Massachusetts Institute of Technology / Artificial Intelligence Laboratory
AI Memo No. 848 / August 1985
Hal Abelson |
Chris Haynes |
Norman Adams |
Eugene Kohlbecker |
David Bartley |
Don Oxley |
Gary Brooks |
Kent Pitman |
William Clinger [editor] |
Jonathan Rees |
Dan Friedman |
Bill Rozas |
Robert Halstead |
Gerald Jay Sussman |
Chris Hanson |
Mitchell Wand |
Data and procedures and the values they amass,
Higher-order functions to combine and mix and match,
Objects with their local state, the messages they pass,
A property, a package, the control point for a catch---
In the Lambda Order they are all first-class.
One Thing to name them all, One Thing to define them.
One Thing to place them in environments and bind them,
In the Lambda Order they are all first-class.
This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology and the Computer Science Department of Indiana University. Support for the MIT research is provided in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract NO0014-80-C-0505. Support for the Indiana University research is provided by NSF Grants NCS 83-0467 and NCS 83-03325. This report is published at Indiana University as Computer Science Department Technical Report 174, June 1985.
Keywords: SCHEME, LISP, functional programming, computer languages.
Acknowledgements
Part I: Introduction to Scheme
-
I.0 Brief history of Scheme
-
I.1 Syntax of Scheme
-
I.2 Semantics of Scheme
Part II: A catalog of Scheme
-
II.0 Notational conventions
-
II.1 Special forms
-
II.2 Booleans
-
II.3 Equivalence predicates
-
II.4 Pairs and lists
-
II.5 Symbols
-
II.6 Numbers
-
II.7 Characters
-
II.8 Strings
-
II.9 Vectors
-
II.10 The object table
-
II.11 Procedures
-
II.12 Ports
-
II.13 Input
-
II.14 Output
Bibliography and References
Index
This report is primarily the work of a group of people who met at Brandeis University for two days in October 1984. Participating in that workshop were Hal Abelson, Norman Adams, David Bartley, Gary Brooks, William Clinger, Dan Friedman, Robert Halstead, Chris Hanson, Chris Haynes, Eugene Kohlbecker, Don Oxley, Jonathan Rees, Bill Rozas, Gerald Sussman, and Mitchell Wand. Kent Pitman made valuable contributions to the agenda for the workshop but was unable to attend the sessions.
We would like to thank the following people for their comments and criticisms in the months following the workshop: George Carrette, Kent Dybvig, Andy Freeman, Yekta Gursel, Paul Hudak, Chris Lindblad, John Ramsdell, and Guy Steele Jr.
We thank Carol Fessenden, Dan Friedman, and Chris Haynes for permission to use text from the Scheme 311 Version 4 reference manual. We thank Gerry Sussman for drafting the chapter on numbers, Chris Hanson for drafting the chapters on characters and strings, and Gary Brooks and William Clinger for drafting the chapters on input and output. We gladly acknowledge the influence of manuals for MIT Scheme, T, Scheme 84, and Common Lisp.
We also thank Betty Dexter for the extreme effort she put into setting this report in (Y)TeX, and Don Knuth for designing the program that caused her troubles.
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 implementors of Scheme to use this report as a starting point for manuals and other documentation, modifying it as necessary.
Editor’s note: This report records the unanimous decisions made through a remarkable spirit of compromise at Brandeis, together with the fruits of subsequent committee work and discussions made possible by various computer networks. I have tried to edit these into a coherent document while remaining faithful to the workshop’s decisions and the community’s consensus. I apologize for any cases in which I have misinterpreted the authors or misjudged the consensus.
William Clinger
Scheme is a statically scoped and properly tail-recursive dialect of the Lisp programming language invented by Guy Lewis Steele Jr and Gerald Jay Sunman. It was designed to have an exceptionally clear and simple semantics and very few different methods of expression formation.
The first description of Scheme was written in 1975 [28]. A Revised Report [24] appeared in 1978, which described the evolution of the language as its MIT implementation was upgraded to support an innovative compiler [21]. Three distinct projects began in 1981 and 1982 to use variants of Scheme for courses at MIT, Yale, and Indiana University [11, 14, 4]. An introductory computer science textbook using Scheme was published in 1984 [1].
As might be expected of a language used-primarily for education and research, Scheme has always evolved rapidly. This was no problem when Scheme was used only within MIT, but as Scheme became more widespread local subdialects 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. This paper reports their unanimous recommendations augmented by committee work in areas of arithmetic, characters, strings, and input/output.
Scheme shares with Common Lisp [23] the goal of a core language common to several implementations. Scheme differs from Common Lisp in its emphasis upon simplicity and function over compatibility with older dialects of Lisp.
Formal definitions of the lexical and context-free syntaxes of Scheme will be included in a separate report.
Most identifiers allowed by other programming languages are also acceptable to Scheme. The precise rules for forming identifiers vary among implementations of Scheme, but in all implementations a sequence of characters that contains no special characters and begins with a character that cannot begin a number is an identifier. There may be other identifiers as well, and in particular the following are identifiers:
+ - 1+ -1+
It is guaranteed that the following characters cannot begin a number, so identifiers other than the four listed above should begin with one of:
a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ! $ % & * / : < = > ? ~
Subsequent characters of the identifier should be drawn from:
a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 0 1 2 3 4 5 6 7 8 9 ! $ % & * / : < = > ? ^ _ . ~
The case in which the letters of an identifier are typed is immaterial. For example, Foo is the same identifier as FOO.
The following characters are special, and should never be used in an identifier:
) ( ] [ } { " ; blank
Scheme deliberately does not specify whether the following characters can be used in identifiers:
# ' ` , @ \ |
Rationale: Some implementations might want to use backslash (\) and vertical bar (|) as in Common Lisp. As for the others there are two schools of thought. One school argues that disallowing special characters in identifiers allows the computer to catch more typing errors. The other school agrees only for special characters that come in pairs, on the grounds that errors involving only the unpaired special characters are easier to see.
A semicolon indicates the start of a comment. The comment continues to the end of the line on which the semicolon appears. Comments are invisible to Scheme, but the end of the line is visible as whitespace. This prevents a comment from appearing in the middle of an identifier or number.
Left and right parentheses are used for grouping and to notate lists as described in section 11.4. Left and right square brackets and curly braces are not used in Scheme right now but are reserved for unspecified future uses.
The quote (') and backquote (`) characters are used to indicate constant or almost-constant data as described in section II.1. The comma is used together with the backquote, and the atsign (@) is used together with the comma.
The doublequote character is used to notate strings as described in section II.8.
The sharp sign (#) is used for a variety of purposes depending on the
character that follows it. A sharp sign followed by a left parenthesis
signals the beginning of a vector, as described in section II.9. A
sharp sign followed by an exclamation point is used to notate one of
the special values #!true, #!false, and #!null. A sharp sign
followed by a backslash is used to notate characters as described in
section II.7. A sharp sign followed by any of a number of letters is
used in the notation for numbers as described in section II.6.
The following grammar is ambiguous because a <special form> looks
like a <procedure call>. Some implementations resolve the ambiguity
by reserving the identifiers that serve as keywords of special forms,
while other implementations allow the keyword meaning of an identifier
to be shadowed by lexical bindings.
<expression> ::= <constant> | <identifier> |
<special form> | <procedure call>
<constant> ::= <numeral> | <string> |
(quote <datum>) | '<datum> |
#!true | #!false | #!null
<special form> ::= (<keyword> <syntactic component> ...)
<procedure call> ::= (<operator> <operands>)
<operator> := <expression>
<operands> := <empty> | <expression> <operands>
<datum> stands for any written representation of a Scheme object, as described in the sections that follow. <identifier> has already been described informally. <numeral> is described in section 1.6, and <string> is described in section II.8. <special form> stands for one of the special forms whose syntax is described in section II.1. For uniformity the other kinds of expressions are also described in that section as though they were special forms.
A formal definition of the semantics of Scheme will be included in a separate report. The detailed informal semantics of Scheme is the subject of Part II. This section gives a quick review of Scheme’s major characteristics.
Scheme is a statically scoped programming language. Each use of an identifier is associated with a lexically apparent binding of that identifier. In this respect Scheme is like Algol 60, Pascal, and C but unlike dynamically scoped languages such as APL and traditional Lisp.
Scheme has latent as opposed to manifest types. Types are associated with values (also called objects) rather than with variables. (Some authors refer to languages with latent types as weally typed or dynamically typed languages.) Other languages with latent types are APL, Snobol, and other dialects of Lisp. Languages with manifest types (sometimes referred to as strongly typed or statically typed languages) include Algol 60, Pascal, and C.
All objects created in the course of a Scheme computation, including all procedures and variables, 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 awe permitted to reclaim the storage occupied by an object if they can prove that the object cannot possibly matter to any future computation. Other languages in which most objects have unlimited extent include APL and other Lisp dialects.
Implementations of Scheme are required to be properly tail-recursive. This allows the execution of an iterative process in constant space, even if the iterative process is described by a syntactically recursive procedure. Thus with a tail-recursive implementation, iteration can be expressed using the ordinary procedure-call mechanics, so that special iteration constructs are useful only as syntactic sugar.
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. Other languages with these properties iuiclude Common Lisp and ML.
Arguments to Scheme procedures are always passed by value, which means that the actual argument expressions are evaluated before the proceduret gains control, whether the procedure needs the result of the evaluation or not. ML, C, and APL are three other languages that always pass arguments by value. Lazy ML passes arguments by name, so that an argument expression is evaluated only if its value is needed by the procedure.
This part of the report is a catalog of the special forms and procedures that make up Scheme. The special forms are described in section II.1, and the procedures are described in the following sections. Each section is organized into entries, with one entry (usually) for each special form or procedure. Each entry begins with a header line that includes the name of the special form or procedure in boldface type within a template for the special form or a call to the procedure. The names of the arguments to a procedure are italicized, as are the syntactic components of a special form. A notation such as
expr ...
indicates zero or more occurrences of expr. Thus
expr1 expr2 ...
indicates at least one expr. At the right of the header line one of the following categories will appear:
-
special form
-
constant
-
variable
-
procedure
-
essential special form
-
essential constant
-
essential variable
-
essential procedure
A special form is a syntactic class of expressions, usually identified by a keyword. A constant is something that is lexically recognizable as a constant. A variable is a location in which values (also called objects) can be stored. An identifier may be bound to a variable. Those variables that initially hold procedure values are identified as procedures.
It is guaranteed that every implementation of Scheme will support the essential special forms, constants, variables, and procedures. Implementations are free to omit other features of Scheme or to add extensions, provided the extensions are not in conflict with the language reported here.
Any Scheme value can be used as a boolean expression for the purpose
of a conditional test. As explained in section 11.2, most values count
as true, but a few-notably #!false-count as false. This manual uses
the word "true" to refer to any Scheme value that counts as true in a
conditional expression, and the word "false" to refer to any Scheme
value that counts as false.
When speaking of an error condition, this manual uses the phrase "an error is signalled" to indicate that implementations must detect and report the error. If the magic word "signalled" 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. An error condition that implementations are not required to detect is usually referred to simply as "an error".
For example, it is an error for a procedure to be passed an argument that the procedure is not explicitly specified to handle, even though such domain errors are seldom mentioned in this manual. Implementations may extend a procedure’s domain of definition to include other arguments.
Identifiers have two uses within Scheme programs. When an identifier appears within a quoted constant (see quote), it is being used as data as described in the section on symbols. Otherwise it is being used as a name. There are two kinds of things that an identifier can name in Scheme: special forms and variables. A special form is a syntactic class of expressions, and an identifier that names a special form is called the keyword of that special form. A variable, on the other hand, is a location where a value can be stored. An identifier that names a variable is said to be bound to that location. The set of all such bindings in effect at some point in a program is known as the environment in effect at that point.
Certain special forms are used to allocate storage for new variables and to bind identifiers to those new variables. The most fundamental of these binding constructs is the lambda special form, because all other binding constructs can be explained in terms of lambda expressions. The other binding constructs are the let, let, letrec, internal definition (see define), rec, namedlambda, and do special forms.
Like Algol or Pascal, and unlike most other dialects of Lisp except for Common Lisp, Scheme is a statically scoped language with block structure. To each place where an identifier is bound in a program there corresponds a region of the program within which the binding is effective. The region varies according to the binding construct that establishes the binding; if the binding is established by a lambda expression, for example, then the region is the entire lambda expression. Every use of an identifier in a variable reference or assignment 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 identifier that was in effect when Scheme started up, if any; if there is no binding for the identifier, it is said to be unbound.
variable [essential special form]
An expression consisting of an identifier that is not the keyword of a apecial form is a variable reference. The value obtained for the variable reference is the value stored in the location to which variable is bound. It is an error to reference an unbound variable.
(operator operand1 …) [essential special form]
A list whose first element is not the keyword of a special form indicates a procedure call. The operator and operand expressions are evaluated and the resulting procedure is passed the resulting arguments. In contrast to other dialects of Lisp the order of evaluation is not specified, and the operator expression and the operand expressions are always evaluated with the same evaluation rules.
(+ 3 4) --> 7 ((if #!false + *) 3 4) --> 12
(quote datum) [essential special form]
'datum [essential special form]
Evaluates to datum. 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) may 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)
Numeric constants, string constants, character constants, vector constants, and the constants # !true, #false, and #!null need not be quoted.
'"abc" --> "abc" "abc" --> "abc" '145932 --> 145932 145932 --> 145932 '#!true --> #!true #!true --> #!true
(lambda (var1 …) expr) [essential special form]
Each var must be an identifier. The lambda expression evaluates to a
procedure with formal argument list (var1 …) and procedure body
expr. 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
identifiers in the formal argument list to fresh locations, the
corresponding actual argument values will be stored in those
locations, and expr will then be evaluated in the extended
environment. The result of expr will be returned as the result of the
procedure call.
(lambda (x) (+ x x)) --> #<PROCEDURE>
((lambda (x) (+ x x)) 4) --> 8
(define reverse-subtract
(lambda (x y) (- y x))) --> unspecified
(reverse-subtract 7 10) --> 3
(define foo
(let ((x 4))
(lambda (y) (+ x y)))) --> unspecified
(foo 6) --> 10
(lambda (var1 …) expr1 expr2 …) [essential special form]
Equivalent to (lambda (var1 …) (begin expr1 expr2 …)).
(lambda var expr1 expr2 …) [essential special form]
Returns a procedure that when later called with some arguments will bind var to a fresh location, convert the sequence of actual arguments into a list, and store that list in the binding of var.
((lambda x x) 3 4 5 6) --> (3 4 5 6)
One last variation on the formal argument list provides for a so-called "rest argument. If a space/dot/space sequence precedes the last argument in the formal argument list, then the value stored in the binding of the last formal argument will be a list of the actual arguments left over after all the other actual arguments have been matched up against the formal arguments.
((lambda (x y . z) z) 3 4 5 6) --> (5 6)
(if condition consequent alternative) [essential special form]
(if condition consequent) [special form]
First evaluates condition. If it yields a true value (see section II.2), then consequent is evaluated and its value is returned. Otherwise alternative is evaluated and its value is returned. If no alternative is specified, then the if expression isevaluated only for its effect, and 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
(cond clause1 clause2 …) [essential special form]
Each clause must be a list of one or more expressions. The first expression in each clause is a boolean expression that serves as the guard for the clause. The guards are evaluated in order until one of them evaluates to a true value (see section II.2). When a guard evaluates true, then the remaining expressions in its clause are evaluated in order, and the result of the last expression in the selected clause is returned as the result of the entire expression. If the selected clause contains only the guard, then the value of the guard is returned as the result. If all guards evaluate to false values, then the result of the conditional expression is unspecified.
(cond ((>? 3 2) 'greater)
((<? 3 2) 'less)) --> greater
The keyword or variable else may be used as a guard to obtain the
effect of a guard that always evaluates true.
(cond ((>? 3 3) 'greater)
((<? 3 3) 'less)
(else 'equal)) --> equal
The above forms for the clauses are essential. Some implementations support yet another form of clause such that
(cond (form1 -> form2) ...)
is equivalent to
(let ((form1-result form1)
(thunk2 (lambda () form2))
(thunk3 (lambda () (cond ...))))
(if form1-result
((thunk2) form1-result)
(thunk3)))
(case expr clause1 clause2 …) [special form]
Each clause is a list whose first element is a selector followed
by one or more expressions. Each selector should be a list of
values. The selector_s are not evaluated. Instead _expr is evaluated
and its result is compared against successive selector_s using the
memv procedure until a match is found. Then the expressions in the
selected _clause are evaluated from left to right and the result of
the last expression in the clause is returned as the result of the
case expression. If no selector matches then the result of the case
expression is unspecified.
(case (* 2 3) ((2 3 5 7) 'prime) ((1 4 6 8 9) 'composite)) --> composite (case (car '(c d)) ((a) 'a) ((b) 'b)) --> unspecified
The special keyword else may be used as a selector to obtain the
effect of a selector that always matches.
(case (car '(c d)) ((a e i o u) 'vowel) ((y) 'y) (else 'consonant)) --> consonant
(and expr1 …) [special form]
Evaluates the _expr_s from left to right, returning false as soon as one evaluates to a false value (see section II.2). Any remaining expressions are not evaluated. If all the expressions evaluate to true values, the value of the last expression is returned.
(and (=? 2 2) (>? 2 1)) --> #!true (and (=? 2 2) (<? 2 1)) --> #!false (and 1 2 'c '(f g)) --> (f g)
(or expr1 …) [special form]
Evaluates the exprs from left to right, returning the value of the first expr that evaluates to a true value (see section II.2). Any remaining expressions are not evaluated. If all expressions evaluate to false values, false is returned.
(or (=? 2 2) (>? 2 1)) --> #!true (or (=? 2 2) (<? 2 1)) --> #!true (or #!false #!false #!false) --> #!false (or (memq 'b '(a b c)) (/ 3 0)) --> (b c)
(let ((var1 form1) …) expr1 expr2 …) [essential special form]
Evaluates the form_s in the current environment (in some unspecified order), binds the _var_s to fresh locations holding the results, and then evaluates the _expr_s in the extended environment from left to right, returning the value of the last one. Each binding of a _var has expr1 expr2 … as its region.
(let ((x 2) (y 3)) (* x y)) --> 6
(let ((x 2) (y 3))
(let ((foo (lambda (z) (+ x y z)))
(x 7))
(foo 4))) --> 9
let and letrec give Scheme a block structure. The difference
between let and letrec is that in a let the _form_s are not
within the region of the _var_s being bound. See letrec.
Some implementations of Scheme permit a "named let" syntax in which
(let name ((var1 form1) ...) expr1 expr2 ...)
is equivalent to
((rec name (lambda (var1 ...) expr1 expr2 ...)) form1 ...)
(let* ((var1 form1) …) expr1 expr2 …) [special form]
Similar to let, but the bindings are performed sequentially from
left to right and the region of a binding indicated by (var form)
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.
(letrec ((var1 form1) …) expr1 expr2 …) [essential special form]
Binds the var_s to fresh locations holding undefined values,
evaluates the _form_s in the resulting environment (in some
unspecified order), assigns to each _var the result of the
corresponding form, evaluates the expr_s sequentially in the
resulting environment, and returns the value of the last _expr. Each
binding of a var has the entire letrec expression as its region,
making it possible to define mutually recursive procedures. See let.
(letrec ((x 2) (y 3))
(letrec ((foo (lambda (z) (+ x y z))) (x 7))
(foo 4))) --> 14
(letrec ((even?
(lambda (n)
(if (zero? n)
#!true
(odd? (-1+ n)))))
(odd?
(lambda (n)
(if (zero? n)
#!false
(even? (-1+ n))))))
(even? 88))
--> #!true
One restriction on letrec is very important: it must be possible to evaluate each form without referring to the value of a var. If this restriction is violated, then the effect is undefined, and an error may be reported during evaluation of the forms. The restriction is necessary because Scheme passes arguments by value rather than by name. In the most common uses of letrec, all the forms are lambda expressions and the restriction is satisfied automatically.
(rec var expr) [special form]
Equivalent to (letrec var expr var). rec is useful for
defining self-recursive procedures.
(named-lambda (name var1 …) expr …) [special form]
Equivalent to (rec name (lambda (var1 …) expr …))
Rationale: Some implementations may find it easier to provide good
edebugging information when named-lambda is used instead of rec.
(define var expr) [essential special form]
When typed at top level, so that it is not nested within any other
expression, this form has essentially the same effect as the
assignment (set! var expr) if var is bound. If var is not bound,
however, then the define form will bind var before performing the
assignment, whereas it would be an error to perform a set! on an
unbound identifier. The value returned by a define form is not
specified.
(define add3 (lambda (x) (+ x 3))) --> unspecified (add3 3) --> 6 (define first car) --> unspecified (first '(1 2)) --> 1
The semantics just described is essential. Some implementations also allow define expressions to appear at the beginning of the body of a lambda, named-lambda, let, let*, or letrec expression. Such expressions are known as internal definitions as opposed to the top level definitions described above. The variable defined by an internal definition is local to the body of the lambda, named-lambda, let, let*, or letrec expression. That is, var is bound rather than assigned, and the region set up by the binding is the entire body of the lambda, named-lambda, let, let*, or letrec expression. For example,
(let ((x 5)) (define foo (lambda (y) (bar x y))) (define bar (lambda (a b) (+ (* a b) a))) (foo (+ x 3))) --> 45
Internal definitions can always be converted into an 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))))
(define (var0 var1 …) expr1 expr2 …) [special form]
(define (form var1 …) expr1 expr2 …) [special form]
The first syntax, where varO is an identifier, is equivalent to
(define var0 (rec var0 (lambda (var1 ...) expr1 expr2)))
The second syntax, where form is a list, is sometimes convenient for
defining a procedure that returns another procedure as its result. It
is equivalent to (define form (lambda (var1 …) expr1 expr2 …)).
(set! var expr) [essential special form]
Stores the value of expr in the location to which var is bound. expr
is evaluated but var is not. The result of the set! expression is
unspecified.
(set! x 4) --> unspecified (1+ x) --> 5
(begin expr1 expr2 …) [essential special form]
Evaluates the expr_s sequentially from left to right and returns the value of the last _expr. Used to sequence side effects such as input and output.
(begin (setl x 5) (1+ x)) --> 6
Also
(begin (display "4 plus 1 equals ")
(display (1+ 4)))
prints 4 plus 1 equals 5
A number of special forms such as lambda and letrec implicitly
treat their bodies as begin expressions.
(sequence expr1 expr2 …) [special form]
sequence is synonymous with begin.
Rationale: sequence was used in the Abelson and Sussman text, but
it should not be used in new code.
(do varspecs exit stmt1 …) [special form]
The do special form is an extremely general albeit complex iteration
macro. The _varspec_s specify variables to be bound, how they are to
be initialized at the start, and how they are to be incremented on
every iteration. The general form looks like:
(do ((var1 init1 step1) ...)
(test expr1 ...)
stmt1 ...)
Each var must be an identifier and each init and step must be expressions. The init expressions are evaluated (in some unspecified order), the var_s are bound to fresh locations, the results of the _init expressions are stored in the bindings of the _var_s, and then the iteration phase begins.
Each iteration begins by evaluating test; if the result is false (see section II.2), then the stmt_s are evaluated in order for effect, the _step_s are evaluated (in some unspecified order), the results of the _step expressions are stored in the bindings of the _var_s, and the next iteration begins.
If test evaluates true, then the expr_s are evaluated from left to
right and the value of the last _expr is returned as the value of the
do expression. If no _expr_s are present, then the value of the do
expression is unspecified.
The region set up by the binding of a var consists of the entire
do expression except for the _init_s.
A step may be omitted, in which case the corresponding var is not updated. When the step is omitted the init may be omitted as well, in which case the initial value is not specified.
(do ((vec (make-vector 5))
(i 0 (1+ i)))
((=? 1 5) vec)
(vector-set vec i 1)) --> #(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
The do special form is essentially the same as the do macro in
Common Lisp. The main difference is that in Scheme the identifier
return is not bound; programmers that want to bind return as in
Common Lisp must do so explicitly (see
call-with-current-continuation).
`pattern [special form]
The backquote special form is useful for constructing a list structure
when most but not all of the desired structure is known in advance. If
no commas appear within the pattern, the result of evaluating
pattern is equivalent (in the sense of equal?) to the result of
evaluating `pattern. If a comma appears within the pattern,
however, the expression following the comma is evaluated and its
result is inserted into the structure instead of the comma and the
expression. If a comma appears followed immediately by an at-sign
(@`), then the following expression must 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 ,(+ 1 2) ,@(map 1+ '(4 5 6)) b) --> (a 3 5 6 7 b) `(((foo ,(- 10 3)) ,@(cdr '(c)) cons)) --> (((foo 7) cons))
Scheme does not have any standard facility for defining new special forms.
Rationale: The ability to define new special forms creates numerous problems. All current implementations of Scheme have macro facilities that solve those problems to one degree or another, but the solutions are quite different and it isn’t clear at this time which solution is best, or indeed whether any of the solutions are truly adequate. Rather than standardize, we are encouraging implementations to continue to experiment with different solutions.
The main problems with traditional macros are: They must be defined to the system before any code using them is loaded; this is a common source of obscure bugs. They are usually global; macros can be made to follow lexical scope rules as in Common Lisp’s macrolet, but many people find the resulting scope rules confusing. Unless they are written very carefully, macros are vulnerable to inadvertant capture of free variables; to get around this, for example, macros may have to generate code in which procedure values appear as quoted constants. There is a similar problem with keywords if the keywords of special forms are not reserved. If keywords are reserved, then either macros introduce new reserved words, invalidating old code, or else special forms defined by the programmer do not have the same status as special forms defined by the system.
The standard boolean objects for truth and falsity are written as
!true and !false. What really matters, though, are the objects
that the Scheme conditional expressions (if, cond, and, or,
do) will treat as though they were 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. All of the conditional expressions are equivalent in that
an object treated as false by any one of them is treated as false by
all of them, and likewise for true values.
Of all the standard Scheme values, only !false and the empty list
count as false in conditional expressions. !true, pairs (and
therefore lists), symbols, numbers, strings, vectors, and procedures
all count as true.
The empty list counts as false for historical reasons only, and programs should not rely on this because future versions of Scheme will probably do away with this nonsense.
Programmers accustomed to other dialects of Lisp should beware that Scheme has already done away with the nonsense that identifies the empty list with the symbol nil.
#!false [essential constant]
!false is the boolean value for falsity. The !false object is
self-evaluating. That is, it does not need to be quoted in programs.
'#!false --> #!false #!false --> #!false
#!true [essential constant]
!true is the boolean value for truth. The !true object is
self-evaluating, and does not need to be quoted in programs.
(not obj) [essential procedure]
Returns !true if obj is false and returns !false otherwise.
nil [variable]
t [variable]
As a crutch for programmers accustomed to other dialects of Lisp, some
implementations provide variables nil and t whose initial values are
!null and !true respectively. These variables should not be
relied upon in new code.
A predicate is a procedure that always returns !true or !false.
Of the equivalence predicates described in this section, eq? is the
most discriminating while equal? is the most liberal. eqv? is very
slightly less discriminating than eq?.
(eq? obj1 obj2) [essential procedure]
Returns !true if obj1 is identical in all respects to obj2,
otherwise returns !false. If there is any way at all that a user
can distinguish obj1 and obj2, then eq? will return #!false.
On the other hand, it is guaranteed that objects maintain their
identity despite being fetched from or stored into variables or data
structures.
The notion of identity used by eq? is stronger than the notions of
equivalence used by the eqv? and equal? predicates. The constants
!true and !false are identical to themselves and are different
from everything else, except that in some implementations the empty
list is identical to #!false for historical reasons. Two symbols are
identical if they print the same way (except that some implementations
may have "uninterned symbols" that violate this rule). For structured
objects such as pairs and vectors the notion of sameness is defined in
terms of the primitive mutation procedures defined on those objects.
For example, two pairs are the same if and only if a set-car!
operation on one changes the car field of the other. The rules for
identity of numbers are extremely implementation-dependent and should
not be relied on.
Generally speaking, the equal? procedure should be used to compare lists, vectors, and arrays. The char=? procedure should be used to compare characters, the string=? procedure should be used to compare strings, and the =? procedure should be used to compare numbers. The eqv? procedure is just like eq? except that it can be used to compare characters and exact numbers as well. (See section II.6 for a discussion of exact numbers.)
(eq? 'a 'a) --> #!true (eq? 'a 'b) --> #!false (eq? '(a) '(a)) --> unspecified
(eq? "a" "a") --> unspecified (eq? 2 2) --> unspecified (eq? (cons 'a 'b) (cons 'a 'b)) --> #!false (let ((x (read))) (eq? (cdr (cons 'b x)) x)) --> #!true
(eqv? obj1 obj2) [essential procedure]
eqv? is just like eq? except that if obj1 and obj2 are exact
numbers then eqv? is guaranteed to return #!true if obj1 and
obj2 are equal according to the *=? procedure.
(eq? 100000 100000) --> unspecified (eqv? 100000 100000) --> #!true
See section II.6 for a discussion of exact numbers.
(equal? obj1 obj2) [essential procedure]
Returns #!true if obj1 and obj2 are identical objects or if they
are equivalent numbers, lists, characters, strings, or vectors. Two
objects are generally considered equivalent if they print the same.
equal? may fail to terminate if its arguments are circular data
structures.
(equal? 'a 'a) --> #!true
(equal? '(a) '(a)) --> #!true
(equal? '(a (b) c) '(a (b) c)) --> #!true
(equal? "abc" "abc") --> #!true
(equal? 2 2) --> #!true
(equal? (make-vector 5 'a)
(make-vector 5 'a)) --> #!true
Lists are Lisp’s—and therefore Scheme’s—characteristic data structures.
The empty list is a special object that is written as an opening
parenthesis followed by a closing parenthesis: () The empty list has
no elements, and its length is zero. The empty list is not a pair.
Larger lists are built out of pairs. 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 named 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!.
The most general notation used 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 whosecdr is 5.
The dotted notation is not often used, because more streamlined
notations exist for the common case where the cdr is the empty list or
a pair. Thus (c1 . ()) is usually written as (c1), and (c1 . (c2
. c3)) is usually written as (c1 c2 . c3). Usually these special
notations permit a structure to be written without any dotted pair
notation at all. For example
(a . (b . (c . (d . (e . ())))))
would normally be written as (a b c d e).
When all the dots can be made to disappear as in the example above, the entire structure is called a proper list. Proper lists are so common that when people speak of a list, they usually mean a proper list. An inductive definition:
-
The empty list is a proper list.
-
If plist is a proper list, then any pair whose cdr is plist is also a proper list.
-
There are no other proper lists.
A proper list is therefore either the empty list or a pair from which the empty list can be obtained by applying the cdr procedure a finite number of times. Whether a given pair is a proper list depends upon what is stored in the cdr field. When the set-cdr! procedure is used, an object can be a proper list one moment and not the next:
(define x '(a b c)) --> unspecified (define y x) --> unspecified y --> (a b c) (set-cdr! x 4) --> unspecified x --> (a . 4) (eq? x y) --> #!true y --> (a . 4)
A pair object, on the other hand, will always be a pair object.
It is often convenient to speak of a homogeneous (proper) list of
objects of some particular data type, as for example (1 2 3) is a
list of integers. To be more precise, suppose D is some data type.
(Any predicate defines a data type consisting of those objects of
which the predicate is true.) Then
-
The empty list is a list of D.
-
If plist is a list of D, then any pair whose cdr is plist and whose car is an element of the data type D is also a list of D.
-
There are no other lists of D.
(pair? obj) [essential procedure]
Returns !true if obj is a pair, otherwise returns !false.
(pair? '(a . b)) --> #!true (pair? '(a b c)) --> #!true (pair? '()) --> #!false (pair? '#(a b)) --> #!false
(cons obj1 obj2) [essential 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 eq?) 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) [essential procedure]
Returns the contents of the car field of pair. pair must be a pair. Note that it is an error to take the car of the empty list.
(car '(abc)) --> a (car '((a) bcd)) --> (a) (car '(1 . 2)) --> 1 (car '()) --> error
(cdr pair) [essential procedure]
Returns the contents of the cdr field of pair. pair must be a 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) [essential procedure]
Stores obj in the car field of pair. pair must be a pair. The value returned by set-car! is unspecified. This procedure can be very confusing if used indiscriminately.
(set-cdr! pair obj) [essential procedure]
Stores obj in the cdr field of pair. pair must be a pair. The value returned by set-cdr! is unspecified. This procedure can be very confusing if used indiscriminately.
(caar pair) [essential procedure]
(cadr pair) [essential procedure]
(cdar pair) [essential procedure]
(cddr pair) [essential procedure]
(caaar pair) [essential procedure]
(caadr pair) [essential procedure]
(cadar pair) [essential procedure]
(caddr pair) [essential procedure]
(cdaar pair) [essential procedure]
(cdadr pair) [essential procedure]
(cddar pair) [essential procedure]
(cdddr pair) [essential procedure]
(caaaar pair) [essential procedure]
(caaadr pair) [essential procedure]
(caadar pair) [essential procedure]
(caaddr pair) [essential procedure]
(cadaar pair) [essential procedure]
(cadadr pair) [essential procedure]
(caddar pair) [essential procedure]
(cadddr pair) [essential procedure]
(cdaaar pair) [essential procedure]
(cdaadr pair) [essential procedure]
(cdadar pair) [essential procedure]
(cdaddr pair) [essential procedure]
(cddaar pair) [essential procedure]
(cddadr pair) [essential procedure]
(cdddar pair) [essential procedure]
(cddddr pair) [essential procedure]
These procedures are compositions of car and cdr, where for example caddr could be defined by
(define caddr (lambda (x) (car (cdr (cdr x)))))
'() [essential constant]
#!null [constant]
'() and !null are notations for the empty list. The !null
notation does not have to be quoted in programs. The () notation
must be quoted in programs, however, because otherwise it would be a
procedure call without a expression in the procedure position.
Rationale: Because many current Scheme interpreters deal with
expressions as list structures rather than as character strings, they
will treat an unquoted () as though it were quoted. It is entirely
possible, however, that some implementations of Scheme will be able to
detect an unquoted () as an error.
(null? obj) [essential procedure]
Returns !true if obj is the empty list, otherwise returns
!false.
(list obj1 …) [essential procedure]
Returns a proper list of its arguments.
(list 'a (+ 3 4) 'c) --> (a 7 c)
(length plist) [essential procedure]
Returns the length of plist, which must be a proper list.
(length '()) --> 0 (length '(a b c)) --> 3 (length '(a (b) (c d e))) --> 3
(append plist1 plist2) [essential procedure]
(append plist …) [procedure]
All plists should be proper lists. Roturns a list consisting of the elements of the first plist followed by the elements of the other plists.
(append '(x) '(y)) --> (x y) (append '(a) '(b c d)) --> (a b c d) (append '(a (b)) '((c))) --> (a (b) (c))
(append! plist …) [procedure]
Like append but may side effect all but its last argument.
(reverse plist) [procedure]
plist must be a proper list. Returns a list consisting of the elements of plist in reverse order.
(reverse '(a b c)) --> (c b a) (reverse '(a (b c) d (e (f)))) --> ((e (f)) d (b c) a)
(list-ref z n) [procedure]
Returns the car of (list-tail z n).
(list-tail z n) [procedure]
Returns the sublist of z obtained by omitting the first n elements. Could be defined by
(define list-tail
(lambda (x n)
(if (zero? n)
x
(list-tail (cdr x) (- n 1)))))
(last-pair x) [procedure]
Returns the last pair in the nonempty list x. Could be defined by
(define last-pair
(lambda (x)
(if (pair? (cdr x))
(last-pair (cdr x))
x)))
(memq obj plist) [essential procedure]
(memv obj plist) [essential procedure]
(member obj plist) [essential procedure]
Finds the first occurrence of obj in the proper list plist and
returns the first sublist of plist beginning with obj. If obj
does not occur in plist, returns #!false. memq uses eq? to
compare obj with the elements of plist, while memv uses eqv?
and member uses equal?.
(memq 'a '(a b c) --> (a b c) (memq 'b '(a b c) --> (b c) (memq 'a '(b c d)) --> #!false (memq (list 'a) '(b (a) c)) --> #!false (memq 101 '(100 101 102)) --> unspecified (memv 101 '(100 101 102)) --> (101 102) (member (list 'a) '(b (a) c)) --> ((a) c)
(assq obj alist) [essential procedure]
(assv obj alist) [essential procedure]
(assoc obj alist) [essential procedure]
alist must be a proper list of pairs. Finds the first pair in
alist whose car field is obj and returns that pair. If no pair in
alist has obj as its car, returns #!false. assq uses eq? to
compare obj with the car fields of the pairs in alist, while
assv uses eqv? and assoc uses equal?.
(assq 'a '((a 1) (b 2) (c 3))) --> (a 1)
(assq 'b '((a 1) (b 2) (c 3))) --> (b 2)
(assq 'd '((a 1) (b 2) (c 3))) --> #!false
(assq (list 'a)
'(((a)) ((b)) ((c)))) --> #!false
(assq 5 '((2 3) (5 7) (11 13))) --> unspecified
(assv 5 '((2 3) (5 7) (11 13))) --> (5 7)
(assoc (list 'a)
'(((a)) ((b)) ((c)))) --> ((a))
Rationale: memq, memv, member, assq, assv, and assoc do
not have question marks in their names because they return useful
values rather than just #!true.
Symbols are objects whose usefulness rests entirely on the fact that two symbols are identical (in the sense of eq?) if and only if their names are spelled the same way. This is exactly the property needed to represent identifiers in programs, and so most implementations of Scheme use them internally for that purpose. Programmers may also use symbols as they use enumerated values in Pascal.
The rules for writing a symbol are the same as the rules for writing an identifier (see section I.2). As with identifiers, different implementations of Scheme use slightly different rules, but it is always the case that a sequence of characters that contains no special characters and begins with a character that cannot begin a number is taken to be a symbol; in addition , - 1, and -1+ are symbols.
The case in which a symbol is written is unimportant. Some implementations of Scheme convert any upper case letters to lower case, and others convert lower case to upper case.
It is guaranteed that any symbol that has been 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 eq?). The string→symbol procedure, however, can create symbols for which this write/read invariance may not hold because their names contain special characters or letters in the non-standard case.
Rationale: Some implementations of Lisp have a feature known as "slashification" in order to guarantee write/read invariance for all symbols, but historically the most important use of this feature has been to compensate for the lack of a string data type. Some implementations have "uninterned symbols", which defeat write/read invariance even in implementations with slashification and also generate exceptions to the rule that two symbols are the same if and only if their names are spelled the same. It is questionable whether these features are worth their complexity, so they are not standard in Scheme.
(symbol? obj) [essential procedure]
Returns !true if obj is a symbol, otherwise returns !false.
(symbol? 'foo) --> #!true (symbol? (car '(a b))) --> #!true (symbol? "bar") --> #!false
(symbol→string symbol) [essential procedure]
Returns the name of symbol as a string. symbol→string performs no case conversion. See string→syabol. The following examples assume the read procedure converts to lower case:
(symbol->string 'flying-fish) --> "flying-fish" (symbol->string 'Martin) --> "martin" (symbol->string (string->symbol "Malvina")) --> "Malvina"
(string→symbol string) [essential procedure]
Returns the symbol whose name is string. string→symbol can create symbols with special characters or letters in the non-standard case, but it is usually a bad idea to create such symbols because in some implementations of Scheme they cannot be read as themselves. See symbol→string.
'mISSISSIppi --> mississippi
(string->symbol mISSISSIppi") --> mISSISSIppi
(eq? 'bitBlt
(string->symbol "bitBlt")) --> unspecified
(eq? 'JollyWog
(string->symbol
(symbol->string 'JollyWog))) --> #!true
(string=?
"K. Harper, M.D."
(symbol->string
(string->symbol
"K. Harper, M.D."))) --> #!true
Numerical computation has traditionally been neglected by the Lisp community. Until Common Lisp there has been no carefully thought out strategy for organizing numerical computation, and with the exception of the MacLisp system there has been little effort to execute numerical code efficiently. We applaud the excellent work of the Common Lisp committee and we accept many of their recommendations. In some ways we simplify and generalize their proposals in a manner consistent with the purposes of Scheme.
Scheme’s numerical operations treat numbers as abstract data, as independent of their representation as is possible. Thus, the casual user should be able to write simple programs without having to know that the implementation may use fixed-point, floating-point, and perhaps other representations for his data. Unfortunately, this illusion of uniformity can be sustained only approximately — the implementation of numbers will leak out of its abstraction whenever the user must be in control of precision, or accuracy, or when he must construct especially efficient computations. Thus the language must also provide escape mechanisms so that a sophisticated programmer can exercise more control over the execution of his code and the represntation of his data when necessary.
It is important to distinguish between the abstract numbers, their machine representations, and their written representations. We will use mathematical words such as NUMBER, COMPLEX, REAL, RATIONAL, and INTEGER for properties of the abstract numbers, names such as FIXNUM, BIGNUM, RATNUM, and FLONUM for machine representations, and names like INT, FIX, FLO, SCI, RAT, POLAR, and RECT for input/output formats.
Numbers
A Scheme system provides data of type NUMBER, which is the most general numerical type supported by that system. NUMBER is likely to be a complicated union type implemented in terms of FIXNUMS, BIGNUMS, FLONUMS, and so forth, but this should not be apparent to a naive user. What the user should see is that the usual operations on numbers produce the mathematically expected results, within the limits of the implementation. Thus if the user divides the exact number 3 by the exact number 2, he should get something like 1.5 (or the exact fraction 3/2). If he adds that result to itself, and the implementation is good enough, he should get an exact 3.
Mathematically, numbers may be arranged into a tower of subtypes with projections and injections relating adjacent levels of the tower:
NUMBER
COMPLEX
REAL
RATIONAL
INTEGER
We impose a uniform rule of downward coercion — a number of one type is also of a lower type if the injection (up) of the projection (down) of a number leaves the number unchanged. Since this tower is a genuine mathematical structure, Scheme provides predicates and procedures to access the tower.
Not all implementations of Scheme must provide the whole tower, but they must implement a coherent subset consistent with both the purposes of the implementation and the spirit of the Scheme language.
Exactness
Numbers are either EXACT or INEXACT. A number is exact if it was derived from EXACT numbers using only EXACT operations. A number is INEXACT if it models a quantity known only approximately, if it was derived using INEXACT ingredients, or if it was derived using INEXACT operations. Thus INEXACTness is a contagious property of a number. Some operations, such as the square root (of non-square numbers) must be INEXACT because of the finite precision of our representations. Other operations are inexact because of implementation requirements. We emphasize that exactness is independent of the position of the number on the tower. It is perfectly possible to have an INEXACT INTEGER or an EXACT REAL; 355/113 may be an EXACT RATIONAL or it may be an INEXACT RATIONAL approximation to pi, depending on the application.
Operationally, it is the system’s responsibility to combine EXACT numbers using exact methods, such as infinite precision integer and rational arithmetic, where possible. An implementation may not be able to do this (if it does not use infinite precision integers and rationals), but if a number becomes inexact for implementation reasons there is likely to be an important error condition, such as integer overflow, to be reported. Arithmetic on INEXACT numbers is not so constrained. The system may use floating point and other ill-behaved represntation strategies for INEXACT numbers. This is not to say that implementors need not use the best known algorithms for INEXACT computations-only that approximate methods of high quality are allowed. In a system that cannot explicitly distinguish exact from inexact numbers the system must do its best to maintain precision. Scheme systems must not burden users with numerical operations described in terms of hardware and operating-system dependent representations such as FIXNUM and FLONUM, however, because these representation issues are hardly ever germane to the user’s problems.
We highly recommend that the IEEE 32-bit and 64-bit floating-point standards be adopted for implementations that use floating-point representations internally. To minimize loss of precision we adopt the following rules: If an implementation uses several different sizes of floating-point formats, the results of any operation with a floating-point result must be expressed in the largest format used to express any of the floating-point arguments to that operation. It is desirable (but not required) for potentially irrational operations such as sqrt, when applied to EXACT arguments, to produce EXACT answers whenever possible (for example the square root of an exact 4 ought to be an exact 2). If an EXACT number (or an INEXACT number represented as a FIXNUM, a BIGNUM, or a RATNUM) is operated upon so as to produce an INEXACT result (as by sqrt), and if the result is represented as a FLONUM, then the largest available FLONUM format must be used; but if the result is expressed as a RATNUM then the rational approximation must have at least as much precision as the largest available FLONUM.
Numerical operations
Scheme provides the usual set of operations for manipulating numbers. In general, numerical operations require numerical arguments. For succintness we let the following meta-symbols range over the indicated types of object in our descriptions, and we let these meta-symbols specify the types of the arguments to numeric operations. It is an error for an operation to be presented with an argument that it is not specified to handle.
obj |
any object |
z, z1, … zi, … |
complex, real, rational, integer |
x, x1, … xi, … |
real, rational, integer |
q, q1, … qi, … |
rational, integer |
n, n1, … ni, … |
integer |
(number? obj) [essential procedure]
(complex? obj) [essential procedure]
(real? obj) [essential procedure]
(rational? obj) [essential procedure]
(integer? obj) [essential procedure]
These numerical type predicates can be applied to any kind of argument. They return true if the object is of the named type. In general, if a type predicate is true of a number then all higher type predicates are also true of that number. Not every system supports all of these types; for example, it is entirely possible to have a Scheme system that has only INTEGERs. Nonetheless every implementation of Scheme must have all of these predicates.
(zero? z) [essential procedure]
(positive? x) [essential procedure]
(negative? x) [essential procedure]
(odd? n) [essential procedure]
(even? n) [essential procedure]
(exact? z) [essential procedure]
(inexact? z) [essential procedure]
These numerical predicates test a number for a particular property,
returning #!true or #!false.
(= z1 z2) [essential procedure]
(=? z1 z2) [essential procedure]
(< x1 x2) [essential procedure]
(<? x1 x2) [essential procedure]
(> x1 x2) [essential procedure]
(>? x1 x2) [essential procedure]
(<= x1 x2) [essential procedure]
(<=? x1 x2) [essential procedure]
(>= x1 x2) [essential procedure]
(>=? x1 x2) [essential procedure]
These numerical comparison predicates have redundant names (with and
without the terminal "?") to make all user populations happy. Some
implementations allow them to take many arguments, as in Common Lisp,
to facilitate range checks. These procedures return #!true if their
arguments are (respectively): numerically equal, monotonically
increasing, monotonically decreasing, monotonically nondecreasing, or
monotonically nonincreasing. Warning: On INEXACT numbers the equality
tests will give unreliable results, and the other numerical
comparisons will be useful only heuristically; when in doubt, consult
a numerical analyst.
(max x1 x2) [essential procedure]
(max x1 x2 …) [procedure]
(min x1 x2) [essential procedure]
(min x1 x2 …) [procedure]
Returns the maximum or minimum of its arguments, respectively.
(+ z1 z2) [essential procedure]
(+ z1 … ) [procedure]
(* z1 z2) [essential procedure]
(* z1 … ) [procedure]
These procedures return the sum or product of their arguments.
(+ 3 4) --> 7 (+ 3) --> 3 (+) --> 0 (* 4) --> 4 (*) --> 1
(- z1 z2) [essential procedure]
(- z1 z2 …) [procedure]
(/ z1 z2) [essential procedure]
(/ z1 z2 …) [procedure]
With two or more arguments, these procedures return the difference or (complex) quotient of their arguments, associating to the left. With one argument, however, they return the additive or multiplicative inverse of their argument.
(- 3 4) --> -1 (- 3 4 5) --> -6 (- 3) --> -3 (/ 3 4 5) --> 3/20 (/ 3) --> 1/3
(1+ z) [procedure]
(-1+ z) [procedure]
These procedures return the result of adding 1 to or subtracting 1 from their argument.
(abs z) [essential procedure]
Returns the magnitude of its argument.
(abs -7) --> 7 (abs -3+4i) --> 5
(quotient n1 n2) [essential procedure]
(remainder n1 n2) [essential procedure]
(modulo n1 n2) [procedure]
In general, these are intended to implement number-theoretic (integer) division: For positive integers n1 and n2, if n3 and n4 are integers such that
n1 = n2 * n3 + n4 and 0 < n4 < n2, then
(quotient n1 n2) --> n3 (remainder n1 n2) --> n4 (modulo n1 n2) --> n4
The value returned by quotient always has the sign of the product of its arguments. Remainder and modulo differ on negative arguments as do the Common Lisp rem and mod procedures — the remainder always has the sign of the dividend, the modulo always has the sign of the divisor:
(modulo 13 4) --> 1 (remainder 13 4) --> 1 (modulo -13 4) --> 3 (remainder -13 4) --> -1 (modulo 13 -4) --> -3 (remainder 13 -4) --> 1 (modulo -13 -4) --> -1 (remainder -13 -4) --> -1
(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) --> 1
(floor x) [procedure]
(ceiling x) [procedure]
(truncate x) [procedure]
(round x) [procedure]
(rationalize x y) [procedure]
(rationalize x) [procedure]
These procedures create integers and rationals. Their results are not EXACT-in fact, their results are clearly INEXACT, though they can be made EXACT with an explicit exactness coercion.
Floor returns the largest integer not larger than x. C*eiling returns the smallest integer not smaller than x. *Truncate returns the integer of maximal absolute value not larger than the absolute value of x. Round returns the closest integer to x, rounding to even when x is halfway between two integers. With two arguments, rationalize produces the best rational approximation to x within the tolerance specified by y. With one argument, rationalize produces the best rational approximation to x, preserving all of the precision in its representation.
(exp x) [procedure]
(log x) [procedure]
(expt _z1_ _z2_)
procedure
(sqrt
(cos z)
(tan z)
(asin z)
(acos z)
procedure
procedure
procedure
procedure
procedure
procedure
(atan _Z1_ _Z2_)
procedure
)
(sin z)
These procedures are part of every implementation that supports real
numbers. Their meanings conform with the Common Lisp standard. (Implementors should be careful of the branch cuts if complex numbers are allowed.)
(make-rectangular _z1_ _z2_)
(make-polar z3 z4)
(real-part z)
procedure
procedure
procedure
(Imag-part z)
rocedure
(magnitude z)
(angle z)
procedure
procedure
These procedures are part of every implementation that supports complex
numbers. Suppose ZI, x2, x3, and z4 are real numbers and z is a complex
number such that
z = X1 + Z21 = z3' Iz 4
Then make-rectangular and make-polar return z, real-part returns zi,
inag-part returns z2, magnitude returns z, and angle returns X4.
(exact->lnexact z)
(nexact->exact )
procedure
procedure
exact->inexact returns an INEXACT representation of z,which is a
fairly harmless thing to do. inexact->exact returns an EXACT representation of z. Since the law of 'garbage in, garbage out" remains in force,
inexact->exact should not be used casually.
,I
42
The Revised Revised Report on Scheme
Numerical Input and Output
Scheme allows all the traditional ways of writing numerical constants,
though any particular implementation may support only some of them. These
syntaxes are intended to be purely notational; any kind of number may be
written in any form that the user deems convenient. Of course, writing 1/7 as
a limited-precision decimal fraction will not express the number exactly, but
this approximate form of expression may be just what the user wants to see.
Scheme numbers are written according to the grammar described below. In
that description, z *means zero or more occurrences of z. Spaces never appear
inside a number, so all spaces in the grammar are for legibility. <empty> stands
for the empty string.
bit
-->
oct
--> 0
I 1
0
I 1 I 2 I 3
--> oct I 8 I 9
IbIc
--> dit Ia
dit
hit
IA
IC
IB
--> *b
#3B
--> #o
S0
radlxlO --> <empty> [
radix16 --> #x I #X
I 4
7
I 5 I 6
Icd
ID
I
IF
IE
radix2
radix8
exactness
precision
prefix2
d
I #D
SI
[ #1 i
I ft I #S
--> <empty>
--> <empty>
-->
"
[ #e
I #1
SE
I #L
radix2 exactness precision
radix2 precision exactness
exactness radix2 precision
exactness precision radix2
precision radix2 exactness
precision exactness radix2
prefix8
-->
radix8 exactness precision
radix8 precision exactness
exactness radix8 precision
exactness precision radix8
precision radix8 exactness
precision exactness radix8
The Revised Revised Report on Scheme
prefixlO
43
exactness precision
IradixlO precision exactness
Iexactness radixlO precision
Iexactness precision radixlO
Iprecision radixlO exactness
Iprecision exactness radixlO
->radixlO
prefixie
-
radixl6 exactness precision
IradixiC precision exactness
Iexactness radixl6 precision
Iexactness precision radixl6
Iprecision radixIG exactness
Iprecision exactness radixl6
sign -->
empty> I+
Isuffix -><empty>
I
sign dit dit*
ureal
IE sign dit dit*
bit bit* 8* suffix
Iprefix2 bit bit* 8*/bit
bit* 8*suffix
Iprefix2 . bit bit* 8*suffix
-
>prefix2
Iprefix2 bit bit*
Iprefix2 bit bit*
Iprefixe
Ipre-fix:8
IprefIx8
Iprefix8
Iprefix8
real number
->
--
.bit*
8* suffix
*.8*suffix
oct octe *
suffix
oct oct* 8*/oct oct* ** suffix
.oct oct* 8*suffix
oct oct* .oct* 8* suffix
oct oct* 8 .8*suffix
IprefixlO
IprefixlO
IprefixlO
IprefixlO
IprefIx1O
dit dits *
suffix
dit dit* 8*/dit dit* 8* suffix
.dit dit* 8*suffix
dit dit* . dit* 8* suffix
dit dit* 8*. *
suffix
IprefixIC
Iprefixl6
IprefixiS
Iprefixl6
Iprefixl6
hit hit* 8*suffix
hit hit* 8*/hit hit* 8* suffix
. hit hit* 8*suffix
hit hit* .hit* 8* suffix
hit hit* 8* *
suffix
sign ureal
> real
I real +ureal i
I real -ureal i
IrealO6 real
The conventions used to print a number can be specified by a format, as
described later in this section. The system provides a procedure, number-
44
The Revised Revised Report on Scheme
>string, that takes a number and a format and returns as a string the printed
expression of the given number in the given format.
procedure
(number->strlng mumber format)
This procedure will mostly be used by sophisticated users and in system
programs. In general, a naive user will need to know nothing about the
formats because the system printer will have reasonable default formats for
all types of NUMBERs. The system reader will construct reasonable default
numerical types for numbers expressed in each of the formats it recognizes.
If a user needs control of the coercion from strings to numbers he will use
string->number, which takes a string, an exactness, and a radix and produces
a number of the maximally precise applicable type expressed by the given
string.
procedure
(strlng->number string exactnes radix)
S(or
The exactness is a symbol, either E (or EXACT) or I (or INEXACT). The
radix is also a symbol: B (or BINARY), 0 (or OCTAL), D (or DECIMAL), and X
HEXADECIMAL). Returns a number of the maximally precise representation
expressed by the given string. It is an error if string does not express a number
according to the grammar presented above.
Formats
%
Formats may have parameters. For example, the (SCI 5 2) format specifies that a number is to be expressed in Fortran scientific format with 5
significant places and two places after the radix point.
In the following examples, the comment shows the format that was used to
produce the output shown:
%
* *d
123 .123 -123
123456789012345678901234567
355/113 4355/113 -355/113
.123.45 -123.45
3.14159265368979
; (int)
; (int); a big one!
; (rat)
; (fix 2)
; (fix 14)
3.14159265358979
; (fio 15)
123.450
-123.46e-i
123.3 123e-3
-1+21
1.261.570796
;
;
;
;
;
-123o-3
(fo 6)
(sci 5 2)
(@ci 30)
(rect (int) (int))
(polar (fix 1) (fio 7))
."!
The Revised Revised Report on Scheme
45
A numerical constant may be specified with an explicit radix by a prefix.
The prefixes are: #B (binary), #0 (octal), #D (decimal), #X (hex). A format
may specify that a number should be expressed in a particular radix. The
radix prefix may also be suppressed. For example, one may express a complex
number in polar form with the magnitude in octal and the angle in decimal
as follows:
#ol . 2#d1.670796327 ; (polar (fio 2 (radix o)) (fio (radix d)))
#ol.2Q1.570796327
; (polar (fio 2 (radix o)) (fio (radix d s)))
A numerical constant may be specified to be either EXACT or INEXACT by
a prefix. The prefixes are: #I (inexact), #E (exact). An exactness prefix may
appear before or after any radix prefix that is used. A format may specify
that a number should be expressed with an explicit exactness prefix, or it may
force the exactness to be suppressed. For example, the following are ways to
output an inexact value for pi:
#355/113
355/113
#13.1416
; (rat (exactness))
; (rat (exactness s))
; (fix 4 (exactness))
An attempt to produce more digits than are available in the internal machine
representation of a number will be marked with a "#" filling the extra digits.
This is not a statement that the implementation knows or keeps track of the
significance of a number, just that the machine will flag attempts to produce
20 digits of a number that has only 15 digits of machine representation:
"
3. 14158265358979#####
; (fio 20 (exactness a))
In systems with both single and double precision FLONUMs we may want
to specify which size we want to use to represent a constant internally. For
example, we may want a constant that has the value of pi rounded to the
single precision length, or we might want a long number that has the value
6/10. In either case, we are specifying an explicit way to represent an INEXACT number. For this purpose, we may express a number with a prefix that
indicates short or long FLONUM representation:
#S3.14159266358979
; Round to short - 3.141593
; Extend to long - .600000000000000
#L.6
Details of formats
The format of a number is a list beginning with a format descriptor,
which is a symbol such as SCI. Following the descriptor are parameters used
by that descriptor, such as the number of significant digits to be used. Default
values are supplied for any parameters that are omitted. Modifiers may appear
The Revised Revised Report on Scheme
46
next, such as the RADIX and EXACTNES descriptor. described below, which
themselves take parameters. The format descriptors are:
(INT)
Express as an integer. The radix point is implicit. If there are not
enough significant places then insignificant digits will be flagged. For example,
6.0238E23 (represented internally as a 7 digit FLONUM) would be printed as
(RAT n)
Express as a rational fraction. n specifies the largest denominator to be
used in constructing a rational approximation to the number being expressed.
If n is omitted it defaults to infinity.
(FIX n)
Express with a fixed radix point, n specifies the number of places to the
right of the radix point. ta defaults to the size of a single-precision FLONUM. If
there are not enough significant places, then insignificant digits will be flagged.
For example, 6.0238E23 (represented internally as a 7 digit FLONUM) would
be printed with a (FIX 2) format as 6023800##########
#.8
(FLO n)
Express with a floating radix point. a specifies the total number of places
to be displayed. n defaults to the size of a single-precision FLONUM. If the
number is out of range, it is converted to (SCI). (FLO H) allows the system
to express a FLO heuristically for human consumption.
(P
)
(SCI nM)
Express in exponential notation. n specifies the total number of places to
be displayed. n defaults to the size of a single-precision FLONUM. m specifies
the number of places to the right of the radix point. m defaults to n-1. (SCI
H) does heuristic expression.
(RECTr s)
Express as a rectangular form complex number. r and i are formats for
the real and imaginary parts respectively. They default to H
).
. ...
The Revised Revised Report on Scheme
47
(POLAR m a)
Express as a polar form complex number. m and a are formats for the
magnitude and angle respectively. m and a default to (HEUR).
(HEUR)
Express heuristically using the minimum number of digits required to
get an expression that when coerced back to a number produces the original
machine representation. EXACT numbers are expressed as (INT) or (RAT).
INEXACT numbers are expressed as (FLO H) or (SCI H) depending on their
range. Complex numbers are expressed in (RECT). This is the normal default
of the system printer.
The following modifiers may be added to a numerical format specification:
(EXACTNESS s)
This controls the expression of the exactness label of a number. a indicates whether the exactness is to be E (expressed) or S (suppressed). s defaults
to E. If no exactness modifier is specified for a format then the exactness is
by default not expressed.
(RADII
a)
This forces a number to be expressed in the radix r. r may be the symbol
B (binary), 0 (octal), D (decimal), or X (hex). a indicates whether the radix
label is to be E (expressed) or S (suppressed). s defaults to E. If no radix
modifier is specified then the default is decimal and the label is suppressed.
L,,.
The Revised Revised Report on Scheme
48
11.7 Characters
Characters are written using the #\ notation of Common Lisp. For example:
#\a
*\A
.\ (
lower case letter
;upper case letter
; the left parentheses as a character
; the space character
; the preferred way to write a space
; the newline character
#\space
#\newline
Characters written in the #\ notation are self-evaluating. That is, they do
not have to be quoted in programs. The #\ notation is not an essential part
of Scheme, however. Even implementations that support the #\ notation for
input do not have to support it for output, and there is no requirement that
the data type of characters be disjoint from data types such as integers or
strings.
Some of the procedures that operate on characters ignore the difference between upper case and lower case. The procedures that ignore case have the
suffix "-ci' (for *case insensitive"). If the operation is a predicate, then the
'-ci* suffix precedes the '?' at the end of the name.
(char?
obj)
[essential procedure]
Returns #!true if obj is a character, otherwise returns #!false.
(char=? char1 chart)
[essential procedure]
(char<? char1 chart)
[essential procedure]
(char>? chari char2)
[essential procedure]
(char<=? chari chart)
[essential procedure]
(char>=? charI char2)
[essential procedure]
Both chari and char2 must be characters. These procedures impose
a total ordering on the set of characters. It is guaranteed that under this
ordering:
*
The upper case characters are in order.
#\B) returns #!true.
*
*
The lower case characters are in order. For example, (char<? #\a #\b)
returns # true.
The digits are in order. For example, (char<? 8\o #\9) returns `#!true`.
*
*
Either all the digits precede all the upper case letters, or vice versa.
Either all the digits precede all the lower case letters, or vice versa.
For example, (char<?
#\A
49
The Revised Revised Report on Scheme
Some implementations may generalize these procedures to take more than two
arguments, as with the corresponding numeric predicates.
procedure
(char-ct=? charl chart)
procedure
(char-c<? charl chart)
procedure
(char-cl>? charl chart)
procedure
(char-cl<=? charl chart)
(char-ci>=? charl chart)
procedure
Both charl and chartmust be characters. These procedures are similar to
char-? et cetera, but they treat upper case and lower case letters as the same.
For example, (char-c i-? *\A #\a) returns # true. Some implementations
may generalize these procedures to take more than two arguments, as with
the corresponding arithmetic predicates.
*:
(char-upper-case?
char)
procedure
(char-lower-case? char)
procedure
(char-alphabetic? char)
procedure
(char-numeric? char)
procedure
(char-whitespace? char)
procedure
Char must be a character These procedures return # true if their arguments are upper case, lower case, alphabetic, numeric, or whitespace characters, respectively, otherwise they return `#!false`. The following remarks,
which are specific to the ASCII character set, are intended only as a guide.
The alphabetic characters are the 52 upper and lower case letters. The numeric characters are the 10 decimal digits. The whitespace characters are tab,
line feed, form feed, carriage return, and space.
(char->Integer char)
[essential procedure]
(integer->char n)
[essential procedure]
Given a character, char->integer returns an integer representation of
the character. Given an integer that is the image of a character under char>integer, Integer->char returns a character. These procedures implement
order isomorphisns between the set of characters under the char<=? ordering
and the set of integers under the <-? ordering. That is, if
(char<-? a
(<-? z g)
b)
-->
-->
`#!true`
`#!true`
and z and y.are in the range of char->integer, then
(<a? (char->integer a)
(char->integer
))
-->
#ttrue
(char<=? (integer->char z)
(integer->char y))
-->
#itrue
,4€_M
*~
%.
The Revised Revised Report on Scheme
50
(char-upcase char)
procedure
(char-dowiacase char)
procedure
char must be a character. These procedures return a character char2
such that (char-c i-? char char2). In addition, if char is alphabetic, then
the result of char-upcase is upper case and the result of char-dowucase is
lower case.
v
-
%%
-
--
The Revised Revised Report on Scheme
51
U.S. Strings
Strings are sequences of characters. In some implementations of Scheme
they are immutable; other implementations provide destructive procedures
such as string-set I that alter string objects.
Strings are written as sequences of characters enclosed within doublequotes
("). A doublequote can be written inside a string only by escaping it with a
backslash (\), as in
"The word \"Recursion\" has many different meanings."
A backslash can be written inside a string only by escaping it with another
backslash. Scheme does not specify the effect of a backslash within a string
that is not followed by a doublequote or backslash.
A string may continue from one line to the next, but this is usually a bad idea
because the exact effect varies from one computer system to another.
The length of a string is the number of characters that it contains. This
number is a non-negative integer that is fixed when the string is created. The
valid indexes of a string are the nonnegative 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.
In phrases such as "the characters of string beginning with index start and
ending with index end," it is understood that the index start is inclusive, and
the index end is exclusive. Thus if start and end are the same index, a null
substring is referred to, and if start is zero and end is the length of string,
then the entire string is referred to.
Some of the procedures that operate on strings ignore the difference between
upper and lower case. The versions that ignore case have the suffix "-ci"
(for "case insensitive"). If the operation is a predicate, then the "-ci" suffix
precedes the "?" at the end of the name.
(string?
obj)
[essential procedure]
Returns `#!true` if obi is a string, otherwise returns `#!false`.
(string-nullstring)
[essential procedure]
string must be a string. Returns #1 true if string has zero length, otherwise returns `#!false`.
.9.
.9.
52
The Revised Revised Report on Scheme
[essential procedure]
(string=? stringi string2)
procedure
(string-ci=? stringl stringf)
Returns # true if the two strings are the same length and contain the
same characters in the same positions, otherwise returns `#!false`. stringci-? treats upper and lower case letters as though they were the same character, but string-? treats upper and lower case as distinct characters.
[essential procedure]
etringi string)
-(string<?
(string>? stringl string)
(string<=? string string2)
[essential procedure]
[essential procedure]
[essential procedure]
(string>=? stringl string2)
procedure
(string-c<? stringi string2)
procedure
(string-cl>? stringi string2)
procedure
(string-ci<=? stringistring2)
procedure
(string-ci>=? stringi string2)
These procedures are the lexicographic extensions to strings of the corresponding orderings on characters. For example, string<? is the lexicographic
ordering on strings induced by the ordering char<? on characters. Some
implementations may generalize these and the string-? and string-ci?
procedures to take more than two arguments.
procedure
(make-string n)
procedure
(make-string n char)
n must be a non-negative integer, and char must be a character. Returns
a newly allocated string of length n. If char is given, then all elements of
the string are initialized to char, otherwise the contents of the string are
unspecified.
[essential procedure]
(string-length string)
Returns the number of characters in the given string.
[essential procedure]
(string-ref string n)
n must be a nonnegative integer less than the string-length of string.
Returns character n using zero-origin indexing.
[essential procedure]
(substring string start end)
string must be a string, and start and end must be valid indexes of string
with start <- end. Returns a newly allocated string formed from the characters
of string beginning with index start and ending with index end.
AL
53
The Revised Revised Report on Scheme
(string-append etringl string2)
[essential procedure]
procedure
(string-append etringi ...
)
Returns a new string whose characters form the catenation of the given
strings.
[essential procedure]
(string->llst string)
(list->string chars)
[essential procedure]
string->list returns a list of the characters that make up the given
string. list->string returns a string formed from the proper list of characters chars. string->list and list->string are inverses so far as equal?
is concerned. Implementations that provide destructive operations on strings
should ensure that the results of these procedures are newly allocated objects.
(string-set! string n char)
procedure
string must be a string, n must be a valid index of string, and char must
be a character. Stores char in element n of string and returns an unspecified
value.
(string-fll]! string char)
procedure
Stores char in every element of the given string and returns an unspecified
value.
(string-copy string)
Returns a newly allocated copy of the given string.
procedure
(substring-fl]U!
procedure
string start end char)
.
Stores char in elements start through end of the given string and returns
an unspecified value.
(substring-move-rghtl 81 ml ni 82 m2)
procedure
(substring-move-left! 81 ml ni s2 m2)
procedure
81 and 82 must be strings, ml and n1 must be valid indexes of 81 with
ml <- nl and m2 must be a valid index of 82. These procedures store the
elements ml through n1 of 81 into the string s2 starting at element m2 and
return an unspecified value.
The procedures differ only when .1 and 82 are eq? and the substring being
moved overlaps the substring being replaced. In this case, substring-moveright I copies serially, starting with the rightmost element and proceeding to
the left, while substring-move-left I begins with the leftmost element and
proceeds to the right.
L.
The Revised Revised Report on Scheme
54
11.9. Vectors
Vectors are heterogenous mutable structures whose elements are indexed
by integers. 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. 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 #(0 (2 2 2 2) "Anna")
Implementations are not required to support this notation.
Vectors are created by the constructor procedure make-vector. The elements
are accessed and assigned by the procedures vector-ref and vector-set 1.
(vector?
obj)
[essential procedure]
Returns `#!true` if obj isa vector, otherwise returns `#!false`.
(make-vector size)
(make-vector size fill)
[essential procedure]
procedure
Returns a newly allocated vector of size elements. If a second argument
is given, then each element is initialized to fidL Otherwise the initial contents
of each element is unspecified.
(vector obj
[essential procedure]
... )
Returns a newly allocated vector whose elements contain the given arguments. Analogous to list.
(vector 'a 'b 'c)
(a b c)
-->
(vector-length vec)
[essential procedure]
Returns the number of elements in the vector vec.
(vector-ref wee k)
[essential procedure]
Returns the contents of element k of the vector vec. k must be a nonnegative integer less than (vector-length wec).
(vector-ref '#(1 1 2 3 5 8 13 21) 6) -->
(vector-set! wee k obj)
8
[essential procedure]
Stores obi in element k of the vector ee. k must be a nonnegative integer
less than (vector-length wc). The value returned by vector-set I is not
.p .. .
The Revised Revised Report on Scheme
55s
specified.
(let ((vec '#(O (2 2 2 2) "Anna")))
(vector-setl vec 1 '("Sue" "Sue"))
vec)
*O
S("Sue" "Sue")
"Anna")L
(vector->list tvec)
[essential procedure]
Returns a list of the objects contained in the elements of vec. See
list->vector.
(vector-list '6 (dali dali didali))
- ->
(dali dali didali)
(llut->vector elts)
[essential procedure]
Returns a newly created vector whose elements are initialized to the
elements of the proper list cit..
(liat->vector '(dididit dali))
-->
*(dididit dali)
(vector-fill! vec fill
procedure
Stores fill in every element of the vector vec. The value returned by
vector-f ill I is not specified.
.4
..
L
rr7A
The Revised Revised Report on Scheme
56
11.10. The object table
procedure
(object-hash obj)
procedure
(object-unhash a)
obJ ect-hash associates an integer with obi in a global table and returns
obj. object-hash guarantees that distinct objects (in the sense of eq?) are
associated with distinct integers. object -unhash takes an integer and returns
the object associated with that integer if there is one, returning #tfalse
otherwise.
Rationale: obj ect-hash and obj ect-unhash can be implemented using association lists and the assq procedure, but the intent is that they be efficient
hash functions for general objects. Furthermore it is intended that the Scheme
system is free to destroy and reclaim the storage of objects that are accessible
only through the object table. It follows that object-unhash is of questionable utility, as illustrated by the following scenario.
>>> (define x (cons 0 0))
x
>>> (object-hash x)
77
>>> (set! x 0)
; garbage collection occurs for some reason
>>> (gc)
>>> (obJect-unhash 77)
ill-defined: `#!false` or (0.0)
The Revised Revised Report on Scheme
5T
11.11. Procedures
Procedures are created when lambda expressions are evaluated. Procedures do not have a standard printed representation.
The most common thing to do with a procedure is to call it with zero or more
arguments. A Scheme procedure may also be stored in data structures or
passed as an argument to procedures such as those described below.
(apply proc args)
[essential procedure]
(apply proc argl ... args)
procedure
proc must be a procedure and args must be a proper list of arguments.
The first (essential) form calls proc with the elements of arg. as the actual
arguments. The second form is a generalization of the first that calls proc
with the elements of (append (list argI ... ) args) as the actual arguments.
(apply + (list 3 4))
-->
(define compose
(lambda (f g)
(lambda args
(f (apply g args)))))
-->
((compose 1+ *) 3 4)
-->
7
unspecified
13
(map f phiet)
[essential procedure]
(map f plietl pliat2 ... )
procedure
f must be a procedure of one argument and the plists must be proper
lists. If more than one plut is given, then they should all be the same length.
Applies f element-wise to the elements of the pliuts and returns a list of the
results. The order in which j is applied to the elements of the plists is not
specified.
(map cadr '((a b) (d e) (g h)))
-->
(b e h)
(map (lambda (a) (expt n n))
'(1 2 3 4 5))
-->
(1 4 27 256 3125)
(map + '(1 2 3) '(4 5 6))
-->
(5 7 9)
(let ((count 0))
(map (lambda (ignored)
(setl count (1. count))
count)
'(a b c)))
-->
.'4
un.pecified
.
The Revised Revised Report on Scheme
(for-each f pliat)
(for-each f plisti plistf
55
[essential procedure]
procedure
... )
The arguments to for-each are like the arguments to map, but for-each
calls f for its side effects rather than for its values. Unlike map, for-each is
guaranteed to call f on the elements of the pliets in order from the first element
to the last, and the value returned by for-each is not specified.
(let ((v (make-vector 5)))
(for-each (lambda Wi)
(vector-set! v i (* i 1)))
'(0 1 2 3 4))
v)
-#(0 1 4 9 16)
(call-with-current-continuation 1)
[essential procedure]
f must be a procedure of one argument. call-with-current-continuation
packages up the current continuation (see the Rationale below) as an "escape
procedure" and passes it as an argument to f. The escape procedure is an ordinary Scheme procedure of one argument that, if it is later passed a value, will
ignore whatever continuation is in effect at that later time and will give the
value instead to the continuation that was in effect when the escape procedure
was created.
The escape procedure created by call-with-current-continuation has unlimited extent just like any other procedure in Scheme. Itmay be stored in
variables or data structures and may be called as many times as desired.
The following examples show only the most common uses of call-withcurrent-continuation. If all real programs were as simple as these examplea, there would be no need for a procedure with the power of call-withcurrent-continuation.
"-L
(call-vith-current-continuation
(lambda (exit)
(for-each (lambda (x)
(if (negative? x)
(exit x)))
'(54 0 37 -3 245 19))
*#true))
-->
-3
.V
'S
%"~'~
/
The Revised Revised Report on Scheme
59
S.
(define list-length
(lambda (obj)
(call-with-current-continuation
(lambda (return)
((rec loop (lambda (obj)
(cond ((null? obJ) 0)
((pair? obJ)
(1+ (loop (cdr obj))))
(else (return `#!false`)))))
obJ)))))
-->
list-length
(list-length '(1 2 3 4))
-->
4
(list-length '(a b . c))
-->
`#!false`
Rationale: The classic use of call-with-current-continuation isfor structured, non-local exits from loops or procedure bodies, but infact call-withcurrent-continuation is extremely useful for implementing a wide variety
of advanced control structures.
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. Ifthe expression is evaluated at top level, for
example, then the continuation will 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 top level continuation to be printed.
Normally these ubiquitous continuations are hidden behind the scenes and
programmers don't think much about them. On rare occasions, however, when
programmers need to do something fancy, then they may need to deal with
continuations explicitly, call-with-current-continuation allows Scheme
programmers to do that by creating a procedure that acts just like the current
continuation.
Most serious programming languages incorporate one or more special purpose
escape constructs with names like exit, return, or even goto. In 1965,
however, Peter Landin invented a general purpose escape operator called the
J-operator. John Reynolds described a simpler but equally powerful construct
in 1972. The catch special form described by Sussman and Steele in the 1975
report on Scheme is exactly the same as Reynolds's construct, though its name
The Revised Revised Report on Scheme
60
came from a less general construct in MacLisp. The fact that the full power
of Scheme's catch could be obtained using a procedure rather than a special
form was noticed in 1982 by the implementors of Scheme 311, and the name
call-with-current-continuation was coined later that year. Although the
name is descriptive, some people feel it is too long and have taken to calling
the procedure call/cc.
The Revised Revised Report on Scheme
61
TT.12. Ports
Ports represent input and output devices. To Scheme, an input device is
a Scheme object that can deliver characters upon command, while an output
device is a Scheme object that can accept characters.
(call-with-Input-file string proc)
[essential procedure]
(call-with-output-file string proc)
[essential procedure]
Proc is a procedure of one argument, and string is a string naming a
file. For call-with-input-file, the file must already exist; for call-withoutput-file, the effect is unspecified if the file already exists. Calls proc
with one argument: the port obtained by opening the named file for input or
output. If the file cannot be opened, an error is signalled. If the procedure
returns, then the port is closed automatically and the value yielded by the
procedure is returned. If the procedure does not return, then Scheme will not
close the port unless it can 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 escape back
in. 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-input-port
or call-with-output-port.
*
(input-port? obj)
[essential procedure]
(output-port? obj)
[essential procedure]
Returns `#!true` if obi is an input port or output port (respectively),
otherwise returns #false.
(current-nput-port)
(current-output-port)
Returns the current default input or output port.
[essential procedure]
[essential procedure]
(with-Input-from-file string thunk)
procedure
(with-output-to-file 8tring thnk)
procedure
thunk is a procedure of no arguments, and string is a string naming a file.
For with-input-from-file, the file must already exist; for with-outputto-f ile, the effect is unspecified if the file already exists. The file is opened
for input or output, an input or output port connected to it is made the
default value returned by current-input-port or current-output-port,
The Revised Revised Report on Scheme
62
and the tuk in called with no arguments. When the thunk returns, the
port is cosed and the previous default is restored. with-input-from-file
procedures
will attempt
and with-output-to-file
the value yielded by thunk Furthermore,
to return
close the
default port
in contrast to call-with-input-file and call-with-output-file,
and restore
these
the previous
default whenever the current continuation changes in such a way as to make
it doubtful that the thunk will ever return.
(open-input-file fikeame)
procedure
Takes a string naming an existing file and returns an input port capable
of delivering characters from the file. If the file cannot be opened, an error is
signalled.
(open-output-file fdename)
procedure
Takes a string naming an output file to be created and returns an output
port capable of writing characters to a new file by that name. If the file cannot
be opened, an error is signalled. If a file with the given name already exists,
the effect is unspecified.
(close-nput-port port)
procedure
(close-output-port port)
procedure
Closes the file associated with port, rendering the port incapable of delivering or accepting characters. The value returned is not specified.
V[
d!
d
e
The Revised Revised Report on Scheme
63
13.13. Input
*
The read procedure converts written representations of Scheme objects
into the objects themselves. The written representations for Scheme objects
are described in the sections devoted to the operations on those objects.
I
(eof-object? obj)
[essential procedure]
Returns * Itrue if o bj is an end of file object, otherwise returns `#!false`.
The precise set of end of file objects will vary among implementations, but in
any case no end of file object will ever be a character or an object that can
be read in using read.
(read)
[essential procedure]
(read port)
[essential procedure]
Returns the next object parsable from the given input port, updating port
to point to the first character past the end of the written representation of the
object. 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. If an end
of file is encountered after the beginning of an object's written representation,
but the written representation is incomplete and therefore not parsable, an
error is signalled. The port argument may be omitted, in which case it defaults
to the value returned by current- input -port.
Rationale: This corresponds to Common Lisp's read-preserving-white space,
but for simplicity it is never an error to encounter end of file except in the
middle of an object.
(read-char)
(read-char port)
[essential procedure]
[essential procedure]
Returns the next character available from the input port, updating the
port to point to the following character. If no more characters are available,
an end of file object is returned, port may be omitted, in which case it defaults
to the value returned by current- input -port.
(char-ready?)
procedure
(char-ready? port)
procedure
Returns 8#true if a character is ready on the input port and returns
# 1f alse otherwise. If char-ready returns `#!true` 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 `#!true`. port may be omitted, in which case it
defaults to the value returned by current -input -port.
m*
The Revised Revised Report on Scheme
*
64
Rationale: char-ready? exists to make it possible for a program to accept
characters from interactive ports without getting stuck waiting for input. Any
rubout handlers associated with such ports must ensure that characters whose
existence has been asserted by char-ready? cannot be rubbed out. If charready? were to return #1Ifalse at end of file, a port at end of file would be
indistinguishable from an interactive port that has no ready characters.
(load filename)
[essential procedure]
filename should be a string naming an existing file containing Scheme
source code. The load procedure reads expressions from the file and evaluates
them sequentially as though they had been typed interactively. It is not
specified whether the results of the expressions are printed, however. The
load procedure does not affect the values returned by current- input -port
and current -output -port. load returns an unspecified value.
Rationale: For portability load must operate on source files. Its operation on
other kinds of files necessarily varies among implementations.
O.
40%
65
The Revised Revised Report on Scheme
11.14. Output
(write obj)
[essential procedure]
(write obj port)
[essential procedure]
Writes a representation of o6j to the given port. Strings that appear in the
written representation are enclosed in doublequotes, and within those strings
backslash and doublequote characters are escaped by backslashes. write returns an unspecified value. The port argument may be omitted, in which case
it defaults to the value returned by current-output-port. See display.
(display obj)
[essential procedure]
(display obj port)
[essential procedure]
Writes a representation of obj to the given port. Strings that appear in
the written representation are not enclosed in doublequotes, and no characters
are escaped within those strings, display returns an unspecified value. The
port argument may be omitted, in which case it defaults to the value returned
by current-output-port. See write.
Rationale: Like Common Lisp's prinl and princ, write is for producing
machine-readable output and display is for producing human-readable output. Implementations that allow "slashification" within symbols will probably
want write but not display to slashify funny characters in symbols.
(newline)
[essential procedure]
(newline port)
[essential procedure]
Writes an end of line to port. Exactly how this is done differs from
one operating system to another. Returns an unspecified value. The port
argument may be omitted, in which case it defaults to the value returned by
current -output-port.
(write-char char)
[essential procedure]
(write-char char port)
[essential procedure]
Writes the character char (not a written representation of the character)
to the given port and returns an unspecified value. The port argument may be
omitted, in which case it defaults to the value returned by current-outputport.
The Revised Revised Report on Scheme
66
(transcript-on filename)
procedure
(transcript-off)
procedure
Filename must be a string naming an output file to be created. The
effect of transcript-on is to open the named file for output, and to cause a
transcript of subsequent interaction between the user and the Scheme system
to be written to the file. The transcript is ended by a call to transcriptoff, which closes the transcript file. Only one transcript may be in progress
at any time, though some implementations may relax this restriction. The
values returned by these procedures are unspecified.
Rationale: These procedures are redundant in some systems, but systems that
need them should provide them.
The Revised Revised Report on Scheme
67
-
Harold Abelson and Gerald Jay Sussman with Julie Sussman, Structure and Interpretation of Computer Programs. MIT Press, Cambridge MA, 1985.
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John Batali, Chris Hanson, Neil Mayle, Howard Shrobe, Richard M. Stallman, and Gerald Jay Sussman, The Scheme-81 Architecture — System and Chip. In Proceedings of the MIT Conference on Advanced Research in VLSI, Paul Penfield Jr [ed], Artech House, Dedham MA, 1982.
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William Clinger, The Scheme 311 Compiler: an Exercise in Denotational Semantics. In Conference Record of the 1984 ACM Symposium on Lisp and FunctionalProgramming,August 1984, pages 356-364.
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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.
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D Friedman, C Haynes, E Kohlbecker, and M Wand, Scheme 84 Interim Reference Manual. Indiana University Computer Science Technical Report 153, January 1985.
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Daniel P Friedman and Christopher T Haynes, Constraining Control. In Proceedings of the Twelfth Annual ACM Symposium on Principles of ProgrammingLanguages, January 1985, pages 245-254.
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Christopher T Haynes, Daniel P Friedman, and Mitchell Wand, Continuations and coroutines. In Conference Record of the 1984 A CM Symposium on Lisp and FunctionalProgramming,August 1984, pages 293-298.
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Peter Landin, A Correspondence Between Algol 60 and Church’s Lambda Notation: Part I. In Communications of the ACM, 8(2), February 1965, pages 89-101.
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Drew McDermott, An Efficient Environment Allocation Scheme in an Interpreter for a Lexically-scoped Lisp. In Conference Record of the 1980 Lisp Conference, August 1980, pages 154-162.
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Steven S Muchnick and Uwe F Pleban, A Semantic Comparison of Lisp and Scheme. In Conference Record of the 1980 Lisp Conference, August 1980, pages 56-64.
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MIT Scheme Manual, Seventh Edition, September 1984.
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Peter Naur et al, Revised Report on the Algorithmic Language Algol
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In Communications of the ACM, 6(1), January 1963, pages 1-17.
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Kent M Pitman, The Revised MacLisp Manual. MIT Artificial Intelligence Laboratory Technical Report 295, 21 May 1983 (Saturday Evening Edition).
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Jonathan A Rees and Norman I Adams IV, T: A Dialect of Lisp or, LAMBDA: The Ultimate Software Tool. In Proceedings of the 1982 A CM Symposium on Lisp and Functional Programming, August 1982, pages 114-122.
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Jonathan A Rees, Norman I Adams IV, and James R Meehan, The T Manual. Fourth Edition, 10 January 1984.
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John Reynolds, Definitional Interpreters for Higher Order Programming Languages. In ACM Conference Proceedings, 1972, pages 717-740.
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Richard M Staliman, Phantom Stacks-If You Look Too Hard, They Aren’t There. MIT Artificial Intelligence Memo 556, July 1980.
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Guy Lewis Steele Jr, and Gerald Jay Sussman, Lambda, the Ultimate Imperative. MIT Artificial Intelligence Memo 353, March 1976.
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Guy Lewis Steele Jr, Lambda, The Ultimate Declarative. MIT Artificial Intelligence Memo 379, November 1976.
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Guy Lewis Steele Jr, Debunking the "Expensive Procedure Call" Myth, or Procedure Call Implementations Considered Harmful, or Lambda, The Ultimate GOTO. In A CM Conference Proceedings, 1977, pages 153-162.
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Guy Lewis Steele Jr, Rabbit: a Compiler for Scheme. MIT Artificial Intelligence Laboratory Technical Report 474, May 1978.
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Guy Lewis Steele Jr, An overview of Common Lisp. In Conference Record of the 1982 ACM Symposium on Lisp and FunctionalProgramming,August 1982, pages 98-107.
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Guy Lewis Steele Jr, Common Lisp: the Language. Digital Press, 1984.
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Guy Lewis Steele Jr and Gerald Jay Sussman, The revised report on Scheme, a dialect of Lisp. MIT Artificial Intelligence Memo 452, January 1978.
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Guy Lewis Steele Jr and Gerald Jay Sussman, The Art of the Interpreter, or The Modularity Complex (Parts Zero, One, and Two). MIT Artificial Intelligence Memo 453, May 1978.
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Guy Lewis Steele Jr and Gerald Jay Sussman, Design of a Lisp>-Based Processor. In Communications of the ACM, 23(11), November 1980, pages 628-645.
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Guy Lewis Steele Jr and Gerald Jay Sussman, The Dream of a Lifetime: A Lazy Variable Extent Mechanism. In Conference Record of the 1950 Lisp Conference, August 1980, pages 163-172.
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Gerald Jay Sussman and Guy Lewis Steele Jr, Scheme: an Interpreter for Extended Lambda Calculus. MIT Artificial Intelligence Memo 349, December 1975.
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Gerald Jay Suasman, Jack Holloway, Guy Lewis Steele Jr, and Alan Bell, Scheme-79-Lisp on a chip. In IEEE Computer, 14(7), July 1981, pages 10-21.
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Mitchell Wand, Continuation-based Program Transformation Strategies. In Journal of the ACM, 27(1), 1978, pages 174-180. 31. Mitchell Wand, Continuation-based Multiprocessing. In Conference Record of the 1980 Lisp Conference, August 1978, pages 19-28.