Assignment 5: Parameter-Passing Conventions
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empty-env extend-env apply-env make-closure apply-closure begin2
random
(define value-of
(lambda (exp env)
(match exp
[`,b #:when (boolean? b) b]
[`,n #:when (number? n) n]
[`(zero? ,n) (zero? (value-of n env))]
[`(sub1 ,n) (sub1 (value-of n env))]
[`(* ,n1 ,n2) (* (value-of n1 env) (value-of n2 env))]
[`(if ,test ,conseq ,alt) (if (value-of test env)
(value-of conseq env)
(value-of alt env))]
[`(begin2 ,e1 ,e2) (begin (value-of e1 env) (value-of e2 env))]
[`(random ,n) (random (value-of n env))]
[`,y #:when (symbol? y) (apply-env env y)]
[`(lambda (,x) ,body) (make-closure x body env)]
[`(,rator ,rand) (apply-closure (value-of rator env)
(value-of rand env))])))
Convention
Interpreter Name
val-of-cbv
val-of-cbr
val-of-cbname
val-of-cbneed
functional representation
empty-env extend-env apply-env make-closure apply-closure make-closure
make-closure val-of-cbr val-of-cbv
lambda
zero? sub1 * if begin2 set!
random
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;; Making sure set! works
> (val-of-cbr
‘((lambda (x) (begin2 (set! x #t)
(if x 3 5))) #f)
(empty-env))
3
;; Returns 4 under CBR…
> (val-of-cbr
‘((lambda (a)
((lambda (p)
(begin2
(p a)
a)) (lambda (x) (set! x 4)))) 3)
(empty-env))
4
;; …but returns 3 under CBV.
> (val-of-cbv
‘((lambda (a)
((lambda (p)
(begin2
(p a)
a)) (lambda (x) (set! x 4)))) 3)
(empty-env))
3
;; returns 44 under CBR…
(test “interesting-cbr-2”
(val-of-cbr
‘((lambda (f)
((lambda (g)
((lambda (z) (begin2
(g z) z))
55))
(lambda (y) (f y)))) (lambda (x) (set! x 44)))
(empty-env))
44)
;; …but returns 55 under CBV! You can change the “begin2” to
;; “begin” and evaluate this in the Racket REPL as evidence that
;; Racket uses CBV.
> (val-of-cbv
‘((lambda (f)
((lambda (g)
((lambda (z) (begin2
(g z)
z))
55))
(lambda (y) (f y)))) (lambda (x) (set! x 44)))
(empty-env))
55
;; Returns 44 under CBR…
> (val-of-cbr
‘((lambda (swap)
((lambda (a)
((lambda (b)
(begin2
((swap a) b)
a)) 44)) 33))
(lambda (x)
(lambda (y)
((lambda (temp)
(begin2
(set! x y)
(set! y temp))) x))))
(empty-env))
44
;; …but returns 33 under CBV.
> (val-of-cbv
‘((lambda (swap)
((lambda (a)
((lambda (b)
(begin2
((swap a) b)
a)) 44)) 33))
(lambda (x)
(lambda (y)
((lambda (temp)
(begin2
(set! x y)
(set! y temp))) x))))
(empty-env))
33
> (define random-sieve
‘((lambda (n)
(if (zero? n)
(if (zero? n) (if (zero? n) (if (zero? n) (if (zero? n) (if (zero? n) (if (zero? n) #t #f) #f) #f) #f) #f) #f)
(if (zero? n) #f (if (zero? n) #f (if (zero? n) #f (if (zero? n) #f (if (zero? n) #f (if (zero? n) #f #t))))))))
(random 2)))
;; call-by-name
;;P(false positive) <= .01
> (val-of-cbname random-sieve (empty-env))
#f
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val-of-cbv
> (define cons-test
‘(let ((fix (lambda (f)
((lambda (x) (f (lambda (v) ((x x) v))))
(lambda (x) (f (lambda (v) ((x x) v))))))))
(let ((map (fix (lambda (map)
(lambda (f)
(lambda (l)
(if (null? l)
‘()
(cons^ (f (car^ l))
((map f) (cdr^ l))))))))))
(let ((take (fix (lambda (take)
(lambda (l)
(lambda (n)
(if (zero? n)
‘()
(cons (car^ l)
((take (cdr^ l)) (sub1 n))))))))))
((take ((fix (lambda (m)
(lambda (i)
(cons^ 1 ((map (lambda (x) (add1 x))) (m i)))))) 0)) 5)))))
> (val-of-cbv cons-test (empty-env))
(1 2 3 4 5)
;; call-by-need
> (val-of-cbneed random-sieve (empty-env))
#t
;; Does not terminate with val-of-cbr or val-of-cbv — try it!
> (val-of-cbname
‘((lambda (z) 100)
((lambda (x) (x x)) (lambda (x) (x x))))
(empty-env))
100
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