Let’s agree that serif fonts do not always carry boring stuff. And have a taste of it:

Programming languages should be designed not by piling feature on top of feature, but by removing the weaknesses and restrictions that make additional features appear necessary. — Revised 7 Report on the Algorithmic Language Scheme, Introduction.

Otherwise said, Scheme offers a minimalist core of powerful primitives upon which one can build abstractions to solve (real world) problems.

The Scheme universe is vast and prolific. As programming languages, Scheme dialects target various niches and implement various paradigms. Some of them are part of the de facto standards (namely RnRS and SRFIs).

The best-known paradigm of agreed-upon practices revolve around Functional Programming.

Scheme might be a dynamically typed language, but it can compete with its scions and siblings when performance matters.

Few programming languages can compete with Scheme when it comes to computer science whether it is Programming Language Theory, or Artificial Intelligence.

That being said, Scheme implementations might be missing some love. That’s a good opportunity for you to learn something useful and give something back.

Or, like others, to make it your secret sauce.

Discourse

Tutorial

Specification

Standard Libraries

Source, and single page files

You can find the source over the rainbow. There is available a single markdown file, and a single html file and a pdf;

LICENSE

Except otherwise noted, this documentation is licensed under the SRFI license:

Copyright (C) Amirouche Amazigh BOUBEKKI, and contributors (2021).

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. # A cheatsheet on Discourse.

The three gates of speech

Before you speak, let your words pass through three gates.

Rogerian rhetoric

  1. You should attempt to re-express your target’s position so clearly, vividly, and fairly that your target says, “Thanks, I wish I’d thought of putting it that way.”

  2. You should list any points of agreement (especially if they are not matters of general or widespread agreement).

  3. You should mention anything you have learned from your target.

  4. Only then are you permitted to say so much as a word of rebuttal or criticism.

Dennett’s version of Rapoport’s Rules

Argument Ranking

“How to apologize: Quickly, specifically, sincerely.”

— Kevin Kelly

Arguments

Responses

Beliefs

“A leader is best when people barely know they exists, when their work is done, their aim fulfilled, people will say: we did it ourselves.”

— 老子(Lao Tse), 道德經(Dao De Jing)

The first principle of Wikipedia etiquette has been said to be Assume Good Faith, also they Be Bold, but not Reckless.

Wrong discourse

Good discourse

Social rules are expected to be broken from time to time, in that regard they are different from a code of conduct.

Response Ranking

Interaction Ranking

Discussion

Low-Effort

Emotional Reaction

Quotes

“Kings speak for the realm, governors for the state, popes for the church. Indeed, the titled, as titled, cannot speak with annyone.”

— James P. Carse, Finite and Infinite Games

“Instead of trying to prove your opponent wrong, try to see in what sense he might be right.” — Robert Nozick, Anarchy, State, and Utopia

“I don’t argue: I just say what I know or what I believe, as the case may be.” — John W. Cohan

“You should mention anything you have learned from your target.”

LICENSE

The whole page is licensed under cc-by-nc-sa; it is slightly adapted from https://wiki.xxiivv.com/site/discourse.html to be able to support the static site generator used on https://scheme.rs and to avoid the words “bad” (replaced with “wrong”) and “faith” (replaced with “discourse”), a few other changes, see history for complete log. # Tutorial

Basics

Continuation

After reading this section you will be able to write basic Scheme programs. In particular, you will study:

How to comment code

You can comment code with the semi-colon, that is ;. Idiomatic code use two semi-colons:

;; Everything after one semi-colon is a comment.

The following sections will use two semi-colons with followed by an arrow => to describe the return value.

How to write literals for builtin types

number

boolean

characters

Characters can be written with their natural representation prefixed with #\\, for instance the character x is represented in Scheme code as follow:

#\x

string

A string is written with double quotes, that is ", for instance:

"hello world"

symbol

A symbol is most of the time written with a simple quote prefix, that is '. For instance:

'unique

pair

A pair of the symbol 'pi and the value 3.1415 can be written as:

'(pi . 3.1415)

list

A list can be written as literals separated by one space and enclosed by parenthesis. For instance, the following list has three items:

'(unique "hello world" (pi . 3.1415))`

The first item is the symbol 'unique, the second item is a string, the third item is a pair.

The empty list is written '().

vector

A vector looks somewhat like a list but without the explicit simple quote. It use a hash prefix. For instance, the following vector has three items:

#(unique "hello world" 42)

The first item is the symbol 'unique, the second item is a string, the third item is a number.

bytevector

A bytevector is like vector but can contain only bytes. It looks like a list of integers, prefixed with #vu8. For instance, the following bytevector has three bytes:

#vu8(0 42 255)

How to call a procedure

A procedure call looks like a list without the simple quote prefix.

The following describe the addition 21 and 21:

(+ 21 21) ;; => 42

It returns 42. So does the following multiplication:

(* 21 2) ;; => 42

The first item is a procedure object. Most of the time, procedure names are made of letters separated with dashes. That usually called kebab-case.

Here is another procedure call:

(string-append "hello" " " "world") ;; => "hello world"

It will return a string "hello world".

How to define a variable

The first kind of variables that you encountered are procedures, things like +, * or string-append.

Variables can also contain constants. You can use define:

(define %thruth 42)

The above code will create a variable called %thruth that contains 42.

Look at this very complicated computation:

(+ %thruth 1 (* 2 647)) ;; => 1337

How to compare objects

Identity equivalence

To compare by identity, in pratice, whether two object represent the same memory location, you can use the procedure eq?.

In the case where you are comparing symbols you can use the procedure eq?:

(eq? 'unique 'unique) ;; => #t
(eq? 'unique 'singleton) ;; => #f

Equivalence

If you do not know the type of the compared objects, or the objects can be of different types, you can use the procedure equal?:

(equal? #t "true") ;; => #f

The string "true" is not equivalent to the boolean #t.

It is rare to use equal?, because, usually, you know the type of the compared objects and the compared object have the same type.

Equivalence predicates

The astute reader might have recognized a pattern in the naming of the equivalence procedures eq? and equal?: both end with a question mark. That is a convention that all procedures that can only return a boolean should end with a question mark. Those are called predicates.

They are predicates for every builtin types. For instance string type has a string equivalence predicate written string=?:

(string=? "hello" "hello world" "hello, world!") ;; => #f

The predicate procedure string=? will return #t if all arguments are the same string, in the sense they contain the same characters.

How to define a procedure

The simplest procedure ever, is the procedure that takes no argument and returns itself:

(define (ruse)
  ruse)

The above is sugar syntax for the following:

(define ruse (lambda () ruse))

A procedure that takes no arguments is called a thunk. Indentation and the newline are cosmetic conventions. If you call the procedure ruse, it will return ruse:

(eq? ruse (ruse))

One can define a procedure that adds one as follow:

(define (add1 number)
  (+ number 1))

The predicate to compare numbers is =. Hence, the following:

(= 2006 (add1 2005)) ;; => #t

Mind the fact that it returns a new number. It does not mutate the value even if it is passed as a variable.

Let’s imagine a procedure that appends a name to the string "Hello". For instance, given "Aziz" or a variable containing "Aziz", it will return "Hello Aziz".

(define name "Aziz")

(define (say-hello name)
  (string-append "Hello " name))

(string=? "Hello Aziz" (say-hello name)) ;; => #t

;; XXX: the variable name still contains "Aziz"

(string=? name "Aziz")) ;; => #t

It does not matter for the callee whether the arguments are passed as variables or literals:

(string=? "Hello John"  (say-hello "John")) ;; => #t

Backtrack

In this section you learned:

Forward

Continuation

After reading this section you will be able to write more complex Scheme code. In particular you will study:

How to create lexical bindings

Lexical bindings can be created with let, let*, letrec and letrec*. They have slightly different behaviors, but the same syntax:

(let (<binding> ...) <expression> ...)

Where <binding> looks like an association of a variable name with the initial value it is holding. For instance:

(let ((a 1)
      (b 2))
  (+ a b 3)) ;; => 6

The above let form will bind a to 1, b to 2 and return the output of (+ a b 3) that is 6.

How to set a variable

To change what a variable holds without overriding it or mutating the object contained in the varialbe, you can use set!. Mind the exclamation mark, it is a convention that forms that have a side-effect ends with a exclamation mark. For instance:

(define %thruth 42)

(display %truth)
(newline)

(set! %thruth 101)

(display %truth)
(newline)

How to do a branch if

Scheme if will consider false, only the object #f. Hence, one can do the following:

(if #t
  (display "true")
  (display "never executed"))

Similarly:

(if #f
  (display "never executed")
  (display "false"))

In particular, the number zero is true according to scheme if:

(if 0
  (display "zero is true")
  (display "never executed"))

If you want to check whether a value is zero you can use the predicate zero? like so:

(if (zero? %thruth)
   (display "%thruth is zero")
   (display "%thruth is not zero"))

Or the less idiomatic predicate =:

(if (= %truth 0)
  (display "%thruth is zero")
  (display "%thruth is not zero"))

How to create a new type

To create a new type you can use the macro define-record-type. For instance, in a todo list application, we will need an <item> type that can be defined as:

(define-record-type <item>
  (make-item title body status)
  item?
  (title item-title item-title!)
  (body item-body item-body!)
  (status item-status item-status!))

Where:

Here is an example use of the above <item> definition:

(define item (make-item "Learn Scheme" "The Scheme programming language is awesome, I should learn it" 'todo))

;; To change the status, one can do the following:

(item-status! item 'wip)

;; to get the title, one can do the following:

(display (item-title item))
(newline)

How to write a named-let

A named-let allows to do recursion without going through the ceremony of defining a separate procedure. In pratice, it used in similar contexts such as for or while loop in other languages. Given the procedure (cons item items) that will return a new list with ITEMS as tail and ITEM as first item, study the following code:

(let loop ((index 0)
           (out '())
  (if (= index 10)
      (display out)
      (loop (+ index 1) (cons index out))))

It is equivalent to the following:

(define (loop index out)
  (if (= index 10)
      (display out)
      (loop (+ index 1) (cons index out))))

(loop 0 '())

A named-let, look like a let form that can be used to bind variables prefixed with a name. Here is some pseudo-code that describe the syntax of the named-let form:

(let <name> (<binding> ...) expression ...))

So <binding> and <expression> are very similar to a let. <name> will be bound to a procedure that takes as many argument as there is <binding> and its body will be <expression> .... It will be called with the associated objects in <binding> .... expression can call <name> most likely in tail call position but not necessarly. If the named-let is not tail-recursive, it is also known to be a grow the stack recursive call. Another way to see the named-let is pseudo-code:

(define <name> (lambda <formals> <expression> ...))

(<name> <arguments> ...)

Where:

That is all.

Backtrack

(define-record-type <record-name>
  (make-record-name field0 ...)
  record-name?
  (field0 record-name-field0 record-name-field0!))
(let loop ((index 0))
  (display index)
  (loop (+ index 1)))

Beyond

Continuation

After reading this section you will be able to create libraries.

Backtrack

Elements of Style

R7RS small specification

Note: This is a port of R7RS specification from tex to markdown that is rendered to html. It does not include formal semantics.

Summary

The report gives a defining description of the programming language Scheme. Scheme is a statically scoped and properly tail recursive dialect of the Lisp programming language  invented by Guy Lewis Steele Jr. and Gerald Jay Sussman. It was designed to have exceptionally clear and simple semantics and few different ways to form expressions. A wide variety of programming paradigms, including imperative, functional, and object-oriented styles, find convenient expression in Scheme.

The introduction offers a brief history of the language and of the report.

The first three chapters present the fundamental ideas of the language and describe the notational conventions used for describing the language and for writing programs in the language.

Chapters [expressionchapter] and [programchapter] describe the syntax and semantics of expressions, definitions, programs, and libraries.

Chapter [builtinchapter] describes Scheme’s built-in procedures, which include all of the language’s data manipulation and input/output primitives.

Chapter [formalchapter] provides a formal syntax for Scheme written in extended BNF, along with a formal denotational semantics. An example of the use of the language follows the formal syntax and semantics.

Appendix [stdlibraries] provides a list of the standard libraries and the identifiers that they export.

Appendix [stdfeatures] provides a list of optional but standardized implementation feature names.

The report concludes with a list of references and an alphabetic index.

Note: The editors of the R5RS and R6RS reports are listed as authors of this report in recognition of the substantial portions of this report that are copied directly from R5RS and R6RS. There is no intended implication that those editors, individually or collectively, support or do not support this report.

Contents

Programming languages should be designed not by piling feature on top of feature, but by removing the weaknesses and restrictions that make additional features appear necessary. Scheme demonstrates that a very small number of rules for forming expressions, with no restrictions on how they are composed, suffice to form a practical and efficient programming language that is flexible enough to support most of the major programming paradigms in use today.

Scheme was one of the first programming languages to incorporate first-class procedures as in the lambda calculus, thereby proving the usefulness of static scope rules and block structure in a dynamically typed language. Scheme was the first major dialect of Lisp to distinguish procedures from lambda expressions and symbols, to use a single lexical environment for all variables, and to evaluate the operator position of a procedure call in the same way as an operand position. By relying entirely on procedure calls to express iteration, Scheme emphasized the fact that tail-recursive procedure calls are essentially GOTOs that pass arguments, thus allowing a programming style that is both coherent and efficient. Scheme was the first widely used programming language to embrace first-class escape procedures, from which all previously known sequential control structures can be synthesized. A subsequent version of Scheme introduced the concept of exact and inexact numbers, an extension of Common Lisp’s generic arithmetic. More recently, Scheme became the first programming language to support hygienic macros, which permit the syntax of a block-structured language to be extended in a consistent and reliable manner.

Background

The first description of Scheme was written in 1975 . A revised report  appeared in 1978, which described the evolution of the language as its MIT implementation was upgraded to support an innovative compiler . Three distinct projects began in 1981 and 1982 to use variants of Scheme for courses at MIT, Yale, and Indiana University . An introductory computer science textbook using Scheme was published in 1984 .

As Scheme became more widespread, local dialects began to diverge until students and researchers occasionally found it difficult to understand code written at other sites. Fifteen representatives of the major implementations of Scheme therefore met in October 1984 to work toward a better and more widely accepted standard for Scheme. Their report, the RRRS , was published at MIT and Indiana University in the summer of 1985. Further revision took place in the spring of 1986, resulting in the R3RS . Work in the spring of 1988 resulted in R4RS , which became the basis for the IEEE Standard for the Scheme Programming Language in 1991 . In 1998, several additions to the IEEE standard, including high-level hygienic macros, multiple return values, and eval, were finalized as the R5RS .

In the fall of 2006, work began on a more ambitious standard, including many new improvements and stricter requirements made in the interest of improved portability. The resulting standard, the R6RS, was completed in August 2007 , and was organized as a core language and set of mandatory standard libraries. Several new implementations of Scheme conforming to it were created. However, most existing R5RS implementations (even excluding those which are essentially unmaintained) did not adopt R6RS, or adopted only selected parts of it.

In consequence, the Scheme Steering Committee decided in August 2009 to divide the standard into two separate but compatible languages — a “small” language, suitable for educators, researchers, and users of embedded languages, focused on R5RS compatibility, and a “large” language focused on the practical needs of mainstream software development, intended to become a replacement for R6RS. The present report describes the “small” language of that effort: therefore it cannot be considered in isolation as the successor to R6RS.

We intend this report to belong to the entire Scheme community, and so we grant permission to copy it in whole or in part without fee. In particular, we encourage implementers of Scheme to use this report as a starting point for manuals and other documentation, modifying it as necessary.

Acknowledgments

We would like to thank the members of the Steering Committee, William Clinger, Marc Feeley, Chris Hanson, Jonathan Rees, and Olin Shivers, for their support and guidance.

This report is very much a community effort, and we’d like to thank everyone who provided comments and feedback, including the following people: David Adler, Eli Barzilay, Taylan Ulrich Bayırlı/Kammer, Marco Benelli, Pierpaolo Bernardi, Peter Bex, Per Bothner, John Boyle, Taylor Campbell, Raffael Cavallaro, Ray Dillinger, Biep Durieux, Sztefan Edwards, Helmut Eller, Justin Ethier, Jay Reynolds Freeman, Tony Garnock-Jones, Alan Manuel Gloria, Steve Hafner, Sven Hartrumpf, Brian Harvey, Moritz Heidkamp, Jean-Michel Hufflen, Aubrey Jaffer, Takashi Kato, Shiro Kawai, Richard Kelsey, Oleg Kiselyov, Pjotr Kourzanov, Jonathan Kraut, Daniel Krueger, Christian Stigen Larsen, Noah Lavine, Stephen Leach, Larry D. Lee, Kun Liang, Thomas Lord, Vincent Stewart Manis, Perry Metzger, Michael Montague, Mikael More, Vitaly Magerya, Vincent Manis, Vassil Nikolov, Joseph Wayne Norton, Yuki Okumura, Daichi Oohashi, Jeronimo Pellegrini, Jussi Piitulainen, Alex Queiroz, Jim Rees, Grant Rettke, Andrew Robbins, Devon Schudy, Bakul Shah, Robert Smith, Arthur Smyles, Michael Sperber, John David Stone, Jay Sulzberger, Malcolm Tredinnick, Sam Tobin-Hochstadt, Andre van Tonder, Daniel Villeneuve, Denis Washington, Alan Watson, Mark H. Weaver, Göran Weinholt, David A. Wheeler, Andy Wingo, James Wise, Jörg F. Wittenberger, Kevin A. Wortman, Sascha Ziemann.

In addition we would like to thank all the past editors, and the people who helped them in turn: Hal Abelson, Norman Adams, David Bartley, Alan Bawden, Michael Blair, Gary Brooks, George Carrette, Andy Cromarty, Pavel Curtis, Jeff Dalton, Olivier Danvy, Ken Dickey, Bruce Duba, Robert Findler, Andy Freeman, Richard Gabriel, Yekta Gürsel, Ken Haase, Robert Halstead, Robert Hieb, Paul Hudak, Morry Katz, Eugene Kohlbecker, Chris Lindblad, Jacob Matthews, Mark Meyer, Jim Miller, Don Oxley, Jim Philbin, Kent Pitman, John Ramsdell, Guillermo Rozas, Mike Shaff, Jonathan Shapiro, Guy Steele, Julie Sussman, Perry Wagle, Mitchel Wand, Daniel Weise, Henry Wu, and Ozan Yigit. We thank Carol Fessenden, Daniel Friedman, and Christopher Haynes for permission to use text from the Scheme 311 version 4 reference manual. We thank Texas Instruments, Inc. for permission to use text from the TI Scheme Language Reference Manual . We gladly acknowledge the influence of manuals for MIT Scheme , T , Scheme 84 , Common Lisp , and Algol 60 , as well as the following SRFIs: 0, 1, 4, 6, 9, 11, 13, 16, 30, 34, 39, 43, 46, 62, and 87, all of which are available at http://srfi.schemers.org.

Overview of Scheme

Semantics

This section gives an overview of Scheme’s semantics. A detailed informal semantics is the subject of chapters [basicchapter] through [builtinchapter]. For reference purposes, section [formalsemanticssection] provides a formal semantics of Scheme.

Scheme is a statically scoped programming language. Each use of a variable is associated with a lexically apparent binding of that variable.

Scheme is a dynamically typed language. Types are associated with values (also called objects) rather than with variables. Statically typed languages, by contrast, associate types with variables and expressions as well as with values.

All objects created in the course of a Scheme computation, including procedures and continuations, have unlimited extent. No Scheme object is ever destroyed. The reason that implementations of Scheme do not (usually!) run out of storage is that they are permitted to reclaim the storage occupied by an object if they can prove that the object cannot possibly matter to any future computation.

Implementations of Scheme are required to be properly tail-recursive. This allows the execution of an iterative computation in constant space, even if the iterative computation is described by a syntactically recursive procedure. Thus with a properly tail-recursive implementation, iteration can be expressed using the ordinary procedure-call mechanics, so that special iteration constructs are useful only as syntactic sugar. See section [proper tail recursion].

Scheme procedures are objects in their own right. Procedures can be created dynamically, stored in data structures, returned as results of procedures, and so on.

One distinguishing feature of Scheme is that continuations, which in most other languages only operate behind the scenes, also have “first-class” status. Continuations are useful for implementing a wide variety of advanced control constructs, including non-local exits, backtracking, and coroutines. See section [continuations].

Arguments to Scheme procedures are always passed by value, which means that the actual argument expressions are evaluated before the procedure gains control, regardless of whether the procedure needs the result of the evaluation.

Scheme’s model of arithmetic is designed to remain as independent as possible of the particular ways in which numbers are represented within a computer. In Scheme, every integer is a rational number, every rational is a real, and every real is a complex number. Thus the distinction between integer and real arithmetic, so important to many programming languages, does not appear in Scheme. In its place is a distinction between exact arithmetic, which corresponds to the mathematical ideal, and inexact arithmetic on approximations. Exact arithmetic is not limited to integers.

Syntax

Scheme, like most dialects of Lisp, employs a fully parenthesized prefix notation for programs and other data; the grammar of Scheme generates a sublanguage of the language used for data. An important consequence of this simple, uniform representation is that Scheme programs and data can easily be treated uniformly by other Scheme programs. For example, the eval procedure evaluates a Scheme program expressed as data.

The read procedure performs syntactic as well as lexical decomposition of the data it reads. The read procedure parses its input as data (section [datumsyntax]), not as program.

The formal syntax of Scheme is described in section [BNF].

Notation and terminology

Base and optional features

Every identifier defined in this report appears in one or more of several libraries. Identifiers defined in the base library are not marked specially in the body of the report. This library includes the core syntax of Scheme and generally useful procedures that manipulate data. For example, the variable abs is bound to a procedure of one argument that computes the absolute value of a number, and the variable + is bound to a procedure that computes sums. The full list all the standard libraries and the identifiers they export is given in Appendix [stdlibraries].

All implementations of Scheme:

Error situations and unspecified behavior

When speaking of an error situation, this report uses the phrase “an error is signaled” to indicate that implementations must detect and report the error. An error is signaled by raising a non-continuable exception, as if by the procedure raise as described in section [exceptionsection]. The object raised is implementation-dependent and need not be distinct from objects previously used for the same purpose. In addition to errors signaled in situations described in this report, programmers can signal their own errors and handle signaled errors.

The phrase “an error that satisfies predicate is signaled” means that an error is signaled as above. Furthermore, if the object that is signaled is passed to the specified predicate (such as file-error? or read-error?), the predicate returns #t.

If such wording does not appear in the discussion of an error, then implementations are not required to detect or report the error, though they are encouraged to do so. Such a situation is sometimes, but not always, referred to with the phrase “an error.” In such a situation, an implementation may or may not signal an error; if it does signal an error, the object that is signaled may or may not satisfy the predicates error-object?, file-error?, or read-error?. Alternatively, implementations may provide non-portable extensions.

For example, it is an error for a procedure to be passed an argument of a type that the procedure is not explicitly specified to handle, even though such domain errors are seldom mentioned in this report. Implementations may signal an error, extend a procedure’s domain of definition to include such arguments, or fail catastrophically.

This report uses the phrase “may report a violation of an implementation restriction” to indicate circumstances under which an implementation is permitted to report that it is unable to continue execution of a correct program because of some restriction imposed by the implementation. Implementation restrictions are discouraged, but implementations are encouraged to report violations of implementation restrictions.

For example, an implementation may report a violation of an implementation restriction if it does not have enough storage to run a program, or if an arithmetic operation would produce an exact number that is too large for the implementation to represent.

If the value of an expression is said to be “unspecified,” then the expression must evaluate to some object without signaling an error, but the value depends on the implementation; this report explicitly does not say what value is returned.

Finally, the words and phrases “must,” “must not,” “shall,” “shall not,” “should,” “should not,” “may,” “required,” “recommended,” and “optional,” although not capitalized in this report, are to be interpreted as described in RFC 2119 . They are used only with reference to implementer or implementation behavior, not with reference to programmer or program behavior.

Entry format

Chapters [expressionchapter] and [builtinchapter] are organized into entries. Each entry describes one language feature or a group of related features, where a feature is either a syntactic construct or a procedure. An entry begins with one or more header lines of the form

template category

for identifiers in the base library, or

template name library category

where name is the short name of a library as defined in Appendix [stdlibraries].

If category is “syntax,” the entry describes an expression type, and the template gives the syntax of the expression type. Components of expressions are designated by syntactic variables, which are written using angle brackets, for example expression and variable. Syntactic variables are intended to denote segments of program text; for example, expression stands for any string of characters which is a syntactically valid expression. The notation

thing ...

indicates zero or more occurrences of a thing, and

thing thing ...

indicates one or more occurrences of a thing.

If category is “auxiliary syntax,” then the entry describes a syntax binding that occurs only as part of specific surrounding expressions. Any use as an independent syntactic construct or variable is an error.

If category is “procedure,” then the entry describes a procedure, and the header line gives a template for a call to the procedure. Argument names in the template are italicized. Thus the header line

(vector-ref vector k) procedure

indicates that the procedure bound to the vector-ref variable takes two arguments, a vector vector and an exact non-negative integer k (see below). The header lines

(make-vector k) procedure

(make-vector k fill) procedure

indicate that the make-vector procedure must be defined to take either one or two arguments.

It is an error for a procedure to be presented with an argument that it is not specified to handle. For succinctness, we follow the convention that if an argument name is also the name of a type listed in section [disjointness], then it is an error if that argument is not of the named type. For example, the header line for vector-ref given above dictates that the first argument to vector-ref is a vector. The following naming conventions also imply type restrictions:

alist association list (list of pairs)
boolean boolean value (#t or #f)
byte exact integer 0 ≤ byte < 256
bytevector bytevector
char character
end exact non-negative integer
k, k1, … kj, … exact non-negative integer
letters alphabetic character
list, list1, … listj, … list (see section [listsection])
n, n1, … nj, … integer
obj any object
pair pair
port port
proc procedure
q, q1, … qj, … rational number
start exact non-negative integer
string string
symbol symbol
thunk zero-argument procedure
vector vector
x, x1, … xj, … real number
y, y1, … yj, … real number
z, z1, … zj, … complex number

The names start and end are used as indexes into strings, vectors, and bytevectors. Their use implies the following:

Evaluation examples

The symbol “=>” used in program examples is read “evaluates to.” For example,

(* 5 8) ;; => 40

means that the expression (* 5 8) evaluates to the object 40. Or, more precisely: the expression given by the sequence of characters “(* 5 8)” evaluates, in an environment containing the base library, to an object that can be represented externally by the sequence of characters “40.” See section [externalreps] for a discussion of external representations of objects.

Naming conventions

By convention, ? is the final character of the names of procedures that always return a boolean value. Such procedures are called predicates. Predicates are generally understood to be side-effect free, except that they may raise an exception when passed the wrong type of argument.

Similarly, ! is the final character of the names of procedures that store values into previously allocated locations (see section [storagemodel]). Such procedures are called mutation procedures. The value returned by a mutation procedure is unspecified.

By convention, “->” appears within the names of procedures that take an object of one type and return an analogous object of another type. For example, list->vector takes a list and returns a vector whose elements are the same as those of the list.

A command is a procedure that does not return useful values to its continuation.

A thunk is a procedure that does not accept arguments.

Lexical conventions

This section gives an informal account of some of the lexical conventions used in writing Scheme programs. For a formal syntax of Scheme, see section [BNF].

Identifiers

An identifier is any sequence of letters, digits, and “extended identifier characters” provided that it does not have a prefix which is a valid number. However, the . token (a single period) used in the list syntax is not an identifier.

All implementations of Scheme must support the following extended identifier characters:

!\ \$ \% & * + - . / :\ < = > ? @ ^ _ ~ %

Alternatively, an identifier can be represented by a sequence of zero or more characters enclosed within vertical lines (|), analogous to string literals. Any character, including whitespace characters, but excluding the backslash and vertical line characters, can appear verbatim in such an identifier. In addition, characters can be specified using either an inline hex escape or the same escapes available in strings.

For example, the identifier |H\x65;llo| is the same identifier as Hello, and in an implementation that supports the appropriate Unicode character the identifier |\x3BB;| is the same as the identifier λ. What is more, |\t\t| and |\x9;\x9;| are the same. Note that || is a valid identifier that is different from any other identifier.

Here are some examples of identifiers:

...                      {+}
+soup+                   <=?
->string                 a34kTMNs
lambda                   list->vector
q                        V17a
|two words|              |two\x20;words|
the-word-recursion-has-many-meanings

See section [extendedalphas] for the formal syntax of identifiers.

Identifiers have two uses within Scheme programs:

In contrast with earlier revisions of the report , the syntax distinguishes between upper and lower case in identifiers and in characters specified using their names. However, it does not distinguish between upper and lower case in numbers, nor in inline hex escapes used in the syntax of identifiers, characters, or strings. None of the identifiers defined in this report contain upper-case characters, even when they appear to do so as a result of the English-language convention of capitalizing the first word of a sentence.

The following directives give explicit control over case folding.

#!fold-case
#!no-fold-case

These directives can appear anywhere comments are permitted (see section [wscommentsection]) but must be followed by a delimiter. They are treated as comments, except that they affect the reading of subsequent data from the same port. The #!fold-case directive causes subsequent identifiers and character names to be case-folded as if by string-foldcase (see section [stringsection]). It has no effect on character literals. The #!no-fold-case directive causes a return to the default, non-folding behavior.

Whitespace and comments

Whitespace characters include the space, tab, and newline characters. (Implementations may provide additional whitespace characters such as page break.) Whitespace is used for improved readability and as necessary to separate tokens from each other, a token being an indivisible lexical unit such as an identifier or number, but is otherwise insignificant. Whitespace can occur between any two tokens, but not within a token. Whitespace occurring inside a string or inside a symbol delimited by vertical lines is significant.

The lexical syntax includes several comment forms. Comments are treated exactly like whitespace.

A semicolon (;) indicates the start of a line comment. The comment continues to the end of the line on which the semicolon appears.

Another way to indicate a comment is to prefix a datum (cf. section [datumsyntax]) with #; and optional whitespace. The comment consists of the comment prefix #;, the space, and the datum together. This notation is useful for “commenting out” sections of code.

Block comments are indicated with properly nested #| and |# pairs.

#|
The FACT procedure computes the factorial
of a non-negative integer.
|#
(define fact
  (lambda (n)
    (if (= n 0)
        #;(= n 1)
        1        ;Base case: return 1
        (* n (fact (- n 1))))))

Other notations

For a description of the notations used for numbers, see section [numbersection].

Datum labels

#n=datum lexicalsyntax

#n# lexical syntax

The lexical syntax #n=datum reads the same as datum, but also results in datum being labelled by n. It is an error if n is not a sequence of digits.

The lexical syntax #n# serves as a reference to some object labelled by #n=; the result is the same object as the #n= (see section [equivalencesection]).

Together, these syntaxes permit the notation of structures with shared or circular substructure.

(let ((x (list 'a 'b 'c)))
  (set-cdr! (cddr x) x)
  x) ;; => #0=(a b c . #0#)

The scope of a datum label is the portion of the outermost datum in which it appears that is to the right of the label. Consequently, a reference #n# can occur only after a label #n=; it is an error to attempt a forward reference. In addition, it is an error if the reference appears as the labelled object itself (as in #n= #n#), because the object labelled by #n= is not well defined in this case.

It is an error for a program or library to include circular references except in literals. In particular, it is an error for quasiquote (section [quasiquote]) to contain them.

#1=(begin (display #\x) #1#)
;; => error

Basic concepts

Variables, syntactic keywords, and regions

An identifier can name either a type of syntax or a location where a value can be stored. An identifier that names a type of syntax is called a syntactic keyword and is said to be bound to a transformer for that syntax. An identifier that names a location is called a variable and is said to be bound to that location. The set of all visible bindings in effect at some point in a program is known as the environment in effect at that point. The value stored in the location to which a variable is bound is called the variable’s value. By abuse of terminology, the variable is sometimes said to name the value or to be bound to the value. This is not quite accurate, but confusion rarely results from this practice.

Certain expression types are used to create new kinds of syntax and to bind syntactic keywords to those new syntaxes, while other expression types create new locations and bind variables to those locations. These expression types are called binding constructs.

Those that bind syntactic keywords are listed in section [macrosection]. The most fundamental of the variable binding constructs is the lambda expression, because all other variable binding constructs (except top-level bindings) can be explained in terms of lambda expressions. The other variable binding constructs are let, let*, letrec, letrec*, let-values, let*-values, and do expressions (see sections [lambda], [letrec], and [do]).

Scheme is a language with block structure. To each place where an identifier is bound in a program there corresponds a region of the program text within which the binding is visible. The region is determined by the particular binding construct that establishes the binding; if the binding is established by a lambda expression, for example, then its region is the entire lambda expression. Every mention of an identifier refers to the binding of the identifier that established the innermost of the regions containing the use. If there is no binding of the identifier whose region contains the use, then the use refers to the binding for the variable in the global environment, if any (chapters [expressionchapter] and [initialenv]); if there is no binding for the identifier, it is said to be unbound.

Disjointness of types

No object satisfies more than one of the following predicates:

boolean?          bytevector?
char?             eof-object?
null?             number?
pair?             port?
procedure?        string?
symbol?           vector?

and all predicates created by define-record-type.

These predicates define the types boolean, bytevector, character, the empty list object, eof-object, number, pair, port, procedure, string, symbol, vector, and all record types.

Although there is a separate boolean type, any Scheme value can be used as a boolean value for the purpose of a conditional test. As explained in section [booleansection], all values count as true in such a test except for #f. This report uses the word “true” to refer to any Scheme value except #f, and the word “false” to refer to #f.

External representations

An important concept in Scheme (and Lisp) is that of the external representation of an object as a sequence of characters. For example, an external representation of the integer 28 is the sequence of characters “28”, and an external representation of a list consisting of the integers 8 and 13 is the sequence of characters “(8 13)”.

The external representation of an object is not necessarily unique. The integer 28 also has representations “#e28.000” and “#x1c”, and the list in the previous paragraph also has the representations “( 08 13 )” and “(8 . (13 . ()))” (see section [listsection]).

Many objects have standard external representations, but some, such as procedures, do not have standard representations (although particular implementations may define representations for them).

An external representation can be written in a program to obtain the corresponding object (see quote, section [quote]).

External representations can also be used for input and output. The procedure read (section [read]) parses external representations, and the procedure write (section [write]) generates them. Together, they provide an elegant and powerful input/output facility.

Note that the sequence of characters “(+ 2 6)” is not an external representation of the integer 8, even though it is an expression evaluating to the integer 8; rather, it is an external representation of a three-element list, the elements of which are the symbol + and the integers 2 and 6. Scheme’s syntax has the property that any sequence of characters that is an expression is also the external representation of some object. This can lead to confusion, since it is not always obvious out of context whether a given sequence of characters is intended to denote data or program, but it is also a source of power, since it facilitates writing programs such as interpreters and compilers that treat programs as data (or vice versa).

The syntax of external representations of various kinds of objects accompanies the description of the primitives for manipulating the objects in the appropriate sections of chapter [initialenv].

Storage model

Variables and objects such as pairs, strings, vectors, and bytevectors implicitly denote locations or sequences of locations. A string, for example, denotes as many locations as there are characters in the string. A new value can be stored into one of these locations using the string-set! procedure, but the string continues to denote the same locations as before.

An object fetched from a location, by a variable reference or by a procedure such as car, vector-ref, or string-ref, is equivalent in the sense of eqv? (section [equivalencesection]) to the object last stored in the location before the fetch.

Every location is marked to show whether it is in use. No variable or object ever refers to a location that is not in use.

Whenever this report speaks of storage being newly allocated for a variable or object, what is meant is that an appropriate number of locations are chosen from the set of locations that are not in use, and the chosen locations are marked to indicate that they are now in use before the variable or object is made to denote them. Notwithstanding this, it is understood that the empty list cannot be newly allocated, because it is a unique object. It is also understood that empty strings, empty vectors, and empty bytevectors, which contain no locations, may or may not be newly allocated.

Every object that denotes locations is either mutable or immutable. Literal constants, the strings returned by symbol->string, and possibly the environment returned by scheme-report-environment are immutable objects. All objects created by the other procedures listed in this report are mutable. It is an error to attempt to store a new value into a location that is denoted by an immutable object.

These locations are to be understood as conceptual, not physical. Hence, they do not necessarily correspond to memory addresses, and even if they do, the memory address might not be constant.

Rationale: In many systems it is desirable for constants (i.e. the values of literal expressions) to reside in read-only memory. Making it an error to alter constants permits this implementation strategy, while not requiring other systems to distinguish between mutable and immutable objects.

Proper tail recursion

Implementations of Scheme are required to be properly tail-recursive. Procedure calls that occur in certain syntactic contexts defined below are tail calls. A Scheme implementation is properly tail-recursive if it supports an unbounded number of active tail calls. A call is active if the called procedure might still return. Note that this includes calls that might be returned from either by the current continuation or by continuations captured earlier by call-with-current-continuation that are later invoked. In the absence of captured continuations, calls could return at most once and the active calls would be those that had not yet returned. A formal definition of proper tail recursion can be found in .

Rationale:

Intuitively, no space is needed for an active tail call because the continuation that is used in the tail call has the same semantics as the continuation passed to the procedure containing the call. Although an improper implementation might use a new continuation in the call, a return to this new continuation would be followed immediately by a return to the continuation passed to the procedure. A properly tail-recursive implementation returns to that continuation directly.

Proper tail recursion was one of the central ideas in Steele and Sussman’s original version of Scheme. Their first Scheme interpreter implemented both functions and actors. Control flow was expressed using actors, which differed from functions in that they passed their results on to another actor instead of returning to a caller. In the terminology of this section, each actor finished with a tail call to another actor.

Steele and Sussman later observed that in their interpreter the code for dealing with actors was identical to that for functions and thus there was no need to include both in the language.

A tail call is a procedure call that occurs in a tail context. Tail contexts are defined inductively. Note that a tail context is always determined with respect to a particular lambda expression.

where

cond clause ⟶  (test tail sequence)
case clause ⟶  ((datum) tail sequence)
tail body ⟶  definition tail sequence
tail sequence ⟶  expression tail expression

Certain procedures defined in this report are also required to perform tail calls. The first argument passed to apply and to call-with-current-continuation, and the second argument passed to call-with-values, must be called via a tail call. Similarly, eval must evaluate its first argument as if it were in tail position within the eval procedure.

In the following example the only tail call is the call to f. None of the calls to g or h are tail calls. The reference to x is in a tail context, but it is not a call and thus is not a tail call.

(lambda ()
  (if (g)
      (let ((x (h)))
        x)
      (and (g) (f))))

Note: Implementations may recognize that some non-tail calls, such as the call to h above, can be evaluated as though they were tail calls. In the example above, the let expression could be compiled as a tail call to h. (The possibility of h returning an unexpected number of values can be ignored, because in that case the effect of the let is explicitly unspecified and implementation-dependent.)

Expressions

Expression types are categorized as primitive or derived. Primitive expression types include variables and procedure calls. Derived expression types are not semantically primitive, but can instead be defined as macros. Suitable syntax definitions of some of the derived expressions are given in section [derivedsection].

The procedures force, promise?, make-promise, and make-parameter are also described in this chapter because they are intimately associated with the delay, delay-force, and parameterize expression types.

Primitive expression types

Variable references

variable  syntax An expression consisting of a variable (section [variablesection]) is a variable reference. The value of the variable reference is the value stored in the location to which the variable is bound. It is an error to reference an unbound variable.

(define x 28)
x ;; => 28

Literal expressions

(quote datum)  syntax datum  syntax constant  syntax (quote datum) evaluates to datum. Datum can be any external representation of a Scheme object (see section [externalreps]). This notation is used to include literal constants in Scheme code.

(quote a) ;; => a
(quote #(a b c)) ;; => #(a b c)
(quote (+ 1 2)) ;; => (+ 1 2)

(quote datum) can be abbreviated as datum. The two notations are equivalent in all respects.

'a ;; => a
'#(a b c) ;; => #(a b c)
'() ;; => ()
'(+ 1 2) ;; => (+ 1 2)
'(quote a) ;; => (quote a)
''a ;; => (quote a)

Numerical constants, string constants, character constants, vector constants, bytevector constants, and boolean constants evaluate to themselves; they need not be quoted.

'145932 ;; => 145932
145932 ;; => 145932
'"abc" ;; => "abc"
"abc" ;; => "abc"
'#\a ;; => #\a
#\a ;; => #\a
'#(a 10) ;; => #(a 10)
#(a 10) ;; => #(a 10)
'#u8(64 65) ;; => #u8(64 65)
#u8(64 65) ;; => #u8(64 65)
'#t ;; => #t
#t ;; => #t

As noted in section [storagemodel], it is an error to attempt to alter a constant (i.e. the value of a literal expression) using a mutation procedure like set-car! or string-set!.

Procedure calls

(operator operand1 … )  syntax A procedure call is written by enclosing in parentheses an expression for the procedure to be called followed by expressions for the arguments to be passed to it. The operator and operand expressions are evaluated (in an unspecified order) and the resulting procedure is passed the resulting arguments.

(+ 3 4) ;; => 7
((if #f + *) 3 4) ;; => 12

The procedures in this document are available as the values of variables exported by the standard libraries. For example, the addition and multiplication procedures in the above examples are the values of the variables + and * in the base library. New procedures are created by evaluating lambda expressions (see section [lambda]).

Procedure calls can return any number of values (see values in section [proceduresection]). Most of the procedures defined in this report return one value or, for procedures such as apply, pass on the values returned by a call to one of their arguments. Exceptions are noted in the individual descriptions.

Note: In contrast to other dialects of Lisp, the order of evaluation is unspecified, and the operator expression and the operand expressions are always evaluated with the same evaluation rules.

Note: Although the order of evaluation is otherwise unspecified, the effect of any concurrent evaluation of the operator and operand expressions is constrained to be consistent with some sequential order of evaluation. The order of evaluation may be chosen differently for each procedure call.

Note: In many dialects of Lisp, the empty list, (), is a legitimate expression evaluating to itself. In Scheme, it is an error.

Procedures

(lambda formals body)  syntax Syntax: Formals is a formal arguments list as described below, and body is a sequence of zero or more definitions followed by one or more expressions.

Semantics: A lambda expression evaluates to a procedure. The environment in effect when the lambda expression was evaluated is remembered as part of the procedure. When the procedure is later called with some actual arguments, the environment in which the lambda expression was evaluated will be extended by binding the variables in the formal argument list to fresh locations, and the corresponding actual argument values will be stored in those locations. (A fresh location is one that is distinct from every previously existing location.) Next, the expressions in the body of the lambda expression (which, if it contains definitions, represents a letrec* form — see section [letrecstar]) will be evaluated sequentially in the extended environment. The results of the last expression in the body will be returned as the results of the procedure call.

(lambda (x) (+ x x)) ;; => a procedure
((lambda (x) (+ x x)) 4) ;; => 8

(define reverse-subtract
  (lambda (x y) (- y x)))
(reverse-subtract 7 10) ;; => 3

(define add4
  (let ((x 4))
    (lambda (y) (+ x y))))
(add4 6) ;; => 10

Formals have one of the following forms:

It is an error for a variable to appear more than once in formals.

((lambda x x) 3 4 5 6) ;; => (3 4 5 6)
((lambda (x y . z) z) 3 4 5 6) ;; => (5 6)

Each procedure created as the result of evaluating a lambda expression is (conceptually) tagged with a storage location, in order to make eqv? and eq? work on procedures (see section [equivalencesection]).

Conditionals

(if test consequent alternate) syntax

(if test consequent) syntax

Syntax: Test, consequent, and alternate are expressions.

Semantics: An if expression is evaluated as follows: first, test is evaluated. If it yields a true value (see section [booleansection]), then consequent is evaluated and its values are returned. Otherwise alternate is evaluated and its values are returned. If test yields a false value and no alternate is specified, then the result of the expression is unspecified.

(if (> 3 2) 'yes 'no) ;; => yes
(if (> 2 3) 'yes 'no) ;; => no
(if (> 3 2)
    (- 3 2)
    (+ 3 2)) ;; => 1

Assignments

(set! variable expression) syntax

Semantics: Expression is evaluated, and the resulting value is stored in the location to which variable is bound. It is an error if variable is not bound either in some region enclosing the set! expression or else globally. The result of the set! expression is unspecified.

(define x 2)
(+ x 1) ;; => 3
(set! x 4) ;; => unspecified
(+ x 1) ;; => 5

Inclusion

(include string ...) syntax

(include-ci sitring ... *) syntax

Semantics: Both include and include-ci take one or more filenames expressed as string literals, apply an implementation-specific algorithm to find corresponding files, read the contents of the files in the specified order as if by repeated applications of read, and effectively replace the include or include-ci expression with a begin expression containing what was read from the files. The difference between the two is that include-ci reads each file as if it began with the #!fold-case directive, while include does not.

Note: Implementations are encouraged to search for files in the directory which contains the including file, and to provide a way for users to specify other directories to search.

Derived expression types

The constructs in this section are hygienic, as discussed in section [macrosection]. For reference purposes, section [derivedsection] gives syntax definitions that will convert most of the constructs described in this section into the primitive constructs described in the previous section.

Conditionals

(cond clause ... ) syntax

else auxiliary syntax

=> auxiliary syntax

Syntax: Clauses take one of two forms, either

(<test> <expression> ...)

where test is any expression, or

(<test> => <expression>)

The last clause can be an “else clause,” which has the form

(else <expression> <expression> ...)

Semantics: A cond expression is evaluated by evaluating the test expressions of successive clauses in order until one of them evaluates to a true value (see section [booleansection]). When a test evaluates to a true value, the remaining expressions in its clause are evaluated in order, and the results of the last expression in the clause are returned as the results of the entire cond expression.

If the selected clause contains only the test and no expressions, then the value of the test is returned as the result. If the selected clause uses the => alternate form, then the expression is evaluated. It is an error if its value is not a procedure that accepts one argument. This procedure is then called on the value of the test and the values returned by this procedure are returned by the cond expression.

If all tests evaluate to #f, and there is no else clause, then the result of the conditional expression is unspecified; if there is an else clause, then its expressions are evaluated in order, and the values of the last one are returned.

(cond ((> 3 2) 'greater)
      ((< 3 2) 'less)) ;; => greater

(cond ((> 3 3) 'greater)
      ((< 3 3) 'less)
      (else 'equal)) ;; => equal

(cond ((assv 'b '((a 1) (b 2))) => cadr)
      (else #f)) ;; => 2

(case key clause ...) syntax

Syntax: Key can be any expression. Each clause has the form

((<datum> ...) <expression> <expression> ...)

where each datum is an external representation of some object. It is an error if any of the datums are the same anywhere in the expression. Alternatively, a clause can be of the form

((<datum> ...) => <expression>)

The last clause can be an “else clause,” which has one of the forms

(else <expression> <expression> ...)

or

(else => <expression>)

Semantics: A case expression is evaluated as follows. Key is evaluated and its result is compared against each datum. If the result of evaluating key is the same (in the sense of eqv?; see section [eqv?]) to a datum, then the expressions in the corresponding clause are evaluated in order and the results of the last expression in the clause are returned as the results of the case expression.

If the result of evaluating key is different from every datum, then if there is an else clause, its expressions are evaluated and the results of the last are the results of the case expression; otherwise the result of the case expression is unspecified.

If the selected clause or else clause uses the => alternate form, then the expression is evaluated. It is an error if its value is not a procedure accepting one argument. This procedure is then called on the value of the key and the values returned by this procedure are returned by the case expression.

(case (* 2 3)
  ((2 3 5 7) 'prime)
  ((1 4 6 8 9) 'composite)) ;; => composite
(case (car '(c d))
  ((a) 'a)
  ((b) 'b)) ;; => unspecified
(case (car '(c d))
  ((a e i o u) 'vowel)
  ((w y) 'semivowel)
  (else => (lambda (x) x))) ;; => c

(and test ... *) syntax

Semantics: The test expressions are evaluated from left to right, and if any expression evaluates to #f (see section [booleansection]), then #f is returned. Any remaining expressions are not evaluated. If all the expressions evaluate to true values, the values of the last expression are returned. If there are no expressions, then #t is returned.

(and (= 2 2) (> 2 1)) ;; => #t
(and (= 2 2) (< 2 1)) ;; => #f
(and 1 2 'c '(f g)) ;; => (f g)
(and) ;; => #t

(or test .... *) syntax

Semantics: The test expressions are evaluated from left to right, and the value of the first expression that evaluates to a true value (see section [booleansection]) is returned. Any remaining expressions are not evaluated. If all expressions evaluate to #f or if there are no expressions, then #f is returned.

(or (= 2 2) (> 2 1)) ;; => #t
(or (= 2 2) (< 2 1)) ;; => #t
(or #f #f #f) ;; => #f
(or (memq 'b '(a b c))
    (/ 3 0)) ;; => (b c)

(when test expression ...) syntax

Syntax: The test is an expression.

Semantics: The test is evaluated, and if it evaluates to a true value, the expressions are evaluated in order. The result of the when expression is unspecified.

(when (= 1 1.0)
  (display "1")
  (display "2")) ;; => unspecified
;; and prints 12

`(unless test expression …) syntax

Syntax: The test is an expression.

Semantics: The test is evaluated, and if it evaluates to #f, the expressions are evaluated in order. The result of the unless expression is unspecified.

(unless (= 1 1.0)
  (display "1")
  (display "2")) ;; => unspecified
;; and prints nothing

(cond-expand ce-clause ...) syntax

Syntax: The cond-expand expression type provides a way to statically expand different expressions depending on the implementation. A ce-clause takes the following form:

(feature requirement expression ...)

The last clause can be an “else clause,” which has the form

(else expression ...)

A feature requirement takes one of the following forms:

Semantics: Each implementation maintains a list of feature identifiers which are present, as well as a list of libraries which can be imported. The value of a feature requirement is determined by replacing each feature identifier and (library library name) on the implementation’s lists with #t, and all other feature identifiers and library names with #f, then evaluating the resulting expression as a Scheme boolean expression under the normal interpretation of and, or, and not.

A cond-expand is then expanded by evaluating the feature requirements of successive ce-clauses in order until one of them returns #t. When a true clause is found, the corresponding expressions are expanded to a begin, and the remaining clauses are ignored. If none of the feature requirements evaluate to #t, then if there is an else clause, its expressions are included. Otherwise, the behavior of the cond-expand is unspecified. Unlike cond, cond-expand does not depend on the value of any variables.

The exact features provided are implementation-defined, but for portability a core set of features is given in appendix [stdfeatures].

Binding constructs

The binding constructs let, let*, letrec, letrec*, let-values, and let*-values give Scheme a block structure, like Algol 60. The syntax of the first four constructs is identical, but they differ in the regions they establish for their variable bindings. In a let expression, the initial values are computed before any of the variables become bound; in a let* expression, the bindings and evaluations are performed sequentially; while in letrec and letrec* expressions, all the bindings are in effect while their initial values are being computed, thus allowing mutually recursive definitions. The let-values and let*-values constructs are analogous to let and let* respectively, but are designed to handle multiple-valued expressions, binding different identifiers to the returned values.

(let bindings body) syntax

Syntax: Bindings has the form

((<variable> <init>) ...)

where each init is an expression, and body is a sequence of zero or more definitions followed by a sequence of one or more expressions as described in section [lambda]. It is an error for a variable to appear more than once in the list of variables being bound.

Semantics: The inits are evaluated in the current environment (in some unspecified order), the variables are bound to fresh locations holding the results, the body is evaluated in the extended environment, and the values of the last expression of body are returned. Each binding of a variable has body as its region.

(let ((x 2) (y 3))
  (* x y)) ;; => 6

(let ((x 2) (y 3))
  (let ((x 7)
        (z (+ x y)))
    (* z x))) ;; => 35

See also “named let,” section [namedlet].

(let* bindings body) syntax

Syntax: Bindings has the form

((<variable> <init>) ...)

and body is a sequence of zero or more definitions followed by one or more expressions as described in section [lambda].

Semantics: The let* binding construct is similar to let, but the bindings are performed sequentially from left to right, and the region of a binding indicated by (variable init) is that part of the let* expression to the right of the binding. Thus the second binding is done in an environment in which the first binding is visible, and so on. The variables need not be distinct.

(let ((x 2) (y 3))
  (let* ((x 7)
         (z (+ x y)))
    (* z x))) ;; => 70

(letrec bindings body) syntax

Syntax: Bindings has the form

((<variable> <init>) ...)

and body is a sequence of zero or more definitions followed by one or more expressions as described in section [lambda]. It is an error for a variable to appear more than once in the list of variables being bound.

Semantics: The variables are bound to fresh locations holding unspecified values, the inits are evaluated in the resulting environment (in some unspecified order), each variable is assigned to the result of the corresponding init, the body is evaluated in the resulting environment, and the values of the last expression in body are returned. Each binding of a variable has the entire letrec expression as its region, making it possible to define mutually recursive procedures.

(letrec ((even?
          (lambda (n)
            (if (zero? n)
                #t
                (odd? (- n 1)))))
         (odd?
          (lambda (n)
            (if (zero? n)
                #f
                (even? (- n 1))))))
  (even? 88))
;; => #t

One restriction on letrec is very important: if it is not possible to evaluate each init without assigning or referring to the value of any variable, it is an error. The restriction is necessary because letrec is defined in terms of a procedure call where a lambda expression binds the variables to the values of the inits. In the most common uses of letrec, all the inits are lambda expressions and the restriction is satisfied automatically.

(letrec* bindings body) syntax

Syntax: Bindings has the form

((<variable> <init>) ...)

and body is a sequence of zero or more definitions followed by one or more expressions as described in section [lambda]. It is an error for a variable to appear more than once in the list of variables being bound.

Semantics: The variables are bound to fresh locations, each variable is assigned in left-to-right order to the result of evaluating the corresponding init (interleaving evaluations and assignments), the body is evaluated in the resulting environment, and the values of the last expression in body are returned. Despite the left-to-right evaluation and assignment order, each binding of a variable has the entire letrec* expression as its region, making it possible to define mutually recursive procedures.

If it is not possible to evaluate each init without assigning or referring to the value of the corresponding variable or the variable of any of the bindings that follow it in bindings, it is an error. Another restriction is that it is an error to invoke the continuation of an init more than once.

;; Returns the arithmetic, geometric, and
;; harmonic means of a nested list of numbers
(define (means ton)
  (letrec*
      ((mean
        (lambda (f g)
          (f (/ (sum g ton) n))))
       (sum
        (lambda (g ton)
          (if (null? ton)
              (+)
              (if (number? ton)
                  (g ton)
                  (+ (sum g (car ton))
                     (sum g (cdr ton)))))))
       (n (sum (lambda (x) 1) ton)))
    (values (mean values values)
            (mean exp log)
            (mean / /))))

Evaluating (means ’(3 (1 4))) returns three values: 8/3, 2.28942848510666 (approximately), and 36/19.

(let-values mv binding spec body) syntax

Syntax: Mv binding spec has the form

((<formals> <init>) ...)

where each init is an expression, and body is zero or more definitions followed by a sequence of one or more expressions as described in section [lambda]. It is an error for a variable to appear more than once in the set of formals.

Semantics: The inits are evaluated in the current environment (in some unspecified order) as if by invoking call-with-values, and the variables occurring in the formals are bound to fresh locations holding the values returned by the inits, where the formals are matched to the return values in the same way that the formals in a lambda expression are matched to the arguments in a procedure call. Then, the body is evaluated in the extended environment, and the values of the last expression of body are returned. Each binding of a variable has body as its region.

It is an error if the formals do not match the number of values returned by the corresponding init.

(let-values (((root rem) (exact-integer-sqrt 32)))
  (* root rem)) ;; => 35

(let*-values mv binding spec body) syntax

Syntax: Mv binding spec has the form

((<formals> <init>) ...)

and body is a sequence of zero or more definitions followed by one or more expressions as described in section [lambda]. In each formals, it is an error if any variable appears more than once.

Semantics: The let*-values construct is similar to let-values, but the inits are evaluated and bindings created sequentially from left to right, with the region of the bindings of each formals including the inits to its right as well as body. Thus the second init is evaluated in an environment in which the first set of bindings is visible and initialized, and so on.

(let ((a 'a) (b 'b) (x 'x) (y 'y))
  (let*-values (((a b) (values x y))
                ((x y) (values a b)))
    (list a b x y))) ;; => (x y x y)

Sequencing

Both of Scheme’s sequencing constructs are named begin, but the two have slightly different forms and uses:

(begin expression-or-definition ...) syntax

This form of begin can appear as part of a body, or at the outermost level of a program, or at the REPL, or directly nested in a begin that is itself of this form. It causes the contained expressions and definitions to be evaluated exactly as if the enclosing begin construct were not present.

Rationale: This form is commonly used in the output of macros (see section [macrosection]) which need to generate multiple definitions and splice them into the context in which they are expanded.

(begin expression ...) syntax

This form of begin can be used as an ordinary expression. The expressions are evaluated sequentially from left to right, and the values of the last expression are returned. This expression type is used to sequence side effects such as assignments or input and output.

(define x 0)

(and (= x 0)
     (begin (set! x 5)
            (+ x 1))) ;; => 6

(begin (display "4 plus 1 equals ")
       (display (+ 4 1))) ;; => unspecified
;; and prints 4 plus 1 equals 5

Note that there is a third form of begin used as a library declaration: see section [librarydeclarations].

Iteration

(do ((variable<sub>1</sub> init<sub>1</sub> step<sub>1</sub>) ...) (test expression ...) command ...) syntax

Syntax: All of init, step, test, and command are expressions.

Semantics: A do expression is an iteration construct. It specifies a set of variables to be bound, how they are to be initialized at the start, and how they are to be updated on each iteration. When a termination condition is met, the loop exits after evaluating the expressions.

A do expression is evaluated as follows: The init expressions are evaluated (in some unspecified order), the variables are bound to fresh locations, the results of the init expressions are stored in the bindings of the variables, and then the iteration phase begins.

Each iteration begins by evaluating test; if the result is false (see section [booleansection]), then the command expressions are evaluated in order for effect, the step expressions are evaluated in some unspecified order, the variables are bound to fresh locations, the results of the steps are stored in the bindings of the variables, and the next iteration begins.

If test evaluates to a true value, then the expressions are evaluated from left to right and the values of the last expression are returned. If no expressions are present, then the value of the do expression is unspecified.

The region of the binding of a variable consists of the entire do expression except for the inits. It is an error for a variable to appear more than once in the list of do variables.

A step can be omitted, in which case the effect is the same as if (variable init variable) had been written instead of (variable init).

(do ((vec (make-vector 5))
     (i 0 (+ i 1)))
    ((= i 5) vec)
  (vector-set! vec i i)) ;; => #(0 1 2 3 4)

(let ((x '(1 3 5 7 9)))
  (do ((x x (cdr x))
       (sum 0 (+ sum (car x))))
      ((null? x) sum))) ;; => 25

(let bindings body ...) syntax

Semantics: “Named let” is a variant on the syntax of let which provides a more general looping construct than do and can also be used to express recursion. It has the same syntax and semantics as ordinary let except that variable is bound within body to a procedure whose formal arguments are the bound variables and whose body is body. Thus the execution of body can be repeated by invoking the procedure named by variable.

(let loop ((numbers '(3 -2 1 6 -5))
           (nonneg '())
           (neg '()))
  (cond ((null? numbers) (list nonneg neg))
        ((>= (car numbers) 0)
         (loop (cdr numbers)
               (cons (car numbers) nonneg)
               neg))
        ((< (car numbers) 0)
         (loop (cdr numbers)
               nonneg
               (cons (car numbers) neg)))))
;; => ((6 1 3) (-5 -2))

Delayed evaluation

(delay expression) lazy library syntax

Semantics: The delay construct is used together with the procedure force to implement lazy evaluation or call by need. (delay expression) returns an object called a promise which at some point in the future can be asked (by the force procedure) to evaluate expression, and deliver the resulting value.

The effect of expression returning multiple values is unspecified.

(delay-force expression) lazy library syntax

Semantics: The expression (delay-force *expression*) is conceptually similar to (delay (force *expression*)), with the difference that forcing the result of delay-force will in effect result in a tail call to (force *expression*), while forcing the result of (delay (force *expression*)) might not. Thus iterative lazy algorithms that might result in a long series of chains of delay and force can be rewritten using delay-force to prevent consuming unbounded space during evaluation.

(force *promise*) lazy library procedure

The force procedure forces the value of a promise created by delay, delay-force, or make-promise. If no value has been computed for the promise, then a value is computed and returned. The value of the promise must be cached (or “memoized”) so that if it is forced a second time, the previously computed value is returned. Consequently, a delayed expression is evaluated using the parameter values and exception handler of the call to force which first requested its value. If promise is not a promise, it may be returned unchanged.

(force (delay (+ 1 2))) ;; => 3
(let ((p (delay (+ 1 2))))
  (list (force p) (force p)))
;; => (3 3)

(define integers
  (letrec ((next
            (lambda (n)
              (delay (cons n (next (+ n 1)))))))
    (next 0)))
(define head
  (lambda (stream) (car (force stream))))
(define tail
  (lambda (stream) (cdr (force stream))))

(head (tail (tail integers)))
;; => 2

The following example is a mechanical transformation of a lazy stream-filtering algorithm into Scheme. Each call to a constructor is wrapped in delay, and each argument passed to a deconstructor is wrapped in force. The use of (delay-force …) instead of (delay (force …)) around the body of the procedure ensures that an ever-growing sequence of pending promises does not exhaust available storage, because force will in effect force such sequences iteratively.

(define (stream-filter p? s)
  (delay-force
   (if (null? (force s))
       (delay '())
       (let ((h (car (force s)))
             (t (cdr (force s))))
         (if (p? h)
             (delay (cons h (stream-filter p? t)))
             (stream-filter p? t))))))

(head (tail (tail (stream-filter odd? integers))))
;; => 5

The following examples are not intended to illustrate good programming style, as delay, force, and delay-force are mainly intended for programs written in the functional style. However, they do illustrate the property that only one value is computed for a promise, no matter how many times it is forced.

(define count 0)
(define p
  (delay (begin (set! count (+ count 1))
                (if (> count x)
                    count
                    (force p)))))
(define x 5)
p ;; => a promise
(force p) ;; => 6
p ;; => a promise, still
(begin (set! x 10)
       (force p)) ;; => 6

Various extensions to this semantics of delay, force and delay-force are supported in some implementations:

(promise? obj) lazy library procedure

The promise? procedure returns #t if its argument is a promise, and #f otherwise. Note that promises are not necessarily disjoint from other Scheme types such as procedures.

(make-promise obj) lazy library procedure

The make-promise procedure returns a promise which, when forced, will return obj. It is similar to delay, but does not delay its argument: it is a procedure rather than syntax. If obj is already a promise, it is returned.

Dynamic bindings

The dynamic extent of a procedure call is the time between when it is initiated and when it returns. In Scheme, call-with-current-continuation (section [continuations]) allows reentering a dynamic extent after its procedure call has returned. Thus, the dynamic extent of a call might not be a single, continuous time period.

This sections introduces parameter objects, which can be bound to new values for the duration of a dynamic extent. The set of all parameter bindings at a given time is called the dynamic environment.

(make-parameter init) procedure

(make-parameter init converter) procedure

Returns a newly allocated parameter object, which is a procedure that accepts zero arguments and returns the value associated with the parameter object. Initially, this value is the value of (converter init), or of init if the conversion procedure converter is not specified. The associated value can be temporarily changed using parameterize, which is described below.

The effect of passing arguments to a parameter object is implementation-dependent.

(parameterize ((param value) …)) syntax

Syntax: Both param and value are expressions.

It is an error if the value of any param expression is not a parameter object.

Semantics: A parameterize expression is used to change the values returned by specified parameter objects during the evaluation of the body.

The param and value expressions are evaluated in an unspecified order. The body is evaluated in a dynamic environment in which calls to the parameters return the results of passing the corresponding values to the conversion procedure specified when the parameters were created. Then the previous values of the parameters are restored without passing them to the conversion procedure. The results of the last expression in the body are returned as the results of the entire parameterize expression.

Note: If the conversion procedure is not idempotent, the results of (parameterize ((x (x))) …), which appears to bind the parameter x to its current value, might not be what the user expects.

If an implementation supports multiple threads of execution, then parameterize must not change the associated values of any parameters in any thread other than the current thread and threads created inside body.

Parameter objects can be used to specify configurable settings for a computation without the need to pass the value to every procedure in the call chain explicitly.

(define radix
  (make-parameter
   10
   (lambda (x)
     (if (and (exact-integer? x) (<= 2 x 16))
         x
         (error "invalid radix")))))

(define (f n) (number->string n (radix)))

(f 12) ;; => "12"
(parameterize ((radix 2))
  (f 12)) ;; => "1100"
(f 12) ;; => "12"

(radix 16) ;; => unspecified

(parameterize ((radix 0))
  (f 12)) ;; => error

Exception handling

(guard (variable cond_clause …) express …)` syntax

Syntax: Each cond_clause is as in the specification of cond.

Semantics: The body is evaluated with an exception handler that binds the raised object (see raise in section [exceptionsection]) to variable and, within the scope of that binding, evaluates the clauses as if they were the clauses of a cond expression. That implicit cond expression is evaluated with the continuation and dynamic environment of the guard expression. If every cond clause’s test evaluates to #f and there is no else clause, then raise-continuable is invoked on the raised object within the dynamic environment of the original call to raise or raise-continuable, except that the current exception handler is that of the guard expression.

See section [exceptionsection] for a more complete discussion of exceptions.

(guard (condition
        ((assq 'a condition) => cdr)
        ((assq 'b condition)))
       (raise (list (cons 'a 42))))
;; => 42

(guard (condition
        ((assq 'a condition) => cdr)
        ((assq 'b condition)))
       (raise (list (cons 'b 23))))
;; => (b . 23)

Quasiquotation

(quasiquote qq template) syntax

qq_template syntax

unquote auxiliary syntax

' auxiliary syntax

unquote-splicing auxiliary syntax

` auxiliary syntax

“Quasiquote” expressions are useful for constructing a list or vector structure when some but not all of the desired structure is known in advance. If no commas appear within the qq template, the result of evaluating `qq template is equivalent to the result of evaluatingqq template. If a comma appears within the qq template, however, the expression following the comma is evaluated (“unquoted”) and its result is inserted into the structure instead of the comma and the expression. If a comma appears followed without intervening whitespace by a commercial at-sign (’`), then it is an error if the following expression does not evaluate to a list; the opening and closing parentheses of the list are then “stripped away” and the elements of the list are inserted in place of the comma at-sign expression sequence. A comma at-sign normally appears only within a list or vector qq template.

Note: In order to unquote an identifier beginning with @, it is necessary to use either an explicit unquote or to put whitespace after the comma, to avoid colliding with the comma at-sign sequence.

`(list ,(+ 1 2) 4) ;; => (list 3 4)
(let ((name 'a)) `(list ,name ',name))
;; => (list a (quote a))
`(a ,(+ 1 2) ,@(map abs '(4 -5 6)) b)
;; => (a 3 4 5 6 b)
`((foo ,(- 10 3)) ,@(cdr '(c)) . ,(car '(cons)))
;; => ((foo 7) . cons)
`#(10 5 ,(sqrt 4) ,@(map sqrt '(16 9)) 8)
;; => #(10 5 2 4 3 8)
(let ((foo '(foo bar)) (@baz 'baz))
  `(list ,@foo , @baz))
;; => (list foo bar baz)

Quasiquote expressions can be nested. Substitutions are made only for unquoted components appearing at the same nesting level as the outermost quasiquote. The nesting level increases by one inside each successive quasiquotation, and decreases by one inside each unquotation.

`(a `(b ,(+ 1 2) ,(foo ,(+ 1 3) d) e) f)
;; => (a `(b ,(+ 1 2) ,(foo 4 d) e) f)
(let ((name1 'x)
      (name2 'y))
  `(a `(b ,,name1 ,',name2 d) e))
;; => (a `(b ,x ,'y d) e)

A quasiquote expression may return either newly allocated, mutable objects or literal structure for any structure that is constructed at run time during the evaluation of the expression. Portions that do not need to be rebuilt are always literal. Thus,

(let ((a 3)) `((1 2) ,a ,4 ,'five 6))

may be treated as equivalent to either of the following expressions:

`((1 2) 3 4 five 6)

(let ((a 3))
  (cons '(1 2)
        (cons a (cons 4 (cons 'five '(6))))))

However, it is not equivalent to this expression:

(let ((a 3)) (list (list 1 2) a 4 'five 6))

The two notations `qq template and(quasiquote qq template)are identical in all respects. ,expression is identical to (unquote expression), and ,@expression is identical to (unquote-splicing expression). Thewrite` procedure may output either format.

(quasiquote (list (unquote (+ 1 2)) 4))
;; => (list 3 4)
'(quasiquote (list (unquote (+ 1 2)) 4))
;; => `(list ,(+ 1 2) 4)
;; i.e., (quasiquote (list (unquote (+ 1 2)) 4))

It is an error if any of the identifiers quasiquote, unquote, or unquote-splicing appear in positions within a qq template otherwise than as described above.

Case-lambda

(case-lambda clause ...) case-lambda library syntax

Syntax: Each clause is of the form (formals body), where formals and body have the same syntax as in a lambda expression.

Semantics: A case-lambda expression evaluates to a procedure that accepts a variable number of arguments and is lexically scoped in the same manner as a procedure resulting from a lambda expression. When the procedure is called, the first clause for which the arguments agree with formals is selected, where agreement is specified as for the formals of a lambda expression. The variables of formals are bound to fresh locations, the values of the arguments are stored in those locations, the body is evaluated in the extended environment, and the results of body are returned as the results of the procedure call.

It is an error for the arguments not to agree with the formals of any clause.

(define range
  (case-lambda
   ((e) (range 0 e))
   ((b e) (do ((r '() (cons e r))
               (e (- e 1) (- e 1)))
              ((< e b) r)))))

(range 3) ;; => (0 1 2)
(range 3 5) ;; => (3 4)

Macros

Scheme programs can define and use new derived expression types, called macros. Program-defined expression types have the syntax

(<keyword> <datum> ...)

where keyword is an identifier that uniquely determines the expression type. This identifier is called the syntactic keyword, or simply keyword, of the macro. The number of the datums, and their syntax, depends on the expression type.

Each instance of a macro is called a use of the macro. The set of rules that specifies how a use of a macro is transcribed into a more primitive expression is called the transformer of the macro.

The macro definition facility consists of two parts:

The syntactic keyword of a macro can shadow variable bindings, and local variable bindings can shadow syntactic bindings. Two mechanisms are provided to prevent unintended conflicts:

In consequence, all macros defined using the pattern language are “hygienic” and “referentially transparent” and thus preserve Scheme’s lexical scoping. 

Implementations may provide macro facilities of other types.

Binding constructs for syntactic keywords

The let-syntax and letrec-syntax binding constructs are analogous to let and letrec, but they bind syntactic keywords to macro transformers instead of binding variables to locations that contain values. Syntactic keywords can also be bound globally or locally with define-syntax; see section [define-syntax].

(let-syntax bindings body) syntax

Syntax: Bindings has the form

((<keyword> <transformer-spec>) ...)

Each keyword is an identifier, each transformer spec is an instance of syntax-rules, and body is a sequence of zero or more definitions followed by one or more expressions. It is an error for a keyword to appear more than once in the list of keywords being bound.

Semantics: The body is expanded in the syntactic environment obtained by extending the syntactic environment of the let-syntax expression with macros whose keywords are the keywords, bound to the specified transformers. Each binding of a keyword has body as its region.

(let-syntax ((given-that (syntax-rules ()
                           ((given-that test stmt1 stmt2 ...)
                            (if test
                                (begin stmt1
                                       stmt2 ...))))))
  (let ((if #t))
    (given-that if (set! if 'now))
    if)) ;; => now

(let ((x 'outer))
  (let-syntax ((m (syntax-rules () ((m) x))))
    (let ((x 'inner))
      (m)))) ;; => outer

(letrec-syntax bindings body) syntax

Syntax: Same as for let-syntax.

Semantics: The body is expanded in the syntactic environment obtained by extending the syntactic environment of the letrec-syntax expression with macros whose keywords are the keywords, bound to the specified transformers. Each binding of a keyword has the transformer specs as well as the body within its region, so the transformers can transcribe expressions into uses of the macros introduced by the letrec-syntax expression.

(letrec-syntax
    ((my-or (syntax-rules ()
              ((my-or) #f)
              ((my-or e) e)
              ((my-or e1 e2 ...)
               (let ((temp e1))
                 (if temp
                     temp
                     (my-or e2 ...)))))))
  (let ((x #f)
        (y 7)
        (temp 8)
        (let odd?)
        (if even?))
    (my-or x
           (let temp)
           (if y)
           y))) ;; => 7

Pattern language

A transformer spec has one of the following forms:

scheme TODO FIXME > `(syntax-rules (pattern literal … )` *syntax* ` ...) ` (syntax-rules ellipsis (pattern literal … )  syntax ` ...)` \_  auxiliary syntax …   auxiliary syntax

Syntax: It is an error if any of the pattern literals, or the ellipsis in the second form, is not an identifier. It is also an error if syntax rule is not of the form

(<pattern> <template>)

The pattern in a syntax rule is a list pattern whose first element is an identifier.

A pattern is either an identifier, a constant, or one of the following

    (<pattern> ...)
    (<pattern> <pattern> ... . <pattern>)
    (<pattern> ... <pattern> ... <pattern> ...)
    (<pattern> ... <pattern> ... <pattern> ...
      . <pattern>)
    #(<pattern> ...)
    #(<pattern> ... <pattern> ... <pattern> ...)

and a template is either an identifier, a constant, or one of the following

    (<element> ...)
    (<element> <element> ... . <template>)
    (... <template>)
    #(<element> ...)

where an element is a template optionally followed by an ellipsis. An ellipsis is the identifier specified in the second form of syntax-rules, or the default identifier … (three consecutive periods) otherwise.

Semantics: An instance of syntax-rules produces a new macro transformer by specifying a sequence of hygienic rewrite rules. A use of a macro whose keyword is associated with a transformer specified by syntax-rules is matched against the patterns contained in the syntax rules, beginning with the leftmost syntax rule. When a match is found, the macro use is transcribed hygienically according to the template.

An identifier appearing within a pattern can be an underscore (_), a literal identifier listed in the list of pattern literals, or the ellipsis. All other identifiers appearing within a pattern are pattern variables.

The keyword at the beginning of the pattern in a syntax rule is not involved in the matching and is considered neither a pattern variable nor a literal identifier.

Pattern variables match arbitrary input elements and are used to refer to elements of the input in the template. It is an error for the same pattern variable to appear more than once in a pattern.

Underscores also match arbitrary input elements but are not pattern variables and so cannot be used to refer to those elements. If an underscore appears in the pattern literals list, then that takes precedence and underscores in the pattern match as literals. Multiple underscores can appear in a pattern.

Identifiers that appear in (pattern literal … ) are interpreted as literal identifiers to be matched against corresponding elements of the input. An element in the input matches a literal identifier if and only if it is an identifier and either both its occurrence in the macro expression and its occurrence in the macro definition have the same lexical binding, or the two identifiers are the same and both have no lexical binding.

A subpattern followed by ellipsis can match zero or more elements of the input, unless ellipsis appears in the pattern literals, in which case it is matched as a literal.

More formally, an input expression E matches a pattern P if and only if:

It is an error to use a macro keyword, within the scope of its binding, in an expression that does not match any of the patterns.

When a macro use is transcribed according to the template of the matching syntax rule, pattern variables that occur in the template are replaced by the elements they match in the input. Pattern variables that occur in subpatterns followed by one or more instances of the identifier ellipsis are allowed only in subtemplates that are followed by as many instances of ellipsis. They are replaced in the output by all of the elements they match in the input, distributed as indicated. It is an error if the output cannot be built up as specified.

Identifiers that appear in the template but are not pattern variables or the identifier ellipsis are inserted into the output as literal identifiers. If a literal identifier is inserted as a free identifier then it refers to the binding of that identifier within whose scope the instance of syntax-rules appears. If a literal identifier is inserted as a bound identifier then it is in effect renamed to prevent inadvertent captures of free identifiers.

A template of the form (ellipsis template) is identical to template, except that ellipses within the template have no special meaning. That is, any ellipses contained within template are treated as ordinary identifiers. In particular, the template (ellipsis ellipsis) produces a single ellipsis. This allows syntactic abstractions to expand into code containing ellipses.

(define-syntax be-like-begin
  (syntax-rules ()
    ((be-like-begin name)
     (define-syntax name
       (syntax-rules ()
         ((name expr (... ...))
          (begin expr (... ...))))))))

(be-like-begin sequence)
(sequence 1 2 3 4) ;; => 4

As an example, if let and cond are defined as in section [derivedsection] then they are hygienic (as required) and the following is not an error.

(let ((=> #f))
  (cond (#t => 'ok))) ;; => ok

The macro transformer for cond recognizes => as a local variable, and hence an expression, and not as the base identifier =>, which the macro transformer treats as a syntactic keyword. Thus the example expands into

(let ((=> #f))
  (if #t (begin => 'ok)))

instead of

(let ((=> #f))
  (let ((temp #t))
    (if temp ('ok temp))))

which would result in an invalid procedure call.

Signaling errors in macro transformers

(syntax-error message args … ) syntax

syntax-error behaves similarly to error ([exceptionsection]) except that implementations with an expansion pass separate from evaluation should signal an error as soon as syntax-error is expanded. This can be used as a syntax-rules template for a pattern that is an invalid use of the macro, which can provide more descriptive error messages. message is a string literal, and args arbitrary expressions providing additional information. Applications cannot count on being able to catch syntax errors with exception handlers or guards.

(define-syntax simple-let
  (syntax-rules ()
    ((_ (head ... ((x . y) val) . tail)
      body1 body2 ...)
     (syntax-error
      "expected an identifier but got"
      (x . y)))
    ((_ ((name val) ...) body1 body2 ...)
     ((lambda (name ...) body1 body2 ...)
      val ...))))

Program structure

Programs

A Scheme program consists of one or more import declarations followed by a sequence of expressions and definitions. Import declarations specify the libraries on which a program or library depends; a subset of the identifiers exported by the libraries are made available to the program. Expressions are described in chapter [expressionchapter]. Definitions are either variable definitions, syntax definitions, or record-type definitions, all of which are explained in this chapter. They are valid in some, but not all, contexts where expressions are allowed, specifically at the outermost level of a program and at the beginning of a body.

At the outermost level of a program, (begin expression or definition_1 ...) is equivalent to the sequence of expressions and definitions in the begin. Similarly, in a body, (begin definition_1 ...) is equivalent to the sequence definition1 … . Macros can expand into such begin forms. For the formal definition, see [sequencing].

Import declarations and definitions cause bindings to be created in the global environment or modify the value of existing global bindings. The initial environment of a program is empty, so at least one import declaration is needed to introduce initial bindings.

Expressions occurring at the outermost level of a program do not create any bindings. They are executed in order when the program is invoked or loaded, and typically perform some kind of initialization.

Programs and libraries are typically stored in files, although in some implementations they can be entered interactively into a running Scheme system. Other paradigms are possible. Implementations which store libraries in files should document the mapping from the name of a library to its location in the file system.

Import declarations

An import declaration takes the following form:

(import <import-set> ...)

An import declaration provides a way to import identifiers exported by a library. Each import set names a set of bindings from a library and possibly specifies local names for the imported bindings. It takes one of the following forms:

In the first form, all of the identifiers in the named library’s export clauses are imported with the same names (or the exported names if exported with rename). The additional import set forms modify this set as follows:

In a program or library declaration, it is an error to import the same identifier more than once with different bindings, or to redefine or mutate an imported binding with a definition or with set!, or to refer to an identifier before it is imported. However, a REPL should permit these actions.

Variable definitions

A variable definition binds one or more identifiers and specifies an initial value for each of them. The simplest kind of variable definition takes one of the following forms:

Top level definitions

At the outermost level of a program, a definition

(define <variable> <expression>)

has essentially the same effect as the assignment expression

(set! <variable> <expression>)

if variable is bound to a non-syntax value. However, if variable is not bound, or is a syntactic keyword, then the definition will bind variable to a new location before performing the assignment, whereas it would be an error to perform a set! on an unbound variable.

(define add3
  (lambda (x) (+ x 3)))
(add3 3) ;; => 6
(define first car)
(first '(1 2)) ;; => 1

Internal definitions

Definitions can occur at the beginning of a body (that is, the body of a lambda, let, let*, letrec, letrec*, let-values, let*-values, let-syntax, letrec-syntax, parameterize, guard, or case-lambda). Note that such a body might not be apparent until after expansion of other syntax. Such definitions are known as internal definitions as opposed to the global definitions described above. The variables defined by internal definitions are local to the body. That is, variable is bound rather than assigned, and the region of the binding is the entire body. For example,

(let ((x 5))
  (define foo (lambda (y) (bar x y)))
  (define bar (lambda (a b) (+ (* a b) a)))
  (foo (+ x 3))) ;; => 45

An expanded body containing internal definitions can always be converted into a completely equivalent letrec* expression. For example, the let expression in the above example is equivalent to

(let ((x 5))
  (letrec* ((foo (lambda (y) (bar x y)))
            (bar (lambda (a b) (+ (* a b) a))))
    (foo (+ x 3))))

Just as for the equivalent letrec* expression, it is an error if it is not possible to evaluate each expression of every internal definition in a body without assigning or referring to the value of the corresponding variable or the variable of any of the definitions that follow it in body.

It is an error to define the same identifier more than once in the same body.

Wherever an internal definition can occur, (begin definition_1 ...) is equivalent to the sequence of definitions that form the body of the begin.

Multiple-value definitions

Another kind of definition is provided by define-values, which creates multiple definitions from a single expression returning multiple values. It is allowed wherever define is allowed.

(define-values formals expression)  syntax

It is an error if a variable appears more than once in the set of formals.

Semantics: Expression is evaluated, and the formals are bound to the return values in the same way that the formals in a lambda expression are matched to the arguments in a procedure call.

(define-values (x y) (exact-integer-sqrt 17))
(list x y) ;; => (4 1)

(let ()
  (define-values (x y) (values 1 2))
  (+ x y)) ;; => 3

Syntax definitions

Syntax definitions have this form:

(define-syntax keyword transformer spec)

Keyword is an identifier, and the transformer spec is an instance of syntax-rules. Like variable definitions, syntax definitions can appear at the outermost level or nested within a body.

If the define-syntax occurs at the outermost level, then the global syntactic environment is extended by binding the keyword to the specified transformer, but previous expansions of any global binding for keyword remain unchanged. Otherwise, it is an internal syntax definition, and is local to the body in which it is defined. Any use of a syntax keyword before its corresponding definition is an error. In particular, a use that precedes an inner definition will not apply an outer definition.

(let ((x 1) (y 2))
  (define-syntax swap!
    (syntax-rules ()
      ((swap! a b)
       (let ((tmp a))
         (set! a b)
         (set! b tmp)))))
  (swap! x y)
  (list x y)) ;; => (2 1)

Macros can expand into definitions in any context that permits them. However, it is an error for a definition to define an identifier whose binding has to be known in order to determine the meaning of the definition itself, or of any preceding definition that belongs to the same group of internal definitions. Similarly, it is an error for an internal definition to define an identifier whose binding has to be known in order to determine the boundary between the internal definitions and the expressions of the body it belongs to. For example, the following are errors:

(define define 3)

(begin (define begin list))

(let-syntax
    ((foo (syntax-rules ()
            ((foo (proc args ...) body ...)
             (define proc
               (lambda (args ...)
                 body ...))))))
  (let ((x 3))
    (foo (plus x y) (+ x y))
    (define foo x)
    (plus foo x)))

Record-type definitions

Record-type definitions are used to introduce new data types, called record types. Like other definitions, they can appear either at the outermost level or in a body. The values of a record type are called records and are aggregations of zero or more fields, each of which holds a single location. A predicate, a constructor, and field accessors and mutators are defined for each record type.

(define-record-type name ... TODO FIXME) syntax

Syntax: name and pred are identifiers. The constructor is of the form

(<constructore-name> <field-name> ...)

and each field is either of the form

(<field-name> <accessor-name>)

or of the form

(<field-name> <accessor-name> <modified-name>)

It is an error for the same identifier to occur more than once as a field name. It is also an error for the same identifier to occur more than once as an accessor or mutator name.

The define-record-type construct is generative: each use creates a new record type that is distinct from all existing types, including Scheme’s predefined types and other record types — even record types of the same name or structure.

An instance of define-record-type is equivalent to the following definitions:

For instance, the following record-type definition

(define-record-type <pare>
  (kons x y)
  pare?
  (x kar set-kar!)
  (y kdr))

defines kons to be a constructor, kar and kdr to be accessors, set-kar! to be a modifier, and pare? to be a predicate for instances of <pare>.

(pare? (kons 1 2)) ;; => #t
(pare? (cons 1 2)) ;; => #f
(kar (kons 1 2)) ;; => 1
(kdr (kons 1 2)) ;; => 2
(let ((k (kons 1 2)))
  (set-kar! k 3)
  (kar k)) ;; => 3

Libraries

Libraries provide a way to organize Scheme programs into reusable parts with explicitly defined interfaces to the rest of the program. This section defines the notation and semantics for libraries.

Library Syntax

A library definition takes the following form:

(define-library <library-name>
  <library-declaration> ...)

library name is a list whose members are identifiers and exact non-negative integers. It is used to identify the library uniquely when importing from other programs or libraries. Libraries whose first identifier is scheme are reserved for use by this report and future versions of this report. Libraries whose first identifier is srfi are reserved for libraries implementing Scheme Requests for Implementation. It is inadvisable, but not an error, for identifiers in library names to contain any of the characters | ' ? * < ” : > + [ ] / or control characters after escapes are expanded.

A library declaration is any of:

An export declaration specifies a list of identifiers which can be made visible to other libraries or programs. An export spec takes one of the following forms:

In an export spec, an identifier names a single binding defined within or imported into the library, where the external name for the export is the same as the name of the binding within the library. A rename spec exports the binding defined within or imported into the library and named by identifier1 in each (identifier_1 identifier_2) pairing, using identifier2 as the external name.

An import declaration provides a way to import the identifiers exported by another library. It has the same syntax and semantics as an import declaration used in a program or at the REPL (see section [import]).

The begin, include, and include-ci declarations are used to specify the body of the library. They have the same syntax and semantics as the corresponding expression types. This form of begin is analogous to, but not the same as, the two types of begin defined in section [sequencing].

The include-library-declarations declaration is similar to include except that the contents of the file are spliced directly into the current library definition. This can be used, for example, to share the same export declaration among multiple libraries as a simple form of library interface.

The cond-expand declaration has the same syntax and semantics as the cond-expand expression type, except that it expands to spliced-in library declarations rather than expressions enclosed in begin.

One possible implementation of libraries is as follows: After all cond-expand library declarations are expanded, a new environment is constructed for the library consisting of all imported bindings. The expressions from all begin, include and include-ci library declarations are expanded in that environment in the order in which they occur in the library. Alternatively, cond-expand and import declarations may be processed in left to right order interspersed with the processing of other declarations, with the environment growing as imported bindings are added to it by each import declaration.

When a library is loaded, its expressions are executed in textual order. If a library’s definitions are referenced in the expanded form of a program or library body, then that library must be loaded before the expanded program or library body is evaluated. This rule applies transitively. If a library is imported by more than one program or library, it may possibly be loaded additional times.

Similarly, during the expansion of a library (foo), if any syntax keywords imported from another library (bar) are needed to expand the library, then the library (bar) must be expanded and its syntax definitions evaluated before the expansion of (foo).

Regardless of the number of times that a library is loaded, each program or library that imports bindings from a library must do so from a single loading of that library, regardless of the number of import declarations in which it appears. That is, (import (only (foo) a)) followed by (import (only (foo) b)) has the same effect as (import (only (foo) a b)).

Library example

The following example shows how a program can be divided into libraries plus a relatively small main program . If the main program is entered into a REPL, it is not necessary to import the base library.

(define-library (example grid)
  (export make rows cols ref each
          (rename put! set!))
  (import (scheme base))
  (begin
    ;; Create an NxM grid.
    (define (make n m)
      (let ((grid (make-vector n)))
        (do ((i 0 (+ i 1)))
            ((= i n) grid)
          (let ((v (make-vector m \sharpfalse{})))
            (vector-set! grid i v)))))
    (define (rows grid)
      (vector-length grid))
    (define (cols grid)
      (vector-length (vector-ref grid 0)))
    ;; Return \sharpfalse{} if out of range.
    (define (ref grid n m)
      (and (< -1 n (rows grid))
           (< -1 m (cols grid))
           (vector-ref (vector-ref grid n) m)))
    (define (put! grid n m v)
      (vector-set! (vector-ref grid n) m v))
    (define (each grid proc)
      (do ((j 0 (+ j 1)))
          ((= j (rows grid)))
        (do ((k 0 (+ k 1)))
            ((= k (cols grid)))
          (proc j k (ref grid j k)))))))

(define-library (example life)
  (export life)
  (import (except (scheme base) set!)
          (scheme write)
          (example grid))
  (begin
    (define (life-count grid i j)
      (define (count i j)
        (if (ref grid i j) 1 0))
      (+ (count (- i 1) (- j 1))
         (count (- i 1) j)
         (count (- i 1) (+ j 1))
         (count i (- j 1))
         (count i (+ j 1))
         (count (+ i 1) (- j 1))
         (count (+ i 1) j)
         (count (+ i 1) (+ j 1))))
    (define (life-alive? grid i j)
      (case (life-count grid i j)
        ((3) \sharptrue{})
        ((2) (ref grid i j))
        (else \sharpfalse{})))
    (define (life-print grid)
      (display "\x1B;[1H\x1B;[J")  ; clear vt100
      (each grid
            (lambda (i j v)
              (display (if v "*" " "))
              (when (= j (- (cols grid) 1))
                (newline)))))
    (define (life grid iterations)
      (do ((i 0 (+ i 1))
           (grid0 grid grid1)
           (grid1 (make (rows grid) (cols grid))
                  grid0))
          ((= i iterations))
        (each grid0
              (lambda (j k v)
                (let ((a (life-alive? grid0 j k)))
                  (set! grid1 j k a))))
        (life-print grid1)))))

;; Main program.
(import (scheme base)
        (only (example life) life)
        (rename (prefix (example grid) grid-)
                (grid-make make-grid)))

;; Initialize a grid with a glider.
(define grid (make-grid 24 24))
(grid-set! grid 1 1 \sharptrue{})
(grid-set! grid 2 2 \sharptrue{})
(grid-set! grid 3 0 \sharptrue{})
(grid-set! grid 3 1 \sharptrue{})
(grid-set! grid 3 2 \sharptrue{})

;; Run for 80 iterations.
(life grid 80)

The REPL

Implementations may provide an interactive session called a REPL (Read-Eval-Print Loop), where import declarations, expressions and definitions can be entered and evaluated one at a time. For convenience and ease of use, the global Scheme environment in a REPL must not be empty, but must start out with at least the bindings provided by the base library. This library includes the core syntax of Scheme and generally useful procedures that manipulate data. For example, the variable abs is bound to a procedure of one argument that computes the absolute value of a number, and the variable + is bound to a procedure that computes sums. The full list of (scheme base) bindings can be found in Appendix [stdlibraries].

Implementations may provide an initial REPL environment which behaves as if all possible variables are bound to locations, most of which contain unspecified values. Top level REPL definitions in such an implementation are truly equivalent to assignments, unless the identifier is defined as a syntax keyword.

An implementation may provide a mode of operation in which the REPL reads its input from a file. Such a file is not, in general, the same as a program, because it can contain import declarations in places other than the beginning.

Standard procedures

This chapter describes Scheme’s built-in procedures.

The procedures force, promise?, and make-promise are intimately associated with the expression types delay and delay-force, and are described with them in section [force]. In the same way, the procedure make-parameter is intimately associated with the expression type parameterize, and is described with it in section [make-parameter].

A program can use a global variable definition to bind any variable. It may subsequently alter any such binding by an assignment (see section [assignment]). These operations do not modify the behavior of any procedure defined in this report or imported from a library (see section [libraries]). Altering any global binding that has not been introduced by a definition has an unspecified effect on the behavior of the procedures defined in this chapter.

When a procedure is said to return a newly allocated object, it means that the locations in the object are fresh.

Equivalence predicates

A predicate is a procedure that always returns a boolean value (#t or #f). An equivalence predicate is the computational analogue of a mathematical equivalence relation; it is symmetric, reflexive, and transitive. Of the equivalence predicates described in this section, eq? is the finest or most discriminating, equal? is the coarsest, and eqv? is slightly less discriminating than eq?.

(eqv? obj1 obj2)  procedure The eqv? procedure defines a useful equivalence relation on objects. Briefly, it returns #t if obj1 and obj2 are normally regarded as the same object. This relation is left slightly open to interpretation, but the following partial specification of eqv? holds for all implementations of Scheme.

The eqv? procedure returns #t if:

The eqv? procedure returns #f if:

(eqv? 'a 'a) ;; => #t
(eqv? 'a 'b) ;; => #f
(eqv? 2 2) ;; => #t
(eqv? 2 2.0) ;; => #f
(eqv? '() '()) ;; => #t
(eqv? 100000000 100000000) ;; => #t
(eqv? 0.0 +nan.0) ;; => #f
(eqv? (cons 1 2) (cons 1 2)) ;; => #f
(eqv? (lambda () 1)
      (lambda () 2)) ;; => #f
(let ((p (lambda (x) x)))
  (eqv? p p)) ;; => #t
(eqv? #f 'nil) ;; => #f

The following examples illustrate cases in which the above rules do not fully specify the behavior of eqv?. All that can be said about such cases is that the value returned by eqv? must be a boolean.

(eqv? "" "") ;; => unspecified
(eqv? '#() '#()) ;; => unspecified
(eqv? (lambda (x) x)
      (lambda (x) x)) ;; => unspecified
(eqv? (lambda (x) x)
      (lambda (y) y)) ;; => unspecified
(eqv? 1.0e0 1.0f0) ;; => unspecified
(eqv? +nan.0 +nan.0) ;; => unspecified

Note that (eqv? 0.0 -0.0) will return #f if negative zero is distinguished, and #t if negative zero is not distinguished.

The next set of examples shows the use of eqv? with procedures that have local state. The gen-counter procedure must return a distinct procedure every time, since each procedure has its own internal counter. The gen-loser procedure, however, returns operationally equivalent procedures each time, since the local state does not affect the value or side effects of the procedures. However, eqv? may or may not detect this equivalence.

(define gen-counter
  (lambda ()
    (let ((n 0))
      (lambda () (set! n (+ n 1)) n))))
(let ((g (gen-counter)))
  (eqv? g g)) ;; => #t
(eqv? (gen-counter) (gen-counter))
;; => #f
(define gen-loser
  (lambda ()
    (let ((n 0))
      (lambda () (set! n (+ n 1)) 27))))
(let ((g (gen-loser)))
  (eqv? g g)) ;; => #t
(eqv? (gen-loser) (gen-loser))
;; => unspecified

(letrec ((f (lambda () (if (eqv? f g) 'both 'f)))
         (g (lambda () (if (eqv? f g) 'both 'g))))
  (eqv? f g))
;; => unspecified

(letrec ((f (lambda () (if (eqv? f g) 'f 'both)))
         (g (lambda () (if (eqv? f g) 'g 'both))))
  (eqv? f g))
;; => #f

Since it is an error to modify constant objects (those returned by literal expressions), implementations may share structure between constants where appropriate. Thus the value of eqv? on constants is sometimes implementation-dependent.

(eqv? '(a) '(a)) ;; => unspecified
(eqv? "a" "a") ;; => unspecified
(eqv? '(b) (cdr '(a b))) ;; => unspecified
(let ((x '(a)))
  (eqv? x x)) ;; => #t

The above definition of eqv? allows implementations latitude in their treatment of procedures and literals: implementations may either detect or fail to detect that two procedures or two literals are equivalent to each other, and can decide whether or not to merge representations of equivalent objects by using the same pointer or bit pattern to represent both.

Note: If inexact numbers are represented as IEEE binary floating-point numbers, then an implementation of eqv? that simply compares equal-sized inexact numbers for bitwise equality is correct by the above definition.

(eq? obj1 obj2)  procedure The eq? procedure is similar to eqv? except that in some cases it is capable of discerning distinctions finer than those detectable by eqv?. It must always return #f when eqv? also would, but may return #f in some cases where eqv? would return #t.

On symbols, booleans, the empty list, pairs, and records, and also on non-empty strings, vectors, and bytevectors, eq? and eqv? are guaranteed to have the same behavior. On procedures, eq? must return true if the arguments’ location tags are equal. On numbers and characters, eq?’s behavior is implementation-dependent, but it will always return either true or false. On empty strings, empty vectors, and empty bytevectors, eq? may also behave differently from eqv?.

(eq? 'a 'a) ;; => #t
(eq? '(a) '(a)) ;; => unspecified
(eq? (list 'a) (list 'a)) ;; => #f
(eq? "a" "a") ;; => unspecified
(eq? "" "") ;; => unspecified
(eq? '() '()) ;; => #t
(eq? 2 2) ;; => unspecified
(eq? #\A #\A) ;; => unspecified
(eq? car car) ;; => #t
(let ((n (+ 2 3)))
  (eq? n n)) ;; => unspecified
(let ((x '(a)))
  (eq? x x)) ;; => #t
(let ((x '#()))
  (eq? x x)) ;; => #t
(let ((p (lambda (x) x)))
  (eq? p p)) ;; => #t

Rationale: It will usually be possible to implement eq? much more efficiently than eqv?, for example, as a simple pointer comparison instead of as some more complicated operation. One reason is that it is not always possible to compute eqv? of two numbers in constant time, whereas eq? implemented as pointer comparison will always finish in constant time.

(equal? obj1 obj2)  procedure The equal? procedure, when applied to pairs, vectors, strings and bytevectors, recursively compares them, returning #t when the unfoldings of its arguments into (possibly infinite) trees are equal (in the sense of equal?) as ordered trees, and #f otherwise. It returns the same as eqv? when applied to booleans, symbols, numbers, characters, ports, procedures, and the empty list. If two objects are eqv?, they must be equal? as well. In all other cases, equal? may return either #t or #f.

Even if its arguments are circular data structures, equal? must always terminate.

(equal? 'a 'a) ;; => #t
(equal? '(a) '(a)) ;; => #t
(equal? '(a (b) c)
        '(a (b) c)) ;; => #t
(equal? "abc" "abc") ;; => #t
(equal? 2 2) ;; => #t
(equal? (make-vector 5 'a)
        (make-vector 5 'a)) ;; => #t
(equal? '#1=(a b . #1#)
        '#2=(a b a b . #2#)) ;; => #t
(equal? (lambda (x) x)
        (lambda (y) y)) ;; => unspecified

Note: A rule of thumb is that objects are generally equal? if they print the same.

Numbers

It is important to distinguish between mathematical numbers, the Scheme numbers that attempt to model them, the machine representations used to implement the Scheme numbers, and notations used to write numbers. This report uses the types number, complex, real, rational, and integer to refer to both mathematical numbers and Scheme numbers.

Numerical types

Mathematically, numbers are arranged into a tower of subtypes in which each level is a subset of the level above it:

number
complex number
real number
rational number
integer

For example, 3 is an integer. Therefore 3 is also a rational, a real, and a complex number. The same is true of the Scheme numbers that model 3. For Scheme numbers, these types are defined by the predicates number?, complex?, real?, rational?, and integer?.

There is no simple relationship between a number’s type and its representation inside a computer. Although most implementations of Scheme will offer at least two different representations of 3, these different representations denote the same integer.

Scheme’s numerical operations treat numbers as abstract data, as independent of their representation as possible. Although an implementation of Scheme may use multiple internal representations of numbers, this ought not to be apparent to a casual programmer writing simple programs.

Exactness

It is useful to distinguish between numbers that are represented exactly and those that might not be. For example, indexes into data structures must be known exactly, as must some polynomial coefficients in a symbolic algebra system. On the other hand, the results of measurements are inherently inexact, and irrational numbers may be approximated by rational and therefore inexact approximations. In order to catch uses of inexact numbers where exact numbers are required, Scheme explicitly distinguishes exact from inexact numbers. This distinction is orthogonal to the dimension of type.

A Scheme number is exact if it was written as an exact constant or was derived from exact numbers using only exact operations. A number is inexact if it was written as an inexact constant, if it was derived using inexact ingredients, or if it was derived using inexact operations. Thus inexactness is a contagious property of a number. In particular, an exact complex number has an exact real part and an exact imaginary part; all other complex numbers are inexact complex numbers.

If two implementations produce exact results for a computation that did not involve inexact intermediate results, the two ultimate results will be mathematically equal. This is generally not true of computations involving inexact numbers since approximate methods such as floating-point arithmetic may be used, but it is the duty of each implementation to make the result as close as practical to the mathematically ideal result.

Rational operations such as + should always produce exact results when given exact arguments. If the operation is unable to produce an exact result, then it may either report the violation of an implementation restriction or it may silently coerce its result to an inexact value. However, (/ 3 4) must not return the mathematically incorrect value 0. See section [restrictions].

Except for exact, the operations described in this section must generally return inexact results when given any inexact arguments. An operation may, however, return an exact result if it can prove that the value of the result is unaffected by the inexactness of its arguments. For example, multiplication of any number by an exact zero may produce an exact zero result, even if the other argument is inexact.

Specifically, the expression (* 0 +inf.0) may return 0, or +nan.0, or report that inexact numbers are not supported, or report that non-rational real numbers are not supported, or fail silently or noisily in other implementation-specific ways.

Implementation restrictions

Implementations of Scheme are not required to implement the whole tower of subtypes given in section [numericaltypes], but they must implement a coherent subset consistent with both the purposes of the implementation and the spirit of the Scheme language. For example, implementations in which all numbers are real, or in which non-real numbers are always inexact, or in which exact numbers are always integer, are still quite useful.

Implementations may also support only a limited range of numbers of any type, subject to the requirements of this section. The supported range for exact numbers of any type may be different from the supported range for inexact numbers of that type. For example, an implementation that uses IEEE binary double-precision floating-point numbers to represent all its inexact real numbers may also support a practically unbounded range of exact integers and rationals while limiting the range of inexact reals (and therefore the range of inexact integers and rationals) to the dynamic range of the IEEE binary double format. Furthermore, the gaps between the representable inexact integers and rationals are likely to be very large in such an implementation as the limits of this range are approached.

An implementation of Scheme must support exact integers throughout the range of numbers permitted as indexes of lists, vectors, bytevectors, and strings or that result from computing the length of one of these. The length, vector-length, bytevector-length, and string-length procedures must return an exact integer, and it is an error to use anything but an exact integer as an index. Furthermore, any integer constant within the index range, if expressed by an exact integer syntax, must be read as an exact integer, regardless of any implementation restrictions that apply outside this range. Finally, the procedures listed below will always return exact integer results provided all their arguments are exact integers and the mathematically expected results are representable as exact integers within the implementation:

-                     *
+                     abs
ceiling               denominator
exact-integer-sqrt    expt
floor                 floor/
floor-quotient        floor-remainder
gcd                   lcm
max                   min
modulo                numerator
quotient              rationalize
remainder             round
square                truncate
truncate/             truncate-quotient
truncate-remainder

It is recommended, but not required, that implementations support exact integers and exact rationals of practically unlimited size and precision, and to implement the above procedures and the / procedure in such a way that they always return exact results when given exact arguments. If one of these procedures is unable to deliver an exact result when given exact arguments, then it may either report a violation of an implementation restriction or it may silently coerce its result to an inexact number; such a coercion can cause an error later. Nevertheless, implementations that do not provide exact rational numbers should return inexact rational numbers rather than reporting an implementation restriction.

An implementation may use floating-point and other approximate representation strategies for inexact numbers. This report recommends, but does not require, that implementations that use floating-point representations follow the IEEE 754 standard, and that implementations using other representations should match or exceed the precision achievable using these floating-point standards . In particular, the description of transcendental functions in IEEE 754-2008 should be followed by such implementations, particularly with respect to infinities and NaNs.

Although Scheme allows a variety of written notations for numbers, any particular implementation may support only some of them. For example, an implementation in which all numbers are real need not support the rectangular and polar notations for complex numbers. If an implementation encounters an exact numerical constant that it cannot represent as an exact number, then it may either report a violation of an implementation restriction or it may silently represent the constant by an inexact number.

Implementation extensions

Implementations may provide more than one representation of floating-point numbers with differing precisions. In an implementation which does so, an inexact result must be represented with at least as much precision as is used to express any of the inexact arguments to that operation. Although it is desirable for potentially inexact operations such as sqrt to produce exact answers when applied to exact arguments, if an exact number is operated upon so as to produce an inexact result, then the most precise representation available must be used. For example, the value of (sqrt 4) should be 2, but in an implementation that provides both single and double precision floating point numbers it may be the latter but must not be the former.

It is the programmer’s responsibility to avoid using inexact number objects with magnitude or significand too large to be represented in the implementation.

In addition, implementations may distinguish special numbers called positive infinity, negative infinity, NaN, and negative zero.

Positive infinity is regarded as an inexact real (but not rational) number that represents an indeterminate value greater than the numbers represented by all rational numbers. Negative infinity is regarded as an inexact real (but not rational) number that represents an indeterminate value less than the numbers represented by all rational numbers.

Adding or multiplying an infinite value by any finite real value results in an appropriately signed infinity; however, the sum of positive and negative infinities is a NaN. Positive infinity is the reciprocal of zero, and negative infinity is the reciprocal of negative zero. The behavior of the transcendental functions is sensitive to infinity in accordance with IEEE 754.

A NaN is regarded as an inexact real (but not rational) number so indeterminate that it might represent any real value, including positive or negative infinity, and might even be greater than positive infinity or less than negative infinity. An implementation that does not support non-real numbers may use NaN to represent non-real values like (sqrt -1.0) and (asin 2.0).

A NaN always compares false to any number, including a NaN. An arithmetic operation where one operand is NaN returns NaN, unless the implementation can prove that the result would be the same if the NaN were replaced by any rational number. Dividing zero by zero results in NaN unless both zeros are exact.

Negative zero is an inexact real value written -0.0 and is distinct (in the sense of eqv?) from 0.0. A Scheme implementation is not required to distinguish negative zero. If it does, however, the behavior of the transcendental functions is sensitive to the distinction in accordance with IEEE 754. Specifically, in a Scheme implementing both complex numbers and negative zero, the branch cut of the complex logarithm function is such that (imag-part (log -1.0-0.0i)) is  − π rather than π.

Furthermore, the negation of negative zero is ordinary zero and vice versa. This implies that the sum of two or more negative zeros is negative, and the result of subtracting (positive) zero from a negative zero is likewise negative. However, numerical comparisons treat negative zero as equal to zero.

Note that both the real and the imaginary parts of a complex number can be infinities, NaNs, or negative zero.

Syntax of numerical constants

The syntax of the written representations for numbers is described formally in section [numbersyntax]. Note that case is not significant in numerical constants.

A number can be written in binary, octal, decimal, or hexadecimal by the use of a radix prefix. The radix prefixes are #b (binary), #o (octal), #d (decimal), and #x (hexadecimal). With no radix prefix, a number is assumed to be expressed in decimal.

A numerical constant can be specified to be either exact or inexact by a prefix. The prefixes are #e for exact, and #i for inexact. An exactness prefix can appear before or after any radix prefix that is used. If the written representation of a number has no exactness prefix, the constant is inexact if it contains a decimal point or an exponent. Otherwise, it is exact.

In systems with inexact numbers of varying precisions it can be useful to specify the precision of a constant. For this purpose, implementations may accept numerical constants written with an exponent marker that indicates the desired precision of the inexact representation. If so, the letter s, f, d, or l, meaning short, single, double, or long precision, respectively, can be used in place of e. The default precision has at least as much precision as double, but implementations may allow this default to be set by the user.

3.14159265358979F0
;; Round to single --- 3.141593
0.6L0
;; Extend to long --- .600000000000000

The numbers positive infinity, negative infinity, and NaN are written +inf.0, -inf.0 and +nan.0 respectively. NaN may also be written -nan.0. The use of signs in the written representation does not necessarily reflect the underlying sign of the NaN value, if any. Implementations are not required to support these numbers, but if they do, they must do so in general conformance with IEEE 754. However, implementations are not required to support signaling NaNs, nor to provide a way to distinguish between different NaNs.

There are two notations provided for non-real complex numbers: the rectangular notation a+bi, where a is the real part and b is the imaginary part; and the polar notation r@θ, where r is the magnitude and θ is the phase (angle) in radians. These are related by the equation a + *b**i = rcos θ + (rsinθ)i. All of a, b, r, and θ* are real numbers.

Numerical operations

The reader is referred to section [typeconventions] for a summary of the naming conventions used to specify restrictions on the types of arguments to numerical routines. The examples used in this section assume that any numerical constant written using an exact notation is indeed represented as an exact number. Some examples also assume that certain numerical constants written using an inexact notation can be represented without loss of accuracy; the inexact constants were chosen so that this is likely to be true in implementations that use IEEE binary doubles to represent inexact numbers.

(number? obj)  procedure

(complex? obj)  procedure

(real? obj)  procedure

(rational? obj)  procedure

(integer? obj)  procedure

These numerical type predicates can be applied to any kind of argument, including non-numbers. They return #t if the object is of the named type, and otherwise they return #f. In general, if a type predicate is true of a number then all higher type predicates are also true of that number. Consequently, if a type predicate is false of a number, then all lower type predicates are also false of that number.

If z is a complex number, then (real? z) is true if and only if (zero? (imag-part z)) is true. If x is an inexact real number, then (integer? x) is true if and only if (= x (round x)).

The numbers +inf.0, -inf.0, and +nan.0 are real but not rational.

(complex? 3+4i) ;; => #t
(complex? 3) ;; => #t
(real? 3) ;; => #t
(real? -2.5+0i) ;; => #t
(real? -2.5+0.0i) ;; => #f
(real? #e1e10) ;; => #t
(real? +inf.0) ;; => #t
(real? +nan.0) ;; => #t
(rational? -inf.0) ;; => #f
(rational? 3.5) ;; => #t
(rational? 6/10) ;; => #t
(rational? 6/3) ;; => #t
(integer? 3+0i) ;; => #t
(integer? 3.0) ;; => #t
(integer? 8/4) ;; => #t

Note: The behavior of these type predicates on inexact numbers is unreliable, since any inaccuracy might affect the result.

Note: In many implementations the complex? procedure will be the same as number?, but unusual implementations may represent some irrational numbers exactly or may extend the number system to support some kind of non-complex numbers.

(exact? z)  procedure

(inexact? z)  procedure

These numerical predicates provide tests for the exactness of a quantity. For any Scheme number, precisely one of these predicates is true.

(exact? 3.0) ;; => #f
(exact? #e3.0) ;; => #t
(inexact? 3.) ;; => #t

(exact-integer? z)  procedure

Returns #t if z is both exact and an integer; otherwise returns #f.

(exact-integer? 32) ;; => #t{}
(exact-integer? 32.0) ;; => #f
(exact-integer? 32/5) ;; => #f

(finite? z)  inexact library procedure

The finite? procedure returns #t on all real numbers except +inf.0, -inf.0, and +nan.0, and on complex numbers if their real and imaginary parts are both finite. Otherwise it returns #f.

(finite? 3) ;; => #t
(finite? +inf.0) ;; => #f
(finite? 3.0+inf.0i) ;; => #f

(infinite? z)  inexact library procedure

The infinite? procedure returns #t on the real numbers +inf.0 and -inf.0, and on complex numbers if their real or imaginary parts or both are infinite. Otherwise it returns #f.

(infinite? 3) ;; => #f
(infinite? +inf.0) ;; => #t
(infinite? +nan.0) ;; => #f
(infinite? 3.0+inf.0i) ;; => #t

(nan? z)  inexact library procedure

The nan? procedure returns #t on +nan.0, and on complex numbers if their real or imaginary parts or both are +nan.0. Otherwise it returns #f.

(nan? +nan.0) ;; => #t
(nan? 32) ;; => #f
(nan? +nan.0+5.0i) ;; => #t
(nan? 1+2i) ;; => #f

(= **z1 z2 z3 … )  procedure

(< **x1 x2 x3 … )  procedure

(> **x1 x2 x3 … )  procedure

(<= **x1 x2 x3 … )  procedure

(>= **x1 x2 x3 … )  procedure

These procedures return #t if their arguments are (respectively): equal, monotonically increasing, monotonically decreasing, monotonically non-decreasing, or monotonically non-increasing, and #f otherwise. If any of the arguments are +nan.0, all the predicates return #f. They do not distinguish between inexact zero and inexact negative zero.

These predicates are required to be transitive.

Note: The implementation approach of converting all arguments to inexact numbers if any argument is inexact is not transitive. For example, let big be (expt 2 1000), and assume that big is exact and that inexact numbers are represented by 64-bit IEEE binary floating point numbers. Then (= (- big 1) (inexact big)) and (= (inexact big) (+ big 1)) would both be true with this approach, because of the limitations of IEEE representations of large integers, whereas (= (- big 1) (+ big 1)) is false. Converting inexact values to exact numbers that are the same (in the sense of =) to them will avoid this problem, though special care must be taken with infinities.

Note: While it is not an error to compare inexact numbers using these predicates, the results are unreliable because a small inaccuracy can affect the result; this is especially true of = and zero?. When in doubt, consult a numerical analyst.

(zero? z)  procedure

(positive? x)  procedure

(negative? x)  procedure

(odd? n)  procedure

(even? n)  procedure

These numerical predicates test a number for a particular property, returning #t or #f. See note above.

(max **x1 x2 … )  procedure

(min **x1 x2 … )  procedure

These procedures return the maximum or minimum of their arguments.

(max 3 4) ;; => 4    ; exact
(max 3.9 4) ;; => 4.0  ; inexact

Note: If any argument is inexact, then the result will also be inexact (unless the procedure can prove that the inaccuracy is not large enough to affect the result, which is possible only in unusual implementations). If min or max is used to compare numbers of mixed exactness, and the numerical value of the result cannot be represented as an inexact number without loss of accuracy, then the procedure may report a violation of an implementation restriction.

(+ z1 … )  procedure (* z1 … )  procedure These procedures return the sum or product of their arguments.

(+ 3 4) ;; => 7
(+ 3) ;; => 3
(+) ;; => 0
(* 4) ;; => 4
(*) ;; => 1

(- z)  procedure

(- **z1 z2 … )  procedure

(/ z)  procedure

(/ **z1 z2 … )  procedure

With two or more arguments, these procedures return the difference or quotient of their arguments, associating to the left. With one argument, however, they return the additive or multiplicative inverse of their argument.

It is an error if any argument of / other than the first is an exact zero. If the first argument is an exact zero, an implementation may return an exact zero unless one of the other arguments is a NaN.

(- 3 4) ;; => -1
(- 3 4 5) ;; => -6
(- 3) ;; => -3
(/ 3 4 5) ;; => 3/20
(/ 3) ;; => 1/3

(abs x)  procedure

The abs procedure returns the absolute value of its argument.

(abs -7) ;; => 7

(floor/ **n1 n2)  procedure

(floor-quotient **n1 n2)  procedure

(floor-remainder **n1 n2)  procedure

(truncate/ **n1 n2)  procedure

(truncate-quotient **n1 n2)  procedure

(truncate-remainder **n1 n2)  procedure

These procedures implement number-theoretic (integer) division. It is an error if n2 is zero. The procedures ending in / return two integers; the other procedures return an integer. All the procedures compute a quotient nq and remainder nr such that ${\\hbox{$n_1$\\/}} = {\\hbox{$n_2$\\/}} {\\hbox{$n_q$\\/}} + {\\hbox{$n_r$\\/}}$. For each of the division operators, there are three procedures defined as follows:

(<operator>/ \vri{n} \vrii{n}) ;; => \vr{n_q} \vr{n_r}
(<operator>-quotient \vri{n} \vrii{n}) ;; => \vr{n_q}
(<operator>-remainder \vri{n} \vrii{n}) ;; => \vr{n_r}

The remainder nr is determined by the choice of integer nq: ${\\hbox{$n_r$\\/}} = {\\hbox{$n_1$\\/}} - {\\hbox{$n_2$\\/}} {\\hbox{$n_q$\\/}}$. Each set of operators uses a different choice of nq:

floor ${\\hbox{$n_q$\\/}} = \\lfloor{\\hbox{$n_1$\\/}} / {\\hbox{$n_2$\\/}}\\rfloor$
truncate ${\\hbox{$n_q$\\/}} = \\text{truncate}({\\hbox{$n_1$\\/}} / {\\hbox{$n_2$\\/}})$

For any of the operators, and for integers n1 and n2 with n2 not equal to 0,

(= \vri{n} (+ (* \vrii{n} (<operator>-quotient \vri{n} \vrii{n}))
              (<operator>-remainder \vri{n} \vrii{n})))
 ;; => #t

provided all numbers involved in that computation are exact.

Examples:

(floor/ 5 2) ;; => 2 1
(floor/ -5 2) ;; => -3 1
(floor/ 5 -2) ;; => -3 -1
(floor/ -5 -2) ;; => 2 -1
(truncate/ 5 2) ;; => 2 1
(truncate/ -5 2) ;; => -2 -1
(truncate/ 5 -2) ;; => -2 1
(truncate/ -5 -2) ;; => 2 -1
(truncate/ -5.0 -2) ;; => 2.0 -1.0

(quotient **n1 n2)  procedure

(remainder **n1 n2)  procedure

(modulo **n1 n2)  procedure

The quotient and remainder procedures are equivalent to truncate-quotient and truncate-remainder, respectively, and modulo is equivalent to floor-remainder.

Note: These procedures are provided for backward compatibility with earlier versions of this report.

(gcd **n1 … )  procedure

(lcm **n1 … )  procedure

These procedures return the greatest common divisor or least common multiple of their arguments. The result is always non-negative.

(gcd 32 -36) ;; => 4
(gcd) ;; => 0
(lcm 32 -36) ;; => 288
(lcm 32.0 -36) ;; => 288.0  ; inexact
(lcm) ;; => 1

(numerator q)  procedure

(denominator q)  procedure

These procedures return the numerator or denominator of their argument; the result is computed as if the argument was represented as a fraction in lowest terms. The denominator is always positive. The denominator of 0 is defined to be 1.

(numerator (/ 6 4)) ;; => 3
(denominator (/ 6 4)) ;; => 2
(denominator
 (inexact (/ 6 4))) ;; => 2.0

(floor x)  procedure

(ceiling x)  procedure

(truncate x)  procedure

(round x)  procedure

These procedures return integers. The floor procedure returns the largest integer not larger than x. The ceiling procedure returns the smallest integer not smaller than x, truncate returns the integer closest to x whose absolute value is not larger than the absolute value of x, and round returns the closest integer to x, rounding to even when x is halfway between two integers.

Rationale: The round procedure rounds to even for consistency with the default rounding mode specified by the IEEE 754 IEEE floating-point standard.

Note: If the argument to one of these procedures is inexact, then the result will also be inexact. If an exact value is needed, the result can be passed to the exact procedure. If the argument is infinite or a NaN, then it is returned.

(floor -4.3) ;; => -5.0
(ceiling -4.3) ;; => -4.0
(truncate -4.3) ;; => -4.0
(round -4.3) ;; => -4.0

(floor 3.5) ;; => 3.0
(ceiling 3.5) ;; => 4.0
(truncate 3.5) ;; => 3.0
(round 3.5) ;; => 4.0  ; inexact

(round 7/2) ;; => 4    ; exact
(round 7) ;; => 7

(rationalize x y)  procedure

The rationalize procedure returns the simplest rational number differing from x by no more than y. A rational number r1 is simpler than another rational number r2 if r1 = p1/q1 and r2 = p2/q2 (in lowest terms) and |p1| ≤ |p2| and |q1| ≤ |q2|. Thus 3/5 is simpler than 4/7. Although not all rationals are comparable in this ordering (consider 2/7 and 3/5), any interval contains a rational number that is simpler than every other rational number in that interval (the simpler 2/5 lies between 2/7 and 3/5). Note that 0 = 0/1 is the simplest rational of all.

(rationalize
 (exact .3) 1/10) ;; => 1/3    ; exact
(rationalize .3 1/10) ;; => #i1/3  ; inexact

(exp z)  inexact library procedure

(log z)  inexact library procedure

(log **z1 z2)  inexact library procedure

(sin z)  inexact library procedure

(cos z)  inexact library procedure

(tan z)  inexact library procedure

(asin z)  inexact library procedure

(acos z)  inexact library procedure

(atan z)  inexact library procedure

(atan y x)  inexact library procedure

These procedures compute the usual transcendental functions. The log procedure computes the natural logarithm of z (not the base ten logarithm) if a single argument is given, or the base-z2 logarithm of z1 if two arguments are given. The asin, acos, and atan procedures compute arcsine (sin−1), arc-cosine (cos−1), and arctangent (tan−1), respectively. The two-argument variant of atan computes (angle (make-rectangular x y)) (see below), even in implementations that don’t support complex numbers.

In general, the mathematical functions log, arcsine, arc-cosine, and arctangent are multiply defined. The value of log z is defined to be the one whose imaginary part lies in the range from  − π (inclusive if -0.0 is distinguished, exclusive otherwise) to π (inclusive). The value of log 0 is mathematically undefined. With log  defined this way, the values of sin−1z, cos−1z, and tan−1z are according to the following formulæ: $$\\sin^{- 1}z = - i\\log\\left( iz + \\sqrt{1 - z^{2}} \\right)$$ cos−1z = π/2 − sin−1z tan−1z = (log(1+iz)−log(1−iz))/(2i)

However, (log 0.0) returns -inf.0 (and (log -0.0) returns -inf.0+πi) if the implementation supports infinities (and -0.0).

The range of (atan y x) is as in the following table. The asterisk (*) indicates that the entry applies to implementations that distinguish minus zero.

y condition x condition range of result r
y = 0.0 x > 0.0 0.0
* y =  + 0.0 x > 0.0  + 0.0
* y =  − 0.0 x > 0.0  − 0.0
y > 0.0 x > 0.0 $0.0 \< r \< \\frac{\\pi}{2}$
y > 0.0 x = 0.0 $\\frac{\\pi}{2}$
y > 0.0 x < 0.0 $\\frac{\\pi}{2} \< r \< \\pi$
y = 0.0 x < 0 π
* y =  + 0.0 x < 0.0 π
* y =  − 0.0 x < 0.0  − π
y < 0.0 x < 0.0 $- \\pi \< r \< - \\frac{\\pi}{2}$
y < 0.0 x = 0.0 $- \\frac{\\pi}{2}$
y < 0.0 x > 0.0 $- \\frac{\\pi}{2} \< r \< 0.0$
y = 0.0 x = 0.0 undefined
* y =  + 0.0 x =  + 0.0  + 0.0
* y =  − 0.0 x =  + 0.0  − 0.0
* y =  + 0.0 x =  − 0.0 π
* y =  − 0.0 x =  − 0.0  − π
* y =  + 0.0 x = 0 $\\frac{\\pi}{2}$
* y =  − 0.0 x = 0 $- \\frac{\\pi}{2}$

The above specification follows , which in turn cites ; refer to these sources for more detailed discussion of branch cuts, boundary conditions, and implementation of these functions. When it is possible, these procedures produce a real result from a real argument.

(square z)  procedure Returns the square of z. This is equivalent to (* z z).

(square 42) ;; => 1764
(square 2.0) ;; => 4.0

(sqrt z)  inexact library procedure Returns the principal square root of z. The result will have either a positive real part, or a zero real part and a non-negative imaginary part.

(sqrt 9) ;; => 3
(sqrt -1) ;; => +i

(exact-integer-sqrt k)  procedure Returns two non-negative exact integers s and r where $\\hbox{\\it{}k\\/} = s^2 + r$ and $\\hbox{\\it{}k\\/} \< (s+1)^2$.

(exact-integer-sqrt 4) ;; => 2 0
(exact-integer-sqrt 5) ;; => 2 1

(expt **z1 z2)  procedure

Returns z1 raised to the power z2. For nonzero z1, this is z1z2 = ez2log z1 The value of 0z is 1 if (zero? z), 0 if (real-part z) is positive, and an error otherwise. Similarly for 0.0z, with inexact results.

(make-rectangular **x1 x2) complex library procedure

(make-polar **x3 x4)  complex library procedure

(real-part z)  complex library procedure

(imag-part z)  complex library procedure

(magnitude z)  complex library procedure

(angle z)  complex library procedure

Let x1, x2, x3, and x4 be real numbers and z be a complex number such that $${\\hbox{$z$\\/}} = {\\hbox{$x_1$\\/}} + {\\hbox{$x_2$\\/}}\\hbox{$i$} = {\\hbox{$x_3$\\/}} \\cdot e^{i x_4}$$ Then all of

(make-rectangular \vri{x} \vrii{x}) ;; => \vr{z}
(make-polar \vriii{x} \vriv{x}) ;; => \vr{z}
(real-part \vr{z}) ;; => \vri{x}
(imag-part \vr{z}) ;; => \vrii{x}
(magnitude \vr{z}) ;; => $|\vriii{x}|$
(angle \vr{z}) ;; => $x_{angle}$

are true, where  − π ≤ xangle ≤ π with $x_{angle} = {\\hbox{$x_4$\\/}} + 2\\pi n$ for some integer n.

The make-polar procedure may return an inexact complex number even if its arguments are exact. The real-part and imag-part procedures may return exact real numbers when applied to an inexact complex number if the corresponding argument passed to make-rectangular was exact.

Rationale: The magnitude procedure is the same as abs for a real argument, but abs is in the base library, whereas magnitude is in the optional complex library.

(inexact z)  procedure

(exact z)  procedure

The procedure inexact returns an inexact representation of z. The value returned is the inexact number that is numerically closest to the argument. For inexact arguments, the result is the same as the argument. For exact complex numbers, the result is a complex number whose real and imaginary parts are the result of applying inexact to the real and imaginary parts of the argument, respectively. If an exact argument has no reasonably close inexact equivalent (in the sense of =), then a violation of an implementation restriction may be reported.

The procedure exact returns an exact representation of z. The value returned is the exact number that is numerically closest to the argument. For exact arguments, the result is the same as the argument. For inexact non-integral real arguments, the implementation may return a rational approximation, or may report an implementation violation. For inexact complex arguments, the result is a complex number whose real and imaginary parts are the result of applying exact to the real and imaginary parts of the argument, respectively. If an inexact argument has no reasonably close exact equivalent, (in the sense of =), then a violation of an implementation restriction may be reported.

These procedures implement the natural one-to-one correspondence between exact and inexact integers throughout an implementation-dependent range. See section [restrictions].

Note: These procedures were known in R5RS as exact->inexact and inexact->exact, respectively, but they have always accepted arguments of any exactness. The new names are clearer and shorter, as well as being compatible with R6RS.

Numerical input and output

(number->string z)  procedure

(number->string z radix)  procedure

It is an error if radix is not one of 2, 8, 10, or 16.

The procedure numberstring takes a number and a radix and returns as a string an external representation of the given number in the given radix such that

(let ((number \vr{number})
      (radix \vr{radix}))
  (eqv? number
        (string->number (number->string number
                                        radix)
                        radix)))

is true. It is an error if no possible result makes this expression true. If omitted, radix defaults to 10.

If z is inexact, the radix is 10, and the above expression can be satisfied by a result that contains a decimal point, then the result contains a decimal point and is expressed using the minimum number of digits (exclusive of exponent and trailing zeroes) needed to make the above expression true ; otherwise the format of the result is unspecified.

The result returned by numberstring never contains an explicit radix prefix.

Note: The error case can occur only when z is not a complex number or is a complex number with a non-rational real or imaginary part.

Rationale: If z is an inexact number and the radix is 10, then the above expression is normally satisfied by a result containing a decimal point. The unspecified case allows for infinities, NaNs, and unusual representations.

(string->number string)  procedure

(string->number string radix)  procedure

Returns a number of the maximally precise representation expressed by the given *string. It is an error if radi**x* is not 2, 8, 10, or 16.

If supplied, radix is a default radix that will be overridden if an explicit radix prefix is present in *strin**g* (e.g. "#o177"). If radix is not supplied, then the default radix is 10. If *strin**g* is not a syntactically valid notation for a number, or would result in a number that the implementation cannot represent, then string->number returns #f. An error is never signaled due to the content of *strin**g*.

(string->number "100") ;; => 100
(string->number "100" 16) ;; => 256
(string->number "1e2") ;; => 100.0

Note: The domain of string->number may be restricted by implementations in the following ways. If all numbers supported by an implementation are real, then string->number is permitted to return #f whenever *strin**g* uses the polar or rectangular notations for complex numbers. If all numbers are integers, then string->number may return #f whenever the fractional notation is used. If all numbers are exact, then string->number may return #f whenever an exponent marker or explicit exactness prefix is used. If all inexact numbers are integers, then string->number may return #f whenever a decimal point is used.

The rules used by a particular implementation for string->number must also be applied to read and to the routine that reads programs, in order to maintain consistency between internal numeric processing, I/O, and the processing of programs. As a consequence, the R5RS permission to return #f when string has an explicit radix prefix has been withdrawn.

Booleans

The standard boolean objects for true and false are written as #t and #f. Alternatively, they can be written #true and #false, respectively. What really matters, though, are the objects that the Scheme conditional expressions (if, cond, and, or, when, unless, do) treat as true or false. The phrase “a true value” (or sometimes just “true”) means any object treated as true by the conditional expressions, and the phrase “a false value” (or “false”) means any object treated as false by the conditional expressions.

Of all the Scheme values, only #f counts as false in conditional expressions. All other Scheme values, including #t, count as true.

Note: Unlike some other dialects of Lisp, Scheme distinguishes #f and the empty list from each other and from the symbol nil.

Boolean constants evaluate to themselves, so they do not need to be quoted in programs.

#t ;; => #t
#f ;; => #f
'#f ;; => #f

(not obj)  procedure

The not procedure returns #t if obj is false, and returns #f otherwise.

(not #t) ;; => #f
(not 3) ;; => #f
(not (list 3)) ;; => #f
(not #f) ;; => #t
(not '()) ;; => #f
(not (list)) ;; => #f
(not 'nil) ;; => #f

(boolean? obj)  procedure

The boolean? predicate returns #t if obj is either #t or #f and returns #f otherwise.

(boolean? #f) ;; => #t
(boolean? 0) ;; => #f
(boolean? '()) ;; => #f

(boolean=? **boolean1 boolean2 boolean3 … ) procedure

Returns #t if all the arguments are #t or all are #f.

Pairs and lists

A pair (sometimes called a dotted pair) is a record structure with two fields called the car and cdr fields (for historical reasons). Pairs are created by the procedure cons. The car and cdr fields are accessed by the procedures car and cdr. The car and cdr fields are assigned by the procedures set-car! and set-cdr!.

Pairs are used primarily to represent lists. A list can be defined recursively as either the empty list or a pair whose cdr is a list. More precisely, the set of lists is defined as the smallest set X such that

The objects in the car fields of successive pairs of a list are the elements of the list. For example, a two-element list is a pair whose car is the first element and whose cdr is a pair whose car is the second element and whose cdr is the empty list. The length of a list is the number of elements, which is the same as the number of pairs.

The empty list is a special object of its own type. It is not a pair, it has no elements, and its length is zero.

Note: The above definitions imply that all lists have finite length and are terminated by the empty list.

The most general notation (external representation) for Scheme pairs is the “dotted” notation (c1 . c2) where c1 is the value of the car field and c2 is the value of the cdr field. For example (4 . 5) is a pair whose car is 4 and whose cdr is 5. Note that (4 . 5) is the external representation of a pair, not an expression that evaluates to a pair.

A more streamlined notation can be used for lists: the elements of the list are simply enclosed in parentheses and separated by spaces. The empty list is written (). For example,

(a b c d e)

and

(a . (b . (c . (d . (e . ())))))

are equivalent notations for a list of symbols.

A chain of pairs not ending in the empty list is called an improper list. Note that an improper list is not a list. The list and dotted notations can be combined to represent improper lists:

(a b c . d)

is equivalent to

(a . (b . (c . d)))

Whether a given pair is a list depends upon what is stored in the cdr field. When the set-cdr! procedure is used, an object can be a list one moment and not the next:

(define x (list 'a 'b 'c))
(define y x)
y ;; => (a b c)
(list? y) ;; => #t
(set-cdr! x 4) ;; => unspecified
x ;; => (a . 4)
(eqv? x y) ;; => #t
y ;; => (a . 4)
(list? y) ;; => #f
(set-cdr! x x) ;; => unspecified
(list? x) ;; => #f

Within literal expressions and representations of objects read by the read procedure, the forms datum, `datum,,datum, and,@datum denote two-element lists whose first elements are the symbolsquote,quasiquote,unquote, andunquote-splicing`, respectively. The second element in each case is datum. This convention is supported so that arbitrary Scheme programs can be represented as lists. That is, according to Scheme’s grammar, every expression is also a datum (see section [datum]). Among other things, this permits the use of the read procedure to parse Scheme programs. See section [externalreps].

(pair? obj)  procedure

The pair? predicate returns #t if obj is a pair, and otherwise returns #f.

(pair? '(a . b)) ;; => #t
(pair? '(a b c)) ;; => #t
(pair? '()) ;; => #f
(pair? '#(a b)) ;; => #f

(cons obj1 obj2)  procedure

Returns a newly allocated pair whose car is obj1 and whose cdr is obj2. The pair is guaranteed to be different (in the sense of eqv?) from every existing object.

(cons 'a '()) ;; => (a)
(cons '(a) '(b c d)) ;; => ((a) b c d)
(cons "a" '(b c)) ;; => ("a" b c)
(cons 'a 3) ;; => (a . 3)
(cons '(a b) 'c) ;; => ((a b) . c)

(car pair)  procedure

Returns the contents of the car field of pair. Note that it is an error to take the car of the empty list.

(car '(a b c)) ;; => a
(car '((a) b c d)) ;; => (a)
(car '(1 . 2)) ;; => 1
(car '()) ;; => error

(cdr pair)  procedure

Returns the contents of the cdr field of pair. Note that it is an error to take the cdr of the empty list.

(cdr '((a) b c d)) ;; => (b c d)
(cdr '(1 . 2)) ;; => 2
(cdr '()) ;; => error

(set-car! pair obj)  procedure

Stores obj in the car field of pair.

(define (f) (list 'not-a-constant-list))
(define (g) '(constant-list))
(set-car! (f) 3) ;; => unspecified
(set-car! (g) 3) ;; => error

(set-cdr! pair obj)  procedure

Stores obj in the cdr field of pair.

(cadr pair) procedure

(caar pair)  procedure

(cadr pair)  procedure

(cdar pair)  procedure

(cddr pair)  procedure

These procedures are compositions of car and cdr as follows:

(define (caar x) (car (car x)))
(define (cadr x) (car (cdr x)))
(define (cdar x) (cdr (car x)))
(define (cddr x) (cdr (cdr x)))

(caaar pair)  cxr library procedure

(caadr pair)  cxr library procedure

(cdddar pair)  cxr library procedure

(cddddr pair)  cxr library procedure

These twenty-four procedures are further compositions of car and cdr on the same principles. For example, caddr could be defined by

(define caddr (lambda (x) (car (cdr (cdr x)))))

Arbitrary compositions up to four deep are provided.

(null? obj)  procedure

Returns #t if obj is the empty list, otherwise returns #f.

(list? obj)  procedure

Returns #t if obj is a list. Otherwise, it returns #f. By definition, all lists have finite length and are terminated by the empty list.

(list? '(a b c)) ;; => #t
(list? '()) ;; => #t
(list? '(a . b)) ;; => #f
(let ((x (list 'a)))
  (set-cdr! x x)
  (list? x)) ;; => #f

(make-list k)  procedure

(make-list k fill)  procedure

Returns a newly allocated list of k elements. If a second argument is given, then each element is initialized to fill. Otherwise the initial contents of each element is unspecified.

(make-list 2 3) ;; => (3 3)

(list **obj … )  procedure

Returns a newly allocated list of its arguments.

(list 'a (+ 3 4) 'c) ;; => (a 7 c)
(list) ;; => ()

(length list)  procedure

Returns the length of list.

(length '(a b c)) ;; => 3
(length '(a (b) (c d e))) ;; => 3
(length '()) ;; => 0

(append list … )  procedure

The last argument, if there is one, can be of any type.

Returns a list consisting of the elements of the first list followed by the elements of the other lists. If there are no arguments, the empty list is returned. If there is exactly one argument, it is returned. Otherwise the resulting list is always newly allocated, except that it shares structure with the last argument. An improper list results if the last argument is not a proper list.

(append '(x) '(y)) ;; => (x y)
(append '(a) '(b c d)) ;; => (a b c d)
(append '(a (b)) '((c))) ;; => (a (b) (c))

(append '(a b) '(c . d)) ;; => (a b c . d)
(append '() 'a) ;; => a

(reverse list)  procedure

Returns a newly allocated list consisting of the elements of list in reverse order.

(reverse '(a b c)) ;; => (c b a)
(reverse '(a (b c) d (e (f)))) ;; => ((e (f)) d (b c) a)

(list-tail list k**)  procedure

It is an error if list has fewer than k elements.

Returns the sublist of list obtained by omitting the first k elements. The list-tail procedure could be defined by

(define list-tail
  (lambda (x k)
    (if (zero? k)
        x
        (list-tail (cdr x) (- k 1)))))

(list-ref list k**)  procedure

The list argument can be circular, but it is an error if list has k or fewer elements.

Returns the kth element of list. (This is the same as the car of (list-tail list k).)

(list-ref '(a b c d) 2) ;; => c
(list-ref '(a b c d)
          (exact (round 1.8))) ;; => c

(list-set! list k obj)  procedure

It is an error if k is not a valid index of list.

The list-set! procedure stores obj in element k of list.

(let ((ls (list 'one 'two 'five!)))
  (list-set! ls 2 'three)
  ls) ;; => (one two three)

(list-set! '(0 1 2) 1 "oops") ;; => error  ; constant list

(memq obj list)  procedure

(memv obj list)  procedure

(member obj list)  procedure

(member obj list compare)  procedure

These procedures return the first sublist of list whose car is obj, where the sublists of list are the non-empty lists returned by (list-tail list k) for k less than the length of list. If obj does not occur in list, then #f (not the empty list) is returned. The memq procedure uses eq? to compare obj with the elements of list, while memv uses eqv? and member uses compare, if given, and equal? otherwise.

(memq 'a '(a b c)) ;; => (a b c)
(memq 'b '(a b c)) ;; => (b c)
(memq 'a '(b c d)) ;; => #f
(memq (list 'a) '(b (a) c)) ;; => #f
(member (list 'a)
        '(b (a) c)) ;; => ((a) c)
(member "B"
        '("a" "b" "c")
        string-ci=?) ;; => ("b" "c")
(memq 101 '(100 101 102)) ;; => unspecified
(memv 101 '(100 101 102)) ;; => (101 102)

(assq obj alist)  procedure

(assv obj alist)  procedure

(assoc obj alist)  procedure

(assoc obj alist compare)  procedure

It is an error if alist (for “association list”) is not a list of pairs.

These procedures find the first pair in alist whose car field is obj, and returns that pair. If no pair in alist has obj as its car, then #f (not the empty list) is returned. The assq procedure uses eq? to compare obj with the car fields of the pairs in alist, while assv uses eqv? and assoc uses compare if given and equal? otherwise.

(define e '((a 1) (b 2) (c 3)))
(assq 'a e) ;; => (a 1)
(assq 'b e) ;; => (b 2)
(assq 'd e) ;; => #f
(assq (list 'a) '(((a)) ((b)) ((c))))
;; => #f
(assoc (list 'a) '(((a)) ((b)) ((c))))
;; => ((a))
(assoc 2.0 '((1 1) (2 4) (3 9)) =)
;; => (2 4)
(assq 5 '((2 3) (5 7) (11 13)))
;; => unspecified
(assv 5 '((2 3) (5 7) (11 13)))
;; => (5 7)

Rationale: Although they are often used as predicates, memq, memv, member, assq, assv, and assoc do not have question marks in their names because they return potentially useful values rather than just #t or #f.

(list-copy obj)  procedure

Returns a newly allocated copy of the given obj if it is a list. Only the pairs themselves are copied; the cars of the result are the same (in the sense of eqv?) as the cars of list. If obj is an improper list, so is the result, and the final cdrs are the same in the sense of eqv?. An obj which is not a list is returned unchanged. It is an error if obj is a circular list.

(define a '(1 8 2 8)) ; a may be immutable
(define b (list-copy a))
(set-car! b 3)        ; b is mutable
b ;; => (3 8 2 8)
a ;; => (1 8 2 8)

Symbols

Symbols are objects whose usefulness rests on the fact that two symbols are identical (in the sense of eqv?) if and only if their names are spelled the same way. For instance, they can be used the way enumerated values are used in other languages.

The rules for writing a symbol are exactly the same as the rules for writing an identifier; see sections [syntaxsection] and [identifiersyntax].

It is guaranteed that any symbol that has been returned as part of a literal expression, or read using the read procedure, and subsequently written out using the write procedure, will read back in as the identical symbol (in the sense of eqv?).

Note: Some implementations have values known as “uninterned symbols,” which defeat write/read invariance, and also violate the rule that two symbols are the same if and only if their names are spelled the same. This report does not specify the behavior of implementation-dependent extensions.

(symbol? obj)  procedure

Returns #t if obj is a symbol, otherwise returns #f.

(symbol? 'foo) ;; => #t
(symbol? (car '(a b))) ;; => #t
(symbol? "bar") ;; => #f
(symbol? 'nil) ;; => #t
(symbol? '()) ;; => #f
(symbol? #f) ;; => #f

(symbol=? **symbol1 symbol2 symbol3 … ) procedure

Returns #t if all the arguments all have the same names in the sense of string=?.

Note: The definition above assumes that none of the arguments are uninterned symbols.

(symbol->string symbol)  procedure

Returns the name of symbol as a string, but without adding escapes. It is an error to apply mutation procedures like string-set! to strings returned by this procedure.

(symbol->string 'flying-fish)
;; => "flying-fish"
(symbol->string 'Martin) ;; => "Martin"
(symbol->string
 (string->symbol "Malvina"))
;; => "Malvina"

(string->symbol string)  procedure

Returns the symbol whose name is string. This procedure can create symbols with names containing special characters that would require escaping when written, but does not interpret escapes in its input.

(string->symbol "mISSISSIppi")  ;; => mISSISSIppi
(eqv? 'bitBlt (string->symbol "bitBlt")) ;; => #t
(eqv? 'LollyPop
      (string->symbol
       (symbol->string 'LollyPop))) ;; => #t
    (string=? "K. Harper, M.D."
              (symbol->string
               (string->symbol "K. Harper, M.D."))) ;; => #t

Characters

Characters are objects that represent printed characters such as letters and digits. All Scheme implementations must support at least the ASCII character repertoire: that is, Unicode characters U+0000 through U+007F. Implementations may support any other Unicode characters they see fit, and may also support non-Unicode characters as well. Except as otherwise specified, the result of applying any of the following procedures to a non-Unicode character is implementation-dependent.

Characters are written using the notation #``'character or #``'character name or #``'xhex scalar value.

The following character names must be supported by all implementations with the given values. Implementations may add other names provided they cannot be interpreted as hex scalar values preceded by x.

; U+0007
; U+0008
; U+007F
; U+001B
; the linefeed character, U+000A
; the null character, U+0000
; the return character, U+000D
; the preferred way to write a space
; the tab character, U+0009

Here are some additional examples:

; lower case letter
; upper case letter
; left parenthesis
; the space character
; λ (if character is supported)
; ι (if character and name are supported)

Case is significant in #``'character, and in #``'⟨character name⟩, but not in #``'xhex scalar value. If character in #``'character is alphabetic, then any character immediately following character cannot be one that can appear in an identifier. This rule resolves the ambiguous case where, for example, the sequence of characters “#' space” could be taken to be either a representation of the space character or a representation of the character “#' s” followed by a representation of the symbol “pace.”

Characters written in the #``' notation are self-evaluating. That is, they do not have to be quoted in programs.

Some of the procedures that operate on characters ignore the difference between upper case and lower case. The procedures that ignore case have “-ci” (for “case insensitive”) embedded in their names.

(char? obj)  procedure

Returns #t if obj is a character, otherwise returns #f.

(char=? char1 char2 char3 … ) procedure

(char<? char1 char2 char3 … ) procedure

(char>? char1 char2 char3 … ) procedure

(char<=? char1 char2 char3 … ) procedure

(char>=? char1 char2 char3 … ) procedure

These procedures return #t if the results of passing their arguments to charinteger are respectively equal, monotonically increasing, monotonically decreasing, monotonically non-decreasing, or monotonically non-increasing.

These predicates are required to be transitive.

(char-ci=? char1 char2 char3 … ) char library procedure

(char-ci<? char1 char2 char3 … ) char library procedure

(char-ci>? char1 char2 char3 … ) char library procedure

(char-ci<=? char1 char2 char3 … ) char library procedure

(char-ci>=? char1 char2 char3 … ) char library procedure

These procedures are similar to char=? et cetera, but they treat upper case and lower case letters as the same. For example, (char-ci=? #'A #'a) returns #t.

Specifically, these procedures behave as if char-foldcase were applied to their arguments before they were compared.

(char-alphabetic? char)  char library procedure

(char-numeric? char)  char library procedure

(char-whitespace? char)  char library procedure

(char-upper-case? letter)  char library procedure

(char-lower-case? letter)  char library procedure

These procedures return #t if their arguments are alphabetic, numeric, whitespace, upper case, or lower case characters, respectively, otherwise they return #f.

Specifically, they must return #t when applied to characters with the Unicode properties Alphabetic, Numeric_Type=Decimal, White_Space, Uppercase, and Lowercase respectively, and #f when applied to any other Unicode characters. Note that many Unicode characters are alphabetic but neither upper nor lower case.

(digit-value char)  char library procedure

This procedure returns the numeric value (0 to 9) of its argument if it is a numeric digit (that is, if char-numeric? returns #t), or #f on any other character.

(digit-value #\3) ;; => 3
(digit-value #\x0664) ;; => 4
(digit-value #\x0AE6) ;; => 0
(digit-value #\x0EA6) ;; => #f

(char->integer char)  procedure

(integer->char n)  procedure

Given a Unicode character, charinteger returns an exact integer between 0 and #xD7FF or between #xE000 and #x10FFFF which is equal to the Unicode scalar value of that character. Given a non-Unicode character, it returns an exact integer greater than #x10FFFF. This is true independent of whether the implementation uses the Unicode representation internally.

Given an exact integer that is the value returned by a character when charinteger is applied to it, integerchar returns that character.

(char-upcase char)  char library procedure

(char-downcase char)  char library procedure

(char-foldcase char)  char library procedure

The char-upcase procedure, given an argument that is the lowercase part of a Unicode casing pair, returns the uppercase member of the pair, provided that both characters are supported by the Scheme implementation. Note that language-sensitive casing pairs are not used. If the argument is not the lowercase member of such a pair, it is returned.

The char-downcase procedure, given an argument that is the uppercase part of a Unicode casing pair, returns the lowercase member of the pair, provided that both characters are supported by the Scheme implementation. Note that language-sensitive casing pairs are not used. If the argument is not the uppercase member of such a pair, it is returned.

The char-foldcase procedure applies the Unicode simple case-folding algorithm to its argument and returns the result. Note that language-sensitive folding is not used. If the character that results from folding is not supported by the implementation, the argument is returned. See UAX #44  (part of the Unicode Standard) for details.

Note that many Unicode lowercase characters do not have uppercase equivalents.

Strings

Strings are sequences of characters. Strings are written as sequences of characters enclosed within quotation marks (“). Within a string literal, various escape sequences represent characters other than themselves. Escape sequences always start with a backslash ('):

The result is unspecified if any other character in a string occurs after a backslash.

Except for a line ending, any character outside of an escape sequence stands for itself in the string literal. A line ending which is preceded by 'intraline whitespace expands to nothing (along with any trailing intraline whitespace), and can be used to indent strings for improved legibility. Any other line ending has the same effect as inserting a 'n character into the string.

Examples:

"The word \"recursion\" has many meanings."
"Another example:\ntwo lines of text"
"Here's text \
       containing just one line"
"\x03B1; is named GREEK SMALL LETTER ALPHA."

The length of a string is the number of characters that it contains. This number is an exact, non-negative integer that is fixed when the string is created. The valid indexes of a string are the exact non-negative integers less than the length of the string. The first character of a string has index 0, the second has index 1, and so on.

Some of the procedures that operate on strings ignore the difference between upper and lower case. The names of the versions that ignore case end with “-ci” (for “case insensitive”).

Implementations may forbid certain characters from appearing in strings. However, with the exception of #' null, ASCII characters must not be forbidden. For example, an implementation might support the entire Unicode repertoire, but only allow characters U+0001 to U+00FF (the Latin-1 repertoire without #' null) in strings.

It is an error to pass such a forbidden character to make-string, string, string-set!, or string-fill!, as part of the list passed to liststring, or as part of the vector passed to vectorstring (see section [vectortostring]), or in UTF-8 encoded form within a bytevector passed to utf8string (see section [utf8tostring]). It is also an error for a procedure passed to string-map (see section [stringmap]) to return a forbidden character, or for read-string (see section [readstring]) to attempt to read one.

(string? obj)  procedure

Returns #t if obj is a string, otherwise returns #f.

(make-string k)  procedure

(make-string **k char)  procedure

The make-string procedure returns a newly allocated string of length k. If char is given, then all the characters of the string are initialized to char, otherwise the contents of the string are unspecified.

(string char … )  procedure

Returns a newly allocated string composed of the arguments. It is analogous to list.

(string-length string)  procedure

Returns the number of characters in the given string.

(string-ref string k**)  procedure

It is an error if k is not a valid index of string.

The string-ref procedure returns character k of string using zero-origin indexing. There is no requirement for this procedure to execute in constant time.

(string-set! string k char)  procedure

It is an error if k is not a valid index of string.

The string-set! procedure stores char in element k of string. There is no requirement for this procedure to execute in constant time.

(define (f) (make-string 3 #\*))
(define (g) "***")
(string-set! (f) 0 #\?) ;; => unspecified
(string-set! (g) 0 #\?) ;; => error
(string-set! (symbol->string 'immutable)
             0
             #\?) ;; => error

(string=? string1 string2 string3 … ) procedure

Returns #t if all the strings are the same length and contain exactly the same characters in the same positions, otherwise returns #f.

(string-ci=? string1 string2 string3 … ) char library procedure

Returns #t if, after case-folding, all the strings are the same length and contain the same characters in the same positions, otherwise returns #f. Specifically, these procedures behave as if string-foldcase were applied to their arguments before comparing them.

(string<? string1 string2 string3 … ) procedure

(string-ci<? string1 string2 string3 … ) char library procedure

(string>? string1 string2 string3 … ) procedure

(string-ci>? string1 string2 string3 … ) char library procedure

(string<=? string1 string2 string3 … ) procedure

(string-ci<=? string1 string2 string3 … ) char library procedure

(string>=? string1 string2 string3 … ) procedure

(string-ci>=? string1 string2 string3 … ) char library procedure

These procedures return #t if their arguments are (respectively): monotonically increasing, monotonically decreasing, monotonically non-decreasing, or monotonically non-increasing.

These predicates are required to be transitive.

These procedures compare strings in an implementation-defined way. One approach is to make them the lexicographic extensions to strings of the corresponding orderings on characters. In that case, string<? would be the lexicographic ordering on strings induced by the ordering char<? on characters, and if the two strings differ in length but are the same up to the length of the shorter string, the shorter string would be considered to be lexicographically less than the longer string. However, it is also permitted to use the natural ordering imposed by the implementation’s internal representation of strings, or a more complex locale-specific ordering.

In all cases, a pair of strings must satisfy exactly one of string<?, string=?, and string>?, and must satisfy string<=? if and only if they do not satisfy string>? and string>=? if and only if they do not satisfy string<?.

The “-ci” procedures behave as if they applied string-foldcase to their arguments before invoking the corresponding procedures without “-ci”.

(string-upcase string)  char library procedure

(string-downcase string)  char library procedure

(string-foldcase string)  char library procedure

These procedures apply the Unicode full string uppercasing, lowercasing, and case-folding algorithms to their arguments and return the result. In certain cases, the result differs in length from the argument. If the result is equal to the argument in the sense of string=?, the argument may be returned. Note that language-sensitive mappings and foldings are not used.

The Unicode Standard prescribes special treatment of the Greek letter Σ, whose normal lower-case form is σ but which becomes ς at the end of a word. See UAX #44  (part of the Unicode Standard) for details. However, implementations of string-downcase are not required to provide this behavior, and may choose to change Σ to σ in all cases.

(substring string start end)  procedure

The substring procedure returns a newly allocated string formed from the characters of string beginning with index start and ending with index end. This is equivalent to calling string-copy with the same arguments, but is provided for backward compatibility and stylistic flexibility.

(string-append **string … )  procedure

Returns a newly allocated string whose characters are the concatenation of the characters in the given strings.

(string->list string)  procedure

(string->list string start)  procedure

(string->list string start end)  procedure

(list->string list)  procedure

It is an error if any element of list is not a character.

The stringlist procedure returns a newly allocated list of the characters of string between start and end. liststring returns a newly allocated string formed from the elements in the list list. In both procedures, order is preserved. stringlist and liststring are inverses so far as equal? is concerned.

(string-copy string)  procedure

(string-copy string start)  procedure

(string-copy string start end)  procedure

Returns a newly allocated copy of the part of the given string between start and end.

(string-copy! to at from)  procedure

(string-copy! to at from start)  procedure

(string-copy! to at from start end)  procedure

It is an error if at is less than zero or greater than the length of to. It is also an error if (- (string-length to) at) is less than (- end start).

Copies the characters of string from between start and end to string to, starting at at. The order in which characters are copied is unspecified, except that if the source and destination overlap, copying takes place as if the source is first copied into a temporary string and then into the destination. This can be achieved without allocating storage by making sure to copy in the correct direction in such circumstances.

(define a "12345")
(define b (string-copy "abcde"))
(string-copy! b 1 a 0 2)
b ;; => "a12de"

(string-fill! string fill)  procedure

(string-fill! string fill start)  procedure

(string-fill! string fill start end)  procedure

It is an error if fill is not a character.

The string-fill! procedure stores fill in the elements of string between start and end.

Vectors

Vectors are heterogeneous structures whose elements are indexed by integers. A vector typically occupies less space than a list of the same length, and the average time needed to access a randomly chosen element is typically less for the vector than for the list.

The length of a vector is the number of elements that it contains. This number is a non-negative integer that is fixed when the vector is created. The valid indexes of a vector are the exact non-negative integers less than the length of the vector. The first element in a vector is indexed by zero, and the last element is indexed by one less than the length of the vector.

Vectors are written using the notation #(obj ...). For example, a vector of length 3 containing the number zero in element 0, the list (2 2 2 2) in element 1, and the string “Anna” in element 2 can be written as follows:

#(0 (2 2 2 2) "Anna")

Vector constants are self-evaluating, so they do not need to be quoted in programs.

(vector? obj)  procedure

Returns #t if obj is a vector; otherwise returns #f.

(make-vector k)  procedure

(make-vector k fill)  procedure

Returns a newly allocated vector of k elements. If a second argument is given, then each element is initialized to fill. Otherwise the initial contents of each element is unspecified.

(vector obj … )  procedure

Returns a newly allocated vector whose elements contain the given arguments. It is analogous to list.

(vector 'a 'b 'c) ;; => #(a b c)

(vector-length vector)  procedure

Returns the number of elements in vector as an exact integer.

(vector-ref vector k)  procedure

It is an error if k is not a valid index of vector.

The vector-ref procedure returns the contents of element k of vector.

(vector-ref '#(1 1 2 3 5 8 13 21)
            5) ;; => 8
(vector-ref '#(1 1 2 3 5 8 13 21)
            (exact
             (round (* 2 (acos -1))))) ;; => 13

(vector-set! vector k obj)  procedure

It is an error if k is not a valid index of vector.

The vector-set! procedure stores obj in element k of vector.

(let ((vec (vector 0 '(2 2 2 2) "Anna")))
  (vector-set! vec 1 '("Sue" "Sue"))
  vec) ;; => #(0 ("Sue" "Sue") "Anna")

(vector-set! '#(0 1 2) 1 "doe") ;; => error  ; constant vector

(vector->list vector)  procedure

(vector->list vector start)  procedure

(vector->list vector start end)  procedure

(list->vector list)  procedure

The vector->list procedure returns a newly allocated list of the objects contained in the elements of vector between start and end. The list->vector procedure returns a newly created vector initialized to the elements of the list list.

In both procedures, order is preserved.

(vector->list '#(dah dah didah)) ;; => (dah dah didah)
(vector->list '#(dah dah didah) 1 2) ;; => (dah)
(list->vector '(dididit dah)) ;; => #(dididit dah)

(vector->string vector)  procedure

(vector->string vector start)  procedure

(vector->string vector start end)  procedure

(string->vector string)  procedure

(string->vector string start)  procedure

(string->vector string start end)  procedure

It is an error if any element of vector between start and end is not a character.

The vector->string procedure returns a newly allocated string of the objects contained in the elements of vector between start and end. The string->vector procedure returns a newly created vector initialized to the elements of the string string between start and end.

In both procedures, order is preserved.

(string->vector "ABC") ;; => #(#\A #\B #\C)
(vector->string
 #(#\1 #\2 #\3) ;; => "123"

(vector-copy vector)  procedure

(vector-copy vector start)  procedure

(vector-copy vector start end)  procedure

Returns a newly allocated copy of the elements of the given vector between start and end. The elements of the new vector are the same (in the sense of eqv?) as the elements of the old.

(define a #(1 8 2 8)) ; a may be immutable
(define b (vector-copy a))
(vector-set! b 0 3)   ; b is mutable
b ;; => #(3 8 2 8)
(define c (vector-copy b 1 3))
c ;; => #(8 2)

(vector-copy! to at from)  procedure

(vector-copy! to at from start)  procedure

(vector-copy! to at from start end)  procedure

It is an error if at is less than zero or greater than the length of to. It is also an error if (- (vector-length to) at) is less than (- end start).

Copies the elements of vector from between start and end to vector to, starting at at. The order in which elements are copied is unspecified, except that if the source and destination overlap, copying takes place as if the source is first copied into a temporary vector and then into the destination. This can be achieved without allocating storage by making sure to copy in the correct direction in such circumstances.

(define a (vector 1 2 3 4 5))
(define b (vector 10 20 30 40 50))
(vector-copy! b 1 a 0 2)
b ;; => #(10 1 2 40 50)

(vector-append **vector … )  procedure

Returns a newly allocated vector whose elements are the concatenation of the elements of the given vectors.

(vector-append #(a b c) #(d e f)) ;; => #(a b c d e f)

(vector-fill! vector fill)  procedure

(vector-fill! vector fill start)  procedure

(vector-fill! vector fill start end)  procedure

The vector-fill! procedure stores fill in the elements of vector between start and end.

(define a (vector 1 2 3 4 5))
(vector-fill! a 'smash 2 4)
a ;; => #(1 2 smash smash 5)

Bytevectors

Bytevectors represent blocks of binary data. They are fixed-length sequences of bytes, where a byte is an exact integer in the range from 0 to 255 inclusive. A bytevector is typically more space-efficient than a vector containing the same values.

The length of a bytevector is the number of elements that it contains. This number is a non-negative integer that is fixed when the bytevector is created. The valid indexes of a bytevector are the exact non-negative integers less than the length of the bytevector, starting at index zero as with vectors.

Bytevectors are written using the notation #u8(byte ...). For example, a bytevector of length 3 containing the byte 0 in element 0, the byte 10 in element 1, and the byte 5 in element 2 can be written as follows:

#u8(0 10 5)

Bytevector constants are self-evaluating, so they do not need to be quoted in programs.

(bytevector? obj)  procedure

Returns #t if obj is a bytevector. Otherwise, #f is returned.

(make-bytevector k)  procedure

(make-bytevector k byte)  procedure

The make-bytevector procedure returns a newly allocated bytevector of length k. If byte is given, then all elements of the bytevector are initialized to byte, otherwise the contents of each element are unspecified.

(make-bytevector 2 12) ;; => #u8(12 12)

(bytevector **byte … )  procedure

Returns a newly allocated bytevector containing its arguments.

(bytevector 1 3 5 1 3 5) ;; => #u8(1 3 5 1 3 5)
(bytevector) ;; => #u8()

(bytevector-length bytevector)  procedure

Returns the length of bytevector in bytes as an exact integer.

(bytevector-u8-ref bytevector k)  procedure

It is an error if k is not a valid index of bytevector.

Returns the kth byte of bytevector.

(bytevector-u8-ref '#u8(1 1 2 3 5 8 13 21)
                   5) ;; => 8

(bytevector-u8-set! bytevector k byte)  procedure

It is an error if k is not a valid index of bytevector.

Stores byte as the kth byte of bytevector.

(let ((bv (bytevector 1 2 3 4)))
  (bytevector-u8-set! bv 1 3)
  bv) ;; => #u8(1 3 3 4)

(bytevector-copy bytevector)  procedure

(bytevector-copy bytevector start)  procedure

(bytevector-copy bytevector start end)  procedure

Returns a newly allocated bytevector containing the bytes in bytevector between start and end.

(define a #u8(1 2 3 4 5))
(bytevector-copy a 2 4)) ;; => #u8(3 4)

(bytevector-copy! to at from)  procedure

(bytevector-copy! to at from start)  procedure

(bytevector-copy! to at from start end)  procedure

It is an error if at is less than zero or greater than the length of to. It is also an error if (- (bytevector-length to) at) is less than (- end start).

Copies the bytes of bytevector from between start and end to bytevector to, starting at at. The order in which bytes are copied is unspecified, except that if the source and destination overlap, copying takes place as if the source is first copied into a temporary bytevector and then into the destination. This can be achieved without allocating storage by making sure to copy in the correct direction in such circumstances.

(define a (bytevector 1 2 3 4 5))
(define b (bytevector 10 20 30 40 50))
(bytevector-copy! b 1 a 0 2)
b ;; => #u8(10 1 2 40 50)

Note: This procedure appears in R6RS, but places the source before the destination, contrary to other such procedures in Scheme.

(bytevector-append **bytevector … )  procedure

Returns a newly allocated bytevector whose elements are the concatenation of the elements in the given bytevectors.

(bytevector-append #u8(0 1 2) #u8(3 4 5)) ;; => #u8(0 1 2 3 4 5)

(utf8->string bytevector)  procedure

(utf8->string bytevector start)  procedure

(utf8->string bytevector start end)  procedure

(string->utf8 string)  procedure

(string->utf8 string start)  procedure

(string->utf8 string start end)  procedure

It is an error for bytevector to contain invalid UTF-8 byte sequences.

These procedures translate between strings and bytevectors that encode those strings using the UTF-8 encoding. The utf8string procedure decodes the bytes of a bytevector between start and end and returns the corresponding string; the stringutf8 procedure encodes the characters of a string between start and end and returns the corresponding bytevector.

(utf8->string #u8(#x41)) ;; => "A"
(string->utf8 "λ") ;; => #u8(#xCE #xBB)

Control features

This section describes various primitive procedures which control the flow of program execution in special ways. Procedures in this section that invoke procedure arguments always do so in the same dynamic environment as the call of the original procedure. The procedure? predicate is also described here.

(procedure? obj)  procedure Returns #t if obj is a procedure, otherwise returns #f.

(procedure? car) ;; => #t
(procedure? 'car) ;; => #f
(procedure? (lambda (x) (* x x)))
 ;; => #t
(procedure? '(lambda (x) (* x x)))
;; => #f
(call-with-current-continuation procedure?)
;; => #t

(apply proc arg1 … args)  procedure

The apply procedure calls proc with the elements of the list (append (list *arg<sub>1</sub>* … ) *args*) as the actual arguments.

(apply + (list 3 4)) ;; => 7

(define compose
  (lambda (f g)
    (lambda args
      (f (apply g args)))))

((compose sqrt *) 12 75) ;; => 30

(map proc list1 list2 … )  procedure

It is an error if proc does not accept as many arguments as there are lists and return a single value.

The map procedure applies proc element-wise to the elements of the lists and returns a list of the results, in order. If more than one list is given and not all lists have the same length, map terminates when the shortest list runs out. The lists can be circular, but it is an error if all of them are circular. It is an error for proc to mutate any of the lists. The dynamic order in which proc is applied to the elements of the lists is unspecified. If multiple returns occur from map, the values returned by earlier returns are not mutated.

(map cadr '((a b) (d e) (g h))) ;; => (b e h)

(map (lambda (n) (expt n n))
     '(1 2 3 4 5)) ;; => (1 4 27 256 3125)

(map + '(1 2 3) '(4 5 6 7)) ;; => (5 7 9)

(let ((count 0))
  (map (lambda (ignored)
         (set! count (+ count 1))
         count)
       '(a b))) ;; => (1 2) \var{or} (2 1)

(string-map proc string1 string2 … ) procedure

It is an error if proc does not accept as many arguments as there are strings and return a single character.

The string-map procedure applies proc element-wise to the elements of the strings and returns a string of the results, in order. If more than one string is given and not all strings have the same length, string-map terminates when the shortest string runs out. The dynamic order in which proc is applied to the elements of the strings is unspecified. If multiple returns occur from string-map, the values returned by earlier returns are not mutated.

(string-map char-foldcase "AbdEgH") ;; => "abdegh"

(string-map
 (lambda (c)
   (integer->char (+ 1 (char->integer c))))
 "HAL") ;; => "IBM"

(string-map
 (lambda (c k)
   ((if (eqv? k #\u) char-upcase char-downcase)
    c))
 "studlycaps xxx"
 "ululululul") ;; => "StUdLyCaPs"

(vector-map proc vector1 vector2 … ) procedure

It is an error if proc does not accept as many arguments as there are vectors and return a single value.

The vector-map procedure applies proc element-wise to the elements of the vectors and returns a vector of the results, in order. If more than one vector is given and not all vectors have the same length, vector-map terminates when the shortest vector runs out. The dynamic order in which proc is applied to the elements of the vectors is unspecified. If multiple returns occur from vector-map, the values returned by earlier returns are not mutated.

(vector-map cadr '#((a b) (d e) (g h))) ;; => #(b e h)

(vector-map (lambda (n) (expt n n))
            '#(1 2 3 4 5)) ;; => #(1 4 27 256 3125)

(vector-map + '#(1 2 3) '#(4 5 6 7)) ;; => #(5 7 9)

(let ((count 0))
  (vector-map
   (lambda (ignored)
     (set! count (+ count 1))
     count)
   '#(a b))) ;; => #(1 2) \var{or} #(2 1)

(for-each proc list1 list2 … )  procedure

It is an error if proc does not accept as many arguments as there are lists.

The arguments to for-each are like the arguments to map, but for-each calls proc for its side effects rather than for its values. Unlike map, for-each is guaranteed to call proc on the elements of the lists in order from the first element(s) to the last, and the value returned by for-each is unspecified. If more than one list is given and not all lists have the same length, for-each terminates when the shortest list runs out. The lists can be circular, but it is an error if all of them are circular.

It is an error for proc to mutate any of the lists.

(let ((v (make-vector 5)))
  (for-each (lambda (i)
              (vector-set! v i (* i i)))
            '(0 1 2 3 4))
  v) ;; => #(0 1 4 9 16)

(string-for-each proc string1 string2 … ) procedure

It is an error if proc does not accept as many arguments as there are strings.

The arguments to string-for-each are like the arguments to string-map, but string-for-each calls proc for its side effects rather than for its values. Unlike string-map, string-for-each is guaranteed to call proc on the elements of the strings in order from the first element(s) to the last, and the value returned by string-for-each is unspecified. If more than one string is given and not all strings have the same length, string-for-each terminates when the shortest string runs out. It is an error for proc to mutate any of the strings.

(let ((v '()))
  (string-for-each
   (lambda (c) (set! v (cons (char->integer c) v)))
   "abcde")
  v) ;; => (101 100 99 98 97)

(vector-for-each proc vector1 vector2 … ) procedure

It is an error if proc does not accept as many arguments as there are vectors.

The arguments to vector-for-each are like the arguments to vector-map, but vector-for-each calls proc for its side effects rather than for its values. Unlike vector-map, vector-for-each is guaranteed to call proc on the elements of the vectors in order from the first element(s) to the last, and the value returned by vector-for-each is unspecified. If more than one vector is given and not all vectors have the same length, vector-for-each terminates when the shortest vector runs out. It is an error for proc to mutate any of the vectors.

(let ((v (make-list 5)))
  (vector-for-each
   (lambda (i) (list-set! v i (* i i)))
   '#(0 1 2 3 4))
  v) ;; => (0 1 4 9 16)

(call-with-current-continuation proc)  procedure

(call/cc proc)  procedure

It is an error if proc does not accept one argument.

The procedure call-with-current-continuation (or its equivalent abbreviation call/cc) packages the current continuation (see the rationale below) as an “escape procedure” and passes it as an argument to proc. The escape procedure is a Scheme procedure that, if it is later called, will abandon whatever continuation is in effect at that later time and will instead use the continuation that was in effect when the escape procedure was created. Calling the escape procedure will cause the invocation of before and after thunks installed using dynamic-wind.

The escape procedure accepts the same number of arguments as the continuation to the original call to call-with-current-continuation. Most continuations take only one value. Continuations created by the call-with-values procedure (including the initialization expressions of define-values, let-values, and let*-values expressions), take the number of values that the consumer expects. The continuations of all non-final expressions within a sequence of expressions, such as in lambda, case-lambda, begin, let, let*, letrec, letrec*, let-values, let*-values, let-syntax, letrec-syntax, parameterize, guard, case, cond, when, and unless expressions, take an arbitrary number of values because they discard the values passed to them in any event. The effect of passing no values or more than one value to continuations that were not created in one of these ways is unspecified.

The escape procedure that is passed to proc has unlimited extent just like any other procedure in Scheme. It can be stored in variables or data structures and can be called as many times as desired. However, like the raise and error procedures, it never returns to its caller.

The following examples show only the simplest ways in which call-with-current-continuation is used. If all real uses were as simple as these examples, there would be no need for a procedure with the power of call-with-current-continuation.

(call-with-current-continuation
 (lambda (exit)
   (for-each (lambda (x)
               (if (negative? x)
                   (exit x)))
             '(54 0 37 -3 245 19))
   #t)) ;; => -3

(define list-length
  (lambda (obj)
    (call-with-current-continuation
     (lambda (return)
       (letrec ((r
                 (lambda (obj)
                   (cond ((null? obj) 0)
                         ((pair? obj)
                          (+ (r (cdr obj)) 1))
                         (else (return #f))))))
         (r obj))))))

(list-length '(1 2 3 4)) ;; => 4

(list-length '(a b . c)) ;; => #f

Rationale:

A common use of call-with-current-continuation is for structured, non-local exits from loops or procedure bodies, but in fact call-with-current-continuation is useful for implementing a wide variety of advanced control structures. In fact, raise and guard provide a more structured mechanism for non-local exits.

Whenever a Scheme expression is evaluated there is a continuation wanting the result of the expression. The continuation represents an entire (default) future for the computation. If the expression is evaluated at the REPL, for example, then the continuation might take the result, print it on the screen, prompt for the next input, evaluate it, and so on forever. Most of the time the continuation includes actions specified by user code, as in a continuation that will take the result, multiply it by the value stored in a local variable, add seven, and give the answer to the REPL’s continuation to be printed. Normally these ubiquitous continuations are hidden behind the scenes and programmers do not think much about them. On rare occasions, however, a programmer needs to deal with continuations explicitly. The call-with-current-continuation procedure allows Scheme programmers to do that by creating a procedure that acts just like the current continuation.

(values obj …)  procedure

Delivers all of its arguments to its continuation. The values procedure might be defined as follows:

(define (values . things)
  (call-with-current-continuation
   (lambda (cont) (apply cont things))))

(call-with-values producer consumer)  procedure

Calls its producer argument with no arguments and a continuation that, when passed some values, calls the consumer procedure with those values as arguments. The continuation for the call to consumer is the continuation of the call to call-with-values.

(call-with-values (lambda () (values 4 5))
  (lambda (a b) b))
;; => 5

(call-with-values * -) ;; => -1

(dynamic-wind before thunk after)  procedure

Calls thunk without arguments, returning the result(s) of this call. Before and after are called, also without arguments, as required by the following rules. Note that, in the absence of calls to continuations captured using call-with-current-continuation, the three arguments are called once each, in order. Before is called whenever execution enters the dynamic extent of the call to thunk and after is called whenever it exits that dynamic extent. The dynamic extent of a procedure call is the period between when the call is initiated and when it returns. The before and after thunks are called in the same dynamic environment as the call to dynamic-wind. In Scheme, because of call-with-current-continuation, the dynamic extent of a call is not always a single, connected time period. It is defined as follows:

If a second call to dynamic-wind occurs within the dynamic extent of the call to thunk and then a continuation is invoked in such a way that the afters from these two invocations of dynamic-wind are both to be called, then the after associated with the second (inner) call to dynamic-wind is called first.

If a second call to dynamic-wind occurs within the dynamic extent of the call to thunk and then a continuation is invoked in such a way that the befores from these two invocations of dynamic-wind are both to be called, then the before associated with the first (outer) call to dynamic-wind is called first.

If invoking a continuation requires calling the before from one call to dynamic-wind and the after from another, then the after is called first.

The effect of using a captured continuation to enter or exit the dynamic extent of a call to before or after is unspecified.

(let ((path '())
      (c #f))
  (let ((add (lambda (s)
               (set! path (cons s path)))))
    (dynamic-wind
        (lambda () (add 'connect))
        (lambda ()
          (add (call-with-current-continuation
                (lambda (c0)
                  (set! c c0)
                  'talk1))))
        (lambda () (add 'disconnect)))
    (if (< (length path) 4)
        (c 'talk2)
        (reverse path))))
;; => (connect talk1 disconnect connect talk2 disconnect)

Exceptions

This section describes Scheme’s exception-handling and exception-raising procedures. For the concept of Scheme exceptions, see section [errorsituations]. See also [guard] for the guard syntax.

Exception handlers are one-argument procedures that determine the action the program takes when an exceptional situation is signaled. The system implicitly maintains a current exception handler in the dynamic environment.

The program raises an exception by invoking the current exception handler, passing it an object encapsulating information about the exception. Any procedure accepting one argument can serve as an exception handler and any object can be used to represent an exception.

(with-exception-handler handler thunk)  procedure

It is an error if handler does not accept one argument. It is also an error if thunk does not accept zero arguments.

The with-exception-handler procedure returns the results of invoking thunk. Handler is installed as the current exception handler in the dynamic environment used for the invocation of thunk.

(call-with-current-continuation
 (lambda (k)
   (with-exception-handler
    (lambda (x)
      (display "condition: ")
      (write x)
      (newline)
      (k 'exception))
    (lambda ()
      (+ 1 (raise 'an-error))))))
;; => exception and prints condition: an-error

(with-exception-handler
 (lambda (x)
   (display "something went wrong\n"))
 (lambda ()
   (+ 1 (raise 'an-error))))
;; prints something went wrong

After printing, the second example then raises another exception.

(raise obj)  procedure

Raises an exception by invoking the current exception handler on obj. The handler is called with the same dynamic environment as that of the call to raise, except that the current exception handler is the one that was in place when the handler being called was installed. If the handler returns, a secondary exception is raised in the same dynamic environment as the handler. The relationship between obj and the object raised by the secondary exception is unspecified.

(raise-continuable obj)  procedure

Raises an exception by invoking the current exception handler on obj. The handler is called with the same dynamic environment as the call to raise-continuable, except that: (1) the current exception handler is the one that was in place when the handler being called was installed, and (2) if the handler being called returns, then it will again become the current exception handler. If the handler returns, the values it returns become the values returned by the call to raise-continuable.

(with-exception-handler
 (lambda (con)
   (cond
    ((string? con)
     (display con))
    (else
     (display "a warning has been issued")))
   42)
 (lambda ()
   (+ (raise-continuable "should be a number")
      23)))
;; prints: should be a number
;; => 65

(error **message obj …)  procedure

Message should be a string.

Raises an exception as if by calling raise on a newly allocated implementation-defined object which encapsulates the information provided by message, as well as any objs, known as the irritants. The procedure error-object? must return #t on such objects.

(define (null-list? l)
  (cond ((pair? l) #f)
        ((null? l) #t)
        (else
         (error
          "null-list?: argument out of domain"
          l))))

(error-object? obj)  procedure

Returns #t if obj is an object created by error or one of an implementation-defined set of objects. Otherwise, it returns #f. The objects used to signal errors, including those which satisfy the predicates file-error? and read-error?, may or may not satisfy error-object?.

(error-object-message error-object)  procedure

Returns the message encapsulated by error-object.

(error-object-irritants error-object)  procedure

Returns a list of the irritants encapsulated by error-object.

(read-error? obj)  procedure

(file-error? obj)  procedure

Error type predicates. Returns #t if obj is an object raised by the read procedure or by the inability to open an input or output port on a file, respectively. Otherwise, it returns #f.

Environments and evaluation

(environment list1 … )  eval library procedure

This procedure returns a specifier for the environment that results by starting with an empty environment and then importing each list, considered as an import set, into it. (See section [libraries] for a description of import sets.) The bindings of the environment represented by the specifier are immutable, as is the environment itself.

(scheme-report-environment version)  r5rs library procedure

If version is equal to 5, corresponding to R5RS, scheme-report-environment returns a specifier for an environment that contains only the bindings defined in the R5RS library. Implementations must support this value of version.

Implementations may also support other values of version, in which case they return a specifier for an environment containing bindings corresponding to the specified version of the report. If version is neither 5 nor another value supported by the implementation, an error is signaled.

The effect of defining or assigning (through the use of eval) an identifier bound in a scheme-report-environment (for example car) is unspecified. Thus both the environment and the bindings it contains may be immutable.

(null-environment version)  r5rs library procedure

If version is equal to 5, corresponding to R5RS, the null-environment procedure returns a specifier for an environment that contains only the bindings for all syntactic keywords defined in the R5RS library. Implementations must support this value of version.

Implementations may also support other values of version, in which case they return a specifier for an environment containing appropriate bindings corresponding to the specified version of the report. If version is neither 5 nor another value supported by the implementation, an error is signaled.

The effect of defining or assigning (through the use of eval) an identifier bound in a scheme-report-environment (for example car) is unspecified. Thus both the environment and the bindings it contains may be immutable.

(interaction-environment)  repl library procedure

This procedure returns a specifier for a mutable environment that contains an implementation-defined set of bindings, typically a superset of those exported by (scheme base). The intent is that this procedure will return the environment in which the implementation would evaluate expressions entered by the user into a REPL.

(eval expr-or-def environment-specifier)  eval library procedure

If expr-or-def is an expression, it is evaluated in the specified environment and its values are returned. If it is a definition, the specified identifier(s) are defined in the specified environment, provided the environment is not immutable. Implementations may extend eval to allow other objects.

(eval '(* 7 3) (environment '(scheme base)))
;; => 21

(let ((f (eval '(lambda (f x) (f x x))
               (null-environment 5))))
  (f + 10))
;; => 20
(eval '(define foo 32)
      (environment '(scheme base)))
;; => error is signaled

Input and output

Ports

Ports represent input and output devices. To Scheme, an input port is a Scheme object that can deliver data upon command, while an output port is a Scheme object that can accept data. Whether the input and output port types are disjoint is implementation-dependent.

Different port types operate on different data. Scheme implementations are required to support textual ports and binary ports, but may also provide other port types.

A textual port supports reading or writing of individual characters from or to a backing store containing characters using read-char and write-char below, and it supports operations defined in terms of characters, such as read and write.

A binary port supports reading or writing of individual bytes from or to a backing store containing bytes using read-u8 and write-u8 below, as well as operations defined in terms of bytes. Whether the textual and binary port types are disjoint is implementation-dependent.

Ports can be used to access files, devices, and similar things on the host system on which the Scheme program is running.

(call-with-port port proc)  procedure

It is an error if proc does not accept one argument.

The call-with-port procedure calls proc with port as an argument. If proc returns, then the port is closed automatically and the values yielded by the proc are returned. If proc does not return, then the port must not be closed automatically unless it is possible to prove that the port will never again be used for a read or write operation.

Rationale: Because Scheme’s escape procedures have unlimited extent, it is possible to escape from the current continuation but later to resume it. If implementations were permitted to close the port on any escape from the current continuation, then it would be impossible to write portable code using both call-with-current-continuation and call-with-port.

(call-with-input-file string proc)  file library procedure

(call-with-output-file string proc)  file library procedure

It is an error if proc does not accept one argument.

These procedures obtain a textual port obtained by opening the named file for input or output as if by open-input-file or open-output-file. The port and proc are then passed to a procedure equivalent to call-with-port.

(input-port? obj)  procedure

(output-port? obj)  procedure

(textual-port? obj)  procedure

(binary-port? obj)  procedure

(port? obj)  procedure

These procedures return #t if obj is an input port, output port, textual port, binary port, or any kind of port, respectively. Otherwise they return #f.

(input-port-open? port)  procedure

(output-port-open? port)  procedure

Returns #t if port is still open and capable of performing input or output, respectively, and #f otherwise.

(current-input-port)  procedure

(current-output-port)  procedure

(current-error-port)  procedure

Returns the current default input port, output port, or error port (an output port), respectively. These procedures are parameter objects, which can be overridden with parameterize (see section [make-parameter]). The initial bindings for these are implementation-defined textual ports.

(with-input-from-file string thunk)  file library procedure

(with-output-to-file string thunk)  file library procedure

The file is opened for input or output as if by open-input-file or open-output-file, and the new port is made to be the value returned by current-input-port or current-output-port (as used by (read), (write obj), and so forth). The thunk is then called with no arguments. When the thunk returns, the port is closed and the previous default is restored. It is an error if thunk does not accept zero arguments. Both procedures return the values yielded by thunk. If an escape procedure is used to escape from the continuation of these procedures, they behave exactly as if the current input or output port had been bound dynamically with parameterize.

(open-input-file string)  file library procedure

(open-binary-input-file string)  file library procedure

Takes a string for an existing file and returns a textual input port or binary input port that is capable of delivering data from the file. If the file does not exist or cannot be opened, an error that satisfies file-error? is signaled.

(open-output-file string)  file library procedure

(open-binary-output-file string)  file library procedure

Takes a string naming an output file to be created and returns a textual output port or binary output port that is capable of writing data to a new file by that name.

If a file with the given name already exists, the effect is unspecified. If the file cannot be opened, an error that satisfies file-error? is signaled.

(close-port port)  procedure

(close-input-port port)  procedure

(close-output-port port)  procedure

Closes the resource associated with port, rendering the port incapable of delivering or accepting data. It is an error to apply the last two procedures to a port which is not an input or output port, respectively. Scheme implementations may provide ports which are simultaneously input and output ports, such as sockets; the close-input-port and close-output-port procedures can then be used to close the input and output sides of the port independently.

These routines have no effect if the port has already been closed.

(open-input-string string)  procedure

Takes a string and returns a textual input port that delivers characters from the string. If the string is modified, the effect is unspecified.

(open-output-string)  procedure

Returns a textual output port that will accumulate characters for retrieval by get-output-string.

(get-output-string port)  procedure

It is an error if port was not created with open-output-string.

Returns a string consisting of the characters that have been output to the port so far in the order they were output. If the result string is modified, the effect is unspecified.

(parameterize
    ((current-output-port
      (open-output-string)))
  (display "piece")
  (display " by piece ")
  (display "by piece.")
  (newline)
  (get-output-string (current-output-port)))
;; => "piece by piece by piece.\n"

(open-input-bytevector bytevector)  procedure

Takes a bytevector and returns a binary input port that delivers bytes from the bytevector.

(open-output-bytevector)  procedure

Returns a binary output port that will accumulate bytes for retrieval by get-output-bytevector.

(get-output-bytevector port)  procedure

It is an error if port was not created with open-output-bytevector.

Returns a bytevector consisting of the bytes that have been output to the port so far in the order they were output.

Input

If port is omitted from any input procedure, it defaults to the value returned by (current-input-port). It is an error to attempt an input operation on a closed port.

(read)  read library procedure

(read port)  read library procedure

The read procedure converts external representations of Scheme objects into the objects themselves. That is, it is a parser for the non-terminal datum (see sections [datum] and [listsection]). It returns the next object parsable from the given textual input port, updating port to point to the first character past the end of the external representation of the object.

Implementations may support extended syntax to represent record types or other types that do not have datum representations.

If an end of file is encountered in the input before any characters are found that can begin an object, then an end-of-file object is returned. The port remains open, and further attempts to read will also return an end-of-file object. If an end of file is encountered after the beginning of an object’s external representation, but the external representation is incomplete and therefore not parsable, an error that satisfies read-error? is signaled.

(read-char)  procedure

(read-char port)  procedure

Returns the next character available from the textual input port, updating the port to point to the following character. If no more characters are available, an end-of-file object is returned.

(peek-char)  procedure

(peek-char port)  procedure

Returns the next character available from the textual input port, but without updating the port to point to the following character. If no more characters are available, an end-of-file object is returned.

Note: The value returned by a call to peek-char is the same as the value that would have been returned by a call to read-char with the same port. The only difference is that the very next call to read-char or peek-char on that port will return the value returned by the preceding call to peek-char. In particular, a call to peek-char on an interactive port will hang waiting for input whenever a call to read-char would have hung.

(read-line)  procedure

(read-line port)  procedure

Returns the next line of text available from the textual input port, updating the port to point to the following character. If an end of line is read, a string containing all of the text up to (but not including) the end of line is returned, and the port is updated to point just past the end of line. If an end of file is encountered before any end of line is read, but some characters have been read, a string containing those characters is returned. If an end of file is encountered before any characters are read, an end-of-file object is returned. For the purpose of this procedure, an end of line consists of either a linefeed character, a carriage return character, or a sequence of a carriage return character followed by a linefeed character. Implementations may also recognize other end of line characters or sequences.

(eof-object? obj)  procedure

Returns #t if obj is an end-of-file object, otherwise returns #f. The precise set of end-of-file objects will vary among implementations, but in any case no end-of-file object will ever be an object that can be read in using read.

(eof-object)  procedure

Returns an end-of-file object, not necessarily unique.

(char-ready?)  procedure

(char-ready? port)  procedure

Returns #t if a character is ready on the textual input port and returns #f otherwise. If char-ready returns #t then the next read-char operation on the given port is guaranteed not to hang. If the port is at end of file then char-ready? returns #t.

Rationale: The char-ready? procedure exists to make it possible for a program to accept characters from interactive ports without getting stuck waiting for input. Any input editors associated with such ports must ensure that characters whose existence has been asserted by char-ready? cannot be removed from the input. If char-ready? were to return #f at end of file, a port at end of file would be indistinguishable from an interactive port that has no ready characters.

(read-string k)  procedure

(read-string k port)  procedure

Reads the next k characters, or as many as are available before the end of file, from the textual input port into a newly allocated string in left-to-right order and returns the string. If no characters are available before the end of file, an end-of-file object is returned.

(read-u8)  procedure

(read-u8 port)  procedure

Returns the next byte available from the binary input port, updating the port to point to the following byte. If no more bytes are available, an end-of-file object is returned.

(peek-u8)  procedure

(peek-u8 port)  procedure

Returns the next byte available from the binary input port, but without updating the port to point to the following byte. If no more bytes are available, an end-of-file object is returned.

(u8-ready?)  procedure (u8-ready? port)  procedure

Returns #t if a byte is ready on the binary input port and returns #f otherwise. If u8-ready? returns #t then the next read-u8 operation on the given port is guaranteed not to hang. If the port is at end of file then u8-ready? returns #t.

(read-bytevector k)  procedure

(read-bytevector k port)  procedure

Reads the next k bytes, or as many as are available before the end of file, from the binary input port into a newly allocated bytevector in left-to-right order and returns the bytevector. If no bytes are available before the end of file, an end-of-file object is returned.

(read-bytevector! bytevector)  procedure

(read-bytevector! bytevector port)  procedure

(read-bytevector! bytevector port start)  procedure

(read-bytevector! bytevector port start end)  procedure

Reads the next end − start bytes, or as many as are available before the end of file, from the binary input port into bytevector in left-to-right order beginning at the start position. If end is not supplied, reads until the end of bytevector has been reached. If start is not supplied, reads beginning at position 0. Returns the number of bytes read. If no bytes are available, an end-of-file object is returned.

Output

If port is omitted from any output procedure, it defaults to the value returned by (current-output-port). It is an error to attempt an output operation on a closed port.

(write obj)  write library procedure

(write obj port)  write library procedure

Writes a representation of obj to the given textual output port. Strings that appear in the written representation are enclosed in quotation marks, and within those strings backslash and quotation mark characters are escaped by backslashes. Symbols that contain non-ASCII characters are escaped with vertical lines. Character objects are written using the #' notation.

If obj contains cycles which would cause an infinite loop using the normal written representation, then at least the objects that form part of the cycle must be represented using datum labels as described in section [labelsection]. Datum labels must not be used if there are no cycles.

Implementations may support extended syntax to represent record types or other types that do not have datum representations.

The write procedure returns an unspecified value.

(write-shared obj)  write library procedure

(write-shared obj port)  write library procedure

The write-shared procedure is the same as write, except that shared structure must be represented using datum labels for all pairs and vectors that appear more than once in the output.

(write-simple obj)  write library procedure

(write-simple obj port)  write library procedure

The write-simple procedure is the same as write, except that shared structure is never represented using datum labels. This can cause write-simple not to terminate if obj contains circular structure.

(display obj)  write library procedure

(display obj port)  write library procedure

Writes a representation of obj to the given textual output port. Strings that appear in the written representation are output as if by write-string instead of by write. Symbols are not escaped. Character objects appear in the representation as if written by write-char instead of by write.

The display representation of other objects is unspecified. However, display must not loop forever on self-referencing pairs, vectors, or records. Thus if the normal write representation is used, datum labels are needed to represent cycles as in write.

Implementations may support extended syntax to represent record types or other types that do not have datum representations.

The display procedure returns an unspecified value.

Rationale: The write procedure is intended for producing machine-readable output and display for producing human-readable output.

(newline)  procedure

(newline port)  procedure

Writes an end of line to textual output port. Exactly how this is done differs from one operating system to another. Returns an unspecified value.

(write-char char)  procedure

(write-char char port)  procedure

Writes the character char (not an external representation of the character) to the given textual output port and returns an unspecified value.

(write-string string)  procedure

(write-string string port)  procedure

(write-string string port start)  procedure

(write-string string port start end)  procedure

Writes the characters of string from start to end in left-to-right order to the textual output port.

(write-u8 byte)  procedure

(write-u8 byte port)  procedure

Writes the byte to the given binary output port and returns an unspecified value.

(write-bytevector bytevector)  procedure

(write-bytevector bytevector port)  procedure

(write-bytevector bytevector port start)  procedure

(write-bytevector bytevector port start end)  procedure

Writes the bytes of bytevector from start to end in left-to-right order to the binary output port.

(flush-output-port)  procedure

(flush-output-port port)  procedure

Flushes any buffered output from the buffer of output-port to the underlying file or device and returns an unspecified value.

System interface

Questions of system interface generally fall outside of the domain of this report. However, the following operations are important enough to deserve description here.

(load filename)  load library procedure

(load filename environment-specifier)  load library procedure

It is an error if filename is not a string.

An implementation-dependent operation is used to transform filename into the name of an existing file containing Scheme source code. The load procedure reads expressions and definitions from the file and evaluates them sequentially in the environment specified by environment-specifier. If environment-specifier is omitted, (interaction-environment) is assumed.

It is unspecified whether the results of the expressions are printed. The load procedure does not affect the values returned by current-input-port and current-output-port. It returns an unspecified value.

Rationale: For portability, load must operate on source files. Its operation on other kinds of files necessarily varies among implementations.

(file-exists? filename)  file library procedure

It is an error if filename is not a string.

The file-exists? procedure returns #t if the named file exists at the time the procedure is called, and #f otherwise.

(delete-file filename)  file library procedure

It is an error if filename is not a string.

The delete-file procedure deletes the named file if it exists and can be deleted, and returns an unspecified value. If the file does not exist or cannot be deleted, an error that satisfies file-error? is signaled.

(command-line)  process-context library procedure

Returns the command line passed to the process as a list of strings. The first string corresponds to the command name, and is implementation-dependent. It is an error to mutate any of these strings.

(exit)  process-context library procedure

(exit obj)  process-context library procedure

Runs all outstanding dynamic-wind after procedures, terminates the running program, and communicates an exit value to the operating system. If no argument is supplied, or if obj is #t, the exit procedure should communicate to the operating system that the program exited normally. If obj is #f, the exit procedure should communicate to the operating system that the program exited abnormally. Otherwise, exit should translate obj into an appropriate exit value for the operating system, if possible.

The exit procedure must not signal an exception or return to its continuation.

Note: Because of the requirement to run handlers, this procedure is not just the operating system’s exit procedure.

(emergency-exit)  process-context library procedure

(emergency-exit obj)  process-context library procedure

Terminates the program without running any outstanding dynamic-wind after procedures and communicates an exit value to the operating system in the same manner as exit.

Note: The emergency-exit procedure corresponds to the _exit procedure in Windows and Posix.

(get-environment-variable name)  process-context library procedure

Many operating systems provide each running process with an environment consisting of environment variables. (This environment is not to be confused with the Scheme environments that can be passed to eval: see section [environments].) Both the name and value of an environment variable are strings. The procedure get-environment-variable returns the value of the environment variable name, or #f if the named environment variable is not found. It may use locale information to encode the name and decode the value of the environment variable. It is an error if get-environment-variable can’t decode the value. It is also an error to mutate the resulting string.

(get-environment-variable "PATH") ;; => "/usr/local/bin:/usr/bin:/bin"

(get-environment-variables)  process-context library procedure Returns the names and values of all the environment variables as an alist, where the car of each entry is the name of an environment variable and the cdr is its value, both as strings. The order of the list is unspecified. It is an error to mutate any of these strings or the alist itself.

(get-environment-variables) ;; => (("USER" . "root") ("HOME" . "/"))

(current-second)  time library procedure Returns an inexact number representing the current time on the International Atomic Time (TAI) scale. The value 0.0 represents midnight on January 1, 1970 TAI (equivalent to 8.000082 seconds before midnight Universal Time) and the value 1.0 represents one TAI second later. Neither high accuracy nor high precision are required; in particular, returning Coordinated Universal Time plus a suitable constant might be the best an implementation can do.

As of 2018, a TAI-UTC offset table can be found at .

(current-jiffy)  time library procedure Returns the number of jiffies as an exact integer that have elapsed since an arbitrary, implementation-defined epoch. A jiffy is an implementation-defined fraction of a second which is defined by the return value of the jiffies-per-second procedure. The starting epoch is guaranteed to be constant during a run of the program, but may vary between runs.

Rationale: Jiffies are allowed to be implementation-dependent so that current-jiffy can execute with minimum overhead. It should be very likely that a compactly represented integer will suffice as the returned value. Any particular jiffy size will be inappropriate for some implementations: a microsecond is too long for a very fast machine, while a much smaller unit would force many implementations to return integers which have to be allocated for most calls, rendering current-jiffy less useful for accurate timing measurements.

(jiffies-per-second)  time library procedure

Returns an exact integer representing the number of jiffies per SI second. This value is an implementation-specified constant.

(define (time-length)
  (let ((list (make-list 100000))
        (start (current-jiffy)))
    (length list)
    (/ (- (current-jiffy) start)
       (jiffies-per-second))))

(features)  procedure

Returns a list of the feature identifiers which cond-expand treats as true. It is an error to modify this list. Here is an example of what features might return:

(features) \ev
(r7rs ratios exact-complex full-unicode
      gnu-linux little-endian
      fantastic-scheme
      fantastic-scheme-1.0
      space-ship-control-system)

Derived expression types

This section gives syntax definitions for the derived expression types in terms of the primitive expression types (literal, variable, call, lambda, if, and set!), except for quasiquote.

Conditional derived syntax types:

(define-syntax cond
  (syntax-rules (else =>)
    ((cond (else result1 result2 ...))
     (begin result1 result2 ...))
    ((cond (test => result))
     (let ((temp test))
       (if temp (result temp))))
    ((cond (test => result) clause1 clause2 ...)
     (let ((temp test))
       (if temp
           (result temp)
           (cond clause1 clause2 ...))))
    ((cond (test)) test)
    ((cond (test) clause1 clause2 ...)
     (let ((temp test))
       (if temp
           temp
           (cond clause1 clause2 ...))))
    ((cond (test result1 result2 ...))
     (if test (begin result1 result2 ...)))
    ((cond (test result1 result2 ...)
           clause1 clause2 ...)
     (if test
         (begin result1 result2 ...)
         (cond clause1 clause2 ...)))))

(define-syntax case
  (syntax-rules (else =>)
    ((case (key ...)
       clauses ...)
     (let ((atom-key (key ...)))
       (case atom-key clauses ...)))
    ((case key
       (else => result))
     (result key))
    ((case key
       (else result1 result2 ...))
     (begin result1 result2 ...))
    ((case key
       ((atoms ...) => result))
     (if (memv key '(atoms ...))
         (result key)))
    ((case key
       ((atoms ...) result1 result2 ...))
     (if (memv key '(atoms ...))
         (begin result1 result2 ...)))
    ((case key
       ((atoms ...) => result)
       clause clauses ...)
     (if (memv key '(atoms ...))
         (result key)
         (case key clause clauses ...)))
    ((case key
       ((atoms ...) result1 result2 ...)
       clause clauses ...)
     (if (memv key '(atoms ...))
         (begin result1 result2 ...)
         (case key clause clauses ...)))))

(define-syntax and
  (syntax-rules ()
    ((and) #t)
    ((and test) test)
    ((and test1 test2 ...)
     (if test1 (and test2 ...) #f))))

(define-syntax or
  (syntax-rules ()
    ((or) #f)
    ((or test) test)
    ((or test1 test2 ...)
     (let ((x test1))
       (if x x (or test2 ...))))))

(define-syntax when
  (syntax-rules ()
    ((when test result1 result2 ...)
     (if test
         (begin result1 result2 ...)))))

(define-syntax unless
  (syntax-rules ()
    ((unless test result1 result2 ...)
     (if (not test)
         (begin result1 result2 ...)))))

Binding constructs:

(define-syntax let
  (syntax-rules ()
    ((let ((name val) ...) body1 body2 ...)
     ((lambda (name ...) body1 body2 ...)
      val ...))
    ((let tag ((name val) ...) body1 body2 ...)
     ((letrec ((tag (lambda (name ...)
                      body1 body2 ...)))
        tag)
      val ...))))

(define-syntax let*
  (syntax-rules ()
    ((let* () body1 body2 ...)
     (let () body1 body2 ...))
    ((let* ((name1 val1) (name2 val2) ...)
       body1 body2 ...)
     (let ((name1 val1))
       (let* ((name2 val2) ...)
         body1 body2 ...)))))

The following letrec macro uses the symbol <undefined> in place of an expression which returns something that when stored in a location makes it an error to try to obtain the value stored in the location. (No such expression is defined in Verbatim.) A trick is used to generate the temporary names needed to avoid specifying the order in which the values are evaluated. This could also be accomplished by using an auxiliary macro.

(define-syntax letrec
  (syntax-rules ()
    ((letrec ((var1 init1) ...) body ...)
     (letrec "generate_temp_names"
       (var1 ...)
       ()
       ((var1 init1) ...)
       body ...))
    ((letrec "generate_temp_names"
       ()
       (temp1 ...)
       ((var1 init1) ...)
       body ...)
     (let ((var1 <undefined>) ...)
       (let ((temp1 init1) ...)
         (set! var1 temp1)
         ...
         body ...)))
    ((letrec "generate_temp_names"
       (x y ...)
       (temp ...)
       ((var1 init1) ...)
       body ...)
     (letrec "generate_temp_names"
       (y ...)
       (newtemp temp ...)
       ((var1 init1) ...)
       body ...))))

(define-syntax letrec*
  (syntax-rules ()
    ((letrec* ((var1 init1) ...) body1 body2 ...)
     (let ((var1 <undefined>) ...)
       (set! var1 init1)
       ...
       (let () body1 body2 ...)))))

(define-syntax let-values
  (syntax-rules ()
    ((let-values (binding ...) body0 body1 ...)
     (let-values "bind"
       (binding ...) () (begin body0 body1 ...)))

    ((let-values "bind" () tmps body)
     (let tmps body))

    ((let-values "bind" ((b0 e0)
                         binding ...) tmps body)
     (let-values "mktmp" b0 e0 ()
                 (binding ...) tmps body))

    ((let-values "mktmp" () e0 args
                 bindings tmps body)
     (call-with-values
         (lambda () e0)
       (lambda args
         (let-values "bind"
           bindings tmps body))))

    ((let-values "mktmp" (a . b) e0 (arg ...)
                 bindings (tmp ...) body)
     (let-values "mktmp" b e0 (arg ... x)
                 bindings (tmp ... (a x)) body))

    ((let-values "mktmp" a e0 (arg ...)
                 bindings (tmp ...) body)
     (call-with-values
         (lambda () e0)
       (lambda (arg ... . x)
         (let-values "bind"
           bindings (tmp ... (a x)) body))))))

(define-syntax let*-values
  (syntax-rules ()
    ((let*-values () body0 body1 ...)
     (let () body0 body1 ...))

    ((let*-values (binding0 binding1 ...)
       body0 body1 ...)
     (let-values (binding0)
       (let*-values (binding1 ...)
         body0 body1 ...)))))

(define-syntax define-values
  (syntax-rules ()
    ((define-values () expr)
     (define dummy
       (call-with-values (lambda () expr)
         (lambda args #f))))
    ((define-values (var) expr)
     (define var expr))
    ((define-values (var0 var1 ... varn) expr)
     (begin
       (define var0
         (call-with-values (lambda () expr)
           list))
       (define var1
         (let ((v (cadr var0)))
           (set-cdr! var0 (cddr var0))
           v)) ...
           (define varn
             (let ((v (cadr var0)))
               (set! var0 (car var0))
               v))))
    ((define-values (var0 var1 ... . varn) expr)
     (begin
       (define var0
         (call-with-values (lambda () expr)
           list))
       (define var1
         (let ((v (cadr var0)))
           (set-cdr! var0 (cddr var0))
           v)) ...
           (define varn
             (let ((v (cdr var0)))
               (set! var0 (car var0))
               v))))
    ((define-values var expr)
     (define var
       (call-with-values (lambda () expr)
         list)))))

(define-syntax begin
  (syntax-rules ()
    ((begin exp ...)
     ((lambda () exp ...)))))

The following alternative expansion for begin does not make use of the ability to write more than one expression in the body of a lambda expression. In any case, note that these rules apply only if the body of the begin contains no definitions.

(define-syntax begin
  (syntax-rules ()
    ((begin exp)
     exp)
    ((begin exp1 exp2 ...)
     (call-with-values
         (lambda () exp1)
       (lambda args
         (begin exp2 ...))))))

The following syntax definition of do uses a trick to expand the variable clauses. As with letrec above, an auxiliary macro would also work. The expression (if #f #f) is used to obtain an unspecific value.

(define-syntax do
  (syntax-rules ()
    ((do ((var init step ...) ...)
         (test expr ...)
       command ...)
     (letrec
         ((loop
           (lambda (var ...)
             (if test
                 (begin
                   (if #f #f)
                   expr ...)
                 (begin
                   command
                   ...
                   (loop (do "step" var step ...)
                         ...))))))
       (loop init ...)))
    ((do "step" x)
     x)
    ((do "step" x y)
     y)))

Here is a possible implementation of delay, force and delay-force. We define the expression

(delay-force <expression>)

to have the same meaning as the procedure call

(make-promise #f (lambda () <expression>))

as follows

(define-syntax delay-force
  (syntax-rules ()
    ((delay-force expression)
     (make-promise #f (lambda () expression)))))

and we define the expression

(delay <expression>)

to have the same meaning as:

(delay-force (make-promise #t <expression>))

as follows

(define-syntax delay
  (syntax-rules ()
    ((delay expression)
     (delay-force (make-promise #t expression)))))

where make-promise is defined as follows:

(define make-promise
  (lambda (done? proc)
    (list (cons done? proc))))

Finally, we define force to call the procedure expressions in promises iteratively using a trampoline technique following until a non-lazy result (i.e. a value created by delay instead of delay-force) is returned, as follows:

(define (force promise)
  (if (promise-done? promise)
      (promise-value promise)
      (let ((promise* ((promise-value promise))))
        (unless (promise-done? promise)
          (promise-update! promise* promise))
        (force promise))))

with the following promise accessors:

(define promise-done?
  (lambda (x) (car (car x))))
(define promise-value
  (lambda (x) (cdr (car x))))
(define promise-update!
  (lambda (new old)
    (set-car! (car old) (promise-done? new))
    (set-cdr! (car old) (promise-value new))
    (set-car! new (car old))))

The following implementation of make-parameter and parameterize is suitable for an implementation with no threads. Parameter objects are implemented here as procedures, using two arbitrary unique objects <param-set!> and <param-convert>:

(define (make-parameter init . o)
  (let* ((converter
          (if (pair? o) (car o) (lambda (x) x)))
         (value (converter init)))
    (lambda args
      (cond
       ((null? args)
        value)
       ((eq? (car args) <param-set!>)
        (set! value (cadr args)))
       ((eq? (car args) <param-convert>)
        converter)
       (else
        (error "bad parameter syntax"))))))

Then parameterize uses dynamic-wind to dynamically rebind the associated value:

(define-syntax parameterize
  (syntax-rules ()
    ((parameterize ("step")
       ((param value p old new) ...)
       ()
       body)
     (let ((p param) ...)
       (let ((old (p)) ...
             (new ((p <param-convert>) value)) ...)
         (dynamic-wind
             (lambda () (p <param-set!> new) ...)
             (lambda () . body)
             (lambda () (p <param-set!> old) ...)))))
    ((parameterize ("step")
       args
       ((param value) . rest)
       body)
     (parameterize ("step")
       ((param value p old new) . args)
       rest
       body))
    ((parameterize ((param value) ...) . body)
     (parameterize ("step")
       ()
       ((param value) ...)
       body))))

The following implementation of guard depends on an auxiliary macro, here called guard-aux.

(define-syntax guard
  (syntax-rules ()
    ((guard (var clause ...) e1 e2 ...)
     ((call/cc
       (lambda (guard-k)
         (with-exception-handler
          (lambda (condition)
            ((call/cc
              (lambda (handler-k)
                (guard-k
                 (lambda ()
                   (let ((var condition))
                     (guard-aux
                      (handler-k
                       (lambda ()
                         (raise-continuable condition)))
                      clause ...))))))))
          (lambda ()
            (call-with-values
                (lambda () e1 e2 ...)
              (lambda args
                (guard-k
                 (lambda ()
                   (apply values args)))))))))))))

(define-syntax guard-aux
  (syntax-rules (else =>)
    ((guard-aux reraise (else result1 result2 ...))
     (begin result1 result2 ...))
    ((guard-aux reraise (test => result))
     (let ((temp test))
       (if temp
           (result temp)
           reraise)))
    ((guard-aux reraise (test => result)
                clause1 clause2 ...)
     (let ((temp test))
       (if temp
           (result temp)
           (guard-aux reraise clause1 clause2 ...))))
    ((guard-aux reraise (test))
     (or test reraise))
    ((guard-aux reraise (test) clause1 clause2 ...)
     (let ((temp test))
       (if temp
           temp
           (guard-aux reraise clause1 clause2 ...))))
    ((guard-aux reraise (test result1 result2 ...))
     (if test
         (begin result1 result2 ...)
         reraise))
    ((guard-aux reraise
                (test result1 result2 ...)
                clause1 clause2 ...)
     (if test
         (begin result1 result2 ...)
         (guard-aux reraise clause1 clause2 ...)))))

(define-syntax case-lambda
  (syntax-rules ()
    ((case-lambda (params body0 ...) ...)
     (lambda args
       (let ((len (length args)))
         (letrec-syntax
             ((cl (syntax-rules ::: ()
                                ((cl)
                                 (error "no matching clause"))
                                ((cl ((p :::) . body) . rest)
                                 (if (= len (length '(p :::)))
                                     (apply (lambda (p :::)
                                              . body)
                                            args)
                                     (cl . rest)))
                                ((cl ((p ::: . tail) . body)
                                     . rest)
                                 (if (>= len (length '(p :::)))
                                     (apply
                                      (lambda (p ::: . tail)
                                        . body)
                                      args)
                                     (cl . rest))))))
           (cl (params body0 ...) ...)))))))

This definition of cond-expand does not interact with the features procedure. It requires that each feature identifier provided by the implementation be explicitly mentioned.

(define-syntax cond-expand
  ;; Extend this to mention all feature ids and libraries
  (syntax-rules (and or not else r7rs library verbatim base)
    ((cond-expand)
     (syntax-error "Unfulfilled cond-expand"))
    ((cond-expand (else body ...))
     (begin body ...))
    ((cond-expand ((and) body ...) more-clauses ...)
     (begin body ...))
    ((cond-expand ((and req1 req2 ...) body ...)
                  more-clauses ...)
     (cond-expand
      (req1
       (cond-expand
        ((and req2 ...) body ...)
        more-clauses ...))
      more-clauses ...))
    ((cond-expand ((or) body ...) more-clauses ...)
     (cond-expand more-clauses ...))
    ((cond-expand ((or req1 req2 ...) body ...)
                  more-clauses ...)
     (cond-expand
      (req1
       (begin body ...))
      (else
       (cond-expand
        ((or req2 ...) body ...)
        more-clauses ...))))
    ((cond-expand ((not req) body ...)
                  more-clauses ...)
     (cond-expand
      (req
       (cond-expand more-clauses ...))
      (else body ...)))
    ((cond-expand (r7rs body ...)
                  more-clauses ...)
     (begin body ...))
    ;; Add clauses here for each
    ;; supported feature identifier.
    ;; Samples:
    ;; ((cond-expand (exact-closed body ...)
    ;;               more-clauses ...)
    ;;   (begin body ...))
    ;; ((cond-expand (ieee-float body ...)
    ;;               more-clauses ...)
    ;;   (begin body ...))
    ((cond-expand ((library (verbatim base))
                   body ...)
                  more-clauses ...)
     (begin body ...))
    ;; Add clauses here for each library
    ((cond-expand (feature-id body ...)
                  more-clauses ...)
     (cond-expand more-clauses ...))
    ((cond-expand ((library (name ...))
                   body ...)
                  more-clauses ...)
     (cond-expand more-clauses ...))))

Standard Libraries

This section lists the exports provided by the standard libraries. The libraries are factored so as to separate features which might not be supported by all implementations, or which might be expensive to load.

The scheme library prefix is used for all standard libraries, and is reserved for use by future standards.

Base Library

The (scheme base) library exports many of the procedures and syntax bindings that are traditionally associated with Scheme. The division between the base library and the other standard libraries is based on use, not on construction. In particular, some facilities that are typically implemented as primitives by a compiler or the run-time system rather than in terms of other standard procedures or syntax are not part of the base library, but are defined in separate libraries. By the same token, some exports of the base library are implementable in terms of other exports. They are redundant in the strict sense of the word, but they capture common patterns of usage, and are therefore provided as convenient abbreviations.

*
+
-
...
/
<
<=
=
=>
>
>=
_
abs
and
append
apply
assoc
assq
assv
begin
binary-port?
boolean=?
boolean?
bytevector
bytevector-append
bytevector-copy
bytevector-copy!
bytevector-length
bytevector-u8-ref
bytevector-u8-set!
bytevector?
caar
cadr
call-with-current-continuation
call-with-port
call-with-values
call/cc
car
case
cdar
cddr
cdr
ceiling
char->integer
char-ready?
char<=?
char<?
char=?
char>=?
char>?
char?
close-input-port
close-output-port
close-port
complex?
cond
cond-expand
cons
current-error-port
current-input-port
current-output-port
define
define-record-type
define-syntax
define-values
denominator
do
dynamic-wind
else
eof-object
eof-object?
eq?
equal?
eqv?
error
error-object-irritants
error-object-message
error-object?
even?
exact
exact-integer-sqrt
exact-integer?
exact?
expt
features
file-error?
floor
floor-quotient
floor-remainder
floor/
flush-output-port
for-each
gcd
get-output-bytevector
get-output-string
guard
if
include
include-ci
inexact
inexact?
input-port-open?
input-port?
integer->char
integer?
lambda
lcm
length
let
let*
let*-values
let-syntax
let-values
letrec
letrec*
letrec-syntax
list
list->string
list->vector
list-copy
list-ref
list-set!
list-tail
list?
make-bytevector
make-list
make-parameter
make-string
make-vector
map
max
member
memq
memv
min
modulo
negative?
newline
not
null?
number->string
number?
numerator
odd?
open-input-bytevector
open-input-string
open-output-bytevector
open-output-string
or
output-port-open?
output-port?
pair?
parameterize
peek-char
peek-u8
port?
positive?
procedure?
quasiquote
quote
quotient
raise
raise-continuable
rational?
rationalize
read-bytevector
read-bytevector!
read-char
read-error?
read-line
read-string
read-u8
real?
remainder
reverse
round
set!
set-car!
set-cdr!
square
string
string->list
string->number
string->symbol
string->utf8
string->vector
string-append
string-copy
string-copy!
string-fill!
string-for-each
string-length
string-map
string-ref
string-set!
string<=?
string<?
string=?
string>=?
string>?
string?
substring
symbol->string
symbol=?
symbol?
syntax-error
syntax-rules
textual-port?
truncate
truncate-quotient
truncate-remainder
truncate/
u8-ready?
unless
unquote
unquote-splicing
utf8->string
values
vector
vector->list
vector->string
vector-append
vector-copy
vector-copy!
vector-fill!
vector-for-each
vector-length
vector-map
vector-ref
vector-set!
vector?
when
with-exception-handler
write-bytevector
write-char
write-string
write-u8
zero?

Case-Lambda Library

The (scheme case-lambda) library exports the case-lambda syntax.

case-lambda

Char Library

The (scheme char) library provides the procedures for dealing with characters that involve potentially large tables when supporting all of Unicode.

char-alphabetic?
char-ci<=?
char-ci<?
char-ci=?
char-ci>=?
char-ci>?
char-downcase
char-foldcase
char-lower-case?
char-numeric?
char-upcase
char-upper-case?
char-whitespace?
digit-value
string-ci<=?
string-ci<?
string-ci=?
string-ci>=?
string-ci>?
string-downcase
string-foldcase
string-upcase

Complex Library

The (scheme complex) library exports procedures which are typically only useful with non-real numbers.

angle                   imag-part
magnitude               make-polar
make-rectangular        real-part

CxR Library

The (scheme cxr) library exports twenty-four procedures which are the compositions of from three to four car and cdr operations. For example caddar could be defined by

(define caddar
  (lambda (x) (car (cdr (cdr (car x))))))

The procedures car and cdr themselves and the four two-level compositions are included in the base library. See section [listsection].

caaaar                  caaadr
caaar                   caadar
caaddr                  caadr
cadaar                  cadadr
cadar                   caddar
cadddr                  caddr
cdaaar                  cdaadr
cdaar                   cdadar
cdaddr                  cdadr
cddaar                  cddadr
cddar                   cdddar
cddddr                  cdddr

Eval Library

The (scheme eval) library exports procedures for evaluating Scheme data as programs.

environment
eval

File Library

The (scheme file) library provides procedures for accessing files.

call-with-input-file
call-with-output-file
delete-file
file-exists?
open-binary-input-file
open-binary-output-file
open-input-file
open-output-file
with-input-from-file
with-output-to-file

Inexact Library

The (scheme inexact) library exports procedures which are typically only useful with inexact values.

acos
asin
atan
cos
exp
finite?
infinite?
log
nan?
sin
sqrt
tan

Lazy Library

The (scheme lazy) library exports procedures and syntax keywords for lazy evaluation.

delay                   delay-force
force                   make-promise
promise?

Load Library

The (scheme load) library exports procedures for loading Scheme expressions from files.

load

Process-Context Library

The (scheme process-context) library exports procedures for accessing with the program’s calling context.

command-line            emergency-exit
exit
get-environment-variable
get-environment-variables

Read Library

The (scheme read) library provides procedures for reading Scheme objects.

read

Repl Library

The (scheme repl) library exports the interaction-environment procedure.

interaction-environment

Time Library

The (scheme time) library provides access to time-related values.

current-jiffy           current-second
jiffies-per-second

Write Library

The (scheme write) library provides procedures for writing Scheme objects.

display                 write
write-shared            write-simple

R5RS Library

The (scheme r5rs) library provides the identifiers defined by R5RS, except that transcript-on and transcript-off are not present. Note that the exact and inexact procedures appear under their R5RS names inexact->exact and exact->inexact respectively. However, if an implementation does not provide a particular library such as the complex library, the corresponding identifiers will not appear in this library either.

\* + - ... / \< \<= = => \> \>= _ abs acos and angle append apply asin
assoc assq assv atan begin boolean?  caaaar caaadr caaar caadar caaddr
caadr caar cadaar cadadr cadar caddar cadddr caddr cadr
call-with-current-continuation call-with-input-file
call-with-output-file call-with-values car case cdaaar cdaadr cdaar
cdadar cdaddr cdadr cdar cddaar cddadr cddar cdddar cddddr cdddr cddr
cdr ceiling char->integer char-alphabetic?  char-ci\<=? char-ci\<?
char-ci=? char-ci>=?  char-ci>? char-downcase char-lower-case?
char-numeric?  char-ready? char-upcase char-upper-case?
char-whitespace?  char\<=? char\<?  char=? char>=?  char>? char?
close-input-port close-output-port complex? cond cons cos
current-input-port current-output-port define define-syntax delay
denominator display do dynamic-wind else eof-object? eq?  equal? eqv?
eval even?  exact->inexact exact?  exp expt floor for-each force gcd if
imag-part inexact->exact inexact?  input-port? integer->char integer?
interaction-environment lambda lcm length let let\* let-syntax letrec
letrec-syntax list list->string list->vector list-ref list-tail list?
load log magnitude make-polar make-rectangular make-string make-vector
map max member memq memv min modulo negative? newline not
null-environment null? number->string number? numerator odd?
open-input-file open-output-file or output-port? pair?  peek-char
positive?  procedure? quasiquote quote quotient rational? rationalize
read read-char real-part real?  remainder reverse round
scheme-report-environment set! set-car! set-cdr! sin sqrt string
string->list string->number string->symbol string-append string-ci\<=?
string-ci\<? string-ci=?  string-ci>=? string-ci>?  string-copy
string-fill! string-length string-ref string-set! string\<=?  string\<?
string=?  string>=? string>?  string? substring symbol->string symbol?
syntax-rules tan truncate values vector vector->list vector-fill!
vector-length vector-ref vector-set! vector? with-input-from-file
with-output-to-file write write-char zero?

Standard Feature Identifiers

An implementation may provide any or all of the feature identifiers listed below for use by cond-expand and features, but must not provide a feature identifier if it does not provide the corresponding feature.

r7rs

All R7RS Scheme implementations have this feature.

exact-closed

The algebraic operations +, -, *, and expt where the second argument is a non-negative integer produce exact values given exact inputs.

exact-complex

Exact complex numbers are provided.

ieee-float

Inexact numbers are IEEE 754 binary floating point values.

full-unicode

All Unicode characters present in Unicode version 6.0 are supported as Scheme characters.

ratios

/ with exact arguments produces an exact result when the divisor is nonzero.

posix

This implementation is running on a POSIX system.

windows

This implementation is running on Windows.

unixdarwingnu-linuxbsdfreebsdsolaris, …

Operating system flags (perhaps more than one).

i386x86-64ppcsparcjvmclrllvm, …

CPU architecture flags.

ilp32lp64ilp64, …

C memory model flags.

big-endianlittle-endian

Byte order flags.

The name of this implementation.

The name and version of this implementation.

Language changes

Incompatibilities with R5RS

This section enumerates the incompatibilities between this report and the “Revised5 report” .

This list is not authoritative, but is believed to be correct and complete.

Other language changes since R5RS

This section enumerates the additional differences between this report and the “Revised5 report” .

This list is not authoritative, but is believed to be correct and complete.

Incompatibilities with R6RS

This section enumerates the incompatibilities between R7RS and the “Revised6 report”  and its accompanying Standard Libraries document.

This list is not authoritative, and is possibly incomplete.

Additional material

The Scheme community website at http://schemers.org contains additional resources for learning and programming, job and event postings, and Scheme user group information.

A bibliography of Scheme-related research at http://library.readscheme.org links to technical papers and theses related to the Scheme language, including both classic papers and recent research.

On-line Scheme discussions are held using IRC on the #scheme channel at irc.freenode.net and on the Usenet discussion group comp.lang.scheme.

Example

The procedure integrate-system integrates the system yk = fk(y1,y2,…,yn), k = 1, …, n of differential equations with the method of Runge-Kutta.

The parameter system-derivative is a function that takes a system state (a vector of values for the state variables y1, …, yn) and produces a system derivative (the values y1, …, yn). The parameter initial-state provides an initial system state, and h is an initial guess for the length of the integration step.

The value returned by integrate-system is an infinite stream of system states.

(define (integrate-system system-derivative
                          initial-state
                          h)
  (let ((next (runge-kutta-4 system-derivative h)))
    (letrec ((states
              (cons initial-state
                    (delay (map-streams next
                                        states)))))
      states)))

The procedure runge-kutta-4 takes a function, f, that produces a system derivative from a system state. It produces a function that takes a system state and produces a new system state.

(define (runge-kutta-4 f h)
  (let ((*h (scale-vector h))
        (*2 (scale-vector 2))
        (*1/2 (scale-vector (/ 1 2)))
        (*1/6 (scale-vector (/ 1 6))))
    (lambda (y)
      ;; y is a system state
      (let* ((k0 (*h (f y)))
             (k1 (*h (f (add-vectors y (*1/2 k0)))))
             (k2 (*h (f (add-vectors y (*1/2 k1)))))
             (k3 (*h (f (add-vectors y k2)))))
        (add-vectors y
                     (*1/6 (add-vectors k0
                                        (*2 k1)
                                        (*2 k2)
                                        k3)))))))

(define (elementwise f)
  (lambda vectors
    (generate-vector
     (vector-length (car vectors))
     (lambda (i)
       (apply f
              (map (lambda (v) (vector-ref  v i))
                   vectors))))))

(define (generate-vector size proc)
  (let ((ans (make-vector size)))
    (letrec ((loop
              (lambda (i)
                (cond ((= i size) ans)
                      (else
                       (vector-set! ans i (proc i))
                       (loop (+ i 1)))))))
      (loop 0))))

(define add-vectors (elementwise +))

(define (scale-vector s)
  (elementwise (lambda (x) (* x s))))

The map-streams procedure is analogous to map: it applies its first argument (a procedure) to all the elements of its second argument (a stream).

(define (map-streams f s)
  (cons (f (head s))
        (delay (map-streams f (tail s)))))

Infinite streams are implemented as pairs whose car holds the first element of the stream and whose cdr holds a promise to deliver the rest of the stream.

(define head car)
(define (tail stream)
  (force (cdr stream)))

The following illustrates the use of integrate-system in integrating the system $$C {dv_C \\over dt} = -i_L - {v_C \\over R}$$ $$L {di_L \\over dt} = v_C$$ which models a damped oscillator.

(define (damped-oscillator R L C)
  (lambda (state)
    (let ((Vc (vector-ref state 0))
          (Il (vector-ref state 1)))
      (vector (- 0 (+ (/ Vc (* R C)) (/ Il C)))
              (/ Vc L)))))

(define the-states
  (integrate-system
   (damped-oscillator 10000 1000 .001)
   '#(1 0)
   .01))

Bibliography

Harold Abelson and Gerald Jay Sussman with Julie Sussman. Structure and Interpretation of Computer Programs, second edition. MIT Press, Cambridge, 1996.

Alan Bawden and Jonathan Rees. Syntactic closures. In Proceedings of the 1988 ACM Symposium on Lisp and Functional Programming, pages 86–95.

S. Bradner. Key words for use in RFCs to Indicate Requirement Levels. http://www.ietf.org/rfc/rfc2119.txt, 1997.

Robert G. Burger and R. Kent Dybvig. Printing floating-point numbers quickly and accurately. In Proceedings of the ACM SIGPLAN ’96 Conference on Programming Language Design and Implementation, pages 108–116.

William Clinger. How to read floating point numbers accurately. In Proceedings of the ACM SIGPLAN ’90 Conference on Programming Language Design and Implementation, pages 92–101. Proceedings published as SIGPLAN Notices 25(6), June 1990.

William Clinger. Proper Tail Recursion and Space Efficiency. In Proceedings of the 1998 ACM Conference on Programming Language Design and Implementation, June 1998.

William Clinger. SRFI 6: Basic String Ports. http://srfi.schemers.org/srfi-6/, 1999.

William Clinger, editor. The revised revised report on Scheme, or an uncommon Lisp. MIT Artificial Intelligence Memo 848, August 1985. Also published as Computer Science Department Technical Report 174, Indiana University, June 1985.

William Clinger and Jonathan Rees. Macros that work. In Proceedings of the 1991 ACM Conference on Principles of Programming Languages, pages 155–162.

William Clinger and Jonathan Rees, editors. The revised4 report on the algorithmic language Scheme. In ACM Lisp Pointers 4(3), pages 1–55, 1991.

Mark Davis. Unicode Standard Annex #44, Unicode Character Database. http://unicode.org/reports/tr44/, 2010.

R. Kent Dybvig, Robert Hieb, and Carl Bruggeman. Syntactic abstraction in Scheme. Lisp and Symbolic Computation 5(4):295–326, 1993.

Marc Feeley. SRFI 4: Homogeneous Numeric Vector Datatypes. http://srfi.schemers.org/srfi-4/, 1999.

Carol Fessenden, William Clinger, Daniel P. Friedman, and Christopher Haynes. Scheme 311 version 4 reference manual. Indiana University Computer Science Technical Report 137, February 1983. Superseded by .

D. Friedman, C. Haynes, E. Kohlbecker, and M. Wand. Scheme 84 interim reference manual. Indiana University Computer Science Technical Report 153, January 1985.

Martin Gardner. Mathematical Games: The fantastic combinations of John Conway’s new solitaire game “Life.” In Scientific American, 223:120–123, October 1970.

IEEE Standard 754-2008. IEEE Standard for Floating-Point Arithmetic. IEEE, New York, 2008.

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Richard Kelsey. SRFI 9: Defining Record Types. http://srfi.schemers.org/srfi-9/, 1999.

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Eugene E. Kohlbecker Jr. Syntactic Extensions in the Programming Language Lisp. PhD thesis, Indiana University, August 1986.

Eugene E. Kohlbecker Jr., Daniel P. Friedman, Matthias Felleisen, and Bruce Duba. Hygienic macro expansion. In Proceedings of the 1986 ACM Conference on Lisp and Functional Programming, pages 151–161.

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Jonathan A. Rees and Norman I. Adams IV. T: A dialect of Lisp or, lambda: The ultimate software tool. In Conference Record of the 1982 ACM Symposium on Lisp and Functional Programming, pages 114–122.

Jonathan A. Rees, Norman I. Adams IV, and James R. Meehan. The T manual, fourth edition. Yale University Computer Science Department, January 1984.

Jonathan Rees and William Clinger, editors. The revised3 report on the algorithmic language Scheme. In ACM SIGPLAN Notices 21(12), pages 37–79, December 1986.

Olin Shivers. SRFI 1: List Library. http://srfi.schemers.org/srfi-1/, 1999.

Guy Lewis Steele Jr. and Gerald Jay Sussman. The revised report on Scheme, a dialect of Lisp. MIT Artificial Intelligence Memo 452, January 1978.

Guy Lewis Steele Jr. Rabbit: a compiler for Scheme. MIT Artificial Intelligence Laboratory Technical Report 474, May 1978.

Michael Sperber, R. Kent Dybvig, Mathew Flatt, and Anton van Straaten, editors. The revised6 report on the algorithmic language Scheme. Cambridge University Press, 2010.

Guy Lewis Steele Jr. Common Lisp: The Language, second edition. Digital Press, Burlington MA, 1990.

Gerald Jay Sussman and Guy Lewis Steele Jr. Scheme: an interpreter for extended lambda calculus. MIT Artificial Intelligence Memo 349, December 1975.

Joseph E. Stoy. Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory. MIT Press, Cambridge, 1977.

Texas Instruments, Inc. TI Scheme Language Reference Manual. Preliminary version 1.0, November 1985.

Andre van Tonder. SRFI 45: Primitives for Expressing Iterative Lazy Algorithms. http://srfi.schemers.org/srfi-45/, 2002.

Martin Gasbichler, Eric Knauel, Michael Sperber and Richard Kelsey. How to Add Threads to a Sequential Language Without Getting Tangled Up. Proceedings of the Fourth Workshop on Scheme and Functional Programming, November 2003.

International Earth Rotation Service. Historical table of TAI-UTC offsets. http://maia.usno.navy.mil/ser7/tai-utc.dat # (scheme base)

_

TODO (missing in r7rs?)

...

It is called ellipsis. It signify that a pattern must be repeated.

=>

TODO

else

Used in cond and case form as in the last clause as a fallback.

(* number ...)

Multiplication procedure.

(+ number ...)

Addition procedure.

(- number ...)

Substraction procedure.

(/ number ...)

Division procedure. Raise 'numerical-overflow condition in case where denominator is zero.

(< number number ...)

Less than procedure. Return a boolean.

(<= number number ...)

Less than or equal procedure. Return a boolean.

(= number number ...)

Return #t if the numbers passed as parameters are equal. And #f otherwise.

(> number number ...)

Greater than procedure. Return a boolean.

(>= number number ...)

Greater than or equal. Return a boolean.

(abs number)

Return the absolute value of NUMBER.

(and test1 ...)

The test expressions are evaluated from left to right, and if any expression evaluates to #f, then #f is returned. Any remaining expressions are not evaluated. If all the expressions evaluate to true values, the values of the last expression are returned. If there are no expressions, then #t is returned.

(append lst ...)

Return the list made of the list passed as parameters in the same order.

(apply proc arg1 ... args)

The apply procedure calls proc with the elements of the list (append (list arg1 ...) args) as the actual arguments.

(assoc obj alist)

Return the first pair which car is equal to OBJ according to the predicate equal?. Or it returns #f.

(assq obj alist)

Return the first pair which car is equal to OBJ according to the predicate eq?. Or it returns #f.

(assv obj alist)

Return the first pair which car is equal to OBJ according to the predicate eqv?. Or it returns #f.

begin syntax

There is two uses of begin.

(begin expression-or-definition ...)

This form of begin can appear as part of a body, or at the outermost level of a program, or at the REPL, or directly nested in a begin that is itself of this form. It causes the contained expressions and definitions to be evaluated exactly as if the enclosing begin construct were not present.

TODO: example

(begin expression1 expression2 ...)

This form of begin can be used as an ordinary expression. The expressions are evaluated sequentially from left to right, and the values of the last expression are returned. This expression type is used to sequence side effects such as assignments or input and output.

TODO: example

binary-port?

TODO: not implemented

(boolean=? obj ...)

Return #t if the scheme objects passed as arguments are the same boolean. Otherwise it return #f.

(boolean? obj)

Return #t if OBJ is a boolean. Otherwise #f.

(bytevector byte ...)

Returns a newly allocated bytevector containing its arguments.

(bytevector-append bytevector ...)

Returns a newly allocated bytevector whose elements arethe concatenation of the elements in the given bytevectors.

(bytevector-copy bytevector [start [end]])

Returns a newly allocated bytevector containing the bytes in bytevector between start and end.

(bytevector-copy! to at from [start [end]])

Copies the bytes of bytevector from between start and end to bytevector TO, starting at at. The order in which bytes are copied is unspecified, except that if the source and destination overlap, copying takes place as if the source is first copied into a temporary bytevector and then into the destination. This can be achieved without allocating storage by making sure to copy in the correct direction in such circumstances.

(bytevector-length bytevector)

Returns the length of bytevector in bytes as an exact integer.

bytevector-u8-ref

Returns the Kth byte of BYTEVECTOR. It is an error if K is not a valid index of BYTEVECTOR.

bytevector-u8-set!

Stores BYTE as the Kth byte of BYTEVECTOR.

It is an error if K is not a valid index of BYTEVECTOR.

(bytevector? obj)

Returns #t if OBJ is a bytevector. Otherwise, #f is returned.

caar

TODO

cadr

TODO

(call-with-current-continuation proc)

It is an error if proc does not accept one argument.

The procedure call-with-current-continuation (or its equivalent abbreviation call/cc) packages the current continuation (see the rationale below) as an “escape procedure” and passes it as an argument to proc. The escape procedure is a Scheme procedure that, if it is later called, will abandon whatever continuation is in effect at that later time and will instead use the continuation that was in effect when the escape procedure was created. Calling the escape procedure will cause the invocation of before and after thunks installed using dynamic-wind.

The escape procedure accepts the same number of arguments as the continuation to the original call to call-with-current-continuation. Most continuations take only one value. Continuations created by the call-with-values procedure (including the initialization expressions of define-values, let-values, and let-values expressions), take the number of values that the consumer expects. The continuations of all non-final expressions within a sequence of expressions, such as in lambda, case-lambda, begin, let, let, letrec, letrec, let-values, let-values, let-syntax, letrec-syntax, parameterize, guard, case, cond, when, and unless expressions, take an arbitrary number of values because they discard the values passed to them in any event. The effect of passing no values or more than one value to continuations that were not created in one of these ways is unspecified.

The escape procedure that is passed to proc has unlimited extent just like any other procedure in Scheme. It can be stored in variables or data structures and can be called as many times as desired. However, like the raise and error procedures, it never returns to its caller.

TODO: example

(call-with-port port proc)

The call-with-port procedure calls PROC with PORT as an argument. If PROC returns, then the PORT is closed automatically and the values yielded by the PROC are returned. If PROC does not return, then the PORT must not be closed automatically unless it is possible to prove that the port will never again be used for a read or write operation.

It is an error if PROC does not accept one argument.

(call-with-values producer consumer)

Calls its producer argument with no arguments and a continuation that, when passed some values, calls the consumer procedure with those values as arguments. The continuation for the call to consumer is the continuation of the call to call-with-values.

(call/cc proc)

Abbreviation for call-with-continuation.

(car pair)

Returns the contents of the car field of pair. Note that it is an error to take the car of the empty list.

(case <key> <clause1> <clause2> ...) syntax

TODO

cdar

TODO

cddr

TODO

cdr

Returns the contents of the cdr field of pair. Note that it is an error to take the cdr of the empty list.

(ceiling x)

The ceiling procedure returns the smallest integer not smaller than x.

(char->integer char)

Given a Unicode character, char->integer returns an exact integer between 0 and #xD7FF or between #xE000 and #x10FFFF which is equal to the Unicode scalar value of that character. Given a non-Unicode character, it returns an exact integer greater than #x10FFFF.

(char-ready? [port])

Returns #t if a character is ready on the textual input port and returns #f otherwise. If char-ready returns #t then the next read-char operation on the given port is guaranteed not to hang. If the port is at end of file then char-ready? returns #t.

char<=?

TODO

char<?

TODO

char=?

TODO

char>=?

TODO

char>?

TODO

char?

Returns #t if obj is a character, otherwise returns #f.

(close-input-port port)

Closes the resource associated with port, rendering the port incapable of delivering or accepting data.

(close-output-port port)

Closes the resource associated with port, rendering the port incapable of delivering or accepting data.

(close-port port)

Closes the resource associated with port, rendering the port incapable of delivering or accepting data.

(complex? obj)

Returns #t if obj is a complex number, otherwise returns #f.

(cond <clause1> ...)

TODO

cond-expand

TODO: not implemented

(cons obj1 obj2)

Returns a newly allocated pair whose car is obj1 and whose cdr is obj2. The pair is guaranteed to be different (in the sense of eqv?) from every existing object.

(current-error-port [port])

Returns the current default error port (an output port). That procedure is also a parameter object, which can be overridden with parameterize.

(current-input-port [port])

Returns the current default input port. That procedure is also a parameter object, which can be overridden with parameterize.

current-output-port

Returns the current default output port. That procedure is also a parameter object, which can be overridden with parameterize.

(define <name> <expr>)

TODO

(define (<name> <variable> ...) <expr> ...)

TODO

define-record-type syntax

TODO

define-syntax

TODO

(define-values var1 ... expr) syntax

creates multiple definitions from a single expression returning multiple values. It is allowed wherever define is allowed.

(denominator q)

Return the denominator of their argument; the result is computed as if the argument was represented as a fraction in lowest terms. The denominator is always positive. The denominator of 0 is defined to be 1.

do

TODO

(dynamic-wind before thunk after)

TODO

(eof-object)

Returns an end-of-file object, not necessarily unique.

(eof-object? obj)

Returns #t if obj is an end-of-file object, otherwise returns #f. A end-of-file object will ever be an object that can be read in using read.

(eq? obj1 obj2)

The eq? procedure is similar to eqv? except that in some cases it is capable of discerning distinctions finer than those detectable by eqv?. It must always return #f when eqv? also would, but may return #f in some cases where eqv? would return #t.

On symbols, booleans, the empty list, pairs, and records, and also on non-empty strings, vectors, and bytevectors, eq? and eqv? are guaranteed to have the same behavior. On procedures, eq? must return true if the arguments’ location tags are equal. On numbers and characters, eq?’s behavior is implementation-dependent, but it will always return either true or false. On empty strings, empty vectors, and empty bytevectors, eq? may also behave differently from eqv?.

(equal? obj1 obj2)

The equal? procedure, when applied to pairs, vectors, strings and bytevectors, recursively compares them, returning #t when the unfoldings of its arguments into (possibly infinite) trees are equal (in the sense of equal?) as ordered trees, and #f otherwise. It returns the same as eqv? when applied to booleans, symbols, numbers, characters, ports, procedures, and the empty list. If two objects are eqv?, they must be equal? as well. In all other cases, equal? may return either #t or #f.

Even if its arguments are circular data structures, equal? must always terminate.

(eqv? obj1 obj2)

The eqv? procedure defines a useful equivalence relation on objects. Briefly, it returns #t if obj1 and obj2 are normally regarded as the same object.

TODO: complete based on r7rs small and guile.

(error [who] message . irritants)

Raises an exception as if by calling raise on a newly allocated implementation-defined object which encapsulates the information provided by message, as well as any objs, known as the irritants. The procedure error-object? must return #t on such objects.

(error-object-irritants error)

Returns a list of the irritants encapsulated by error.

(error-object-message error)

Returns the message encapsulated by error.

(error-object? obj)

Returns #t if obj is an object created by error or one of an implementation-defined set of objects. Otherwise, it returns #f. The objects used to signal errors, including those which satisfy the predicates file-error? and read-error?, may or may not satisfy error-object?.

(even? number)

Return #t if NUMBER is even. Otherwise #f.

(exact z)

TODO: FIXME

The procedure exact returns an exact representation of z. The value returned is the exact number that is numerically closest to the argument. For exact arguments, the result is the same as the argument. For inexact non-integral real arguments, the implementation may return a rational approximation, or may report an implementation violation. For inexact complex arguments, the result is a complex number whose real and imaginary parts are the result of applying exact to the real and imaginary parts of the argument, respectively. If an inexact argument has no reasonably close exact equivalent, (in the sense of =), then a violation of an implementation restriction may be reported.

(exact-integer-sqrt k)

TODO

(exact-integer? z)

Returns #t if z is both exact and an integer; otherwise returns #f.

(exact? z)

Return #t if Z is exact. Otherwise #f.

(expt z1 z2)

Returns z1 raised to the power z2.

features

TODO: no implemented

(file-error? error)

TODO: not implemented?

(floor x)

The floor procedure returns the largest integer not larger than x.

floor-quotient

TODO

floor-remainder

TODO

floor/

TODO

(flush-output-port [port])

Flushes any buffered output from the buffer of output-port to the underlying file or device and returns an unspecified value.

(for-each proc list1 ...)

It is an error if proc does not accept as many arguments as there are lists.

The arguments to for-each are like the arguments to map, but for-each calls proc for its side effects rather than for its values. Unlike map, for-each is guaranteed to call proc on the elements of the lists in order from the first element(s) to the last, and the value returned by for-each is unspecified. If more than one list is given and not all lists have the same length, for-each terminates when the shortest list runs out. The lists can be circular, but it is an error if all of them are circular.

(gcd n1 ...)

Return the greatest common divisor.

(get-output-bytevector port)

It is an error if port was not created with open-output-bytevector.

Returns a bytevector consisting of the bytes that have been output to the port so far in the order they were output.

(get-output-string port)

It is an error if port was not created with open-output-string.

Returns a string consisting of the characters that have been output to the port so far in the order they were output.

(guard <clause> ...) syntax

TODO

(if <expr> <then> [<else>])

TODO

include

TODO

include-ci

TODO: not implemented

(inexact z)

The procedure inexact returns an inexact representation of z. The value returned is the inexact number that is numerically closest to the argument. For inexact arguments, the result is the same as the argument. For exact complex numbers, the result is a complex number whose real and imaginary parts are the result of applying inexact to the real and imaginary parts of the argument, respectively. If an exact argument has no reasonably close inexact equivalent (in the sense of =), then a violation of an implementation restriction may be reported.

(inexact? z)

Return #t if Z is inexact. Otherwise #f.

(input-port-open? port)

Returns #t if port is still open and capable of performing input, and #f otherwise.

(input-port? obj)

Return #t if obj is an input port. Otherwise it return #f.

(integer->char integer)

Given an exact integer that is the value returned by a character when char->integer is applied to it, integer->char returns that character.

(integer? obj)

Return #t if OBJ is an integer. Otherwise #f.

(lambda <formals> <expr> ...)

TODO

(lcm n1 ...)

Return the least common multiple of its arguments.

(length list)

Returns the length of list.

let

TODO

let*

TODO

let*-values

TODO

let-syntax

TODO

let-values

TODO

letrec

TODO

letrec*

TODO

letrec-syntax

TODO

(list obj ...)

Returns a newly allocated list of its arguments.

(list->string list)

It is an error if any element of list is not a character.

list->string returns a newly allocated string formed from the elements in the list list.

(list->vector list)

The list->vector procedure returns a newly created vector initialized to the elements of the list list.

(list-copy obj)

Returns a newly allocated copy of the given obj if it is a list. Only the pairs themselves are copied; the cars of the result are the same (in the sense of eqv?) as the cars of list. If obj is an improper list, so is the result, and the final cdrs are the same in the sense of eqv?. An obj which is not a list is returned unchanged. It is an error if obj is a circular list.

(list-ref list k)

The list argument can be circular, but it is an error if list has fewer than k elements.

Returns the kth element of list. (This is the same as the car of (list-tail list k).)

(list-set! list k obj)

It is an error if k is not a valid index of list.

The list-set! procedure stores obj in element k of list.

(list-tail list k)

It is an error if list has fewer than k elements.

Returns the sublist of list obtained by omitting the first k elements.

(list? obj)

Return #t if OBJ is a list. Otherwise #f.

(make-bytevector k [byte])

The make-bytevector procedure returns a newly allocated bytevector of length k. If byte is given, then all elements of the bytevector are initialized to byte, otherwise the contents of each element are unspecified.

(make-list k [fill])

Returns a newly allocated list of k elements. If a second argument is given, then each element is initialized to fill. Otherwise the initial contents of each element is unspecified.

(make-parameter init [converter])

Returns a newly allocated parameter object, which is a procedure that accepts zero arguments and returns the value associated with the parameter object. Initially, this value is the value of (converter init), or of init if the conversion procedure converter is not specified. The associated value can be temporarily changed using parameterize, which is described below.

(make-string k [char])

The make-string procedure returns a newly allocated string of length k. If char is given, then all the characters of the string are initialized to char, otherwise the contents of the string are unspecified.

(make-vector k [fill])

Returns a newly allocated vector of k elements. If a second argument is given, then each element is initialized to fill. Otherwise the initial contents of each element is unspecified.

(map proc list1 ...)

It is an error if proc does not accept as many arguments as there are lists and return a single value.

The map procedure applies proc element-wise to the elements of the lists and returns a list of the results, in order. If more than one list is given and not all lists have the same length, map terminates when the shortest list runs out. The lists can be circular, but it is an error if all of them are circular. It is an error for proc to mutate any of the lists. The dynamic order in which proc is applied to the elements of the lists is unspecified. If multiple returns occur from map, the values returned by earlier returns are not mutated.

(max x1 ...)

Return the maximum of its arguments.

(member obj list [compare])

Return the first sublist of list whose car is obj, where the sublists of list are the non-empty lists returned by (list-tail list k) for k less than the length of list. If obj does not occur in list, then #f (not the empty list) is returned.

Uses compare, if given, and equal? otherwise.

(memq obj list)

Return the first sublist of list whose car is obj, where the sublists of list are the non-empty lists returned by (list-tail list k) for k less than the length of list. If obj does not occur in list, then #f (not the empty list) is returned.

Use eq? for comparison.

(memv obj list)

Return the first sublist of list whose car is obj, where the sublists of list are the non-empty lists returned by (list-tail list k) for k less than the length of list. If obj does not occur in list, then #f (not the empty list) is returned.

Uses eqv? for comparison.

(min x1 ...)

Return the minimum of its arguments.

(modulo n1 n2)

modulo is equivalent to floor-remainder. Provided for backward compatibility.

(negative? x)

Return #t if X is negative. Otherwise #f.

(newline [port])

Writes an end of line to output port.

(not obj)

The not procedure returns #t if obj is false, and returns #f otherwise.

(null? obj)

Returns #t if obj is the empty list, otherwise returns #f.

(number->string z [radix])

It is an error if radix is not one of 2, 8, 10, or 16.

(number? obj)

Return #t if OBJ is a number. Otherwise #f.

(numerator q)

TODO

(odd? number)

Return #t if NUMBER is odd. Otherwise #f.

(open-input-bytevector bytevector)

Takes a bytevector and returns a binary input port that delivers bytes from the bytevector.

(open-input-string string)

Takes a string and returns a textual input port that delivers characters from the string. If the string is modified, the effect is unspecified.

(open-output-bytevector)

Returns a binary output port that will accumulate bytes for retrieval by get-output-bytevector.

(open-output-string)

Returns a textual output port that will accumulate characters for retrieval by get-output-string.

(or test1 ...) syntax

The test expressions are evaluated from left to right, and the value of the first expression that evaluates to a true value is returned. Any remaining expressions are not evaluated. If all expressions evaluate to #f or if there are no expressions, then #f is returned.

(output-port-open? port)

Returns #t if port is still open and capable of performing output, and #f otherwise.

(output-port? obj)

Return #t if obj is an output port. Otherwise return #f.

(pair? obj)

The pair? predicate returns #t if obj is a pair, and otherwise returns #f.

(parameterize ((param1 value1) ...) expr ...)

A parameterize expression is used to change the values returned by specified parameter objects during the evaluation of the body.

The param and value expressions are evaluated in an unspecified order. The body is evaluated in a dynamic environment in which calls to the parameters return the results of passing the corresponding values to the conversion procedure specified when the parameters were created. Then the previous values of the parameters are restored without passing them to the conversion procedure. The results of the last expression in the body are returned as the results of the entire parameterize expression.

Note: If the conversion procedure is not idempotent, the results of (parameterize ((x (x))) …), which appears to bind the parameter x to its current value, might not be what the user expects.

If an implementation supports multiple threads of execution, then parameterize must not change the associated values of any parameters in any thread other than the current thread and threads created inside body.

Parameter objects can be used to specify configurable settings for a computation without the need to pass the value to every procedure in the call chain explicitly.

(peek-char [port])

Returns the next character available from the textual input port, but without updating the port to point to the following character. If no more characters are available, an end-of-file object is returned.

Note: The value returned by a call to peek-char is the same as the value that would have been returned by a call to read-char with the same port. The only difference is that the very next call to read-char or peek-char on that port will return the value returned by the preceding call to peek-char. In particular, a call to peek-char on an interactive port will hang waiting for input whenever a call to read-char would have hung.

(peek-u8 [port])

Returns the next byte available from the binary input port, but without updating the port to point to the following byte. If no more bytes are available, an end-of-file object is returned.

(port? obj)

Return #t if OBJ is port. Otherwise #f.

(positive? x)

Return #t if X is positive. Otherwise #f.

(procedure? obj)

Return #t if OBJ is a procedure. Otherwise #f.

quasiquote

TODO

quote

TODO

quotient

TODO

(raise obj)

Raises an exception by invoking the current exception handler on obj. The handler is called with the same dynamic environment as that of the call to raise, except that the current exception handler is the one that was in place when the handler being called was installed. If the handler returns, a secondary exception is raised in the same dynamic environment as the handler. The relationship between obj and the object raised by the secondary exception is unspecified.

(raise-continuable obj)

Raises an exception by invoking the current exception handler on obj. The handler is called with the same dynamic environment as the call to raise-continuable, except that: (1) the current exception handler is the one that was in place when the handler being called was installed, and (2) if the handler being called returns, then it will again become the current exception handler. If the handler returns, the values it returns become the values returned by the call to raise-continuable.

(rational? obj)

Return #t if OBJ is a rational number. Otherwise #f.

(rationalize x y)

The rationalize procedure returns the simplest rational number differing from x by no more than y.

(read-bytevector k [port])

Reads the next k bytes, or as many as are available before the end of file, from the binary input port into a newly allocated bytevector in left-to-right order and returns the bytevector. If no bytes are available before the end of file, an end-of-file object is returned.

(read-bytevector! bytevector [port [start [end]]])

Reads the next end - start bytes, or as many as are available before the end of file, from the binary input port into bytevector in left-to-right order beginning at the start position. If end is not supplied, reads until the end of bytevector has been reached. If start is not supplied, reads beginning at position 0. Returns the number of bytes read. If no bytes are available, an end-of-file object is returned.

(read-char [port])

Returns the next character available from the textual input port, updating the port to point to the following character. If no more characters are available, an end-of-file object is returned.

(read-error? obj)

Error type predicates. Returns #t if obj is an object raised by the read procedure. Otherwise, it returns #f.

(read-line [port])

Returns the next line of text available from the textual input port, updating the port to point to the following character. If an end of line is read, a string containing all of the text up to (but not including) the end of line is returned, and the port is updated to point just past the end of line. If an end of file is encountered before any end of line is read, but some characters have been read, a string containing those characters is returned. If an end of file is encountered before any characters are read, an end-of-file object is returned. For the purpose of this procedure, an end of line consists of either a linefeed character, a carriage return character, or a sequence of a carriage return character followed by a linefeed character. Implementations may also recognize other end of line characters or sequences.

(read-string k [port])

Reads the next k characters, or as many as are available before the end of file, from the textual input port into a newly allocated string in left-to-right order and returns the string. If no characters are available before the end of file, an end-of-file object is returned.

(read-u8 [port])

Returns the next byte available from the binary input port, updating the port to point to the following byte. If no more bytes are available, an end-of-file object is returned.

(real? obj)

Return #t if OBJ is real number. Otherwise #f.

(remainder n1 n2)

TODO

(reverse list)

Returns a newly allocated list consisting of the elements of list in reverse order.

(round x)

TODO

(set! <variable> <expression>) syntax

Expression is evaluated, and the resulting value is stored in the location to which variable is bound. It is an error if variable is not bound either in some region enclosing the set! expression or else globally. The result of the set! expression is unspecified.

(set-car! pair obj)

Stores obj in the car field of pair.

(set-cdr! pair obj)

Stores obj in the cdr field of pair.

(square z)

Returns the square of z. This is equivalent to (* z z).

(string char ...)

Returns a newly allocated string composed of the arguments. It is analogous to list.

(string->list string [start [end]])

The string->list procedure returns a newly allocated list of the characters of string between start and end.

(string->number string [radix])

Returns a number of the maximally precise representation expressed by the given string. It is an error if radix is not 2, 8, 10, or 16.

If supplied, radix is a default radix that will be overridden if an explicit radix prefix is present in string (e.g. “#o177”). If radix is not supplied, then the default radix is 10. If string is not a syntactically valid notation for a number, or would result in a number that the implementation cannot represent, then string->number returns #f. An error is never signaled due to the content of string.

(string->symbol string)

Returns the symbol whose name is string. This procedure can create symbols with names containing special characters that would require escaping when written, but does not interpret escapes in its input.

(string->utf8 string [start [end]])

The string->utf8 procedure encodes the characters of a string between start and end and returns the corresponding bytevector.

(string->vector string [start [end]])

The string->vector procedure returns a newly created vector initialized to the elements of the string string between start and end.

(string-append string ...)

Returns a newly allocated string whose characters are the concatenation of the characters in the given strings.

(string-copy string [start [end]])

Returns a newly allocated copy of the part of the given string between start and end.

(string-copy! to at from [start [end]])

It is an error if at is less than zero or greater than the length of to. It is also an error if (- (string-length to) at) is less than (- end start).

Copies the characters of string from between start and end to string to, starting at at. The order in which characters are copied is unspecified, except that if the source and destination overlap, copying takes place as if the source is first copied into a temporary string and then into the destination. This can be achieved without allocating storage by making sure to copy in the correct direction in such circumstances.

(string-fill! string fill [start [end]])

It is an error if fill is not a character.

The string-fill! procedure stores fill in the elements of string between start and end.

(string-for-each proc string1 ...)

It is an error if proc does not accept as many arguments as there are strings.

The arguments to string-for-each are like the arguments to string-map, but string-for-each calls proc for its side effects rather than for its values. Unlike string-map, string-for-each is guaranteed to call proc on the elements of the lists in order from the first element(s) to the last, and the value returned by string-for-each is unspecified. If more than one string is given and not all strings have the same length, string-for-each terminates when the shortest string runs out. It is an error for proc to mutate any of the strings.

(string-length string)

Returns the number of characters in the given string.

(string-map proc string1 ...)

It is an error if proc does not accept as many arguments as there are strings and return a single character.

The string-map procedure applies proc element-wise to the elements of the strings and returns a string of the results, in order. If more than one string is given and not all strings have the same length, string-map terminates when the shortest string runs out. The dynamic order in which proc is applied to the elements of the strings is unspecified. If multiple returns occur from string-map, the values returned by earlier returns are not mutated.

(string-ref string k)

It is an error if k is not a valid index of string.

The string-ref procedure returns character k of string using zero-origin indexing. There is no requirement for this procedure to execute in constant time.

(string-set! string k char)

It is an error if k is not a valid index of string.

The string-set! procedure stores char in element k of string. There is no requirement for this procedure to execute in constant time.

string<=?

TODO

string<?

TODO

(string=? string1 string2 ...)

Returns #t if all the strings are the same length and contain exactly the same characters in the same positions, otherwise returns #f.

string>=?

TODO

string>?

TODO

(string? obj)

Return #t if OBJ is string. Otherwise #f.

(substring string start end)

The substring procedure returns a newly allocated string formed from the characters of string beginning with index start and ending with index end. This is equivalent to calling string-copy with the same arguments, but is provided for backward compatibility and stylistic flexibility.

(symbol->string symbol)

Returns the name of symbol as a string, but without adding escapes. It is an error to apply mutation procedures like string-set! to strings returned by this procedure.

(symbol=? symbol1 symbol2 ...)

Returns #t if all the arguments are symbols and all have the same names in the sense of string=?.

(symbol? obj)

Returns #t if obj is a symbol, otherwise returns #f.

syntax-error

TODO

syntax-rules

TODO

textual-port?

TODO

(truncate x)

TODO

truncate-quotient

TODO

truncate-remainder

TODO

truncate/

TODO

(u8-ready? [port])

Returns #t if a byte is ready on the binary input port and returns #f otherwise. If u8-ready? returns #t then the next read-u8 operation on the given port is guaranteed not to hang. If the port is at end of file then u8-ready? returns #t.

(unless <test> <expr> ...) syntax

The test is evaluated, and if it evaluates to #f, the expressions are evaluated in order. The result of the unless expression is unspecified.

unquote

TODO

unquote-splicing

TODO

(utf8->string bytevector [start [end]])

It is an error for bytevector to contain invalid UTF-8 byte sequences.

The utf8->string procedure decodes the bytes of a bytevector between start and end and returns the corresponding string.

(values obj ...)

Delivers all of its arguments to its continuation.

(vector obj ...)

Returns a newly allocated vector whose elements contain the given arguments. It is analogous to list.

(vector->list vector [start [end]])

The vector->list procedure returns a newly allocated list of the objects contained in the elements of vector between start and end. The list->vector procedure returns a newly created vector initialized to the elements of the list list.

(vector->string vector [start [end]])

It is an error if any element of vector between start and end is not a character.

The vector->string procedure returns a newly allocated string of the objects contained in the elements of vector between start and end. The string->vector procedure returns a newly created vector initialized to the elements of the string string between start and end.

(vector-append vector ...)

Returns a newly allocated vector whose elements are the concatenation of the elements of the given vectors.

(vector-copy vector [start [end]])

Returns a newly allocated copy of the elements of the given vector between start and end. The elements of the new vector are the same (in the sense of eqv?) as the elements of the old.

(vector-copy! to at from [start [end]])

It is an error if at is less than zero or greater than the length of to. It is also an error if (- (vector-length to) at) is less than (- end start).

Copies the elements of vector from between start and end to vector to, starting at at. The order in which elements are copied is unspecified, except that if the source and destination overlap, copying takes place as if the source is first copied into a temporary vector and then into the destination. This can be achieved without allocating storage by making sure to copy in the correct direction in such circumstances.

(vector-fill! vector fill [start [end]])

The vector-fill! procedure stores fill in the elements of vector between start and end.

(vector-for-each proc vector1 ...)

It is an error if proc does not accept as many arguments as there are vectors.

The arguments to vector-for-each are like the arguments to vector-map, but vector-for-each calls proc for its side effects rather than for its values. Unlike vector-map, vector-for-each is guaranteed to call proc on the elements of the vectors in order from the first element(s) to the last, and the value returned by vector-for-each is unspecified. If more than one vector is given and not all vectors have the same length, vector-for-each terminates when the shortest vector runs out. It is an error for proc to mutate any of the vectors.

(vector-length vector)

Returns the number of elements in vector as an exact integer.

(vector-map proc vector1 ...)

It is an error if proc does not accept as many arguments as there are vectors and return a single value.

The vector-map procedure applies proc element-wise to the elements of the vectors and returns a vector of the results, in order. If more than one vector is given and not all vectors have the same length, vector-map terminates when the shortest vector runs out. The dynamic order in which proc is applied to the elements of the vectors is unspecified. If multiple returns occur from vector-map, the values returned by earlier returns are not mutated.

(vector-ref vector k)

It is an error if k is not a valid index of vector.

The vector-ref procedure returns the contents of element k of vector.

(vector-set! vector k obj)

It is an error if k is not a valid index of vector.

The vector-set! procedure stores obj in element k of vector.

vector?

Returns #t if obj is a bytevector. Otherwise, #f is returned.

(when <test> <expr> ...) syntax

The test is evaluated, and if it evaluates to a true value, the expressions are evaluated in order. The result of the when expression is unspecified.

with-exception-handler

TODO

(write-bytevector bytevector [port [start [end]]])

Writes the bytes of bytevector from start to end in left-to-right order to the binary output port.

(write-char char [port])

Writes the character char (not an external representation of the character) to the given textual output port and returns an unspecified value.

(write-string string [port [start [end]]])

Writes the characters of string from start to end in left-to-right order to the textual output port.

(write-u8 byte [port])

Writes the byte to the given binary output port and returns an unspecified value.

(zero? z)

Return #t if z is zero. Otherwise #f. # (scheme bitwise)

This library is based on SRFI-151.

This library offers a coherent and comprehensive set of procedures for performing bitwise logical operations on integers.

(bitwise-not i)

Returns the bitwise complement of i; that is, all 1 bits are changed to 0 bits and all 0 bits to 1 bits.

(bitwise-not 10) ;; => -11
(bitwise-not -37) ;; => 36

The following ten procedures correspond to the useful set of non-trivial two-argument boolean functions. For each such function, the corresponding bitwise operator maps that function across a pair of bitstrings in a bit-wise fashion. The core idea of this group of functions is this bitwise “lifting” of the set of dyadic boolean functions to bitstring parameters.

(bitwise-and i ...)

(bitwise-ior i ...)

(bitwise-xor i ...)

(bitwise-eqv i ...)

These operations are associative. When passed no arguments, the procedures return the identity values -1, 0, 0, and -1 respectively.

The bitwise-eqv procedure produces the complement of the bitwise-xor procedure. When applied to three arguments, it does not produce a 1 bit everywhere that a, b and c all agree. That is, it does not produce

     (bitwise-ior (bitwise-and a b c)
                  (bitwise-and (bitwise-not a)
                               (bitwise-not b)
                               (bitwise-not c)))

Rather, it produces (bitwise-eqv a (bitwise-eqv b c)) or the equivalent (bitwise-eqv (bitwise-eqv a b) c).

(bitwise-ior 3  10)     =>  11
(bitwise-and 11 26)     =>  10
(bitwise-xor 3 10)      =>   9
(bitwise-eqv 37 12)     => -42
(bitwise-and 37 12)     =>   4

(bitwise-nand i j)

(bitwise-nor i j)

(bitwise-andc1 i j)

(bitwise-andc2 i j)

(bitwise-orc1 i j)

(bitwise-orc2 i j)

These operations are not associative.

(bitwise-nand 11 26) =>  -11
(bitwise-nor  11 26) => -28
(bitwise-andc1 11 26) => 16
(bitwise-andc2 11 26) => 1
(bitwise-orc1 11 26) => -2
(bitwise-orc2 11 26) => -17

(arithmetic-shift i count)

Returns the arithmetic left shift when count>0; right shift when count < 0.

(arithmetic-shift 8 2) => 32
(arithmetic-shift 4 0) => 4
(arithmetic-shift 8 -1) => 4
(arithmetic-shift -100000000000000000000000000000000 -100) => -79

(bit-count i)

Returns the population count of 1’s (i >= 0) or 0’s (i < 0). The result is always non-negative.

Compatibility note: The R6RS analogue bitwise-bit-count applies bitwise-not to the population count before returning it if i is negative.

(bit-count 0) =>  0
(bit-count -1) =>  0
(bit-count 7) =>  3
(bit-count  13) =>  3 ;Two's-complement binary: ...0001101
(bit-count -13) =>  2 ;Two's-complement binary: ...1110011
(bit-count  30) =>  4 ;Two's-complement binary: ...0011110
(bit-count -30) =>  4 ;Two's-complement binary: ...1100010
(bit-count (expt 2 100)) =>  1
(bit-count (- (expt 2 100))) =>  100
(bit-count (- (1+ (expt 2 100)))) =>  1

(integer-length i)

The number of bits needed to represent i, i.e.

(ceiling (/ (log (if (negative? integer)
                     (- integer)
                     (+ 1 integer)))
            (log 2)))

The result is always non-negative. For non-negative i, this is the number of bits needed to represent i in an unsigned binary representation. For all i, (+ 1 (integer-length i)) is the number of bits needed to represent i in a signed twos-complement representation.

(integer-length  0) => 0
(integer-length  1) => 1
(integer-length -1) => 0
(integer-length  7) => 3
(integer-length -7) => 3
(integer-length  8) => 4
(integer-length -8) => 3

(bitwise-if mask i j)

Merge the bitstrings i and j, with bitstring mask determining from which string to take each bit. That is, if the kth bit of mask is 1, then the kth bit of the result is the kth bit of i, otherwise the kth bit of j.

(bitwise-if 3 1 8) => 9
(bitwise-if 3 8 1) => 0
(bitwise-if 1 1 2) => 3
(bitwise-if #b00111100 #b11110000 #b00001111) => #b00110011

(bit-set? index i)

Is bit index set in bitstring i (where index is a non-negative exact integer)?

Compatibility note: The R6RS analogue bitwise-bit-set? accepts its arguments in the opposite order.

(bit-set? 1 1) =>  false
(bit-set? 0 1) =>  true
(bit-set? 3 10) =>  true
(bit-set? 1000000 -1) =>  true
(bit-set? 2 6) =>  true
(bit-set? 0 6) =>  false

(copy-bit index i boolean)

Returns an integer the same as i except in the indexth bit, which is 1 if boolean is #t and 0 if boolean is #f.

Compatibility note: The R6RS analogue bitwise-copy-bit as originally documented has a completely different interface. (bitwise-copy-bit dest index source) replaces the index’th bit of dest with the index’th bit of source. It is equivalent to (bit-field-replace-same dest source index (+ index 1)). However, an erratum made a silent breaking change to interpret the third argument as 0 for a false bit and 1 for a true bit. Some R6RS implementations applied this erratum but others did not.

(copy-bit 0 0 #t) => #b1
(copy-bit 2 0 #t) => #b100
(copy-bit 2 #b1111 #f) => #b1011

(bit-swap index1 index2 i)

Returns an integer the same as i except that the index1th bit and the index2th bit have been exchanged.

(bit-swap 0 2 4) => #b1

(any-bit-set? test-bits i)

(every-bit-set? test-bits i)

Determines if any/all of the bits set in bitstring test-bits are set in bitstring i. I.e., returns (not (zero? (bitwise-and test-bits i))) and (= test-bits (bitwise-and test-bits i))) respectively.

(any-bit-set? 3 6) => #t
(any-bit-set? 3 12) => #f
(every-bit-set? 4 6) => #t
(every-bit-set? 7 6) => #f

(first-set-bit i)

Return the index of the first (smallest index) 1 bit in bitstring i. Return -1 if i contains no 1 bits (i.e., if i is zero).

(first-set-bit 1) => 0
(first-set-bit 2) => 1
(first-set-bit 0) => -1
(first-set-bit 40) => 3
(first-set-bit -28) => 2
(first-set-bit (expt  2 99)) => 99
(first-set-bit (expt -2 99)) => 99

(bit-field i start end)

Returns the field from i, shifted down to the least-significant position in the result.

(bit-field #b1101101010 0 4) => #b1010
(bit-field #b1101101010 3 9) => #b101101
(bit-field #b1101101010 4 9) => #b10110
(bit-field #b1101101010 4 10) => #b110110
(bit-field 6 0 1) => 0
(bit-field 6 1 3) => 3
(bit-field 6 2 999) => 1
(bit-field #x100000000000000000000000000000000 128 129) => 1

(bit-field-any? i start end)

Returns true if any of the field’s bits are set in bitstring i, and false otherwise.

(bit-field-any? #b1001001 1 6) => #t
(bit-field-any? #b1000001 1 6) => #f

(bit-field-every? i start end)

Returns false if any of the field’s bits are not set in bitstring i, and true otherwise.

(bit-field-every? #b1011110 1 5) => #t
(bit-field-every? #b1011010 1 5) => #f

(bit-field-clear i start end)

(bit-field-set i start end)

Returns i with the field’s bits set to all 0s/1s.

(bit-field-clear #b101010 1 4) => #b100000
(bit-field-set #b101010 1 4) => #b101110

(bit-field-replace dest source start end)

Returns dest with the field replaced by the least-significant end-start bits in source.

(bit-field-replace #b101010 #b010 1 4) => #b100100
(bit-field-replace #b110 1 0 1) => #b111
(bit-field-replace #b110 1 1 2) => #b110

(bit-field-replace-same dest source start end)

Returns dest with its field replaced by the corresponding field in source.

(bit-field-replace-same #b1111 #b0000 1 3) => #b1001

(bit-field-rotate i count start end)

Returns i with the field cyclically permuted by count bits towards high-order.

Compatibility note: The R6RS analogue bitwise-rotate-bit-field uses the argument ordering i start end count.

(bit-field-rotate #b110 0 0 10) => #b110
(bit-field-rotate #b110 0 0 256) => #b110
(bit-field-rotate #x100000000000000000000000000000000 1 0 129) => 1
(bit-field-rotate #b110 1 1 2) => #b110
(bit-field-rotate #b110 1 2 4) => #b1010
(bit-field-rotate #b0111 -1 1 4) => #b1011

(bit-field-reverse i start end)

Returns i with the order of the bits in the field reversed.

(bit-field-reverse 6 1 3) => 6
(bit-field-reverse 6 1 4) => 12
(bit-field-reverse 1 0 32) => #x80000000
(bit-field-reverse 1 0 31) => #x40000000
(bit-field-reverse 1 0 30) => #x20000000
(bit-field-reverse #x140000000000000000000000000000000 0 129) => 5

(bits->list i [ len ])

(bits->vector i [ len ])

Returns a list/vector of len booleans corresponding to each bit of the non-negative integer i, returning bit #0 as the first element, bit #1 as the second, and so on. #t is returned for each 1; #f for 0.

(bits->list #b1110101)) => (#t #f #t #f #t #t #t)
(bits->list 3 5)) => (#t #t #f #f #f)
(bits->list 6 4)) => (#f #t #t #f)

(bits->vector #b1110101)) => #(#t #f #t #f #t #t #t)

(list->bits list)

(vector->bits vector)

Returns an integer formed from the booleans in list/vector, using the first element as bit #0, the second element as bit #1, and so on. It is an error if list/vector contains non-booleans. A 1 bit is coded for each #t; a 0 bit for #f. Note that the result is never a negative integer.

(list->bits '(#t #f #t #f #t #t #t)) => #b1110101
(list->bits '(#f #f #t #f #t #f #t #t #t)) => #b111010100
(list->bits '(#f #t #t)) => 6
(list->bits '(#f #t #t #f)) => 6
(list->bits '(#f #f #t #t)) => 12

(vector->bits '#(#t #f #t #f #t #t #t)) => #b1110101
(vector->bits '#(#f #f #t #f #t #f #t #t #t)) => #b111010100
(vector->bits '#(#f #t #t)) => 6
(vector->bits '#(#f #t #t #f)) => 6
(vector->bits '#(#f #f #t #t)) => 12

For positive integers, bits->list and list->bits are inverses in the sense of equal?, and so are bits->vector and vector->bits.

(bits bool ...)

Returns the integer coded by the bool arguments. The first argument is bit #0, the second argument is bit #1, and so on. Note that the result is never a negative integer.

(bits #t #f #t #f #t #t #t) => #b1110101
(bits #f #f #t #f #t #f #t #t #t) => #b111010100

(bitwise-fold proc seed i)

For each bit b of i from bit #0 (inclusive) to bit (integer-length i) (exclusive), proc is called as (proc b r), where r is the current accumulated result. The initial value of r is seed, and the value returned by proc becomes the next accumulated result. When the last bit has been processed, the final accumulated result becomes the result of bitwise-fold.

(bitwise-fold cons '() #b1010111) => (#t #f #t #f #t #t #t)

(bitwise-for-each proc i)

Repeatedly applies proc to the bits of i starting with bit #0 (inclusive) and ending with bit (integer-length i) (exclusive). The values returned by proc are discarded. Returns an unspecified value.

      (let ((count 0))
        (bitwise-for-each (lambda (b) (if b (set! count (+ count 1))))
                          #b1010111)
       count)

(bitwise-unfold stop? mapper successor seed)

Generates a non-negative integer bit by bit, starting with bit 0. If the result of applying stop? to the current state (whose initial value is seed) is true, return the currently accumulated bits as an integer. Otherwise, apply mapper to the current state to obtain the next bit of the result by interpreting a true value as a 1 bit and a false value as a 0 bit. Then get a new state by applying successor to the current state, and repeat this algorithm.

  (bitwise-unfold (lambda (i) (= i 10))
                  even?
                  (lambda (i) (+ i 1))
                  0)) => #b101010101

(make-bitwise-generator i)

Returns a SRFI 121 generator that generates all the bits of i starting with bit #0. Note that the generator is infinite.

(let ((g (make-bitwise-generator #b110)))
  (test #f (g))
  (test #t (g))
  (test #t (g))
  (test #f (g)))

(scheme box)

This library is based on SRFI-111.

Boxes are objects with a single mutable state. Several Schemes have them, sometimes called cells. A constructor, predicate, accessor, and mutator are provided.

(box value)

Constructor. Returns a newly allocated box initialized to value.

(box? object)

Predicate. Returns #t if object is a box, and #f otherwise.

(unbox box)

Accessor. Returns the current value of box.

(set-box! box value)

Mutator. Changes box to hold value. # (scheme bytevector)

This is based on R6RS bytevectors library

(endianness <endianess symbol>) syntax

(native-endianness)

Returns the endianness symbol associated implementation’s preferred endianness (usually that of the underlying machine architecture). This may be any <endianness symbol>, including a symbol other than big and little.

(bytevector? obj)

Returns #t if obj is a bytevector, otherwise returns #f.

(make-bytevector k [fill])

Returns a newly allocated bytevector of K bytes.

If the FILL argument is missing, the initial contents of the returned bytevector are unspecified.

If the FILL argument is present, it must be an exact integer object in the interval {-128, … 255} that specifies the initial value for the bytes of the bytevector: If FILL is positive, it is interpreted as an octet; if it is negative, it is interpreted as a byte.

(bytevector-length bytevector)

Returns, as an exact integer object, the number of bytes in bytevector.

(bytevector=? bytevector1 bytevector2)

Returns #t if bytevector1 and bytevector2 are equal-that is, if they have the same length and equal bytes at all valid indices. It returns #f otherwise.

(bytevector-fill! bytevector fill)

The fill argument is as in the description of the make-bytevector procedure. The bytevector-fill! procedure stores fill in every element of bytevector and returns unspecified values. Analogous to vector-fill!.

(bytevector-copy! source source-start‌‌ target target-start k)

(bytevector-copy bytevector)‌‌

Returns a newly allocated copy of bytevector.

(bytevector-u8-ref bytevector k)‌‌

The bytevector-u8-ref procedure returns the byte at index k of bytevector, as an octet.

(bytevector-s8-ref bytevector k)‌‌

The bytevector-s8-ref procedure returns the byte at index k of bytevector, as a (signed) byte.

(bytevector-u8-set! bytevector k octet)‌‌

The bytevector-u8-set! procedure stores octet in element k of bytevector.

(bytevector-s8-set! bytevector k byte)‌‌

The bytevector-s8-set! procedure stores the two’s-complement representation of byte in element k of bytevector.

(bytevector->u8-list bytevector)‌‌

The bytevector->u8-list procedure returns a newly allocated list of the octets of bytevector in the same order.

(u8-list->bytevector list)‌‌

The u8-list->bytevector procedure returns a newly allocated bytevector whose elements are the elements of list list, in the same order. It is analogous to list->vector.

(bytevector-uint-ref bytevector k endianness size)‌‌

(bytevector-sint-ref bytevector k endianness size)‌‌

(bytevector-uint-set! bytevector k n endianness size)‌‌

(bytevector-sint-set! bytevector k n endianness size)‌‌

(bytevector->uint-list bytevector endianness size)‌‌

(bytevector->sint-list bytevector endianness sizee‌‌

(uint-list->bytevector list endianness size)‌‌

(sint-list->bytevector list endianness size)‌‌

(bytevector-u16-ref bytevector k endianness)‌‌

(bytevector-s16-ref bytevector k endianness)‌‌

(bytevector-u16-native-ref bytevector k)‌‌

(bytevector-s16-native-ref bytevector k)‌‌

(bytevector-u16-set! bytevector k n endianness)‌‌

(bytevector-s16-set! bytevector k n endianness)‌‌

(bytevector-u16-native-set! bytevector k n)‌‌

(bytevector-s16-native-set! bytevector k n)‌‌

(bytevector-u32-ref bytevector k endianness)‌‌

(bytevector-s32-ref bytevector k endianness)‌‌

(bytevector-u32-native-ref bytevector k)‌‌

(bytevector-s32-native-ref bytevector k)‌‌

(bytevector-u32-set! bytevector k n endianness)‌‌

(bytevector-s32-set! bytevector k n endianness)‌‌

(bytevector-u32-native-set! bytevector k n)‌‌

(bytevector-s32-native-set! bytevector k n)‌‌

(bytevector-u64-ref bytevector k endianness)‌‌

(bytevector-s64-ref bytevector k endianness)‌‌

(bytevector-u64-native-ref bytevector k)‌‌

(bytevector-s64-native-ref bytevector k)‌‌

(bytevector-u64-set! bytevector k n endianness)‌‌

(bytevector-s64-set! bytevector k n endianness)‌‌

(bytevector-u64-native-set! bytevector k n)‌‌

(bytevector-s64-native-set! bytevector k n)‌‌

(bytevector-ieee-single-native-ref bytevector k)‌‌

(bytevector-ieee-single-ref bytevector k endianness)‌‌

(bytevector-ieee-double-native-ref bytevector k)‌‌

(bytevector-ieee-double-ref bytevector k endianness)‌‌

(bytevector-ieee-single-native-set! bytevector k x)‌‌

(bytevector-ieee-single-set! bytevector ‌k x endianness)

(bytevector-ieee-double-native-set! bytevector k x)‌‌

(bytevector-ieee-double-set! bytevector k x endianness)‌

(string->utf8 string)‌‌

(string->utf16 string)‌‌

(string->utf16 string endianness)‌‌

(string->utf32 string)‌‌

(string->utf32 string endianness)‌‌

(utf8->string bytevector)‌‌

(utf16->string bytevector endianness)‌‌

(utf16->string bytevector‌ endianness endianness-mandatory)

(utf32->string bytevector endianness)‌‌

(utf32->string bytevector‌ endianness endianness-mandatory)

(scheme case-lambda)

(case-lambda <clause1> ...) syntax

Each clause is of the form (<formals> <body>), where <formals> and <body> have the same syntax as in a lambda expression.

A case-lambda expression evaluates to a procedure that accepts a variable number of arguments and is lexically scoped in the same manner as a procedure resulting from a lambda expression. When the procedure is called, the first clause for which the arguments agree with <formals> is selected, where agreement is specified as for the <formals> of a lambda expression. The variables of <formals> are bound to fresh locations, the values of the arguments are stored in those locations, the <body> is evaluated in the extended environment, and the results of <body> are returned as the results of the procedure call.

It is an error for the arguments not to agree with the <formals> of any clause`.

Example:

(define add1
  (case-lambda
    ((a) (add1 a 0))
    ((a b) (+ 1 a b))))

(add1 1) ;; => 2
(add1 1 2) ;; => 4

(scheme char)

(char-alphabetic? char)

TODO

(char-alphabetic? char)

TODO

(char-ci<=? char)

TODO

(char-ci<? char)

TODO

(char-ci=? char)

TODO

(char-ci>=? char)

TODO

(char-ci>? char)

TODO

(char-downcase char)

TODO

(char-foldcase char)

TODO

(char-lower-case? char)

TODO

(char-numeric? char)

TODO

(char-upcase char)

TODO

(char-upper-case? char)

TODO

(char-whitespace? char)

TODO

(string-ci<=? string1 string2 ...)

TODO

(string-ci<? string1 string2 ...)

TODO

(string-ci=? string1 string2 ...)

TODO

(string-ci>=? string1 string2 ...)

TODO

(string-ci>? string1 string2 ...)

TODO

(string-downcase string)

TODO

(string-foldcase string)

TODO

(string-upcase string)

TODO # (scheme charset)

This library is based on SRFI-14.

The ability to efficiently represent and manipulate sets of characters is an unglamorous but very useful capability for text-processing code – one that tends to pop up in the definitions of other libraries.

(char-set? obj)

Is the object obj a character set?

(char-set= cs1 ...)

Are the character sets equal?

Boundary cases:

(char-set=) => true
(char-set= cs) => true

Rationale: transitive binary relations are generally extended to n-ary relations in Scheme, which enables clearer, more concise code to be written. While the zero-argument and one-argument cases will almost certainly not arise in first-order uses of such relations, they may well arise in higher-order cases or macro-generated code. E.g., consider

(apply char-set= cset-list)

This is well-defined if the list is empty or a singleton list. Hence we extend these relations to any number of arguments. Implementors have reported actual uses of n-ary relations in higher-order cases allowing for fewer than two arguments. The way of Scheme is to handle the general case; we provide the fully general extension.

A counter-argument to this extension is that R5RS’s transitive binary arithmetic relations (=, <, etc.) require at least two arguments, hence this decision is a break with the prior convention – although it is at least one that is backwards-compatible.

(char-set<= cs1 ...)

Returns true if every character set csi is a subset of character set csi+1.

Boundary cases:

(char-set<=) => true
(char-set<= cs) => true

Rationale: See char-set= for discussion of zero- and one-argument applications. Consider testing a list of char-sets for monotonicity with

(apply char-set<= cset-list)

(char-set-hash cs [bound])

Compute a hash value for the character set cs. Bound is a non-negative exact integer specifying the range of the hash function. A positive value restricts the return value to the range [0,bound).

If bound is either zero or not given, the implementation may use an implementation-specific default value, chosen to be as large as is efficiently practical. For instance, the default range might be chosen for a given implementation to map all strings into the range of integers that can be represented with a single machine word.

Invariant:

(char-set= cs1 cs2) => (= (char-set-hash cs1 b) (char-set-hash cs2 b))

A legal but nonetheless discouraged implementation:

(define (char-set-hash cs . maybe-bound) 1)

Rationale: allowing the user to specify an explicit bound simplifies user code by removing the mod operation that typically accompanies every hash computation, and also may allow the implementation of the hash function to exploit a reduced range to efficiently compute the hash value. E.g., for small bounds, the hash function may be computed in a fashion such that intermediate values never overflow into bignum integers, allowing the implementor to provide a fixnum-specific “fast path” for computing the common cases very rapidly.

(char-set-cursor cset)

(char-set-ref cset cursor)

(char-set-cursor-next cset cursor)

(end-of-char-set? cursor)

Cursors are a low-level facility for iterating over the characters in a set. A cursor is a value that indexes a character in a char set. char-set-cursor produces a new cursor for a given char set. The set element indexed by the cursor is fetched with char-set-ref. A cursor index is incremented with char-set-cursor-next; in this way, code can step through every character in a char set. Stepping a cursor “past the end” of a char set produces a cursor that answers true to end-of-char-set?. It is an error to pass such a cursor to char-set-ref or to char-set-cursor-next.

A cursor value may not be used in conjunction with a different character set; if it is passed to char-set-ref or char-set-cursor-next with a character set other than the one used to create it, the results and effects are undefined.

Cursor values are not necessarily distinct from other types. They may be integers, linked lists, records, procedures or other values. This license is granted to allow cursors to be very “lightweight” values suitable for tight iteration, even in fairly simple implementations.

Note that these primitives are necessary to export an iteration facility for char sets to loop macros.

Example:

    (define cs (char-set #\G #\a #\T #\e #\c #\h))

    ;; Collect elts of CS into a list.
    (let lp ((cur (char-set-cursor cs)) (ans '()))
      (if (end-of-char-set? cur) ans
          (lp (char-set-cursor-next cs cur)
              (cons (char-set-ref cs cur) ans))))
      => (#\G #\T #\a #\c #\e #\h)

    ;; Equivalently, using a list unfold (from SRFI 1):
    (unfold-right end-of-char-set?
                  (curry char-set-ref cs)
              (curry char-set-cursor-next cs)
              (char-set-cursor cs))
      => (#\G #\T #\a #\c #\e #\h)

Rationale: Note that the cursor API’s four functions “fit” the functional protocol used by the unfolders provided by the list, string and char-set SRFIs (see the example above). By way of contrast, here is a simpler, two-function API that was rejected for failing this criterion. Besides char-set-cursor, it provided a single function that mapped a cursor and a character set to two values, the indexed character and the next cursor. If the cursor had exhausted the character set, then this function returned false instead of the character value, and another end-of-char-set cursor. In this way, the other three functions of the current API were combined together.

(char-set-fold kons knil cs)

This is the fundamental iterator for character sets. Applies the function kons across the character set cs using initial state value knil. That is, if cs is the empty set, the procedure returns knil. Otherwise, some element c of cs is chosen; let cs’ be the remaining, unchosen characters. The procedure returns

    (char-set-fold kons (kons c knil) cs')

    Examples:

    ;; CHAR-SET-MEMBERS
    (lambda (cs) (char-set-fold cons '() cs))

    ;; CHAR-SET-SIZE
    (lambda (cs) (char-set-fold (lambda (c i) (+ i 1)) 0 cs))

    ;; How many vowels in the char set?
    (lambda (cs)
      (char-set-fold (lambda (c i) (if (vowel? c) (+ i 1) i))
                     0 cs))

(char-set-unfold f p g seed [base-cs])

(char-set-unfold! f p g seed base-cs)

This is a fundamental constructor for char-sets.

More precisely, the following definitions hold, ignoring the optional-argument issues:

    (define (char-set-unfold p f g seed base-cs)
      (char-set-unfold! p f g seed (char-set-copy base-cs)))

    (define (char-set-unfold! p f g seed base-cs)
      (let lp ((seed seed) (cs base-cs))
            (if (p seed) cs                                 ; P says we are done.
                (lp (g seed)                                ; Loop on (G SEED).
                    (char-set-adjoin! cs (f seed))))))      ; Add (F SEED) to set.

    (Note that the actual implementation may be more efficient.)

Examples:

    (port->char-set p) = (char-set-unfold eof-object? values
                                          (lambda (x) (read-char p))
                                          (read-char p))

    (list->char-set lis) = (char-set-unfold null? car cdr lis)

(char-set-for-each proc cs)

Apply procedure proc to each character in the character set cs. Note that the order in which proc is applied to the characters in the set is not specified, and may even change from one procedure application to another.

Nothing at all is specified about the value returned by this procedure; it is not even required to be consistent from call to call. It is simply required to be a value (or values) that may be passed to a command continuation, e.g. as the value of an expression appearing as a non-terminal subform of a begin expression. Note that in R5RS, this restricts the procedure to returning a single value; non-R5RS systems may not even provide this restriction. char-set-map proc cs -> char-set proc is a char->char procedure. Apply it to all the characters in the char-set cs, and collect the results into a new character set.

Essentially lifts proc from a char->char procedure to a char-set -> char-set procedure.

Example:

(char-set-map char-downcase cset)

(char-set-copy cs)

Returns a copy of the character set cs. “Copy” means that if either the input parameter or the result value of this procedure is passed to one of the linear-update procedures described below, the other character set is guaranteed not to be altered.

A system that provides pure-functional implementations of the linear-operator suite could implement this procedure as the identity function – so copies are not guaranteed to be distinct by eq?.

(char-set char1 ...)

Return a character set containing the given characters.

(list->char-set char-list [base-cs])

(list->char-set! char-list base-cs)

Return a character set containing the characters in the list of characters char-list.

If character set base-cs is provided, the characters from char-list are added to it. list->char-set! is allowed, but not required, to side-effect and reuse the storage in base-cs; list->char-set produces a fresh character set.

(string->char-set s [base-cs])

(string->char-set! s base-cs)

Return a character set containing the characters in the string s.

If character set base-cs is provided, the characters from s are added to it. string->char-set! is allowed, but not required, to side-effect and reuse the storage in base-cs; string->char-set produces a fresh character set.

(char-set-filter pred cs [base-cs])

(char-set-filter! pred cs base-cs)

Returns a character set containing every character c in cs such that (pred c) returns true.

If character set base-cs is provided, the characters specified by pred are added to it. char-set-filter! is allowed, but not required, to side-effect and reuse the storage in base-cs; char-set-filter produces a fresh character set.

An implementation may not save away a reference to pred and invoke it after char-set-filter or char-set-filter! returns – that is, “lazy,” on-demand implementations are not allowed, as pred may have external dependencies on mutable data or have other side-effects.

Rationale: This procedure provides a means of converting a character predicate into its equivalent character set; the cs parameter allows the programmer to bound the predicate’s domain. Programmers should be aware that filtering a character set such as char-set:full could be a very expensive operation in an implementation that provided an extremely large character type, such as 32-bit Unicode. An earlier draft of this library provided a simple predicate->char-set procedure, which was rejected in favor of char-set-filter for this reason.

(ucs-range->char-set lower upper [error? base-cs])

(ucs-range->char-set! lower upper error? base-cs)

Lower and upper are exact non-negative integers; lower <= upper.

Returns a character set containing every character whose ISO/IEC 10646 UCS-4 code lies in the half-open range [lower,upper).

If the requested range includes unassigned UCS values, these are silently ignored (the current UCS specification has “holes” in the space of assigned codes).

If the requested range includes “private” or “user space” codes, these are handled in an implementation-specific manner; however, a UCS- or Unicode-based Scheme implementation should pass them through transparently.

If any code from the requested range specifies a valid, assigned UCS character that has no corresponding representative in the implementation’s character type, then (1) an error is raised if error? is true, and (2) the code is ignored if error? is false (the default). This might happen, for example, if the implementation uses ASCII characters, and the requested range includes non-ASCII characters.

If character set base-cs is provided, the characters specified by the range are added to it. ucs-range->char-set! is allowed, but not required, to side-effect and reuse the storage in base-cs; ucs-range->char-set produces a fresh character set.

Note that ASCII codes are a subset of the Latin-1 codes, which are in turn a subset of the 16-bit Unicode codes, which are themselves a subset of the 32-bit UCS-4 codes. We commit to a specific encoding in this routine, regardless of the underlying representation of characters, so that client code using this library will be portable. I.e., a conformant Scheme implementation may use EBCDIC or SHIFT-JIS to encode characters; it must simply map the UCS characters from the given range into the native representation when possible, and report errors when not possible.

(->char-set x)

Coerces x into a char-set. X may be a string, character or char-set. A string is converted to the set of its constituent characters; a character is converted to a singleton set; a char-set is returned as-is. This procedure is intended for use by other procedures that want to provide “user-friendly,” wide-spectrum interfaces to their clients.

(char-set-size cs)

Returns the number of elements in character set cs.

(char-set-count pred cs)

Apply pred to the chars of character set cs, and return the number of chars that caused the predicate to return true.

(char-set->list cs)

This procedure returns a list of the members of character set cs. The order in which cs’s characters appear in the list is not defined, and may be different from one call to another.

(char-set->string cs)

This procedure returns a string containing the members of character set cs. The order in which cs’s characters appear in the string is not defined, and may be different from one call to another.

(char-set-contains? cs char)

This procedure tests char for membership in character set cs.

The MIT Scheme character-set package called this procedure char-set-member?, but the argument order isn’t consistent with the name.

(char-set-every pred cs)

(char-set-any pred cs)

The char-set-every procedure returns true if predicate pred returns true of every character in the character set cs. Likewise, char-set-any applies pred to every character in character set cs, and returns the first true value it finds. If no character produces a true value, it returns false. The order in which these procedures sequence through the elements of cs is not specified.

Note that if you need to determine the actual character on which a predicate returns true, use char-set-any and arrange for the predicate to return the character parameter as its true value, e.g.

    (char-set-any (lambda (c) (and (char-upper-case? c) c))
                  cs)

(char-set-adjoin cs char1 ...)

(char-set-delete cs char1 ...)

Add/delete the chari characters to/from character set cs.

(char-set-adjoin! cs char1 ...)

(char-set-delete! cs char1 ...)

Linear-update variants. These procedures are allowed, but not required, to side-effect their first parameter.

(char-set-complement cs)

(char-set-union cs1 ...)

(char-set-intersection cs1 ...)

(char-set-difference cs1 cs2 ...)

(char-set-xor cs1 ...)

(char-set-diff+intersection cs1 cs2 ...)

These procedures implement set complement, union, intersection, difference, and exclusive-or for character sets. The union, intersection and xor operations are n-ary. The difference function is also n-ary, associates to the left (that is, it computes the difference between its first argument and the union of all the other arguments), and requires at least one argument.

Boundary cases:

(char-set-union) => char-set:empty
(char-set-intersection) => char-set:full
(char-set-xor) => char-set:empty
(char-set-difference cs) => cs

char-set-diff+intersection returns both the difference and the intersection of the arguments – it partitions its first parameter. It is equivalent to

(values (char-set-difference cs1 cs2 ...)
        (char-set-intersection cs1 (char-set-union cs2 ...)))

but can be implemented more efficiently.

Programmers should be aware that char-set-complement could potentially be a very expensive operation in Scheme implementations that provide a very large character type, such as 32-bit Unicode. If this is a possibility, sets can be complimented with respect to a smaller universe using char-set-difference.

(char-set-complement! cs)

(char-set-union! cs1 cs2 ...)

(char-set-intersection! cs1 cs2 ...)

(char-set-difference! cs1 cs2 ...)

(char-set-xor! cs1 cs2 ...)

(char-set-diff+intersection! cs1 cs2 cs3 ...)

These are linear-update variants of the set-algebra functions. They are allowed, but not required, to side-effect their first (required) parameter.

char-set-diff+intersection! is allowed to side-effect both of its two required parameters, cs1 and cs2.

char-set:lower-case

Lower-case letters

char-set:upper-case

Upper-case letters

char-set:title-case

Title-case letters

char-set:letter

Letters

char-set:digit

Digits

char-set:letter+digit

Letters and digits

char-set:graphic

Printing characters except spaces

char-set:printing

Printing characters including spaces

char-set:whitespace

Whitespace characters

char-set:iso-control

The ISO control characters

char-set:punctuation

Punctuation characters

char-set:symbol

Symbol characters

char-set:hex-digit

A hexadecimal digit: 0-9, A-F, a-f

char-set:blank

Blank characters – horizontal whitespace

char-set:ascii

All characters in the ASCII set.

char-set:empty

Empty set

char-set:full

All characters # (scheme comparator)

This library is based on SRFI-128.

A comparator is an object of a disjoint type. It is a bundle of procedures that are useful for comparing two objects either for equality or for ordering. There are four procedures in the bundle:

It is also the programmer’s responsibility to ensure that all four procedures provide the same result whenever they are applied to the same object(s) (in the sense of eqv?), unless the object(s) have been mutated since the last invocation. In particular, they must not depend in any way on memory addresses in implementations where the garbage collector can move objects in memory.

B> Limitations: The comparator objects defined in this library are not B> applicable to circular structure or to NaNs or objects containing B> them. Attempts to pass any such objects to any procedure defined B> here, or to any procedure that is part of a comparator defined B> here, is an error except as otherwise noted.

(comparator? obj)

Returns #t if obj is a comparator, and #f otherwise.

(comparator-comparison-procedure? comparator)

Returns #t if comparator has a supplied comparison procedure, and #f otherwise.

(comparator-hash-function? comparator)

Returns #t if comparator has a supplied hash function, and #f otherwise.

boolean-comparator

Compares booleans using the total order #f < #t.

char-comparator

Compares characters using the total order implied by char<?. On R6RS and R7RS systems, this is Unicode codepoint order.

char-ci-comparator

Compares characters using the total order implied by char-ci<? On R6RS and R7RS systems, this is Unicode codepoint order after the characters have been folded to lower case.

string-comparator

Compares strings using the total order implied by string<?. Note that this order is implementation-dependent.

string-ci-comparator

Compares strings using the total order implied by string-ci<?. Note that this order is implementation-dependent.

symbol-comparator

Compares symbols using the total order implied by applying symbol->string to the symbols and comparing them using the total order implied by string<?. It is not a requirement that the hash function of symbol-comparator be consistent with the hash function of string-comparator, however.

exact-integer-comparator

integer-comparator

rational-comparator

real-comparator

complex-comparator

number-comparator

These comparators compare exact integers, integers, rational numbers, real numbers, complex numbers, and any numbers using the total order implied by <. They must be compatible with the R5RS numerical tower in the following sense: If S is a subtype of the numerical type T and the two objects are members of S , then the equality predicate and comparison procedures (but not necessarily the hash function) of S-comparator and T-comparator compute the same results on those objects.

Since non-real numbers cannot be compared with <, the following least-surprising ordering is defined: If the real parts are < or >, so are the numbers; otherwise, the numbers are ordered by their imaginary parts. This can still produce surprising results if one real part is exact and the other is inexact.

pair-comparator

This comparator compares pairs using default-comparator (see below) on their cars. If the cars are not equal, that value is returned. If they are equal, default-comparator is used on their cdrs and that value is returned.

list-comparator

This comparator compares lists lexicographically, as follows:

vector-comparator

bytevector-comparator

These comparators compare vectors and bytevectors by comparing their lengths. A shorter argument is always less than a longer one. If the lengths are equal, then each element is compared in turn using default-comparator (see below) until a pair of unequal elements is found, in which case the result is the result of that comparison. If all elements are equal, the arguments are equal.

If the implementation does not support bytevectors, bytevector-comparator has a type testing procedure that always returns #f.

default-comparator

This is a comparator that accepts any two Scheme values (with the exceptions listed in the Limitations section) and orders them in some implementation-defined way, subject to the following conditions:

(make-comparator type-test equality compare hash)

Returns a comparator which bundles the type-test, equality, compare, and hash procedures provided. As a convenience, the following additional values are accepted:

(make-inexact-real-comparator epsilon rounding nan-handling)

Returns a comparator that compares inexact real numbers including NaNs as follows: if after rounding to the nearest epsilon they are the same, they compare equal; otherwise they compare as specified by <. The direction of rounding is specified by the rounding argument, which is either a procedure accepting two arguments (the number and epsilon, or else one of the symbols floor, ceiling, truncate, or round.

The argument nan-handling specifies how to compare NaN arguments to non-NaN arguments. If it is a procedure, the procedure is invoked on the other argument if either argument is a NaN. If it is the symbol min, NaN values precede all other values; if it is the symbol max, they follow all other values, and if it is the symbol error, an error is signaled if a NaN value is compared. If both arguments are NaNs, however, they always compare as equal.

(make-list-comparator element-comparator)

(make-vector-comparator element-comparator)

(make-bytevector-comparator element-comparator)

These procedures return comparators which compare two lists, vectors, or bytevectors in the same way as list-comparator, vector-comparator, and bytevector-comparator respectively, but using element-comparator rather than default-comparator.

If the implementation does not support bytevectors, the result of invoking make-bytevector-comparator is a comparator whose type testing procedure always returns #f.

(make-listwise-comparator type-test element-comparator empty? head tail)

Returns a comparator which compares two objects that satisfy type-test as if they were lists, using the empty? procedure to determine if an object is empty, and the head and tail procedures to access particular elements.

(make-vectorwise-comparator type-test element-comparator length ref)

Returns a comparator which compares two objects that satisfy type-test as if they were vectors, using the length procedure to determine the length of the object, and the ref procedure to access a particular element.

(make-car-comparator comparator)

Returns a comparator that compares pairs on their cars alone using comparator.

(make-cdr-comparator comparator)

Returns a comparator that compares pairs on their cdrs alone using comparator.

(make-pair-comparator car-comparator cdr-comparator)

Returns a comparator that compares pairs first on their cars using car-comparator. If the cars are equal, it compares the cdrs using cdr-comparator.

(make-improper-list-comparator element-comparator)

Returns a comparator that compares arbitrary objects as follows: the empty list precedes all pairs, which precede all other objects. Pairs are compared as if with (make-pair-comparator element-comparator element-comparator). All other objects are compared using element-comparator.

(make-selecting-comparator comparator1 comparator2 ...)

Returns a comparator whose procedures make use of the comparators as follows:

The type test predicate passes its argument to the type test predicates of comparators in the sequence given. If any of them returns #t, so does the type test predicate; otherwise, it returns #f.

The arguments of the equality, compare, and hash functions are passed to the type test predicate of each comparator in sequence. The first comparator whose type test predicate is satisfied on all the arguments is used when comparing those arguments. All other comparators are ignored. If no type test predicate is satisfied, an error is signaled.

(make-refining-comparator comparator1 comparator2 ...)

Returns a comparator that makes use of the comparators in the same way as make-selecting-comparator, except that its procedures can look past the first comparator whose type test predicate is satisfied. If the comparison procedure of that comparator returns zero, then the next comparator whose type test predicate is satisfied is tried in place of it until one returns a non-zero value. If there are no more such comparators, then the comparison procedure returns zero. The equality predicate is defined in the same way. If no type test predicate is satisfied, an error is signaled.

The hash function of the result returns a value which depends, in an implementation-defined way, on the results of invoking the hash functions of the comparators whose type test predicates are satisfied on its argument. In particular, it may depend solely on the first or last such hash function. If no type test predicate is satisfied, an error is signaled.

This procedure is analogous to the expression type refine-compare from SRFI 67.

(make-reverse-comparator comparator)

Returns a comparator that behaves like comparator, except that the compare procedure returns 1, 0, and -1 instead of -1, 0, and 1 respectively. This allows ordering in reverse.

(make-debug-comparator comparator)

Returns a comparator that behaves exactly like comparator, except that whenever any of its procedures are invoked, it verifies all the programmer responsibilities (except stability), and an error is signaled if any of them are violated. Because it requires three arguments, transitivity is not tested on the first call to a debug comparator; it is tested on all future calls using an arbitrarily chosen argument from the previous invocation. Note that this may cause unexpected storage leaks.

eq-comparator

eqv-comparator

equal-comparator

The equality predicates of these comparators are eq?, eqv?, and equal? respectively. When their comparison procedures are applied to non-equal objects, their behavior is implementation-defined. The type test predicates always return #t.

These comparators accept circular structure (in the case of equal-comparator, provided the implementation’s equal does so) and NaNs.

(comparator-type-test-procedure comparator)

Returns the type test predicate of comparator.

(comparator-equality-predicate comparator)

Returns the equality predicate of comparator.

(comparator-comparison-procedure comparator)

Returns the comparison procedure of comparator.

(comparator-hash-function comparator)

Returns the hash function of comparator.

(comparator-test-type comparator obj)

Invokes the type test predicate of comparator on obj and returns what it returns.

(comparator-check-type comparator obj)

Invokes the type test predicate of comparator on obj and returns true if it returns true and signals an error otherwise.

(comparator-equal? comparator obj1 obj2)

Invokes the equality predicate of comparator on obj1 and obj2 and returns what it returns.

(comparator-compare comparator obj1 obj2)

Invokes the comparison procedure of comparator on obj1 and obj2 and returns what it returns.

(comparator-hash comparator obj)

Invokes the hash function of comparator on obj and returns what it returns.

(make-comparison< lt-pred)

(make-comparison> gt-pred)

(make-comparison<= le-pred)

(make-comparison>= ge-pred)

(make-comparison=/< eq-pred lt-pred)

(make-comparison=/> eq-pred gt-pred)

These procedures return a comparison procedure, given a less-than predicate, a greater-than predicate, a less-than-or-equal-to predicate, a greater-than-or-equal-to predicate, or the combination of an equality predicate and either a less-than or a greater-than predicate.

(if3 <expr> <less> <equal> <greater>)

The expression <expr> is evaluated; it will typically, but not necessarily, be a call on a comparison procedure. If the result is -1, <less> is evaluated and its value(s) are returned; if the result is 0, <equal> is evaluated and its value(s) are returned; if the result is 1, <greater> is evaluated and its value(s) are returned. Otherwise an error is signaled.

(if=? <expr> <consequent> [ <alternate> ])

(if<? <expr> <consequent> [ <alternate> ])

(if>? <expr> <consequent> [ <alternate> ])

(if<=? <expr> <consequent> [ <alternate> ])

(if>=? <expr> <consequent> [ <alternate> ])

(if-not=? <expr> <consequent> [ <alternate> ])

The expression <expr> is evaluated; it will typically, but not necessarily, be a call on a comparison procedure. It is an error if its value is not -1, 0, or 1. If the value is consistent with the specified relation, <consequent> is evaluated and its value(s) are returned. Otherwise, if <alternate> is present, it is evaluated and its value(s) are returned; if it is absent, an unspecified value is returned.

(=? comparator object1 object2 object3 ...)

(<? comparator object1 object2 object3 ...)

(>? comparator object1 object2 object3 ...)

(<=? comparator object1 object2 object3 ...)

(>=? comparator object1 object2 object3 ...)

These procedures are analogous to the number, character, and string comparison predicates of Scheme. They allow the convenient use of comparators in situations where the expression types are not usable. They are also analogous to the similarly named procedures SRFI 67, but handle arbitrary numbers of arguments, which in SRFI 67 requires the use of the variants whose names begin with chain.

These procedures apply the comparison procedure of comparator to the objects as follows. If the specified relation returns #t for all objecti and objectj where n is the number of objects and 1 <= i < j <= n, then the procedures return #t, but otherwise #f.

The order in which the values are compared is unspecified. Because the relations are transitive, it suffices to compare each object with its successor.

(make=? comparator)

(make<? comparator)

(make>? comparator)

(make<=? comparator)

(make>=? comparator)

These procedures return predicates which, when applied to two or more arguments, return #t if comparing obj1 and obj2 using the equality or comparison procedures of comparator shows that the objects bear the specified relation to one another. Such predicates can be used in contexts that do not understand or expect comparators.

(in-open-interval? [comparator] obj1 obj2 obj3)

Return #t if obj1 is less than obj2, which is less thanobj3, and #f otherwise.

(in-closed-interval? [comparator] obj1 obj2 obj3)

Returns #t if obj1 is less than or equal to obj2, which is less than or equal to obj3, and #f otherwise.

(in-open-closed-interval? [comparator] obj1 obj2 obj3)

Returns #t if obj1 is less than obj2, which is less than or equal to obj3, and #f otherwise.

(in-closed-open-interval? [comparator] obj1 obj2 obj3)

Returns #t if obj1 is less than or equal to obj2, which is less than obj3, and #f otherwise.

(comparator-min comparator object1 object2 ...)

(comparator-max comparator object1 object2 ...)

These procedures are analogous to min and max respectively. They apply the comparison procedure of comparator to the objects to find and return a minimal (or maximal) object. The order in which the values are compared is unspecified. # (scheme complex)

angle

TODO

imag-part

TODO

magnitude

TODO

make-polar

TODO

make-rectangular

TODO

real-part

TODO # (scheme cxr)

Exports the following procedure which are the compositions of from three to four car and cdr operations. For example caddar could be defined:

(define caddar
  (lambda (x) (car (cdr (cdr (car x))))))

Here is the full list:

This is based on SRFI-141.

This SRFI provides a fairly complete set of integral division and remainder operators.

(floor/ numerator denominator)

(floor-quotient numerator denominator)

(floor-remainder numerator denominator)

q = floor(n/d)

Thus r is negative iff d is negative.

(ceiling/ numerator denominator)

(ceiling-quotient numerator denominator)

(ceiling-remainder numerator denominator)

q = ceiling(n/d)

Thus r is negative iff d is non-negative.

If denominator is the number of units in a block, and is some number of units, then (ceiling-quotient numerator denominator) gives the number of blocks needed to cover numerator units. For example, denominator might be the number of bytes in a disk sector, and numerator the number of bytes in a file; then the quotient is the number of disk sectors needed to store the contents of the file. For another example, denominator might be the number of octets in the output of a cryptographic hash function, and numerator the number of octets desired in a key for a symmetric cipher, to be derived using the cryptographic hash function; then the quotient is the number of hash values needed to concatenate to make a key.

(truncate/ numerator denominator)

(truncate-quotient numerator denominator)

(truncate-remainder numerator denominator)

q = truncate(n/d)

Thus r is negative iff n is negative. However, by any non-unit denominator, the quotient of +1, 0, or -1 is 0; that is, three contiguous numerators by a common denominator share a common quotient. Of the other division operator pairs, only the round pair exhibits this property.

(round/ numerator denominator)

(round-quotient numerator denominator)

(round-remainder numerator denominator)

q = round(n/d)

The round function rounds to the nearest integer, breaking ties by choosing the nearest even integer. Nothing general can be said about the sign of r. Like the truncate operator pair, the quotient of +1, 0, or -1 by any non-unit denominator is 0, so that three contiguous numerators by a common denominator share a common quotient.

(euclidean/ numerator denominator)

(euclidean-quotient numerator denominator)

(euclidean-remainder numerator denominator)

If d > 0, q = floor(n/d); if d < 0, q = ceiling(n/d).

This division operator pair satisfies the stronger property

0 <= r < |d|,

used often in mathematics. Thus, for example, (euclidean-remainder numerator denominator) is always a valid index into a vector whose length is at least the absolute value of denominator. This division operator pair is so named because it is the subject of the Euclidean division algorithm.

(balanced/ numerator denominator)

(balanced-quotient numerator denominator)

(balanced-remainder numerator denominator)

This division operator pair satisfies the property

-|d/2| <= r < |d/2|.

When d is a power of 2, say 2k for some k, this reduces to

-2(k - 1) <= r < 2(k - 1).

Computer scientists will immediately recognize this as the interval of integers representable in two’s-complement with k bits. # (scheme ephemeron)

This library is based on SRFI-124, that is itself based on the MIT Scheme Reference Manual.

An ephemeron is an object with two components called its key and its datum. It differs from an ordinary pair as follows: if the garbage collector (GC) can prove that there are no references to the key except from the ephemeron itself and possibly from the datum, then it is free to break the ephemeron, dropping its reference to both key and datum. In other words, an ephemeron can be broken when nobody else cares about its key. Ephemerons can be used to construct weak vectors or lists and (possibly in combination with finalizers) weak hash tables.

(ephemeron? obj)

Returns #t if object is an ephemeron; otherwise returns #f.

(make-ephemeron key datum)

Returns a newly allocated ephemeron, with components key and datum. Note that if key and datum are the same in the sense of eq?, the ephemeron is effectively a weak reference to the object.

(ephemeron-broken? ephemeron)

Returns #t if ephemeron has been broken; otherwise returns #f.

This procedure must be used with care. If it returns #f, that guarantees only that prior evaluations of ephemeron-key or ephemeron-datum yielded the key or datum that was stored in ephemeron. However, it makes no guarantees about subsequent calls to ephemeron-key or ephemeron-datum, because the GC may run and break the ephemeron immediately after ephemeron-broken? returns. Thus, the correct idiom to fetch an ephemeron’s key and datum and use them if the ephemeron is not broken is:

     (let ((key (ephemeron-key ephemeron))
           (datum (ephemeron-datum ephemeron)))
       (if (ephemeron-broken? ephemeron)
           ... broken case ...
           ... code using key and datum ...))

(ephemeron-key ephemeron)

(ephemeron-value ephemeron)

These return the key or datum component, respectively, of ephemeron. If ephemeron has been broken, these operations return #f, but they can also return #f if that is what was stored as the key or datum.

(reference-barrier key)

This procedure is optional.

This procedure ensures that the garbage collector does not break an ephemeron containing an unreferenced key before a certain point in a program. The program can invoke a reference barrier on the key by calling this procedure, which guarantees that even if the program does not use the key, it will be considered strongly reachable until after reference-barrier returns. # (scheme eval)

(environment list1 ...)

This procedure returns a specifier for the environment that results by starting with an empty environment and then importing each list, considered as an import set, into it. The bindings of the environment represented by the specifier are immutable, as is the environment itself.

(eval expr-or-def environment-specifier)

If expr-or-def is an expression, it is evaluated in the specified environment and its values are returned. If it is a definition, the specified identifier(s) are defined in the specified environment, provided the environment is not immutable. Implementations may extend eval to allow other objects. # (scheme file)

(call-with-input-file)

TODO

(call-with-output-file)

TODO

(delete-file)

TODO

(file-exists?)

TODO

(open-input-file)

TODO

(open-output-file)

TODO

(with-input-from-file)

TODO

(with-output-to-file)

TODO

(open-binary-input-file)

TODO

(open-binary-output-file)

TODO # (scheme fixnum)

This is based on SRFI-143.

This library describes arithmetic procedures applicable to a limited range of exact integers only. These procedures are semantically similar to the corresponding generic-arithmetic procedures, but allow more efficient implementations.

fx-width

Bound to the value w that specifies the implementation-defined range. (R6RS fixnum-width is a procedure that always returns this value.)

fx-greatest

Bound to the value 2w-1-1, the largest representable fixnum. (R6RS greatest-fixnum is a procedure that always returns this value.)

fx-least

Bound to the value -2w-1, the smallest representable fixnum. (R6RS least-fixnum is a procedure that always returns this value.)

(fixnum? obj)

Returns #t if obj is an exact integer within the fixnum range, and #f otherwise.

(fx=? i ...)

Semantically equivalent to =.

(fx<? i ...)

Semantically equivalent to <.

(fx>? i ...)

Semantically equivalent to >.

(fx<=? i ...)

Semantically equivalent to <=.

(fx>=? i ...)

Semantically equivalent to >=.

(fxzero? i)

Semantically equivalent to zero?.

(fxpositive? i)

Semantically equivalent to positive?.

(fxnegative? i)

Semantically equivalent to negative?.

(fxodd? i)

Semantically equivalent to odd?.

(fxeven? i)

Semantically equivalent to even?.

(fxmax i j ...)

Semantically equivalent to max.

(fxmin i j ...)

Semantically equivalent to min.

(fx+ i j)

Semantically equivalent to +, but accepts exactly two arguments.

(fx- i j)

Semantically equivalent to -, but accepts exactly two arguments.

(fxneg i)

Semantically equivalent to -, but accepts exactly one argument.

(fx* i j)

Semantically equivalent to *, but accepts exactly two arguments.

(fxquotient i j)

Semantically equivalent to quotient.

(fxremainder i j)

Semantically equivalent to remainder.

(fxabs i)

Semantically equivalent to abs. In accordance with the fixnum rule, has undefined results when applied to fx-least.

(fxsquare i)

Semantically equivalent to square.

(fxsqrt i)

Semantically equivalent to exact-integer-sqrt (not sqrt).

(fx+/carry i j k)

Returns the two fixnum results of the following computation:

(let*-values (((s) (+ i j k))
       ((q r) (balanced/ s (expt 2 fx-width))))
  (values r q))

(fx-/carry i j k)

Returns the two fixnum results of the following computation:

(let*-values (((d) (- i j k))
       ((q r) (balanced/ d (expt 2 fx-width))))
  (values r q))

(fx*/carry i j k)

Returns the two fixnum results of the following computation:

(let*-values (((s) (+ (* i j) k))
       ((q r) (balanced/ s (expt 2 fx-width))))
  (values r q))

The balanced/ procedure is available in SRFI 141, and also in the R6RS base library under the name of div0-and-mod0. Bitwise operations

The following procedures are the fixnum counterparts of certain bitwise operations from SRFI 151 and the R6RS (rnrs arithmetic fixnums) library. In case of disagreement, SRFI 151 is preferred. The prefixes bitwise- and integer- are dropped for brevity and compatibility.

(fxnot i)

Semantically equivalent to bitwise-not.

(fxand i ...)

Semantically equivalent to bitwise-and.

(fxior i ...)

Semantically equivalent to bitwise-ior.

(fxxor i ...)

Semantically equivalent to bitwise-xor.

(fxarithmetic-shift i count)

Semantically equivalent to arithmetic-shift, except that it is an error for the absolute value of count to exceed w-1.

(fxarithmetic-shift-left i count)

The same as fxarithmetic-shift except that a negative value of count is an error. This is provided for additional efficiency.

(fxarithmetic-shift-right i count)

The same as fxarithmetic-shift except that a non-negative value of count specifies the number of bits to shift right, and a negative value is an error. This is provided for additional efficiency.

(fxbit-count i)

Semantically equivalent to SRFI 151 bit-count.

(fxlength i)

Semantically equivalent to integer-length.

(fxif mask i j)

Semantically equivalent to bitwise-if. It can be implemented as (fxior (fxand mask i) (fxand (fxnot mask) j))).

(fxbit-set? index i)

Semantically equivalent to SRFI 151 bit-set?, except that it is an error for index to be larger than or equal to fx-width.

(fxcopy-bit index i boolean)

Semantically equivalent to SRFI 151 copy-bit, except that it is an error for index to be larger than or equal to fx-width.

(fxfirst-set-bit i)

Semantically equivalent to first-set-bit.

(fxbit-field i start end)

Semantically equivalent to bit-field.

(fxbit-field-rotate i count start end)

Semantically equivalent to SRFI 151 bit-field-rotate.

(fxbit-field-reverse i start end)

Semantically equivalent to bit-field-reverse.

(scheme flonum)

This is based on SRFI-144.

This library describes numeric procedures applicable to flonums, a subset of the inexact real numbers provided by a Scheme implementation. In most Schemes, the flonums and the inexact reals are the same. These procedures are semantically equivalent to the corresponding generic procedures, but allow more efficient implementations.

fl-e

Bound to the mathematical constant e. (C99 M_E)

fl-1/e

Bound to 1/e. (C99 M_E)

fl-e-2

Bound to e2.

fl-e-pi/4

Bound to eπ/4.

fl-log2-e

Bound to log2 e. (C99 M_LOG2E)

fl-log10-e

Bound to log10 e. (C99 M_LOG10E)

fl-log-2

Bound to loge 2. (C99 M_LN2)

fl-1/log-2

Bound to 1/loge 2. (C99 M_LN2)

fl-log-3

Bound to loge 3.

fl-log-pi

Bound to loge π.

fl-log-10

Bound to loge 10. (C99 M_LN10)

fl-1/log-10

Bound to 1/loge 10. (C99 M_LN10)

fl-pi

Bound to the mathematical constant π. (C99 M_PI)

fl-1/pi

Bound to 1/π. (C99 M_1_PI)

fl-2pi

Bound to 2π.

fl-pi/2

Bound to π/2. (C99 M_PI_2)

fl-pi/4

Bound to π/4. (C99 M_PI_4)

fl-pi-squared

Bound to π2.

fl-degree

Bound to π/180, the number of radians in a degree.

fl-2/pi

Bound to 2/π. (C99 M_2_PI)

fl-2/sqrt-pi

Bound to 2/√π. (C99 M_2_SQRTPI)

fl-sqrt-2

Bound to √2. (C99 M_SQRT2)

fl-sqrt-3

Bound to √3.

fl-sqrt-5

Bound to √5.

fl-sqrt-10

Bound to √10.

fl-1/sqrt-2

Bound to 1/√2. (C99 M_SQRT1_2)

fl-cbrt-2

Bound to ∛2.

fl-cbrt-3

Bound to ∛3.

fl-4thrt-2

Bound to ∜2.

fl-phi`

Bound to the mathematical constant φ.

fl-log-phi

Bound to log(φ).

fl-1/log-phi

Bound to 1/log(φ).

fl-euler

Bound to the mathematical constant γ (Euler’s constant).

fl-e-euler

Bound to eγ.

fl-sin-1

Bound to sin 1.

fl-cos-1

Bound to cos 1.

fl-gamma-1/2

Bound to Γ(1/2).

fl-gamma-1/3

Bound to Γ(1/3).

fl-gamma-2/3

Bound to Γ(2/3).

fl-greatest

fl-least

Bound to the largest/smallest positive finite flonum. (e.g. C99 DBL_MAX and C11 DBL_TRUE_MIN)

fl-epsilon

Bound to the appropriate machine epsilon for the hardware representation of flonums. (C99 DBL_EPSILON in <float.h>)

fl-fast-fl+*

Bound to #t if (fl+* x y z) executes about as fast as, or faster than, (fl+ (fl* x y) z); bound to #f otherwise. (C99 FP_FAST_FMA)

So that the value of this variable can be determined at compile time, R7RS implementations and other implementations that provide a features function should provide the feature fl-fast-fl+* if this variable is true, and not if it is false or the value is unknown at compile time.

fl-integer-exponent-zero

Bound to whatever exact integer is returned by (flinteger-exponent 0.0). (C99 FP_ILOGB0)

fl-integer-exponent-nan

Bound to whatever exact integer is returned by (flinteger-exponent +nan.0). (C99 FP_ILOGBNAN)

(flonum number)

If number is an inexact real number and there exists a flonum that is the same (in the sense of =) to number, returns that flonum. If number is a negative zero, an infinity, or a NaN, return its flonum equivalent. If such a flonum does not exist, returns the nearest flonum, where “nearest” is implementation-dependent. If number is not a real number, it is an error. If number is exact, applies inexact or exact->inexact to number first.

(fladjacent x y)

Returns a flonum adjacent to x in the direction of y. Specifically: if x < y, returns the smallest flonum larger than x; if x > y, returns the largest flonum smaller than x; if x = y, returns x. (C99 nextafter)

(flcopysign x y)

Returns a flonum whose magnitude is the magnitude of x and whose sign is the sign of y. (C99 copysign)

(make-flonum x n)

Returns x × 2n, where n is an integer with an implementation-dependent range. (C99 ldexp)

(flinteger-fraction x)

Returns two values, the integral part of x as a flonum and the fractional part of x as a flonum. (C99 modf)

(flexponent x)

Returns the exponent of x. (C99 logb)

(flinteger-exponent x)

Returns the same as flexponent truncated to an exact integer. If x is zero, returns fl-integer-exponent-zero; if x is a NaN, returns fl-integer-exponent-nan; if x is infinite, returns a large implementation-dependent exact integer. (C99 ilogb)

(flnormalized-fraction-exponent x)

Returns two values, a correctly signed fraction y whose absolute value is between 0.5 (inclusive) and 1.0 (exclusive), and an exact integer exponent n such that x = y(2n). (C99 frexp)

(flsign-bit x)

Returns 0 for positive flonums and 1 for negative flonums and -0.0. The value of (flsign-bit +nan.0) is implementation-dependent, reflecting the sign bit of the underlying representation of NaNs. (C99 signbit)

(flonum? obj)

Returns #t if obj is a flonum and #f otherwise.

(fl=? x y z ...)

(fl<? x y z ...)

(fl>? x y z ...)

(fl<=? x y z ...)

(fl>=? x y z ...)

These procedures return #t if their arguments are (respectively): equal, monotonically increasing, monotonically decreasing, monotonically nondecreasing, or monotonically nonincreasing; they return #f otherwise. These predicates must be transitive. (C99 =, <, > <=, >= operators respectively)

(flunordered? x y)

Returns #t if x and y are unordered according to IEEE rules. This means that one of them is a NaN.

These numerical predicates test a flonum for a particular property, returning #t or #f.

(flinteger? x)

Tests whether x is an integral flonum.

(flzero? x)

Tests whether x is zero. Beware of roundoff errors.

(flpositive? x)

Tests whether x is positive.

(flnegative? x)

Tests whether x is negative. Note that (flnegative? -0.0) must return #f; otherwise it would lose the correspondence with (fl<? -0.0 0.0), which is #f according to IEEE 754.

(flodd? x)

Tests whether the flonum x is odd. It is an error if x is not an integer.

(fleven? x)

Tests whether the flonum x is even. It is an error if x is not an integer.

(flfinite? x)

Tests whether the flonum x is finite. (C99 isfinite)

(flinfinite? x)

Tests whether the flonum x is infinite. (C99 isinf)

(flnan? x)

Tests whether the flonum x is NaN. (C99 isnan)

(flnormalized? x)

Tests whether the flonum x is normalized. (C11 isnormal; in C99, use fpclassify(x) == FP_NORMAL)

(fldenormalized? x)

Tests whether the flonum x is denormalized. (C11 issubnormal; in C99, use fpclassify(x) == FP_SUBNORMAL)

(flmax x ...)

(flmin x ...)

Return the maximum/minimum argument. If there are no arguments, these procedures return -inf.0 or +inf.0 if the implementation provides these numbers, and (fl- fl-greatest) or fl-greatest otherwise. (C99 fmax fmin)

(fl+ x ...)

(fl* x ...)

Return the flonum sum or product of their flonum arguments. (C99 + * operators respectively)

(fl+* x y z)

Returns xy + z as if to infinite precision and rounded only once. The boolean constant fl-fast-fl+* indicates whether this procedure executes about as fast as, or faster than, a multiply and an add of flonums. (C99 fma)

(fl- x y ...)

(fl/ x y ...)

With two or more arguments, these procedures return the difference or quotient of their arguments, associating to the left. With one argument, however, they return the additive or multiplicative inverse of their argument. (C99 - / operators respectively)

(flabs x)

Returns the absolute value of x. (C99 fabs)

(flabsdiff x y)

Returns |x - y|.

(flposdiff x y)

Returns the difference of x and y if it is non-negative, or zero if the difference is negative. (C99 fdim)

(flsgn x)

Returns (flcopysign 1.0 x).

(flnumerator x)

(fldenominator x)

Returns the numerator/denominator of x as a flonum; the result is computed as if x was represented as a fraction in lowest terms. The denominator is always positive. The numerator of an infinite flonum is itself. The denominator of an infinite or zero flonum is 1.0. The numerator and denominator of a NaN is a NaN.

(flfloor x)

Returns the largest integral flonum not larger than x. (C99 floor)

(flceiling x)

Returns the smallest integral flonum not smaller than x. (C99 ceil)

(flround x)

Returns the closest integral flonum to x, rounding to even when x represents a number halfway between two integers. (Not the same as C99 round, which rounds away from zero)

(fltruncate x)

Returns the closest integral flonum to x whose absolute value is not larger than the absolute value of x (C99 trunc) Exponents and logarithms

(flexp x)

Returns ex. (C99 exp)

(flexp2 x)

Returns 2x. (C99 exp2)

(flexp-1 x)

Returns ex - 1, but is much more accurate than flexp for very small values of x. It is recommended for use in algorithms where accuracy is important. (C99 expm1)

(flsquare x)

Returns x2.

(flsqrt x)

Returns √x. For -0.0, flsqrt should return -0.0. (C99 sqrt)

(flcbrt x)

Returns ∛x. (C99 cbrt)

(flhypot x y)

Returns the length of the hypotenuse of a right triangle whose sides are of length |x| and |y|. (C99 hypot)

(flexpt x y)

Returns xy. If x is zero, then the result is zero. (C99 pow)

(fllog x)

Returns loge x. (C99 log)

(fllog1+ x)

Returns loge (x+ 1), but is much more accurate than fllog for values of x near 0. It is recommended for use in algorithms where accuracy is important. (C99 log1p)

(fllog2 x)

Returns log2 x. (C99 log2)

(fllog10 x)

Returns log10 x. (C99 log10)

(make-fllog-base x)

Returns a procedure that calculates the base-x logarithm of its argument. If x is 1.0 or less than 1.0, it is an error.

(flsin x)

Returns sin x. (C99 sin)

(flcos x)

Returns cos x. (C99 cos)

(fltan x)

Returns tan x. (C99 tan)

(flasin x)

Returns arcsin x. (C99 asin)

(flacos x)

Returns arccos x. (C99 acos)

(flatan [y] x)

Returns arctan x. (C99 atan)

With two arguments, returns arctan(y/x). in the range [-π,π], using the signs of x and y to choose the correct quadrant for the result. (C99 atan2)

(flsinh x)

Returns sinh x. (C99 sinh)

(flcosh x)

Returns cosh x. (C99 cosh)

(fltanh x)

Returns tanh x. (C99 tanh)

(flasinh x)

Returns arcsinh x. (C99 asinh)

(flacosh x)

Returns arccosh x. (C99 acosh)

(flatanh x)

Returns arctanh x. (C99 atanh)

(flquotient x y)

Returns the quotient of x/y as an integral flonum, truncated towards zero.

(flremainder x y)

Returns the truncating remainder of x/y as an integral flonum.

(flremquo x y)

` Returns two values, the rounded remainder of x/y and the low-order n bits (as a correctly signed exact integer) of the rounded quotient. The value of n is implementation-dependent but at least 3. This procedure can be used to reduce the argument of the inverse trigonometric functions, while preserving the correct quadrant or octant. (C99 remquo)

(flgamma x)

Returns Γ(x), the gamma function applied to x. This is equal to (x-1)! for integers. (C99 tgamma)

(flloggamma x)

Returns two values, log |Γ(x)| without internal overflow, and the sign of Γ(x) as 1.0 if it is positive and -1.0 if it is negative. (C99 lgamma)

(flfirst-bessel n x)

Returns the nth order Bessel function of the first kind applied to x, Jn(x). (jn, which is an XSI Extension of C99)

(flsecond-bessel n x)

Returns the nth order Bessel function of the second kind applied to x, Yn(x). (yn, which is an XSI Extension of C99)

(flerf x)

Returns the error function erf(x). (C99 erf)

(flerfc x)

Returns the complementary error function, 1 - erf(x). (C99 erfc)

(scheme generator)

This is based on SRFI-158

This SRFI defines utility procedures that create, transform, and consume generators. A generator is simply a procedure with no arguments that works as a source of values. Every time it is called, it yields a value. Generators may be finite or infinite; a finite generator returns an end-of-file object to indicate that it is exhausted. For example, read-char, read-line, and read are generators that generate characters, lines, and objects from the current input port. Generators provide lightweight laziness.

This SRFI also defines procedures that return accumulators. An accumulator is the inverse of a generator: it is a procedure of one argument that works as a sink of values.

(generator arg ...)

The simplest finite generator. Generates each of its arguments in turn. When no arguments are provided, it returns an empty generator that generates no values.

(circular-generator arg ...)

The simplest infinite generator. Generates each of its arguments in turn, then generates them again in turn, and so on forever.

(make-iota-generator count [start [step]])

Creates a finite generator of a sequence of count numbers. The sequence begins with start (which defaults to 0) and increases by step (which defaults to 1). If both start and step are exact, it generates exact numbers; otherwise it generates inexact numbers. The exactness of count doesn’t affect the exactness of the results.

(make-range-generator start [end [step]])

Creates a generator of a sequence of numbers. The sequence begins with start, increases by step (default 1), and continues while the number is less than end, or forever if end is omitted. If both start and step are exact, it generates exact numbers; otherwise it generates inexact numbers. The exactness of end doesn’t affect the exactness of the results.

(make-coroutine-generator proc)

Creates a generator from a coroutine.

The proc argument is a procedure that takes one argument, yield. When called, make-coroutine-generator immediately returns a generator g. When g is called, proc runs until it calls yield. Calling yield causes the execution of proc to be suspended, and g returns the value passed to yield.

Whether this generator is finite or infinite depends on the behavior of proc. If proc returns, it is the end of the sequence — g returns an end-of-file object from then on. The return value of proc is ignored.

The following code creates a generator that produces a series 0, 1, and 2 (effectively the same as (make-range-generator 0 3)) and binds it to g.

(define g
  (make-coroutine-generator
   (lambda (yield) (let loop ((i 0))
               (when (< i 3) (yield i) (loop (+ i 1)))))))

(generator->list g) ;; => (0 1 2)

(list->generator list)

Convert LIST into a generator.

(vector->generator vector [start [end]])

(reverse-vector->generator vector [start [end]])

(string->generator string [start [end]])

(bytevector->generator bytevector [start [end]])

These procedures return generators that yield each element of the given argument. Mutating the underlying object will affect the results of the generator.

(generator->list (list->generator '(1 2 3 4 5)))
  ;; => (1 2 3 4 5)
(generator->list (vector->generator '#(1 2 3 4 5)))
  ;; => (1 2 3 4 5)
(generator->list (reverse-vector->generator '#(1 2 3 4 5)))
  ;; => (5 4 3 2 1)
(generator->list (string->generator "abcde"))
  ;; => (#\a #\b #\c #\d #\e)

The generators returned by the constructors are exhausted once all elements are retrieved; the optional start-th and end-th arguments can limit the range the generator walks across.

For reverse-vector->generator, the first value is the element right before the end-th element, and the last value is the start-th element. For all the other constructors, the first value the generator yields is the start-th element, and it ends right before the end-th element.

(generator->list (vector->generator '#(a b c d e) 2))
  ;; => (c d e)
(generator->list (vector->generator '#(a b c d e) 2 4))
  ;; => (c d)
(generator->list (reverse-vector->generator '#(a b c d e) 2))
  ;; => (e d c)
(generator->list (reverse-vector->generator '#(a b c d e) 2 4))
  ;; => (d c)
(generator->list (reverse-vector->generator '#(a b c d e) 0 2))
  ;; => (b a)

(make-for-each-generator for-each obj)

A generator constructor that converts any collection obj to a generator that returns its elements using a for-each procedure appropriate for obj. This must be a procedure that when called as (for-each proc obj) calls proc on each element of obj. Examples of such procedures are for-each, string-for-each, and vector-for-each from R7RS. The value returned by for-each is ignored. The generator is finite if the collection is finite, which would typically be the case.

The collections need not be conventional ones (lists, strings, etc.) as long as for-each can invoke a procedure on everything that counts as a member. For example, the following procedure allows for-each-generator to generate the digits of an integer from least to most significant:

(define (for-each-digit proc n)
  (when (> n 0)
    (let-values (((div rem) (truncate/ n 10)))
      (proc rem)
      (for-each-digit proc div))))

(make-unfold-generator stop? mapper successor seed)

A generator constructor similar to (scheme list) unfold.

The stop? predicate takes a seed value and determines whether to stop. The mapper procedure calculates a value to be returned by the generator from a seed value. The successor procedure calculates the next seed value from the current seed value.

For each call of the resulting generator, stop? is called with the current seed value. If it returns true, then the generator returns an end-of-file object. Otherwise, it applies mapper to the current seed value to get the value to return, and uses successor to update the seed value.

This generator is finite unless stop? never returns true.

(generator->list (make-unfold-generator
                      (lambda (s) (> s 5))
                      (lambda (s) (* s 2))
                      (lambda (s) (+ s 1))
                      0))
  ;; => (0 2 4 6 8 10)

(gcons* item ... generator)

Returns a generator that adds items in front of gen. Once the items have been consumed, the generator is guaranteed to tail-call gen.

(generator->list (gcons* 'a 'b (make-range-generator 0 2)))
 ;; => (a b 0 1)

(gappend generator ...)

Returns a generator that yields the items from the first given generator, and once it is exhausted, from the second generator, and so on.

(generator->list (gappend (make-range-generator 0 3) (make-range-generator 0 2)))
 ;; => (0 1 2 0 1)

(generator->list (gappend))
 ;; => ()

(gflatten generator)

Returns a generator that yields the elements of the lists produced by the given generator.

(ggroup generator k [padding])

Returns a generator that yields lists of k items from the given generator. If fewer than k elements are available for the last list, and padding is absent, the short list is returned; otherwise, it is padded by padding to length k.

(gmerge less-than generator1 ...)

Returns a generator that yields the items from the given generators in the order dictated by less-than. If the items are equal, the leftmost item is used first. When all of given generators are exhausted, the returned generator is exhausted also.

As a special case, if only one generator is given, it is returned.

(gmap proc generator ...)

When only one generator is given, returns a generator that yields the items from the given generator after invoking proc on them.

When more than one generator is given, each item of the resulting generator is a result of applying proc to the items from each generator. If any of input generator is exhausted, the resulting generator is also exhausted.

Note: This differs from generator-map->list, which consumes all values at once and returns the results as a list, while gmap returns a generator immediately without consuming input.

(generator->list (gmap - (make-range-generator 0 3)))
 ;; => (0 -1 -2)

(generator->list (gmap cons (generator 1 2 3) (generator 4 5)))
 ;; => ((1 . 4) (2 . 5))

(gcombine proc seed generator generator2)

A generator for mapping with state. It yields a sequence of sub-folds over proc.

The proc argument is a procedure that takes as many arguments as the input generators plus one. It is called as (proc v1 v2 … seed), where v1, v2, … are the values yielded from the input generators, and seed is the current seed value. It must return two values, the yielding value and the next seed. The result generator is exhausted when any of the genn generators is exhausted, at which time all the others are in an undefined state.

(gfilter predicate generator)

(gremove predicate generator)

Returns generators that yield the items from the source generator, except those on which pred answers false or true respectively.

(gstate-filter proc seed generator)

Returns a generator that obtains items from the source generator and passes an item and a state (whose initial value is seed) as arguments to proc. Proc in turn returns two values, a boolean and a new value of the state. If the boolean is true, the item is returned; otherwise, this algorithm is repeated until gen is exhausted, at which point the returned generator is also exhausted. The final value of the state is discarded.

(gtake gen k [padding])

(gdrop gen k)

These are generator analogues of SRFI 1 take and drop. Gtake returns a generator that yields (at most) the first k items of the source generator, while gdrop returns a generator that skips the first k items of the source generator.

These won’t complain if the source generator is exhausted before generating k items. By default, the generator returned by gtake terminates when the source generator does, but if you provide the padding argument, then the returned generator will yield exactly k items, using the padding value as needed to provide sufficient additional values.

gtake-while pred gen

gdrop-while pred gen

The generator analogues of SRFI-1 take-while and drop-while. The generator returned from gtake-while yields items from the source generator as long as pred returns true for each. The generator returned from gdrop-while first reads and discards values from the source generator while pred returns true for them, then starts yielding items returned by the source.

(gdelete item gen [=])

Creates a generator that returns whatever gen returns, except for any items that are the same as item in the sense of =, which defaults to equal?. The = predicate is passed exactly two arguments, of which the first was generated by gen before the second.

(generator->list (gdelete 3 (generator 1 2 3 4 5 3 6 7)))
  ;; => (1 2 4 5 6 7)

(gdelete-neighbor-dups gen [=])

Creates a generator that returns whatever gen returns, except for any items that are equal to the preceding item in the sense of =, which defaults to equal?. The = predicate is passed exactly two arguments, of which the first was generated by gen before the second.

(generator->list (gdelete-neighbor-dups (list->generator '(a a b c a a a d c))))
  ;; => (a b c a d c)

(gindex value-gen index-gen)

Creates a generator that returns elements of value-gen specified by the indices (non-negative exact integers) generated by index-gen. It is an error if the indices are not strictly increasing, or if any index exceeds the number of elements generated by value-gen. The result generator is exhausted when either generator is exhausted, at which time the other is in an undefined state.

(generator->list (gindex (list->generator '(a b c d e f))
                         (list->generator '(0 2 4))))
  ;; => (a c e)

(gselect value-gen truth-gen)

Creates a generator that returns elements of value-gen that correspond to the values generated by truth-gen. If the current value of truth-gen is true, the current value of value-gen is generated, but otherwise not. The result generator is exhausted when either generator is exhausted, at which time the other is in an undefined state.

(generator->list (gselect (list->generator '(a b c d e f))
                          (list->generator '(#t #f #f #t #t #f))))
  ;; => (a d e)

(generator->list generator [k])

Reads items from generator and returns a newly allocated list of them. By default, it reads until the generator is exhausted.

If an optional argument k is given, it must be a non-negative integer, and the list ends when either k items are consumed, or generator is exhausted; therefore generator can be infinite in this case.

(generator->reverse-list generator [k])

Reads items from generator and returns a newly allocated list of them in reverse order. By default, this reads until the generator is exhausted.

If an optional argument k is given, it must be a non-negative integer, and the list ends when either k items are read, or generator is exhausted; therefore generator can be infinite in this case.

(generator->vector generator [k])

Reads items from generator and returns a newly allocated vector of them. By default, it reads until the generator is exhausted.

If an optional argument k is given, it must be a non-negative integer, and the list ends when either k items are consumed, or generator is exhausted; therefore generator can be infinite in this case.

(generator->vector! vector at generator)

Reads items from generator and puts them into vector starting at index at, until vector is full or generator is exhausted. Generator can be infinite. The number of elements generated is returned.

(generator->string generator [k])

Reads items from generator and returns a newly allocated string of them. It is an error if the items are not characters. By default, it reads until the generator is exhausted.

If an optional argument k is given, it must be a non-negative integer, and the string ends when either k items are consumed, or generator is exhausted; therefore generator can be infinite in this case.

(generator-fold proc seed generator ...)

Works like (scheme list) fold on the values generated by the generator arguments.

When one generator is given, for each value v generated by gen, proc is called as (proc v r), where r is the current accumulated result; the initial value of the accumulated result is seed, and the return value from proc becomes the next accumulated result. When gen is exhausted, the accumulated result at that time is returned from generator-fold.

When more than one generator is given, proc is invoked on the values returned by all the generator arguments followed by the current accumulated result. The procedure terminates when any of the genn generators is exhausted, at which time all the others are in an undefined state.

(with-input-from-string "a b c d e"
  (lambda () (generator-fold cons 'z read)))
  ;; => (e d c b a . z)

(generator-for-each proc generator ...)

A generator analogue of for-each that consumes generated values using side effects. Repeatedly applies proc on the values yielded by gen, gen2 … until any one of the generators is exhausted, at which time all the others are in an undefined state. The values returned from proc are discarded. Returns an unspecified value.

(generator-map->list proc generator ...)

A generator analogue of map that consumes generated values, processes them through a mapping function, and returns a list of the mapped values. Repeatedly applies proc on the values yielded by gen, gen2 … until any one of the generators is exhausted, at which time all the others are in an undefined state. The values returned from proc are accumulated into a list, which is returned.

(generator-find predicate generator)

Returns the first item from the generator gen that satisfies the predicate pred, or #f if no such item is found before gen is exhausted. If gen is infinite, generator-find will not return if it cannot find an appropriate item.

(generator-count predicate generator)

Returns the number of items available from the generator gen that satisfy the predicate pred.

(generator-any predicate generator)

Applies predicate to each item from gen. As soon as it yields a true value, the value is returned without consuming the rest of gen. If gen is exhausted, returns #f.

(generator-every predicate generator)

Applies pred to each item from gen. As soon as it yields a false value, the value is returned without consuming the rest of gen. If gen is exhausted, returns the last value returned by pred, or #t if pred was never called.

(generator-unfold gen unfold arg ...)

Equivalent to (unfold eof-object? (lambda (x) x) (lambda (x) (gen)) (gen) arg ...). The values of gen are unfolded into the collection that unfold creates.

The signature of the unfold procedure is (unfold stop? mapper successor seed args …). Note that the vector-unfold and vector-unfold-right of SRFI 43 and SRFI 133 do not have this signature and cannot be used with this procedure. To unfold into a vector, use SRFI 1’s unfold and then apply list->vector to the result.

;; Iterates over string and unfolds into a list using SRFI 1 unfold
(generator-unfold (make-for-each-generator string-for-each "abc") unfold)
;; => (#\a #\b #\c)

(make-accumulator kons knil finalizer)

Returns an accumulator that, when invoked on an object other than an end-of-file object, invokes kons on its argument and the accumulator’s current state, using the same order as a function passed to fold. It then sets the accumulator’s state to the value returned by kons and returns an unspecified value. The initial state of the accumulator is set to knil. However, if an end-of-file object is passed to the accumulator, it returns the result of tail-calling the procedure finalizer on the state. Repeated calls with an end-of-file object will reinvoke finalizer.

(count-accumulator)

qReturns an accumulator that, when invoked on an object, adds 1 to a count inside the accumulator and returns an unspecified value. However, if an end-of-file object is passed, the accumulator returns the count.

(list-accumulator)

Returns an accumulator that, when invoked on an object, adds that object to a list inside the accumulator in order of accumulation and returns an unspecified value. However, if an end-of-file object is passed, the accumulator returns the list.

(reverse-list-accumulator)

Returns an accumulator that, when invoked on an object, adds that object to a list inside the accumulator in reverse order of accumulation and returns an unspecified value. However, if an end-of-file object is passed, the accumulator returns the list.

(vector-accumulator)

Returns an accumulator that, when invoked on an object, adds that object to a vector inside the accumulator in order of accumulation and returns an unspecified value. However, if an end-of-file object is passed, the accumulator returns the vector.

(reverse-vector-accumulator)

Returns an accumulator that, when invoked on an object, adds that object to a vector inside the accumulator in reverse order of accumulation and returns an unspecified value. However, if an end-of-file object is passed, the accumulator returns the vector.

(vector-accumulator! vector at)

Returns an accumulator that, when invoked on an object, adds that object to consecutive positions of vector starting at at in order of accumulation. It is an error to try to accumulate more objects than vector will hold. An unspecified value is returned. However, if an end-of-file object is passed, the accumulator returns vector.

(string-accumulator)

Returns an accumulator that, when invoked on a character, adds that character to a string inside the accumulator in order of accumulation and returns an unspecified value. However, if an end-of-file object is passed, the accumulator returns the string.

(bytevector-accumulator)

Returns an accumulator that, when invoked on a byte, adds that integer to a bytevector inside the accumulator in order of accumulation and returns an unspecified value. However, if an end-of-file object is passed, the accumulator returns the bytevector.

(bytevector-accumulator! bytevector at)

Returns an accumulator that, when invoked on a byte, adds that byte to consecutive positions of bytevector starting at at in order of accumulation. It is an error to try to accumulate more bytes than vector will hold. An unspecified value is returned. However, if an end-of-file object is passed, the accumulator returns bytevector.

(sum-accumulator)

Returns an accumulator that, when invoked on a number, adds that number to a sum inside the accumulator in order of accumulation and returns an unspecified value. However, if an end-of-file object is passed, the accumulator returns the sum.

(product-accumulator)

Returns an accumulator that, when invoked on a number, multiplies that number to a product inside the accumulator in order of accumulation and returns an unspecified value. However, if an end-of-file object is passed, the accumulator returns the product. # (scheme hash-table)

This library is based on srfi-125.

The library doesn’t implement deprecated features. Application must rely on (scheme comparator) to specify equal predicate and hash function.

This SRFI defines an interface to hash tables, which are widely recognized as a fundamental data structure for a wide variety of applications. A hash table is a data structure that:

(make-hash-table comparator . args)

Returns a newly allocated hash table using (scheme comparator) object COMPARATOR. For the time being, ARGS is ignored.

(hash-table comparator [key value] ...)

Returns a newly allocated hash table using (scheme comparator) object COMPARATOR. For each pair of arguments, an association is added to the new hash table with key as its key and value as its value. If the same key (in the sense of the equality predicate) is specified more than once, it is an error.

(hash-table-unfold stop? mapper successor seed comparator args ...)

Create a new hash table as if by make-hash-table using comparator and the args. If the result of applying the predicate stop? to seed is true, return the hash table. Otherwise, apply the procedure mapper to seed. mapper returns two values, which are inserted into the hash table as the key and the value respectively. Then get a new seed by applying the procedure successor to seed, and repeat this algorithm.

(alist->hash-table alist comparator arg ...)

Returns a newly allocated hash-table as if by make-hash-table using comparator and the args. It is then initialized from the associations of alist. Associations earlier in the list take precedence over those that come later.

(hash-table? obj)

Returns #t if obj is a hash table, and #f otherwise

(hash-table-contains? hash-table key)

Returns #t if there is any association to key in hash-table, and #f otherwise.

(hash-table-empty? hash-table)

Returns #t if hash-table contains no associations, and #f otherwise.

(hash-table=? value-comparator hash-table1 hash-table2)

Returns #t if hash-table1 and hash-table2 have the same keys (in the sense of their common equality predicate) and each key has the same value (in the sense of value-comparator), and #f otherwise.

(hash-table-mutable? hash-table)

Returns #t if the hash table is mutable.

(hash-table-ref hash-table key [failure [success]])

Extracts the value associated to key in hash-table, invokes the procedure success on it, and returns its result; if success is not provided, then the value itself is returned. If key is not contained in hash-table and failure is supplied, then failure is invoked on no arguments and its result is returned.

(hash-table-ref/default hash-table key default)

TODO

(hash-table-set! hash-table key value ...)

Repeatedly mutates hash-table, creating new associations in it by processing the arguments from left to right. The args alternate between keys and values. Whenever there is a previous association for a key, it is deleted. It is an error if the type check procedure of the comparator of hash-table, when invoked on a key, does not return #t. Likewise, it is an error if a key is not a valid argument to the equality predicate of hash-table. Returns an unspecified value.

(hash-table-delete! hash-table key ...)

Deletes any association to each key in hash-table and returns the number of keys that had associations.

(hash-table-intern! hash-table key failure)

Effectively invokes hash-table-ref with the given arguments and returns what it returns. If key was not found in hash-table, its value is set to the result of calling failure.

(hash-table-update! hash-table key updater [failure [success]])

TODO:

(hash-table-pop! hash-table)

Chooses an arbitrary association from hash-table and removes it, returning the key and value as two values. It is an error if hash-table is empty.

(hash-table-clear! hash-table)

Delete all the associations from hash-table.

(hash-table-size hash-table)

Returns the number of associations in hash-table as an exact integer.

(hash-table-keys hash-table)

Returns a newly allocated list of all the keys in hash-table.

(hash-table-values hash-table)

Returns a newly allocated list of all the keys in hash-table.

(hash-table-entries hash-table)

Returns two values, a newly allocated list of all the keys in hash-table and a newly allocated list of all the values in hash-table in the corresponding order.

(hash-table-find proc hash-table failure)

For each association of hash-table, invoke proc on its key and value. If proc returns true, then hash-table-find returns what proc returns. If all the calls to proc return #f, return the result of invoking the thunk failure.

(hash-table-count pred hash-table)

For each association of hash-table, invoke pred on its key and value. Return the number of calls to pred which returned true.

(hash-table-map proc comparator hash-table)

Returns a newly allocated hash table as if by (make-hash-table comparator). Calls PROC for every association in hash-table with the value of the association. The key of the association and the result of invoking proc are entered into the new hash table. Note that this is not the result of lifting mapping over the domain of hash tables, but it is considered more useful.

If comparator recognizes multiple keys in the hash-table as equivalent, any one of such associations is taken.

(hash-table-for-each proc hash-table)

Calls proc for every association in hash-table with two arguments: the key of the association and the value of the association. The value returned by proc is discarded. Returns an unspecified value.

(hash-table-map! proc hash-table)

Calls proc for every association in hash-table with two arguments: the key of the association and the value of the association. The value returned by proc is used to update the value of the association. Returns an unspecified value.

(hash-table-map->list proc hash-table)

Calls proc for every association in hash-table with two arguments: the key of the association and the value of the association. The values returned by the invocations of proc are accumulated into a list, which is returned.

(hash-table-fold proc seed hash-table)

Calls proc for every association in hash-table with three arguments: the key of the association, the value of the association, and an accumulated value val. Val is seed for the first invocation of procedure, and for subsequent invocations of proc, the returned value of the previous invocation. The value returned by hash-table-fold is the return value of the last invocation of proc.

(hash-table-prune! proc hash-table)

Calls proc for every association in hash-table with two arguments, the key and the value of the association, and removes all associations from hash-table for which proc returns true. Returns an unspecified value.

(hash-table-copy hash-table [mutable?])

Returns a newly allocated hash table with the same properties and associations as hash-table. If the second argument is present and is true, the new hash table is mutable. Otherwise it is immutable provided that the implementation supports immutable hash tables.

(hash-table-empty-copy hash-table)

Returns a newly allocated mutable hash table with the same properties as hash-table, but with no associations.

(hash-table->alist hash-table)

Returns an alist with the same associations as hash-table in an unspecified order.

(hash-table-union! hash-table1 hash-table2)

Adds the associations of hash-table2 to hash-table1 and returns hash-table1. If a key appears in both hash tables, its value is set to the value appearing in hash-table1. Returns hash-table1.

(hash-table-intersection! hash-table1 hash-table2)

Deletes the associations from hash-table1 whose keys don’t also appear in hash-table2 and returns hash-table1.

(hash-table-difference! hash-table1 hash-table2)

Deletes the associations of hash-table1 whose keys are also present in hash-table2 and returns hash-table1.

(hash-table-xor! hash-table1 hash-table2)

Deletes the associations of hash-table1 whose keys are also present in hash-table2, and then adds the associations of hash-table2 whose keys are not present in hash-table1 to hash-table1. Returns hash-table1. # (scheme idque)

This is based on SRFI-134.

This SRFI defines immutable deques. A deque is a double-ended queue, a sequence which allows elements to be added or removed efficiently from either end. A structure is immutable when all its operations leave the structure unchanged. Note that none of the procedures specified here ends with an exclamation point.

This SRFI describes immutable deques, or ideques. Immutable structures are sometimes called persistent and are closely related to pure functional (a.k.a. pure) structures. The availability of immutable data structures facilitates writing efficient programs in the pure-functional style. Immutable deques can also be seen as a bidirectional generalization of immutable lists, and some of the procedures documented below are most useful in that context. Unlike the immutable lists of SRFI 116, it is efficient to produce modified versions of an ideque; unlike the list queues of SRFI 117, it is possible to efficiently return an updated version of an ideque without mutating any earlier versions of it.

The specification was designed jointly by Kevin Wortman and John Cowan. John Cowan is the editor and shepherd. The two-list implementation was written by John Cowan.

(ideque element ...)

Returns an ideque containing the elements. The first element (if any) will be at the front of the ideque and the last element (if any) will be at the back. Takes O(n) time, where n is the number of elements.

(ideque-tabulate n proc)

Invokes the predicate proc on every exact integer from 0 (inclusive) to n (exclusive). Returns an ideque containing the results in order of generation. Takes O(n) time.

(ideque-unfold stop? mapper successor seed)

Invokes the predicate stop? on seed. If it returns false, generate the next result by applying mapper to seed, generate the next seed by applying successor to seed, and repeat this algorithm with the new seed. If stop? returns true, return an ideque containing the results in order of accumulation. Takes O(n) time.

(ideque-unfold-right stop? mapper successor seed)

Invokes the predicate stop? on seed. If it returns false, generate the next result by applying mapper to seed, generate the next seed by applying successor to seed, and repeat the algorithm with the new seed. If stop? returns true, return an ideque containing the results in reverse order of accumulation. Takes O(n) time. Predicates

(ideque? x)

Returns #t if x is an ideque, and #f otherwise. Takes O(1) time.

(ideque-empty? idaeque)

Returns #t if ideque contains zero elements, and #f otherwise. Takes O(1) time.

(ideque= elt= ideque ...)

Determines ideque equality, given an element-equality procedure. Ideque A equals ideque B if they are of the same length, and their corresponding elements are equal, as determined by elt=. If the element-comparison procedure’s first argument is from idequei, then its second argument is from idequei+1, i.e. it is always called as (elt= a b) for a an element of ideque A, and b an element of ideque B.

In the n-ary case, every idequei is compared to idequei+1 (as opposed, for example, to comparing ideque1 to every idequei, for i > 1). If there are zero or one ideque arguments, ideque= simply returns true. The name does not end in a question mark for compatibility with the SRFI-1 procedure list=.

Note that the dynamic order in which the elt= procedure is applied to pairs of elements is not specified. For example, if ideque= is applied to three ideques, A, B, and C, it may first completely compare A to B, then compare B to C, or it may compare the first elements of A and B, then the first elements of B and C, then the second elements of A and B, and so forth.

The equality procedure must be consistent with eq?. Note that this implies that two ideques which are eq? are always ideque=, as well; implementations may exploit this fact to “short-cut” the element-by-element comparisons.

(ideque-any pred ideque)

(ideque-every pred ideque)

Invokes pred on the elements of the ideque in order until one call returns a true/false value, which is then returned. If there are no elements, returns #f/#t. Takes O(n) time. Queue operations

(ideque-front ideque)

(ideque-back ideque)

Returns the front/back element of ideque. It is an error for ideque to be empty. Takes O(1) time.

(ideque-remove-front ideque)

(ideque-remove-back ideque)

Returns an ideque with the front/back element of ideque removed. It is an error for ideque to be empty. Takes O(1) time.

(ideque-add-front ideque obj)

(ideque-add-back ideque obj)

Returns an ideque with obj pushed to the front/back of ideque. Takes O(1) time. Other accessors

(ideque-ref ideque n)

Returns the nth element of ideque. It is an error unless n is less than the length of ideque. Takes O(n) time.

(ideque-take ideque n)

(ideque-take-right ideque n)

Returns an ideque containing the first/last n elements of ideque. It is an error if n is greater than the length of ideque. Takes O(n) time.

(ideque-drop ideque n)

(ideque-drop-right ideque n)

Returns an ideque containing all but the first/last n elements of ideque. It is an error if n is greater than the length of ideque. Takes O(n) time.

(ideque-split-at ideque n)

Returns two values, the results of (ideque-take ideque n) and (ideque-drop ideque n) respectively, but may be more efficient. Takes O(n) time. The whole ideque

(ideque-length ideque)

Returns the length of ideque as an exact integer. May take O(n) time, though O(1) is optimal.

(ideque-append ideque ...)

Returns an ideque with the contents of the ideque followed by the others, or an empty ideque if there are none. Takes O(kn) time, where k is the number of ideques and n is the number of elements involved, though O(k log n) is possible.

(ideque-reverse ideque)

Returns an ideque containing the elements of ideque in reverse order. Takes O(1) time.

(ideque-count pred ideque)

Pred is a procedure taking a single value and returning a single value. It is applied element-wise to the elements of ideque, and a count is tallied of the number of elements that produce a true value. This count is returned. Takes O(n) time. The dynamic order of calls to pred is unspecified.

(ideque-zip ideque1 ideque2 ...)

Returns an ideque of lists (not ideques) each of which contains the corresponding elements of ideques in the order specified. Terminates when all the elements of any of the ideques have been processed. Takes O(kn) time, where k is the number of ideques and n is the number of elements in the shortest ideque.

(ideque-map proc ideque)

Applies proc to the elements of ideque and returns an ideque containing the results in order. The dynamic order of calls to proc is unspecified. Takes O(n) time.

(ideque-filter-map proc ideque)

Applies proc to the elements of ideque and returns an ideque containing the true (i.e. non-#f) results in order. The dynamic order of calls to proc is unspecified. Takes O(n) time.

(ideque-for-each proc ideque)

(ideque-for-each-right proc ideque)

Applies proc to the elements of ideque in forward/reverse order and returns an unspecified result. Takes O(n) time.

(ideque-fold proc nil ideque)

(ideque-fold-right proc nil ideque)

Invokes proc on the elements of ideque in forward/reverse order, passing the result of the previous invocation as a second argument. For the first invocation, nil is used as the second argument. Returns the result of the last invocation, or nil if there was no invocation. Takes O(n) time.

(ideque-append-map proc ideque)

Applies proc to the elements of ideque. It is an error if the result is not a list. Returns an ideque containing the elements of the lists in order. Takes O(n) time, where n is the number of elements in all the lists returned.

(ideque-filter pred ideque)

(ideque-remove pred ideque)

Returns an ideque containing the elements of ideque that do/do not satisfy pred. Takes O(n) time.

(ideque-partition proc ideque)

Returns two values, the results of (ideque-filter pred ideque) and (ideque-remove pred ideque) respectively, but may be more efficient. Takes O(n) time.

(ideque-find pred ideque [ failure ])

(ideque-find-right pred ideque [ failure ])

Returns the first/last element of ideque that satisfies pred. If there is no such element, returns the result of invoking the thunk failure; the default thunk is (lambda () #f). Takes O(n) time.

(ideque-take-while pred ideque)

(ideque-take-while-right pred ideque)

Returns an ideque containing the longest initial/final prefix of elements in ideque all of which satisfy pred. Takes O(n) time.

(ideque-drop-while pred ideque)

(ideque-drop-while-right pred ideque)

Returns an ideque which omits the longest initial/final prefix of elements in ideque all of which satisfy pred, but includes all other elements of ideque. Takes O(n) time.

(ideque-span pred ideque)

(ideque-break pred ideque)

Returns two values, the initial prefix of the elements of ideque which do/do not satisfy pred, and the remaining elements. Takes O(n) time.

(list->ideque list)

(ideque->list ideque)

Conversion between ideque and list structures. FIFO order is preserved, so the front of a list corresponds to the front of an ideque. Each operation takes O(n) time.

(generator->ideque generator)

(ideque->generator ideque)

Conversion between SRFI 121 generators and ideques. Each operation takes O(n) time. A generator is a procedure that is called repeatedly with no arguments to generate consecutive values, and returns an end-of-file object when it has no more values to return. # (scheme ilist)

This library is based on SRFI-116.

Scheme currently does not provide immutable pairs corresponding to its existing mutable pairs, although most uses of pairs do not exploit their mutability. The Racket system takes the radical approach of making Scheme’s pairs immutable, and providing a minimal library of mutable pairs with procedures named mpair?, mcons, mcar, mcdr, set-mcar!, set-mcdr!. This SRFI takes the opposite approach of leaving Scheme’s pairs unchanged and providing a full set of routines for creating and dealing with immutable pairs. The sample implementation is portable (to systems with SRFI 9) and efficient.

(ipair a d)

The primitive constructor. Returns a newly allocated ipair whose icar is a and whose icdr is d. The ipair is guaranteed to be different (in the sense of eqv?) from every existing object.

(ipair 'a '())        => (a)
(ipair (iq a) (iq b c d)) => ((a) b c d)
(ipair "a" (iq b c))    => ("a" b c)
(ipair 'a 3)          => (a . 3)
(ipair (iq a b) 'c)     => ((a b ) . c)

(ilist object ...)

Returns a newly allocated ilist of its arguments.

(ilist 'a (+ 3 4) 'c) =>  (a 7 c)
(ilist)               =>  ()

(xipair d a)

(lambda (d a) (ipair a d))

Of utility only as a value to be conveniently passed to higher-order procedures.

(xipair (iq b c) 'a) => (a b c)

The name stands for “eXchanged Immutable PAIR.”

`(ipair* elt1 elt2 …)

Like ilist, but the last argument provides the tail of the constructed ilist, returning

(ipair elt1 (ipair elt2 (ipair ... eltn)))

(ipair* 1 2 3 4) => (1 2 3 . 4)
(ipair* 1) => 1

(make-ilist n [fill])

Returns an n-element ilist, whose elements are all the value fill. If the fill argument is not given, the elements of the ilist may be arbitrary values.

(make-ilist 4 'c) => (c c c c)

(ilist-tabulate n init-proc)

Returns an n-element ilist. Element i of the ilist, where 0 <= i < n, is produced by (init-proc i). No guarantee is made about the dynamic order in which init-proc is applied to these indices.

(ilist-tabulate 4 values) => (0 1 2 3)

(ilist-copy dilist)

Copies the spine of the argument, including the ilist tail.

(iiota count [start step])

Returns an ilist containing the elements

(start start+step ... start+(count-1)*step)

The start and step parameters default to 0 and 1, respectively. This procedure takes its name from the APL primitive.

(iiota 5) => (0 1 2 3 4)
(iiota 5 0 -0.1) => (0 -0.1 -0.2 -0.3 -0.4)

(proper-ilist? x)

(ilist? x)

These identifiers are bound either to the same procedure, or to procedures of equivalent behavior. In either case, true is returned iff x is a proper ilist — a ()-terminated ilist.

More carefully: The empty list is a proper ilist. An ipair whose icdr is a proper ilist is also a proper ilist. Everything else is a dotted ilist. This includes non-ipair, non-() values (e.g. symbols, numbers, mutable pairs), which are considered to be dotted ilists of length 0.

(dotted-ilist? x)

True if x is a finite, non-nil-terminated ilist. That is, there exists an n >= 0 such that icdrn(x) is neither an ipair nor (). This includes non-ipair, non-() values (e.g. symbols, numbers), which are considered to be dotted ilists of length 0.

(dotted-ilist? x) = (not (proper-ilist? x))

(ipair? object)

Returns #t if object is an ipair; otherwise, #f.

(ipair? (ipair 'a 'b)) =>  #t
(ipair? (iq a b c)) =>  #t
(ipair? (cons 1 2)) =>  #f
(ipair? '())        =>  #f
(ipair? '#(a b))    =>  #f
(ipair? 7)          =>  #f
(ipair? 'a)         =>  #f

`(null-ilist? ilist)

Ilist is a proper ilist. This procedure returns true if the argument is the empty list (), and false otherwise. It is an error to pass this procedure a value which is not a proper ilist. This procedure is recommended as the termination condition for ilist-processing procedures that are not defined on dotted ilists.

(not-ipair? x)

(lambda (x) (not (ipair? x)))

Provided as a procedure as it can be useful as the termination condition for ilist-processing procedures that wish to handle all ilists, both proper and dotted.

(ilist= elt= ilist1 ...)

Determines ilist equality, given an element-equality procedure. Proper ilist A equals proper ilist B if they are of the same length, and their corresponding elements are equal, as determined by elt=. If the element-comparison procedure’s first argument is from ilisti, then its second argument is from ilisti+1, i.e. it is always called as (elt= a b) for a an element of ilist A, and b an element of ilist B.

In the n-ary case, every ilisti is compared to ilisti+1 (as opposed, for example, to comparing ilist1 to ilisti, for i>1). If there are no ilist arguments at all, ilist= simply returns true.

It is an error to apply ilist= to anything except proper ilists. It cannot reasonably be extended to dotted ilists, as it provides no way to specify an equality procedure for comparing the ilist terminators.

Note that the dynamic order in which the elt= procedure is applied to pairs of elements is not specified. For example, if ilist= is applied to three ilists, A, B, and C, it may first completely compare A to B, then compare B to C, or it may compare the first elements of A and B, then the first elements of B and C, then the second elements of A and B, and so forth.

The equality procedure must be consistent with eq?. That is, it must be the case that:

(eq? x y) => (elt= x y).

Note that this implies that two ilists which are eq? are always ilist=, as well; implementations may exploit this fact to “short-cut” the element-by-element comparisons.

(ilist= eq?) => #t       ; Trivial cases
(ilist= eq? (iq a)) => #t

(icar ipair)

(icdr ipair)

These procedures return the contents of the icar and icdr field of their argument, respectively. Note that it is an error to apply them to the empty ilist.

(icar (iq a b c))       =>  a        (icdr (iq a b c))     =>  (b c)
(icar (iq (a) b c d))   =>  (a)      (icdr (iq (a) b c d)) =>  (b c d)
(icar (ipair 1 2))      =>  1        (icdr (ipair 1 2))    =>  2
(icar '())              =>  *error*  (icdr '())            =>  *error*

(icaar ipair)

(icadr ipair)

(icdddar ipair)

`(icddddr ipair)

These procedures are compositions of icar and icdr, where for example icaddr could be defined by

(define icaddr (lambda (x) (icar (icdr (icdr x)))))

Arbitrary compositions, up to four deep, are provided. There are twenty-eight of these procedures in all.

(ilist-ref ilist i)

Returns the ith element of ilist. (This is the same as the icar of (idrop ilist i).) It is an error if i >= n, where n is the length of ilist.

(ilist-ref (iq a b c d) 2) => c

(ifirst ipair)

(isecond ipair)

(ithird ipair)

(ifourth ipair)

(ififth ipair)

(isixth ipair)

(iseventh ipair)

(ieighth ipair)

(ininth ipair)

(itenth ipair)

Synonyms for car, cadr, caddr, …

(ithird '(a b c d e)) => c

(icar+icdr ipair)

The fundamental ipair deconstructor:

(lambda (p) (values (icar p) (icdr p)))

This can, of course, be implemented more efficiently by a compiler.

(itake x i)

(idrop x i)

(ilist-tail x i)

itake returns the first i elements of ilist x.

idrop returns all but the first i elements of ilist x.

ilist-tail is either the same procedure as idrop or else a procedure with the same behavior.

``scheme (itake (iq a b c d e) 2) => (a b) (idrop (iq a b c d e) 2) => (c d e)


x may be any value — a proper or dotted ilist:

```scheme
(itake (ipair 1 (ipair 2 (ipair 3 'd)))    => (1 2)
(idrop (ipair 1 (ipair 2 (ipair 3 'd))) 2) => (3 . d)
(itake (ipair 1 (ipair 2 (ipair 3 'd))) 3) => (1 2 3)
(idrop (ipair 1 (ipair 2 (ipair 3 'd))) 3) => d

For a legal i, itake and idrop partition the ilist in a manner which can be inverted with iappend:

(iappend (itake x i) (idrop x i)) = x

idrop is exactly equivalent to performing i icdr operations on x; the returned value shares a common tail with x.

(itake-right dilist i)

(idrop-right dilist i)

itake-right returns the last i elements of dilist. idrop-right returns all but the last i elements of dilist.

(itake-right (iq a b c d e) 2) => (d e)
(idrop-right (iq a b c d e) 2) => (a b c)

The returned ilist may share a common tail with the argument ilist.

dilist may be any ilist, either proper or dotted:

(itake-right (iq ipair 1 (ipair 2 (ipair 3 'd))) 2) => (2 3 . d)
(idrop-right (ipair 1 (ipair 2 (ipair 3 'd))) 2)    => (1)
(itake-right (ipair 1 (ipair 2 (ipair 3 'd))) 0)    => d
(idrop-right (ipair 1 (ipair 2 (ipair 3 'd))) 0)    => (1 2 3)

For a legal i, itake-right and idrop-right partition the ilist in a manner which can be inverted with iappend:

(iappend (itake dilist i) (idrop dilist i)) = dilist

itake-right’s return value is guaranteed to share a common tail with dilist.

(isplit-at x i)

isplit-at splits the ilist x at index i, returning an ilist of the first i elements, and the remaining tail. It is equivalent to

(values (itake x i) (idrop x i))

(ilast ipair)

(last-ipair ipair)

Returns the last element of the non-empty, possibly dotted, ilist ipair. last-ipair returns the last ipair in the non-empty ilist pair.

(ilast (iq a b c))      => c
(last-ipair (iq a b c)) => (c)

(ilength ilist)

Returns the length of its argument. It is an error to pass a value to ilength which is not a proper ilist (()-terminated).

The length of a proper ilist is a non-negative integer n such that icdr applied n times to the ilist produces the empty list.

(iappend ilist1 ...)

Returns an ilist consisting of the elements of ilist1 followed by the elements of the other ilist parameters.

(iappend (iq x) (iq y))        =>  (x y)
(iappend (iq a) (iq b c d))    =>  (a b c d)
(iappend (iq a (b)) (iq (c)))  =>  (a (b) (c))

The resulting ilist is always newly allocated, except that it shares structure with the final ilisti argument. This last argument may be any value at all; an improper ilist results if it is not a proper ilist. All other arguments must be proper ilists.

(iappend (iq a b) (ipair 'c 'd))  =>  (a b c . d)
(iappend '() 'a)           =>  a
(iappend (iq x y))         =>  (x y)
(iappend)                  =>  ()

(iconcatenate ilist-of-ilists)

Appends the elements of its argument together. That is, iconcatenate returns

(iapply iappend ilist-of-ilists)

or, equivalently,

(ireduce-right iappend '() ilist-of-ilists)

Note that some Scheme implementations do not support passing more than a certain number (e.g., 64) of arguments to an n-ary procedure. In these implementations, the (iapply iappend …) idiom would fail when applied to long lists, but iconcatenate would continue to function properly.

As with iappend, the last element of the input list may be any value at all.

(ireverse ilist)

Returns a newly allocated ilist consisting of the elements of ilist in reverse order.

(ireverse (iq a b c)) =>  (c b a)
(ireverse (iq a (b c) d (e (f))))
        =>  ((e (f)) d (b c) a)

(iappend-reverse rev-head tail)

iappend-reverse returns (iappend (ireverse rev-head) tail). It is provided because it is a common operation — a common list-processing style calls for this exact operation to transfer values accumulated in reverse order onto the front of another ilist, and because the implementation is significantly more efficient than the simple composition it replaces. (But note that this pattern of iterative computation followed by a reverse can frequently be rewritten as a recursion, dispensing with the reverse and iappend-reverse steps, and shifting temporary, intermediate storage from the heap to the stack, which is typically a win for reasons of cache locality and eager storage reclamation.)

(izip ilist1 ilist2 ...)

(lambda ilists (iapply imap ilist ilists))

If izip is passed n ilists, it returns an ilist as long as the shortest of these ilists, each element of which is an n-element ilist comprised of the corresponding elements from the parameter ilists.

(izip (iq one two three)
  (iq 1 2 3)
  (iq odd even odd even odd even odd even))
   ;; => ((one 1 odd) (two 2 even) (three 3 odd))

(izip (iq 1 2 3)) => ((1) (2) (3))

(iunzip1 ilist)

(iunzip2 ilist)

(iunzip3 ilist)

(iunzip4 ilist)

(iunzip5 ilist)

iunzip1 takes an ilist of ilists, where every ilist must contain at least one element, and returns an ilist containing the initial element of each such ilist. That is, it returns (imap icar ilists). iunzip2 takes an ilist of ilists, where every ilist must contain at least two elements, and returns two values: an ilist of the first elements, and an ilist of the second elements. iunzip3 does the same for the first three elements of the ilists, and so forth.

(iunzip2 (iq (1 one) (2 two) (3 three))) =>
  (1 2 3)
  (one two three)

(icount pred ilist1 ilist2 ...)

pred is a procedure taking as many arguments as there are ilists and returning a single value. It is applied element-wise to the elements of the ilists, and a count is tallied of the number of elements that produce a true value. This count is returned. count is “iterative” in that it is guaranteed to apply pred to the ilist elements in a left-to-right order. The counting stops when the shortest ilist expires.

(count even? (iq 3 1 4 1 5 9 2 5 6)) => 3
(count < (iq 1 2 4 8) (iq 2 4 6 8 10 12 14 16)) => 3

(ifold kons knil ilist1 ilist2 ...)

The fundamental ilist iterator.

First, consider the single ilist-parameter case. If ilist1 = (e1 e2 … en), then this procedure returns

(kons en ... (kons e2 (kons e1 knil)) ... )

That is, it obeys the (tail) recursion

(ifold kons knil lis) = (ifold kons (kons (icar lis) knil) (icdr lis))
(ifold kons knil '()) = knil

Examples:

(ifold + 0 lis)         ; Add up the elements of LIS.

(ifold ipair '() lis)       ; Reverse LIS.

(ifold ipair tail rev-head) ; See APPEND-REVERSE.

;; How many symbols in LIS?
(ifold (lambda (x count) (if (symbol? x) (+ count 1) count))
       0
       lis)

;; Length of the longest string in LIS:
(ifold (lambda (s max-len) (max max-len (string-length s)))
       0
       lis)

If n ilist arguments are provided, then the kons function must take n+1 parameters: one element from each ilist, and the “seed” or fold state, which is initially knil. The fold operation terminates when the shortest ilist runs out of values:

(ifold ipair* '() (iq a b c) (iq 1 2 3 4 5)) => (c 3 b 2 a 1)

(ifold-right kons knil ilist1 ilist2 ...)

The fundamental ilist recursion operator.

First, consider the single ilist-parameter case. If ilist1 = (e1 e2 … en), then this procedure returns

(kons e1 (kons e2 ... (kons en knil)))

That is, it obeys the recursion

(ifold-right kons knil lis) = (kons (icar lis) (ifold-right kons knil (icdr lis)))
(ifold-right kons knil '()) = knil

Examples:

(ifold-right ipair '() lis)     ; Copy LIS.

;; Filter the even numbers out of LIS.
(ifold-right (lambda (x l) (if (even? x) (ipair x l) l)) '() lis))

If n ilist arguments are provided, then the kons procedure must take n+1 parameters: one element from each ilist, and the “seed” or fold state, which is initially knil. The fold operation terminates when the shortest ilist runs out of values:

(ifold-right ipair* '() (iq a b c) (iq 1 2 3 4 5)) => (a 1 b 2 c 3)

(ipair-fold kons knil ilist1 ilist2 ...)

Analogous to fold, but kons is applied to successive sub-ilists of the ilists, rather than successive elements — that is, kons is applied to the ipairs making up the lists, giving this (tail) recursion:

(ipair-fold kons knil lis) = (let ((tail (icdr lis)))
                               (ipair-fold kons (kons lis knil) tail))
(ipair-fold kons knil '()) = knil

Example:

(ipair-fold ipair '() (iq a b c)) => ((c) (b c) (a b c))

(ipair-fold-right kons knil ilist1 ilist2 ...)

Holds the same relationship with ifold-right that ipair-fold holds with ifold. Obeys the recursion

    (ipair-fold-right kons knil lis) =
        (kons lis (ipair-fold-right kons knil (icdr lis)))
    (ipair-fold-right kons knil '()) = knil

Example:

(ipair-fold-right ipair '() (iq a b c)) => ((a b c) (b c) (c))

(ireduce f ridentity ilist)

ireduce is a variant of ifold.

ridentity should be a “right identity” of the procedure f — that is, for any value x acceptable to f,

(f x ridentity) = x

ireduce has the following definition:

If ilist = (), return ridentity;

Otherwise, return (ifold f (icar ilist) (icdr ilist)).

…in other words, we compute (ifold f ridentity ilist).

Note that ridentity is used only in the empty-list case. You typically use ireduce when applying f is expensive and you’d like to avoid the extra application incurred when ifold applies f to the head of ilist and the identity value, redundantly producing the same value passed in to f. For example, if f involves searching a file directory or performing a database query, this can be significant. In general, however, ifold is useful in many contexts where ireduce is not (consider the examples given in the ifold definition — only one of the five folds uses a function with a right identity. The other four may not be performed with ireduce).

;; take the max of an ilist of non-negative integers.
(ireduce max 0 nums) ; i.e., (iapply max 0 nums)

(ireduce-right f ridentity ilist)

ireduce-right is the fold-right variant of ireduce. It obeys the following definition:

(ireduce-right f ridentity '()) = ridentity
(ireduce-right f ridentity (iq e1)) = (f e1 ridentity) = e1
(ireduce-right f ridentity (iq e1 e2 ...)) =
  (f e1 (ireduce f ridentity (e2 ...)))

…in other words, we compute (ifold-right f ridentity ilist).

;; Append a bunch of ilists together.
;; I.e., (iapply iappend ilist-of-ilists)
(ireduce-right iappend '() ilist-of-ilists)

(iunfold p f g seed [tail-gen])

iunfold is best described by its basic recursion:

    (iunfold p f g seed) =
        (if (p seed) (tail-gen seed)
            (ipair (f seed)
                  (iunfold p f g (g seed))))

In other words, we use g to generate a sequence of seed values

seed, g(seed), g2(seed), g3(seed), ...

These seed values are mapped to ilist elements by f, producing the elements of the result ilist in a left-to-right order. P says when to stop.

iunfold is the fundamental recursive ilist constructor, just as ifold-right is the fundamental recursive ilist consumer. While iunfold may seem a bit abstract to novice functional programmers, it can be used in a number of ways:

    ;; Ilist of squares: 1^2 ... 10^2
    (iunfold (lambda (x) (> x 10))
            (lambda (x) (* x x))
        (lambda (x) (+ x 1))
        1)

    (iunfold null-ilist? icar icdr lis) ; Copy a proper ilist.

    ;; Read current input port into an ilist of values.
    (iunfold eof-object? values (lambda (x) (read)) (read))

    ;; Copy a possibly non-proper ilist:
    (iunfold not-ipair? icar icdr lis
                  values)

    ;; Append HEAD onto TAIL:
    (iunfold null-ilist? icar icdr head
                  (lambda (x) tail))

Interested functional programmers may enjoy noting that ifold-right and iunfold are in some sense inverses. That is, given operations knull?, kar, kdr, kons, and knil satisfying

(kons (kar x) (kdr x)) = x and (knull? knil) = #t

then

(ifold-right kons knil (iunfold knull? kar kdr x)) = x

and

(iunfold knull? kar kdr (ifold-right kons knil x)) = x

This combinator sometimes is called an “anamorphism;” when an explicit tail-gen procedure is supplied, it is called an “apomorphism.”

(iunfold-right p f g seed [tail])

iunfold-right constructs an ilist with the following loop:

    (let lp ((seed seed) (lis tail))
      (if (p seed) lis
          (lp (g seed)
              (ipair (f seed) lis))))

    p
        Determines when to stop unfolding.
    f
        Maps each seed value to the corresponding ilist element.
    g
        Maps each seed value to next seed value.
    seed
        The "state" value for the unfold.
    tail
        ilist terminator; defaults to '().

In other words, we use g to generate a sequence of seed values

    seed, g(seed), g2(seed), g3(seed), ...

These seed values are mapped to ilist elements by f, producing the elements of the result ilist in a right-to-left order. P says when to stop.

iunfold-right is the fundamental iterative ilist constructor, just as ifold is the fundamental iterative ilist consumer. While iunfold-right may seem a bit abstract to novice functional programmers, it can be used in a number of ways:

    ;; Ilist of squares: 1^2 ... 10^2
    (iunfold-right zero?
                  (lambda (x) (* x x))
                  (lambda (x) (- x 1))
                  10)

    ;; Reverse a proper ilist.
    (iunfold-right null-ilist? icar icdr lis)

    ;; Read current input port into an ilist of values.
    (iunfold-right eof-object? values (lambda (x) (read)) (read))

    ;; (iappend-reverse rev-head tail)
    (iunfold-right null-ilist? icar icdr rev-head tail)

Interested functional programmers may enjoy noting that ifold and iunfold-right are in some sense inverses. That is, given operations knull?, kar, kdr, kons, and knil satisfying

(kons (kar x) (kdr x)) = x and (knull? knil) = #t

then

(ifold kons knil (iunfold-right knull? kar kdr x)) = x

and

(iunfold-right knull? kar kdr (ifold kons knil x)) = x.

This combinator presumably has some pretentious mathematical name; interested readers are invited to communicate it to the author.

(imap proc ilist1 ilist2 ...)

proc is a procedure taking as many arguments as there are ilist arguments and returning a single value. imap applies proc element-wise to the elements of the ilists and returns an ilist of the results, in order. The dynamic order in which proc is applied to the elements of the ilists is unspecified.

    (imap icadr (iq (a b) (d e) (g h))) =>  (b e h)

    (imap (lambda (n) (expt n n))
         (iq 1 2 3 4 5))
        =>  (1 4 27 256 3125)

    (imap + (iq 1 2 3) (iq 4 5 6)) =>  (5 7 9)

    (let ((count 0))
      (imap (lambda (ignored)
             (set! count (+ count 1))
             count)
           (iq a b))) =>  (1 2) or (2 1)

(ifor-each proc ilist1 ilist2 ...)

The arguments to ifor-each are like the arguments to imap, but ifor-each calls proc for its side effects rather than for its values. Unlike imap, ifor-each is guaranteed to call proc on the elements of the ilists in order from the first element(s) to the last, and the value returned by ifor-each is unspecified.

    (let ((v (make-vector 5)))
      (ifor-each (lambda (i)
                  (vector-set! v i (* i i)))
                (iq 0 1 2 3 4))
      v)  =>  #(0 1 4 9 16)

(iappend-map f ilist1 ilist2 ...)

Equivalent to

(iapply iappend (imap f ilist1 ilist2 ...))

and

(iapply iappend (imap f ilist1 ilist2 ...))

Map f over the elements of the ilists, just as in the imap function. However, the results of the applications are appended together (using iappend) to make the final result.

The dynamic order in which the various applications of f are made is not specified.

Example:

(iappend-map (lambda (x) (ilist x (- x))) (iq 1 3 8))
  ;; => (1 -1 3 -3 8 -8)

(imap-in-order f ilist1 ilist2 ...)

A variant of the imap procedure that guarantees to apply f across the elements of the ilisti arguments in a left-to-right order. This is useful for mapping procedures that both have side effects and return useful values.

(ipair-for-each f ilist1 ilist2 ...)

Like ifor-each, but f is applied to successive sub-ilists of the argument ilists. That is, f is applied to the cells of the ilists, rather than the ilists’ elements. These applications occur in left-to-right order.

    (ipair-for-each (lambda (ipair) (display ipair) (newline)) (iq a b c)) ==>
        (a b c)
        (b c)
        (c)

(ifilter-map f ilist1 ilist2 ...)

Like imap, but only true values are saved.

    (ifilter-map (lambda (x) (and (number? x) (* x x))) (iq a 1 b 3 c 7))
        => (1 9 49)

The dynamic order in which the various applications of f are made is not specified.

(ifilter pred ilist)

Return all the elements of ilist that satisfy predicate pred. The ilist is not disordered — elements that appear in the result ilist occur in the same order as they occur in the argument ilist. The returned ilist may share a common tail with the argument ilist. The dynamic order in which the various applications of pred are made is not specified.

(ifilter even? (iq 0 7 8 8 43 -4)) => (0 8 8 -4)

(ipartition pred ilist)

Partitions the elements of ilist with predicate pred, and returns two values: the ilist of in-elements and the ilist of out-elements. The ilist is not disordered — elements occur in the result ilists in the same order as they occur in the argument ilist. The dynamic order in which the various applications of pred are made is not specified. One of the returned ilists may share a common tail with the argument ilist.

    (ipartition symbol? (iq one 2 3 four five 6)) =>
        (one four five)
        (2 3 6)

(iremove pred ilist)

Returns ilist without the elements that satisfy predicate pred:

(lambda (pred ilist) (ifilter (lambda (x) (not (pred x))) ilist))

The ilist is not disordered — elements that appear in the result ilist occur in the same order as they occur in the argument ilist. The returned ilist may share a common tail with the argument ilist. The dynamic order in which the various applications of pred are made is not specified.

(iremove even? (iq 0 7 8 8 43 -4)) => (7 43)

(ifind pred ilist)

Return the first element of ilist that satisfies predicate pred; false if no element does.

(ifind even? (iq 3 1 4 1 5 9)) => 4

Note that ifind has an ambiguity in its lookup semantics — if ifind returns #f, you cannot tell (in general) if it found a #f element that satisfied pred, or if it did not find any element at all. In many situations, this ambiguity cannot arise — either the ilist being searched is known not to contain any #f elements, or the ilist is guaranteed to have an element satisfying pred. However, in cases where this ambiguity can arise, you should use ifind-tail instead of ifind — ifind-tail has no such ambiguity:

    (cond ((ifind-tail pred lis) => (lambda (ipair) ...)) ; Handle (icar ipair)
          (else ...)) ; Search failed.

(ifind-tail pred ilist)

Return the first ipair of ilist whose icar satisfies pred. If no ipair does, return false.

ifind-tail can be viewed as a general-predicate variant of the imember function.

Examples:

    (ifind-tail even? (iq 3 1 37 -8 -5 0 0)) => (-8 -5 0 0)
    (ifind-tail even? (iq 3 1 37 -5)) => #f

    ;; IMEMBER X LIS:
    (ifind-tail (lambda (elt) (equal? x elt)) lis)

iqfind-tail is essentially idrop-while, where the sense of the predicate is inverted: Ifind-tail searches until it finds an element satisfying the predicate; idrop-while searches until it finds an element that doesn’t satisfy the predicate.

(itake-while pred ilist)

Returns the longest initial prefix of ilist whose elements all satisfy the predicate pred.

(itake-while even? (iq 2 18 3 10 22 9)) => (2 18)

(idrop-while pred ilist)

idrops the longest initial prefix of ilist whose elements all satisfy the predicate pred, and returns the rest of the ilist.

(idrop-while even? (iq 2 18 3 10 22 9)) => (3 10 22 9)

(ispan pred ilist)

(ibreak pred ilist)

ispan splits the ilist into the longest initial prefix whose elements all satisfy pred, and the remaining tail. ibreak inverts the sense of the predicate: the tail commences with the first element of the input ilist that satisfies the predicate.

In other words: ispan finds the initial span of elements satisfying pred, and ibreak breaks the ilist at the first element satisfying pred.

ispan is equivalent to

    (values (itake-while pred ilist)
            (idrop-while pred ilist))

    (ispan even? (iq 2 18 3 10 22 9)) =>
      (2 18)
      (3 10 22 9)

    (ibreak even? (iq 3 1 4 1 5 9)) =>
      (3 1)
      (4 1 5 9)

(iany pred ilist1 ilist2 ...)

Applies the predicate across the ilists, returning true if the predicate returns true on any application.

If there are n ilist arguments ilist1 … ilistn, then pred must be a procedure taking n arguments and returning a boolean result.

iany applies pred to the first elements of the ilisti parameters. If this application returns a true value, iany immediately returns that value. Otherwise, it iterates, applying pred to the second elements of the ilisti parameters, then the third, and so forth. The iteration stops when a true value is produced or one of the ilists runs out of values; in the latter case, iany returns #f. The application of pred to the last element of the ilists is a tail call.

Note the difference between ifind and iany — ifind returns the element that satisfied the predicate; iany returns the true value that the predicate produced.

Like ievery, iany’s name does not end with a question mark — this is to indicate that it does not return a simple boolean (#t or #f), but a general value.

    (iany integer? (iq a 3 b 2.7))   => #t
    (iany integer? (iq a 3.1 b 2.7)) => #f
    (iany < (iq 3 1 4 1 5)
           (iq 2 7 1 8 2)) => #t

(ievery pred ilist1 ilist2 ...)

Applies the predicate across the ilists, returning true if the predicate returns true on every application.

If there are n ilist arguments ilist1 … ilistn, then pred must be a procedure taking n arguments and returning a boolean result.

ievery applies pred to the first elements of the ilisti parameters. If this application returns false, ievery immediately returns false. Otherwise, it iterates, applying pred to the second elements of the ilisti parameters, then the third, and so forth. The iteration stops when a false value is produced or one of the ilists runs out of values. In the latter case, ievery returns the true value produced by its final application of pred. The application of pred to the last element of the ilists is a tail call.

If one of the ilisti has no elements, ievery simply returns #t.

Like iany, ievery’s name does not end with a question mark — this is to indicate that it does not return a simple boolean (#t or #f), but a general value.

(ilist-index pred ilist1 ilist2 ...)

Return the index of the leftmost element that satisfies pred.

If there are n ilist arguments ilist1 … ilistn, then pred must be a function taking n arguments and returning a boolean result.

ilist-index applies pred to the first elements of the ilisti parameters. If this application returns true, ilist-index immediately returns zero. Otherwise, it iterates, applying pred to the second elements of the ilisti parameters, then the third, and so forth. When it finds a tuple of ilist elements that cause pred to return true, it stops and returns the zero-based index of that position in the ilists.

The iteration stops when one of the ilists runs out of values; in this case, ilist-index returns #f.

    (ilist-index even? (iq 3 1 4 1 5 9)) => 2
    (ilist-index < (iq 3 1 4 1 5 9 2 5 6) (iq 2 7 1 8 2)) => 1
    (ilist-index = (iq 3 1 4 1 5 9 2 5 6) (iq 2 7 1 8 2)) => #f

(imember x ilist [=])

(imemq x ilist)

`(imemv x ilist)

These procedures return the first sub-ilist of ilist whose icar is x, where the sub-ilists of ilist are the non-empty ilists returned by (idrop ilist i) for i less than the length of ilist. If x does not occur in ilist, then #f is returned. imemq uses eq? to compare x with the elements of ilist, while imemv uses eqv?, and imember uses equal?.

        (imemq 'a (iq a b c))           =>  (a b c)
        (imemq 'b (iq a b c))           =>  (b c)
        (imemq 'a (iq b c d))           =>  #f
        (imemq (list 'a)
                (ilist 'b '(a) 'c))     =>  #f
        (imember (list 'a)
                (ilist 'b '(a) 'c)))    =>  ((a) c)
        (imemq 101 (iq 100 101 102))    =>  *unspecified*
        (imemv 101 (iq 100 101 102))    =>  (101 102)

The comparison procedure is used to compare the elements ei of ilist to the key x in this way:

(= x ei) ; ilist is (E1 ... En)

That is, the first argument is always x, and the second argument is one of the ilist elements. Thus one can reliably find the first element of ilist that is greater than five with (imember 5 ilist <)

Note that fully general ilist searching may be performed with the ifind-tail and ifind procedures, e.g.

(ifind-tail even? ilist) ; Find the first elt with an even key.

(idelete x ilist [=])

idelete uses the comparison procedure =, which defaults to equal?, to find all elements of ilist that are equal to x, and deletes them from ilist. The dynamic order in which the various applications of = are made is not specified.

The ilist is not disordered — elements that appear in the result ilist occur in the same order as they occur in the argument ilist. The result may share a common tail with the argument ilist.

Note that fully general element deletion can be performed with the iremove procedures, e.g.:

;; idelete all the even elements from LIS: