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test-numbers.ss
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(load "mk.scm")
(load "numbers.ss")
(test-check "test 1"
(run* (q) (*o (build-num 2) (build-num 3) q))
'((0 1 1)))
(test-check "test 2"
(run* (q)
(fresh (n m)
(*o n m (build-num 6))
(== `(,n ,m) q)))
'(((1) (0 1 1)) ((0 1 1) (1)) ((0 1) (1 1)) ((1 1) (0 1))))
(test-check "sums"
(run 5 (q)
(fresh (x y z)
(pluso x y z)
(== `(,x ,y ,z) q)))
'((_.0 () _.0)
(() (_.0 . _.1) (_.0 . _.1))
((1) (1) (0 1))
((1) (0 _.0 . _.1) (1 _.0 . _.1))
((1) (1 1) (0 0 1))))
(test-check "factors"
(run* (q)
(fresh (x y)
(*o x y (build-num 24))
(== `(,x ,y ,(build-num 24)) q)))
'(((1) (0 0 0 1 1) (0 0 0 1 1))
((0 0 0 1 1) (1) (0 0 0 1 1))
((0 1) (0 0 1 1) (0 0 0 1 1))
((0 0 1) (0 1 1) (0 0 0 1 1))
((0 0 0 1) (1 1) (0 0 0 1 1))
((1 1) (0 0 0 1) (0 0 0 1 1))
((0 1 1) (0 0 1) (0 0 0 1 1))
((0 0 1 1) (0 1) (0 0 0 1 1))))
(define number-primo
(lambda (exp env val)
(fresh (n)
(== `(intexp ,n) exp)
(== `(intval ,n) val)
(not-in-envo 'numo env))))
(define sub1-primo
(lambda (exp env val)
(fresh (e n n-1)
(== `(sub1 ,e) exp)
(== `(intval ,n-1) val)
(not-in-envo 'sub1 env)
(eval-expo e env `(intval ,n))
(minuso n '(1) n-1))))
(define zero?-primo
(lambda (exp env val)
(fresh (e n)
(== `(zero? ,e) exp)
(conde
((zeroo n) (== #t val))
((poso n) (== #f val)))
(not-in-envo 'zero? env)
(eval-expo e env `(intval ,n)))))
(define *-primo
(lambda (exp env val)
(fresh (e1 e2 n1 n2 n3)
(== `(* ,e1 ,e2) exp)
(== `(intval ,n3) val)
(not-in-envo '* env)
(eval-expo e1 env `(intval ,n1))
(eval-expo e2 env `(intval ,n2))
(*o n1 n2 n3))))
(define if-primo
(lambda (exp env val)
(fresh (e1 e2 e3 t)
(== `(if ,e1 ,e2 ,e3) exp)
(not-in-envo 'if env)
(eval-expo e1 env t)
(conde
((== #t t) (eval-expo e2 env val))
((== #f t) (eval-expo e3 env val))))))
(define boolean-primo
(lambda (exp env val)
(conde
((== #t exp) (== #t val))
((== #f exp) (== #f val)))))
(define eval-expo
(lambda (exp env val)
(conde
((boolean-primo exp env val))
((number-primo exp env val))
((sub1-primo exp env val))
((zero?-primo exp env val))
((*-primo exp env val))
((if-primo exp env val))
((symbolo exp) (lookupo exp env val))
((fresh (rator rand x body env^ a)
(== `(,rator ,rand) exp)
(eval-expo rator env `(closure ,x ,body ,env^))
(eval-expo rand env a)
(eval-expo body `((,x . ,a) . ,env^) val)))
((fresh (x body)
(== `(lambda (,x) ,body) exp)
(symbolo x)
(== `(closure ,x ,body ,env) val)
(not-in-envo 'lambda env))))))
(define not-in-envo
(lambda (x env)
(conde
((fresh (y v rest)
(== `((,y . ,v) . ,rest) env)
(=/= y x)
(not-in-envo x rest)))
((== '() env)))))
(define lookupo
(lambda (x env t)
(fresh (rest y v)
(== `((,y . ,v) . ,rest) env)
(conde
((== y x) (== v t))
((=/= y x) (lookupo x rest t))))))
(test-check "push-down problems 2"
(run* (q)
(fresh (x a d)
(absento 'intval x)
(== 'intval a)
(== `(,a . ,d) x)))
'())
(test-check "push-down problems 3"
(run* (q)
(fresh (x a d)
(== `(,a . ,d) x)
(absento 'intval x)
(== 'intval a)))
'())
(test-check "push-down problems 4"
(run* (q)
(fresh (x a d)
(== `(,a . ,d) x)
(== 'intval a)
(absento 'intval x)))
'())
(test-check "push-down problems 6"
(run* (q)
(fresh (x a d)
(== 'intval a)
(== `(,a . ,d) x)
(absento 'intval x)))
'())
(test-check "push-down problems 1"
(run* (q)
(fresh (x a d)
(absento 'intval x)
(== `(,a . ,d) x)
(== 'intval a)))
'())
(test-check "push-down problems 5"
(run* (q)
(fresh (x a d)
(== 'intval a)
(absento 'intval x)
(== `(,a . ,d) x)))
'())
(test-check "zero?"
(run 1 (q)
(eval-expo `(zero? (sub1 (intexp ,(build-num 1)))) '() q))
'(#t))
(test-check "*"
(run 1 (q)
(eval-expo `(* (intexp ,(build-num 3)) (intexp ,(build-num 2))) '() `(intval ,(build-num 6))))
'(_.0))
(test-check "sub1"
(run 1 (q)
(eval-expo q '() `(intval ,(build-num 6))) (== `(sub1 (intexp ,(build-num 7))) q))
'((sub1 (intexp (1 1 1)))))
(test-check "sub1 bigger WAIT a minute"
(run 1 (q)
(eval-expo q '() `(intval ,(build-num 6)))
(== `(sub1 (sub1 (intexp ,(build-num 8)))) q))
'((sub1 (sub1 (intexp (0 0 0 1))))))
(test-check "sub1 biggest WAIT a minute"
(run 1 (q)
(eval-expo q '() `(intval ,(build-num 6)))
(== `(sub1 (sub1 (sub1 (intexp ,(build-num 9))))) q))
'((sub1 (sub1 (sub1 (intexp (1 0 0 1)))))))
(test-check "lots of programs to make a 6"
(run 12 (q) (eval-expo q '() `(intval ,(build-num 6))))
'((intexp (0 1 1)) (sub1 (intexp (1 1 1)))
(* (intexp (1)) (intexp (0 1 1)))
(* (intexp (0 1 1)) (intexp (1)))
(if #t (intexp (0 1 1)) _.0)
(* (intexp (0 1)) (intexp (1 1)))
(if #f _.0 (intexp (0 1 1)))
(sub1 (* (intexp (1)) (intexp (1 1 1))))
(((lambda (_.0) (intexp (0 1 1))) #t)
(=/= ((_.0 numo)))
(sym _.0))
(sub1 (* (intexp (1 1 1)) (intexp (1))))
(sub1 (sub1 (intexp (0 0 0 1))))
(sub1 (if #t (intexp (1 1 1)) _.0))))
(define rel-fact5
`((lambda (f)
((f f) (intexp ,(build-num 5))))
(lambda (f)
(lambda (n)
(if (zero? n)
(intexp ,(build-num 1))
(* n ((f f) (sub1 n))))))))
(test-check "rel-fact5"
(run* (q) (eval-expo rel-fact5 '() q))
`((intval ,(build-num 120))))
(test-check "rel-fact5-backwards"
(run 1 (q)
(eval-expo
`((lambda (f)
((f ,q) (intexp ,(build-num 5))))
(lambda (f)
(lambda (n)
(if (zero? n)
(intexp ,(build-num 1))
(* n ((f f) (sub1 n)))))))
'()
`(intval ,(build-num 120))))
`(f))