This chapter describes Scheme's built-in procedures. The initial (or
"top level") Scheme environment starts out with a number of variables
bound to locations containing useful values, most of which are primitive
procedures that manipulate data. For example, the variable
bound to (a location initially containing) a procedure of one argument
that computes the absolute value of a number, and the variable
is bound to a procedure that computes sums.
The standard boolean objects for true and false are written as
#t and #f. What really
matters, though, are the objects that the Scheme conditional expressions
do) treat as
true or false. The phrase "a true value" (or
sometimes just "true") means any object treated as true by the
conditional expressions, and the phrase "a false value" (or "false")
means any object treated as false by the conditional expressions.
Of all the standard Scheme values, only #f and the empty list count as false in conditional expressions. Everything else, including #t, pairs, symbols, numbers, strings, vectors, and procedures, counts as true.
The empty list counts as false for compatibility with existing programs and implementations that assume this to be the case.
Programmers accustomed to other dialects of Lisp should beware that
Scheme distinguishes false and the empty list from the symbol
Boolean constants evaluate to themselves, so they don't need to be quoted in programs.
#t ==> #t #f ==> #f '#f ==> #f
Not returns #t if obj is false, and returns
(not #t) ==> #f (not 3) ==> #f (not (list 3)) ==> #f (not #f) ==> #t (not '()) ==> #t (not (list)) ==> #t
Boolean? returns #t if obj is either #t or
#f and returns #f otherwise.
(boolean? #f) ==> #t (boolean? 0) ==> #f
Some implementations provide variables
values in the initial environment are #f and #t
t ==> #t nil ==> #f 'nil ==> nil
A predicate is a procedure that always returns a boolean
value (#t or #f). An equivalence predicate is
the computational analogue of a mathematical equivalence relation (it is
symmetric, reflexive, and transitive). Of the equivalence predicates
described in this section,
eq? is the finest or most
equal? is the coarsest.
slightly less discriminating than
Two objects are operationally equivalent if and only if
there is no way that they can be distinguished, using Scheme primitives
eq? or those like
assv whose meaning is defined explicitly in terms of
eq?. It is guaranteed that objects maintain their operational
identity despite being named by variables or fetched from or stored into
This definition can be interpreted in the following ways for various kinds of objects:
=, section see section 6.5.4 Numerical operations) and are either both exact or both inexact (see section see section 6.5.2 Exactness).
char=?(section see section 6.6 Characters).
set-car!which alters a data structure.) For example, two pairs are not operationally equivalent if a
set-car!operation on one does not change the car field of the other.
eqv? procedure implements an approximation to the relation of
It returns #t if it can prove that obj1 and obj2
are operationally equivalent. If it can't, it always errs on the
conservative side and returns #f.
The only situation in which it might fail to prove is when obj1
and obj2 are operationally equivalent procedures that were
created at different times. In general, operational equivalence of
procedures is uncomputable, but it is guaranteed that
recognize a procedure created at a given time by a given lambda expression as
"being itself." This is useful for applications in which procedures
are being used to implement objects with local state.
(eqv? 'a 'a) ==> #t (eqv? 'a 'b) ==> #f (eqv? 2 2) ==> #t (eqv? '() '()) ==> #t (eqv? "" "") ==> #t (eqv? 100000000 100000000) ==> #t (eqv? (cons 1 2) (cons 1 2)) ==> #f (eqv? (lambda () 1) (lambda () 2)) ==> #f (eqv? #f 'nil) ==> #f (let ((p (lambda (x) x))) (eqv? p p)) ==> #t
The following examples illustrate cases in which
permitted to fail to prove operational equivalence, depending on the
implementation. (In every case, it will return either #t or
#f, but which one it returns is implementation-dependent.)
Compare with the last example in the previous set.
(eqv? (lambda (x) x) (lambda (x) x)) ==> unspecified (eqv? (lambda (x) x) (lambda (y) y)) ==> unspecified
The next set of examples shows the use of
eqv? with procedures
that have local state.
Gen-counter must return a distinct
procedure every time, since each procedure has its own internal counter.
Gen-loser, however, returns equivalent procedures each time, since
the local state does not affect the value or side effects of the
(define gen-counter (lambda () (let ((n 0)) (lambda () (set! n (+ n 1)) n)))) (let ((g (gen-counter))) (eqv? g g)) ==> #t (eqv? (gen-counter) (gen-counter)) ==> #f (define gen-loser (lambda () (let ((n 0)) (lambda () (set! n (+ n 1)) 27)))) (let ((g (gen-loser))) (eqv? g g)) ==> #t (eqv? (gen-loser) (gen-loser)) ==> unspecified
Objects of distinct types are never operationally equivalent, except that false and the empty list are permitted to be identical, and the character type need not be disjoint from other types.
(eqv? '() #f) ==> unspecified (eqv? 57 #\A) ==> unspecified
Since it is an error to modify constant objects (those returned by
literal expressions), implementations are permitted, though not
required, to share structure between constants where appropriate. Thus
the value of
eqv? on constants is sometimes
(let ((x '(a))) (eqv? x x)) ==> #t (eqv? '(a) '(a)) ==> unspecified (eqv? "a" "a") ==> unspecified (eqv? '(b) (cdr '(a b))) ==> unspecified
Note: The above definition of
eqv?allows implementations latitude in their treatment of procedures and literals: implementations are free to either detect or fail to detect that two procedures or two literals are operationally equivalent to each other, and can decide whether or not to merge representations of equivalent objects by using the same pointer or bit pattern to represent both.
Eq? is similar to
eqv? except that in some cases it is
capable of discerning distinctions finer than those detectable by
eqv? are guaranteed to have the same
behavior on symbols, booleans, the empty list, pairs, and non-empty
strings and vectors.
Eq?'s behavior on numbers and characters is
implementation-dependent, but it will always return either true or
false, and will return true only when
eqv? would also return
Eq? may also behave differently from
eqv? on empty
vectors and empty strings.
(eq? 'a 'a) ==> #t (eq? '(a) '(a)) ==> unspecified (eq? (list 'a) (list 'a)) ==> #f (eq? "a" "a") ==> unspecified (eq? "" "") ==> unspecified (eq? '() '()) ==> #t (eq? 2 2) ==> unspecified (eq? #\A #\A) ==> unspecified (eq? car car) ==> #t (let ((n (+ 2 3))) (eq? n n)) ==> unspecified (let ((x '(a))) (eq? x x)) ==> #t (let ((x '#())) (eq? x x)) ==> #t (let ((p (lambda (x) x))) (eq? p p)) ==> #t
Note: It will usually be possible to implement
eq?much more efficiently than
eqv?, for example, as a simple pointer comparison instead of as some more complicated operation. One reason is that it may not be possible to compute
eqv?of two numbers in constant time, whereas
eq?implemented as pointer comparison will always finish in constant time.
Eq?may be used like
eqv?in applications using procedures to implement objects with state since it obeys the same constraints as
eqv?. @end quotation
Equal? recursively compares the contents of pairs, vectors, and
eqv? on other objects such as numbers and symbols.
A rule of thumb is that objects are generally
equal? if they print
Equal? may fail to terminate if its arguments are
circular data structures.
(equal? 'a 'a) ==> #t (equal? '(a) '(a)) ==> #t (equal? '(a (b) c) '(a (b) c)) ==> #t (equal? "abc" "abc") ==> #t (equal? 2 2) ==> #t (equal? (make-vector 5 'a) (make-vector 5 'a)) ==> #t (equal? (lambda (x) x) (lambda (y) y)) ==> unspecified
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
The car and cdr fields are accessed by the procedures
cdr. The car and cdr fields are assigned by the procedures
Pairs are used primarily to represent lists. A list can be defined recursively as either the empty list or a pair whose cdr is a list. The objects in the car fields of successive pairs of a list are the elements of the list. For example, a two-element list is a pair whose car is the first element and whose cdr is a pair whose car is the second element and whose cdr is the empty list. The length of a list is the number of elements, which is the same as the number of pairs.
The empty list is a special object of its own type (it is not a pair); it has no elements and its length is zero.
The most general notation (external representation) for Scheme pairs is the "dotted" notation `(c1 . c2)' where c1 is the value of the car field and c2 is the value of the cdr field. For example `(4 . 5)' is a pair whose car is 4 and whose cdr is 5. Note that `(4 . 5)' is the external representation of a pair, not an expression that evaluates to a pair.
A more streamlined notation can be used for lists: the elements of the list are simply enclosed in parentheses and separated by spaces. The empty list is written () . For example,
(a b c d e)
(a . (b . (c . (d . (e . ())))))
are both representations of the same list of symbols.
A chain of pairs not ending in the empty list is called an improper list. Note that an improper list is not a list. The list and dotted notations can be combined to represent improper lists:
(a b c . d)
is equivalent to
(a . (b . (c . d)))
Whether a given pair is a list depends upon what is stored in the cdr
field. When the
set-cdr! procedure is used, an object can be a
list one moment and not the next:
(define x (list 'a 'b 'c)) (define y x) y ==> (a b c) (set-cdr! x 4) ==> unspecified x ==> (a . 4) (eqv? x y) ==> #t y ==> (a . 4)
It is often convenient to speak of a homogeneous 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
Within literal expressions and representations of objects read by the
read procedure, the forms '<datum>,
`<datum>, ,<datum>, and
,@<datum> denote two-element lists whose first elements are
unquote-splicing, respectively. The second element in each case
is <datum>. This convention is supported so that arbitrary Scheme
programs may be represented as lists.
That is, according to Scheme's grammar, every
<expression> is also a <datum> (see section see section 7.1.2 External representations).
Among other things, this permits the use of the
read procedure to
parse Scheme programs. See section 3.3 External representations.
Pair? returns #t if obj is a pair, and otherwise
(pair? '(a . b)) ==> #t (pair? '(a b c)) ==> #t (pair? '()) ==> #f (pair? '#(a b)) ==> #f
Returns a newly allocated pair whose car is obj1 and whose cdr is
obj2. The pair is guaranteed to be different (in the sense of
eqv?) from every existing object.
(cons 'a '()) ==> (a) (cons '(a) '(b c d)) ==> ((a) b c d) (cons "a" '(b c)) ==> ("a" b c) (cons 'a 3) ==> (a . 3) (cons '(a b) 'c) ==> ((a b) . c)
Returns the contents of the car field of pair. Note that it is an error to take the car of the empty list.
(car '(a b c)) ==> a (car '((a) b c d)) ==> (a) (car '(1 . 2)) ==> 1 (car '()) ==> error
Returns the contents of the cdr field of pair. Note that it is an error to take the cdr of the empty list.
(cdr '((a) b c d)) ==> (b c d) (cdr '(1 . 2)) ==> 2 (cdr '()) ==> error
Stores obj in the car field of pair.
The value returned by
set-car! is unspecified.
Stores obj in the cdr field of pair.
The value returned by
set-cdr! is unspecified.
These procedures are compositions of
caddr could be defined by
(define caddr (lambda (x) (car (cdr (cdr x))))).
Arbitrary compositions, up to four deep, are provided. There are twenty-eight of these procedures in all.
Returns #t if obj is the empty list,
otherwise returns #f. (In implementations in which the empty
list is the same as #f,
null? will return #t
if obj is #f.)
Returns a list of its arguments.
(list 'a (+ 3 4) 'c) ==> (a 7 c) (list) ==> ()
Returns the length of list.
(length '(a b c)) ==> 3 (length '(a (b) (c d e))) ==> 3 (length '()) ==> 0
Returns a list consisting of the elements of the first list followed by the elements of the other lists.
(append '(x) '(y)) ==> (x y) (append '(a) '(b c d)) ==> (a b c d) (append '(a (b)) '((c))) ==> (a (b) (c))
The resulting list is always newly allocated, except that it shares structure with the last list argument. The last argument may actually be any object; an improper list results if it is not a proper list.
(append '(a b) '(c . d)) ==> (a b c . d) (append '() 'a) ==> a
Returns a newly allocated list consisting of the elements of list in reverse order.
(reverse '(a b c)) ==> (c b a) (reverse '(a (b c) d (e (f)))) ==> ((e (f)) d (b c) a)
Returns the sublist of list obtained by omitting the first k
List-tail could be defined by
(define list-tail (lambda (x k) (if (zero? k) x (list-tail (cdr x) (- k 1)))))
Returns the kth element of list. (This is the same as the car of (list-tail list k).)
(list-ref '(a b c d) 2) ==> c
Returns the last pair in the nonempty, possibly improper, list list.
Last-pair could be defined by
(define last-pair (lambda (x) (if (pair? (cdr x)) (last-pair (cdr x)) x)))
These procedures return the first sublist of list whose car is
obj. If obj does not occur in list, #f
(n.b.: not the empty list) is returned.
compare obj with the elements of list, while
(memq 'a '(a b c)) ==> (a b c) (memq 'b '(a b c)) ==> (b c) (memq 'a '(b c d)) ==> #f (memq (list 'a) '(b (a) c)) ==> #f (member (list 'a) '(b (a) c)) ==> ((a) c) (memq 101 '(100 101 102)) ==> unspecified (memv 101 '(100 101 102)) ==> (101 102)
Alist (for "association list") must be a list of
pairs. These procedures find the first pair in alist whose car field is obj,
and returns that pair. If no pair in alist has obj as its
car, #f is returned.
eq? to compare obj
with the car fields of the pairs in alist, while
(define e '((a 1) (b 2) (c 3))) (assq 'a e) ==> (a 1) (assq 'b e) ==> (b 2) (assq 'd e) ==> #f (assq (list 'a) '(((a)) ((b)) ((c)))) ==> #f (assoc (list 'a) '(((a)) ((b)) ((c)))) ==> ((a)) (assq 5 '((2 3) (5 7) (11 13))) ==> unspecified (assv 5 '((2 3) (5 7) (11 13))) ==> (5 7)
Note: Although they are ordinarily used as predicates,
assocdo not have question marks in their names because they return useful values rather than just #t or #f.
Symbols are objects whose usefulness rests on the fact that two
symbols are identical (in the sense of
eqv?) if and only if their
names are spelled the same way. This is exactly the property needed to
represent identifiers in programs, and so most
implementations of Scheme use them internally for that purpose. Symbols
are useful for many other applications; for instance, they may be used
the way enumerated values are used in Pascal.
The rules for writing a symbol are exactly the same as the rules for writing an identifier; see sections section 2.1 Identifiers and section 7.1.1 Lexical structure.
It is guaranteed that any symbol that has been returned as part of
a literal expression, or read using the
read procedure, and
subsequently written out using the
write procedure, will read back
in as the identical symbol (in the sense of
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.
Note: Some implementations of Scheme 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 also 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.
Returns #t if obj is a symbol, otherwise returns #f.
(symbol? 'foo) ==> #t (symbol? (car '(a b))) ==> #t (symbol? "bar") ==> #f
Returns the name of symbol as a string. If the symbol was part of
an object returned as the value of a literal expression
(section see section 4.1.2 Literal expressions) or by a call to the
and its name contains alphabetic characters, then the string returned
will contain characters in the implementation's preferred standard
case--some implementations will prefer upper case, others lower case.
If the symbol was returned by
string->symbol, the case of
characters in the string returned will be the same as the case in the
string that was passed to
string->symbol. It is an error
to apply mutation procedures like
string-set! to strings returned
by this procedure.
The following examples assume that the implementation's standard case is lower case:
(symbol->string 'flying-fish) ==> "flying-fish" (symbol->string 'Martin) ==> "martin" (symbol->string (string->symbol "Malvina")) ==> "Malvina"
Returns the symbol whose name is string. This procedure can
create symbols with names containing 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
The following examples assume that the implementation's standard case is lower case:
(eq? 'mISSISSIppi 'mississippi) ==> #t (string->symbol "mISSISSIppi") ==> the symbol with name "mISSISSIppi" (eq? 'bitBlt (string->symbol "bitBlt")) ==> #f (eq? 'JollyWog (string->symbol (symbol->string 'JollyWog))) ==> #t (string=? "K. Harper, M.D." (symbol->string (string->symbol "K. Harper, M.D."))) ==> #t
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 [Pitman83] 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 representation 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 terms number, complex, real, rational, and integer for properties of the abstract numbers, the names fixnum, bignum, ratnum, and flonum for machine representations, and the names int, fix, flo, sci, rat, polar, and rect for input/output formats.
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:
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.
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 (e.g., a measurement) 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 representation 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
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.
Scheme allows 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.
The syntax of numbers is described formally in section 7.1.1 Lexical structure. See section 6.5.6 Formats for many examples of representations of numbers.
A numerical constant may be represented in binary, octal, decimal, or hex by the use of a radix prefix. The radix prefixes are `#b' (binary), `#o' (octal), `#d' (decimal), and `#x' (hex). With no radix prefix, a number is assumed to be expressed in decimal.
A numerical constant may be specified to be either exact or inexact by a prefix. The prefixes are `#e' for exact, and `#i' for inexact. An exactness prefix may appear before or after any radix prefix that is used. If the representation of a numerical constant has no exactness prefix, the constant may be assumed to be exact or inexact at the discretion of the implementation, except that integers expressed without decimal points and without use of exponential notation are assumed exact.
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:
#S3.14159265358979 Round to short --- 3.141593 #L.6 Extend to long --- .600000000000000
The reader is referred to section 1.3.3 Entry format for a summary of the naming conventions used to specify restrictions on the types of arguments to numerical routines.
These numerical type predicates can be applied to any kind of argument, including non-numbers. 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.
These numerical predicates test a number for a particular property, returning #t or #f.
Some implementations allow these procedures to take many arguments, to facilitate range checks. These procedures return #t 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.
These procedures return the maximum or minimum of their arguments.
These procedures return the sum or product of their arguments.
(+ 3 4) ==> 7 (+ 3) ==> 3 (+) ==> 0 (* 4) ==> 4 (*) ==> 1
With two or more arguments, these procedures return the difference or quotient of their arguments, associating to the left. With one argument, however, they return the additive or multiplicative inverse of their argument.
(- 3 4) ==> -1 (- 3 4 5) ==> -6 (- 3) ==> -3 (/ 3 4 5) ==> 3/20 (/ 3) ==> 1/3
Abs returns the magnitude of its argument.
(abs -7) ==> 7 (abs -3+4i) ==> 5
These are intended to implement number-theoretic (integer) division: For positive integers n1 and n2, if n3 and n4 are integers such that n1=n2n3+n4 and 0<= n4<n2, then
(quotient n1 n2) ==> n3 (remainder n1 n2) ==> n4 (modulo n1 n2) ==> n4
For all integers n1 and n2 with n2 not equal to 0,
(= n1 (+ (* n2 (quotient n1 n2)) (remainder n1 n2))) ==> #t
The value returned by
quotient always has the sign of the product of
modulo differ on negative arguments--the
remainder always has the sign of the dividend, the
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
These procedures return the numerator or denominator of their argument.
(numerator (/ 6 4)) ==> 3 (denominator (/ 6 4)) ==> 2
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
These procedures create integers and rationals. Their results are exact if and only if their arguments are exact.
Floor returns the largest integer not larger than x.
Ceiling 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 rational
number with smallest denominator differing from x by no more than
y. With one argument,
rationalize produces the best rational
approximation to x, preserving all of the precision in its
Roundrounds to even for consistency with the rounding modes required by the IEEE floating point standard.
These procedures are part of every implementation that supports real
numbers; they compute the usual transcendental functions.
computes the natural logarithm of z (not the base 10 logarithm).
atan compute arcsine (sin^-1),
arccosine (cos^-1), and arctangent (tan^-1), respectively.
The two-argument variant of
atan computes (angle
(make-rectangular x y)) (see below), even in implementations
that don't support complex numbers.
In general, the mathematical functions log, arcsine, arccosine, and arctangent are multiply defined. For nonzero real x, the value of log x is defined to be the one whose imaginary part lies in the range -pi (exclusive) to pi (inclusive). log 0 is undefined. The value of log z when z is complex is defined according to the formula
log z = log magnitude(z) + i --> angle (z)
With log defined this way, the values of sin^-1 z, cos^-1 z, and tan^-1 z are according to the following formulae:
sin^-1 z = -i log (i z + sqrt1 - z^2)
cos^-1 z = -i log (z + i sqrt1 - z^2)
tan^-1 z = -i log ( (1 + i z) sqrt1/(1 + z^2) )
The above specification follows [CLtL], which in turn follows [Penfield81]; refer to these sources for more detailed discussion of branch cuts, boundary conditions, and implementation of these functions.
Returns the principal square root of z. The result will have either positive real part, or zero real part and non-negative imaginary part.
Returns z1 raised to the power z2:
z_1^z_2 = e^z_2 log z_1
0^0 is defined to be equal to 1.
These procedures are part of every implementation that supports complex numbers. Suppose x1, x2, x3, and x4 are real numbers and z is a complex number such that
z = x1 + x2i = x3 . e^i x4
make-polar return z,
real-part returns x1,
imag-part returns x2,
magnitude returns x3, and
angle returns x4.
In the case of
angle, whose value is not uniquely determined by
the preceding rule, the value returned will be the one in the range
-pi (exclusive) to pi (inclusive).
Magnitudeis the same as
absmust be present in all implementations, whereas
magnitudewill only be present in implementations that support complex numbers.
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
The conventions used to produce the printed representation of a number can
be specified by a format, as described in section 6.5.6 Formats.
number->string takes a
number and a format and returns as a string the printed representation of
the given number in the given 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
The system reader will construct reasonable default numerical types for
numbers expressed in each of the formats it recognizes. A user who
needs control of the coercion from strings to numbers will use
Exactness must be a symbol, either `E' (for exact) or `I' (for inexact). Radix must also be a symbol: `B' for
binary, `O' for octal, `D' for decimal, and `X' for
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 in section 7.1.1 Lexical structure.
A format 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 after the parameters, such as the `radix' and `exactness' formats described below, which themselves take parameters.
Details of particular formats such as sci and fix are given in section 6.5.7 Details of formats.
For example, the format `(sci 5 2 (exactness s))' specifies that a number is to be expressed in Fortran scientific format with 5 significant places and two places after the radix point, and that its exactness prefix is to be suppressed.
In the following examples, the comment shows the format that was used to produce the output shown:
123 +123 -123 ; (int) 123456789012345678901234567 ; (int) 355/113 +355/113 -355/113 ; (rat) +123.45 -123.45 ; (fix 2) 3.14159265358979 ; (fix 14) 3.14159265358979 ; (flo 15) 123.450 ; (flo 6) -123.45e-1 ; (sci 5 2) 123e3 123e-3 -123e-3 ; (sci 3 0) -1+2i ; (rect (int) (int)) email@example.com ; (polar (fix 1) ; (flo 7))
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:
#o1.2@#d1.570796327 ; (polar (flo 2 (radix o)) ; (flo (radix d))) #firstname.lastname@example.org ; (polar (flo 2 (radix o)) ; (flo (radix d s)))
A format may specify that a number should be expressed with an explicit exactness prefix ((exactness e)), or it may force the exactness to be suppressed ((exactness s)). For example, the following are ways to express an inexact value for pi:
#i355/113 ; (rat (exactness e)) 355/113 ; (rat (exactness s)) #i3.1416 ; (fix 4 (exactness e))
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##### ; (flo 20 (exactness s))
The format descriptors are:
Express as an integer. The radix point is implicit. If there are not enough significant places then insignificant digits will be flagged. For example, an inexact integer 6.0238.10^23 (represented internally as a 7 digit flonum) would be printed as
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.
Express with a fixed radix point. n specifies the number of places to the right of the radix point. n defaults to the size of a single-precision flonum. If there are not enough significant places, then insignificant digits will be flagged. For example, an inexact 6.0238.10^23 (represented internally as a 7 digit flonum) would be printed with a (fix 2) format as
Express with a floating radix point. n 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) expresses n in floating point format heuristically for human consumption.
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.
Express as a rectangular form complex number. r and i are formats for the real and imaginary parts respectively. They default to (heur).
Express as a polar form complex number. m and a are formats for the magnitude and angle respectively. m and a default to (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:
This controls the expression of the exactness prefix of a number. s must be a symbol, either E or S, indicating whether the exactness is to be expressed or suppressed, respectively. If no exactness modifier is specified for a format then the exactness is by default suppressed.
This forces a number to be expressed in the radix r. r may be the symbol B (binary), O (octal), D (decimal), or X (hex). s must be a symbol, either E or S, indicating whether the radix prefix is to be expressed or suppressed, respectively. s defaults to E (expressed). If no radix modifier is specified then the default is decimal and the prefix is suppressed.
Characters are objects that represent printed characters such as letters and digits. There is no requirement that the data type of characters be disjoint from other data types; implementations are encouraged to have a separate character data type, but may choose to represent characters as integers, strings, or some other type.
Characters are written using the notation #\<character> or #\<character name>. For example:
- ; lower case letter
- ; upper case letter
- ; left parenthesis
- ; the space character
- ; the preferred way to write a space
- ; the newline character
Case is significant in #\<character>, but not in #\<character name>. If <character> in #\<character> is alphabetic, then the character following <character> must be a delimiter character such as a space or parenthesis. This rule resolves the ambiguous case where, for example, the sequence of characters "#\ space" could be taken to be either a representation of the space character or a representation of the character "#\ s" followed by a representation of the symbol "pace."
Characters written in the #\ notation are self-evaluating. That is, they do not have to be quoted in programs. 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.
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.
Returns #t if obj is a character, otherwise returns #f.
These procedures impose a total ordering on the set of characters. It is guaranteed that under this ordering:
Some implementations may generalize these procedures to take more than two arguments, as with the corresponding numeric predicates.
These procedures are similar to
char=? et cetera, but they treat
upper case and lower case letters as the same. For example, `(char-ci=? #\A #\a)' returns #t. Some
implementations may generalize these procedures to take more than two
arguments, as with the corresponding numeric predicates.
These procedures return #t if their arguments are alphabetic, numeric, or whitespace characters, respectively, otherwise they return #f. 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 ten decimal digits. The whitespace characters are space, tab, line feed, form feed, and carriage return.
Letter must be an alphabetic character. These procedures return #t if their arguments are upper case or lower case characters, respectively, otherwise they return #f.
Given a character,
char->integer returns an integer
representation of the character. Given an integer that is the image of
a character under
returns a character. These procedures implement order isomorphisms
between the set of characters under the
char<=? ordering and some
subset of the integers under the
<= ordering. That is, if
(char<=? a b) => #t and (<= x y) => #t
and x and y are in the range of
(<= (char->integer a) (char->integer b)) ==> #t (char<=? (integer->char x) (integer->char y)) ==> #t
These procedures return a character char2 such that `(char-ci=? char char2)'. In addition, if char is
alphabetic, then the result of
char-upcase is upper case and the
char-downcase is lower case.
Strings are sequences of characters. In some implementations of Scheme
they are immutable; other implementations provide destructive procedures
string-set! 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 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 may vary 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 exact non-negative integers less than the length of the string. The first character of a string has index 0, the second has index 1, and so on.
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.
Returns #t if obj is a string, otherwise returns #f.
k must be a non-negative integer, and char must be
Make-string returns a newly allocated string of
length k. If char is given, then all elements of the string
are initialized to char, otherwise the contents of the
string are unspecified.
Returns the number of characters in the given string.
k must be a valid index of string.
String-ref returns character k of string using zero-origin indexing.
k must be a valid index of string
String-set! stores char in element k of string
and returns an unspecified value.
Returns #t if the two strings are the same length and contain the same
characters in the same positions, otherwise returns #f.
upper and lower case letters as though they were the same character, but
string=? treats upper and lower case as distinct characters.
These procedures are the lexicographic extensions to strings of the
corresponding orderings on characters. For example,
the lexicographic ordering on strings induced by the ordering
char<? on characters. If two strings differ in length but
are the same up to the length of the shorter string, the shorter string
is considered to be lexicographically less than the longer string.
Implementations may generalize these and the
string-ci=? procedures to take more than two arguments, as with
the corresponding numeric predicates.
String must be a string, and start and end must be exact integers satisfying
0 <= start <= end <= (string-length string).
Substring returns a newly allocated string formed from the characters of
string beginning with index start (inclusive) and ending with index
Returns a new string whose characters form the concatenation of the given strings.
String->list returns a newly allocated list of the
characters that make up the given string.
returns a string formed from the characters in the list chars.
list->string are inverses so
equal? is concerned. Implementations that provide
destructive operations on strings should ensure that the result of
list->string is newly allocated.
Returns a newly allocated copy of the given string.
Stores char in every element of the given string and returns an unspecified value.
Vectors are heterogenous mutable structures whose elements are indexed by integers.
The length of a vector is the number of elements that it contains. This number is a non-negative integer that is fixed when the vector is created. The valid indexes of a vector are the exact non-negative integers less than the length of the vector. The first element in a vector is indexed by zero, and the last element is indexed by one less than the length of the vector.
Vectors are written using the notation #(obj ...). For example, a vector of length 3 containing the number zero in element 0, the list `(2 2 2 2)' in element 1, and the string `"Anna"' in element 2 can be written as following:
#(0 (2 2 2 2) "Anna")
Note that this is the external representation of a vector, not an expression evaluating to a vector. Like list constants, vector constants must be quoted:
'#(0 (2 2 2 2) "Anna") ==> #(0 (2 2 2 2) "Anna")
Returns a newly allocated vector of k elements. If a second argument is given, then each element is initialized to fill. Otherwise the initial contents of each element is unspecified.
Returns a newly allocated vector whose elements contain the given
arguments. Analogous to
(vector 'a 'b 'c) ==> #(a b c)
Returns the number of elements in vector.
k must be a valid index of vector.
Vector-ref returns the contents of element k of
(vector-ref '#(1 1 2 3 5 8 13 21) 5) => 8
k must be a valid index of vector.
Vector-set! stores obj in element k of vector.
The value returned by
vector-set! is unspecified.
(let ((vec (vector 0 '(2 2 2 2) "Anna"))) (vector-set! vec 1 '("Sue" "Sue")) vec) ==> #(0 ("Sue" "Sue") "Anna")
Vector->list returns a newly created list of the objects contained
in the elements of vector.
List->vector returns a newly
created vector initialized to the elements of the list list.
(vector->list '#(dah dah didah)) ==> (dah dah didah) (list->vector '(dididit dah)) ==> #(dididit dah)
Stores fill in every element of vector.
The value returned by
vector-fill! is unspecified.
This chapter describes various primitive procedures which control the
flow of program execution in special ways.
procedure? predicate is also described here.
Returns #t if obj is a procedure, otherwise returns #f.
(procedure? car) ==> #t (procedure? 'car) ==> #f (procedure? (lambda (x) (* x x))) ==> #t (procedure? '(lambda (x) (* x x))) ==> #f (call-with-current-continuation procedure?) ==> #t
Proc must be a procedure and args must be a list. The first (essential) form calls proc with the elements of args as the actual arguments. The second form is a generalization of the first that calls proc with the elements of the list `(append (list arg1 ...) args)' as the actual arguments.
(apply + (list 3 4)) ==> 7 (define compose (lambda (f g) (lambda args (f (apply g args))))) ((compose sqrt *) 12 75) ==> 30
The lists must be lists, and proc must be a
procedure taking as many arguments as there are lists. If more
than one list is given, then they must all be the same length.
Map applies proc element-wise to the elements of the
lists and returns a list of the results. The order in which
proc is applied to the elements of the lists is unspecified.
(map cadr '((a b) (d e) (g h))) ==> (b e h) (map (lambda (n) (expt n n)) '(1 2 3 4 5)) ==> (1 4 27 256 3125) (map + '(1 2 3) '(4 5 6)) ==> (5 7 9) (let ((count 0)) (map (lambda (ignored) (set! count (+ count 1)) count) '(a b c))) ==> unspecified
The arguments to
for-each are like the arguments to
for-each calls proc for its side effects rather than for its
for-each is guaranteed to call proc on
the elements of the lists in order from the first element to the
last, and the value returned by
for-each is unspecified.
(let ((v (make-vector 5))) (for-each (lambda (i) (vector-set! v i (* i i))) '(0 1 2 3 4)) v) ==> #(0 1 4 9 16)
Forces the value of promise (see
section see section 4.2.5 Delayed evaluation). If no value has been computed for
the promise, then a value is computed and returned. The value of the
promise is cached (or "memoized") so that if it is forced a second
time, the previously computed value is returned without any
(force (delay (+ 1 2))) ==> 3 (let ((p (delay (+ 1 2)))) (list (force p) (force p))) ==> (3 3) (define a-stream (letrec ((next (lambda (n) (cons n (delay (next (+ n 1))))))) (next 0))) (define head car) (define tail (lambda (stream) (force (cdr stream)))) (head (tail (tail a-stream))) ==> 2
delay are mainly intended for programs written in
functional style. The following examples should not be considered to
illustrate good programming style, but they illustrate the property that
the value of a promise is computed at most once.
(define count 0) (define p (delay (begin (set! count (+ count 1)) (* x 3)))) (define x 5) count ==> 0 p ==> a promise (force p) ==> 15 p ==> a promise, still count ==> 1 (force p) ==> 15 count ==> 1
Here is a possible implementation of
define the expression
to have the same meaning as the procedure call
(make-promise (lambda () <expression>)),
make-promise is defined as follows:
(define make-promise (lambda (proc) (let ((already-run? #f) (result #f)) (lambda () (cond ((not already-run?) (set! result (proc)) (set! already-run? #t))) result))))
Promises are implemented here as procedures of no arguments,
force simply calls its argument.
(define force (lambda (object) (object)))
Various extensions to this semantics of
are supported in some implementations:
forceon an object that is not a promise may simply return the object.
(eqv? (delay 1) 1) ==> unspecified (pair? (delay (cons 1 2))) ==> unspecified
(+ (delay (* 3 7)) 13) ==> 34
Proc must be a procedure of one
argument. The procedure
up the current continuation (see the rationale below) as an "escape
procedure" and passes it as an argument to
proc. The escape procedure is a Scheme procedure 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
The escape procedure created by
unlimited extent just like any other procedure in Scheme. It may 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-with-current-continuation. If all real programs were as
simple as these examples, there would be no need for a procedure with
the power of
(call-with-current-continuation (lambda (exit) (for-each (lambda (x) (if (negative? x) (exit x))) '(54 0 37 -3 245 19)) #t)) ==> -3 (define list-length (lambda (obj) (call-with-current-continuation (lambda (return) (letrec ((r (lambda (obj) (cond ((null? obj) 0) ((pair? obj) (+ (r (cdr obj)) 1)) (else (return #f)))))) (r obj)))))) (list-length '(1 2 3 4)) ==> 4 (list-length '(a b . c)) ==> #f
Rationale: A common use of
call-with-current-continuationis for structured, non-local exits from loops or procedure bodies, but in fact
call-with-current-continuationis 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. If the 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, a programmer may need to deal with continuations explicitly.
Call-with-current-continuationallows Scheme programmers to do that by creating a procedure that acts just like the current continuation.
Most programming languages incorporate one or more special-purpose escape constructs with names like exit,
return, or even goto. In 1965, however, Peter Landin [Landin65] invented a general purpose escape operator called the J-operator. John Reynolds [Reynolds72] described a simpler but equally powerful construct in 1972. The
catchspecial form described by Sussman and Steele in the 1975 report on Scheme is exactly the same as Reynolds's construct, though its name came from a less general construct in MacLisp. Several Scheme implementors noticed that the full power of the
catchconstruct could be provided by a procedure instead of by a special syntactic construct, and the name
call-with-current-continuationwas coined in 1982. This name is descriptive, but opinions differ on the merits of such a long name, and some people use the name
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.
Proc should be a procedure of one argument, and
string should be a string naming a file. For
call-with-input-file, the file must already exist; for
call-with-output-file, the effect is unspecified if the file
already exists. These procedures call 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
Returns #t if obj is an input port or output port respectively, otherwise returns #f.
Thunk must be a procedure of no arguments, and
string must be a string naming a file. For
with-input-from-file, the file must already exist; for
with-output-to-file, 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-output-port, and the
thunk is called with no arguments. When the thunk returns,
the port is closed and the previous default is restored.
with-output-to-file return the
value yielded by thunk.
If an escape procedure
is used to escape from the continuation of these procedures, their
behavior is implementation dependent.
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.
Closes the file associated with port, rendering the port incapable of delivering or accepting characters.
These routines have no effect if the file has already been closed. The value returned is unspecified.
Read converts written representations of Scheme objects into the
objects themselves. That is, it is a parser for the nonterminal
<datum> (see section see section 7.1.2 External representations).
Read 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. The port remains open, and further attempts to read will also return an end of file object. If an end of file is encountered after the beginning of an object's 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. It is an error to read from
a closed port.
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
Returns #t if a character is ready on the input port and
returns #f otherwise. If
char-ready returns #t then
read-char operation on the given port is guaranteed
not to hang. If the port is at end of file then
returns #t. Port may be omitted, in which case it defaults to
the value returned by
Char-ready?exists to make it possible for a program to accept characters from interactive ports without getting stuck waiting for input. Any input editors associated with such ports must ensure that characters whose existence has been asserted by
char-ready?cannot be rubbed out. If
char-ready?were to return #f at end of file, a port at end of file would be indistinguishable from an interactive port that has no ready characters.
Returns #t if obj is an end of file object, otherwise returns
#f. The precise set of end of file objects will vary among
implementations, but in any case no end of file object will ever be a
character or an object that can be read in using
Writes a representation of obj 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
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. In
those implementations that have a distinct character type, character
objects appear in the representation as if written by
instead of by
Display returns an unspecified value.
The port argument may be omitted, in which case it defaults to the
value returned by
Writeis intended for producing machine-readable output and
displayis for producing human-readable output. Implementations that allow "slashification" within symbols will probably want
displayto slashify funny characters in symbols.
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
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
Questions of user interface generally fall outside of the domain of this report. However, the following operations are important enough to deserve description here.
Filename should be a string naming an existing file
containing Scheme source code. The
load procedure reads
expressions and definitions from the file and evaluates them
sequentially. It is unspecified whether the results of the expressions
are printed. The
load procedure does not affect the values
Load returns an unspecified value.
Note: For portability,
loadmust operate on source files. Its operation on other kinds of files necessarily varies among implementations.
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
transcript-off, 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.