# Chapter 19R5RS compatibility

The features described in this chapter are exported from the (rnrs r5rs (6))library and provide some functionality of the preceding revision of this report [7] that was omitted from the main part of the current report.

(exact->inexact z)    procedure
(inexact->exact z)    procedure

These are the same as the inexact and exact procedures; see report section on “Generic conversions”.

(quotient n1 n2)    procedure
(remainder n1 n2)    procedure
(modulo n1 n2)    procedure

These procedures implement number-theoretic (integer) division. n2 must be non-zero. All three procedures return integers. If n1/n2 is an integer:

(quotient n1 n2)           ⇒ n1/n2
(remainder n1 n2)          ⇒ 0
(modulo n1 n2)             ⇒ 0

If n1/n2 is not an integer:

(quotient n1 n2)           ⇒ nq
(remainder n1 n2)          ⇒ nr
(modulo n1 n2)             ⇒ nm

where nq is n1/n2 rounded towards zero, 0 < |nr| < |n2|, 0 < |nm| < |n2|, nr and nm differ from n1 by a multiple of n2, nr has the same sign as n1, and nm has the same sign as n2.

Consequently, for integers n1 and n2 with n2 not equal to 0,

(= n1 (+ (* n2 (quotient n1 n2))
(remainder n1 n2)))
⇒  #t

provided all numbers involved in that computation are exact.

(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

(remainder -13 -4.0)            ⇒  -1.0  ; inexact

Note:   These procedures could be defined in terms of div and mod (see report section on “Arithmetic operations”) as follows (without checking of the argument types): (define (sign n)
(cond
((negative? n) -1)
((positive? n) 1)
(else 0)))

(define (quotient n1 n2)
(* (sign n1) (sign n2) (div (abs n1) (abs n2))))

(define (remainder n1 n2)
(* (sign n1) (mod (abs n1) (abs n2))))

(define (modulo n1 n2)
(* (sign n2) (mod (* (sign n2) n1) (abs n2))))

(delay <expression>)    syntax

The delay construct is used together with the procedure force to implement lazy evaluation or call by need. (delay <expression>) returns an object called a promise which at some point in the future may be asked (by the force procedure) to evaluate <expression>, and deliver the resulting value. The effect of <expression> returning multiple values is unspecified.

(force promise)    procedure

Promise must be a promise.

Forces the value of promise. 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.

(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 tail
(lambda (stream) (force (cdr stream))))

⇒  2

Promises 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 only one value is computed for a promise, no matter how many times it is forced.

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

Here is a possible implementation of delay and force. Promises are implemented here as procedures of no arguments, and force simply calls its argument:

(define force
(lambda (object)
(object)))

The expression

(delay <expression>)

has the same meaning as the procedure call

(make-promise (lambda () <expression>))

as follows

(define-syntax delay
(syntax-rules ()
((delay expression)
(make-promise (lambda () expression))))),

where make-promise is defined as follows:

(define make-promise
(lambda (proc)
(result #f))
(lambda ()
result
(let ((x (proc)))
result