569 lines
19 KiB
Scheme
569 lines
19 KiB
Scheme
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;;; BOYER -- Logic programming benchmark, originally written by Bob Boyer.
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;;; Fairly CONS intensive.
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(define (lookup key table)
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(let loop ((x table))
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(if (null? x)
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#f
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(let ((pair (car x)))
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(if (eq? (car pair) key)
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pair
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(loop (cdr x)))))))
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(define properties '())
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(define (get key1 key2)
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(let ((x (lookup key1 properties)))
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(if x
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(let ((y (lookup key2 (cdr x))))
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(if y
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(cdr y)
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#f))
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#f)))
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(define (put key1 key2 val)
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(let ((x (lookup key1 properties)))
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(if x
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(let ((y (lookup key2 (cdr x))))
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(if y
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(set-cdr! y val)
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(set-cdr! x (cons (cons key2 val) (cdr x)))))
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(set! properties
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(cons (list key1 (cons key2 val)) properties)))))
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(define unify-subst '())
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(define (add-lemma term)
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(cond ((and (pair? term)
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(eq? (car term)
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(quote equal))
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(pair? (cadr term)))
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(put (car (cadr term))
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(quote lemmas)
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(cons term (get (car (cadr term)) (quote lemmas)))))
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(else (fatal-error "ADD-LEMMA did not like term: " term))))
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(define (add-lemma-lst lst)
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(cond ((null? lst)
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#t)
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(else (add-lemma (car lst))
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(add-lemma-lst (cdr lst)))))
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(define (apply-subst alist term)
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(cond ((not (pair? term))
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(cond ((assq term alist) => cdr)
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(else term)))
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(else (cons (car term)
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(apply-subst-lst alist (cdr term))))))
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(define (apply-subst-lst alist lst)
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(cond ((null? lst)
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'())
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(else (cons (apply-subst alist (car lst))
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(apply-subst-lst alist (cdr lst))))))
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(define (falsep x lst)
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(or (equal? x (quote (f)))
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(member x lst)))
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(define (one-way-unify term1 term2)
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(begin (set! unify-subst '())
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(one-way-unify1 term1 term2)))
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(define (one-way-unify1 term1 term2)
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(cond ((not (pair? term2))
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(cond ((assq term2 unify-subst) =>
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(lambda (x) (equal? term1 (cdr x))))
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(else (set! unify-subst (cons (cons term2 term1)
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unify-subst))
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#t)))
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((not (pair? term1))
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#f)
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((eq? (car term1)
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(car term2))
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(one-way-unify1-lst (cdr term1)
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(cdr term2)))
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(else #f)))
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(define (one-way-unify1-lst lst1 lst2)
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(cond ((null? lst1)
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#t)
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((one-way-unify1 (car lst1)
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(car lst2))
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(one-way-unify1-lst (cdr lst1)
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(cdr lst2)))
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(else #f)))
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(define (rewrite term)
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(cond ((not (pair? term))
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term)
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(else (rewrite-with-lemmas (cons (car term)
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(rewrite-args (cdr term)))
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(get (car term)
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(quote lemmas))))))
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(define (rewrite-args lst)
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(cond ((null? lst)
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'())
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(else (cons (rewrite (car lst))
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(rewrite-args (cdr lst))))))
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(define (rewrite-with-lemmas term lst)
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(cond ((or (not lst) (null? lst))
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term)
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((one-way-unify term (cadr (car lst)))
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(rewrite (apply-subst unify-subst (caddr (car lst)))))
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(else (rewrite-with-lemmas term (cdr lst)))))
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(define (setup)
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(add-lemma-lst
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(quote ((equal (compile form)
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(reverse (codegen (optimize form)
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(nil))))
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(equal (eqp x y)
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(equal (fix x)
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(fix y)))
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(equal (greaterp x y)
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(lessp y x))
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(equal (lesseqp x y)
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(not (lessp y x)))
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(equal (greatereqp x y)
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(not (lessp x y)))
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(equal (boolean x)
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(or (equal x (t))
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(equal x (f))))
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(equal (iff x y)
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(and (implies x y)
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(implies y x)))
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(equal (even1 x)
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(if (zerop x)
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(t)
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(odd (_1- x))))
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(equal (countps- l pred)
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(countps-loop l pred (zero)))
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(equal (fact- i)
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(fact-loop i 1))
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(equal (reverse- x)
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(reverse-loop x (nil)))
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(equal (divides x y)
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(zerop (remainder y x)))
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(equal (assume-true var alist)
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(cons (cons var (t))
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alist))
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(equal (assume-false var alist)
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(cons (cons var (f))
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alist))
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(equal (tautology-checker x)
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(tautologyp (normalize x)
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(nil)))
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(equal (falsify x)
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(falsify1 (normalize x)
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(nil)))
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(equal (prime x)
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(and (not (zerop x))
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(not (equal x (add1 (zero))))
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(prime1 x (_1- x))))
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(equal (and p q)
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(if p (if q (t)
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(f))
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(f)))
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(equal (or p q)
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(if p (t)
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(if q (t)
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(f))
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(f)))
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(equal (not p)
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(if p (f)
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(t)))
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(equal (implies p q)
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(if p (if q (t)
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(f))
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(t)))
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(equal (fix x)
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(if (numberp x)
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x
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(zero)))
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(equal (if (if a b c)
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d e)
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(if a (if b d e)
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(if c d e)))
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(equal (zerop x)
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(or (equal x (zero))
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(not (numberp x))))
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(equal (plus (plus x y)
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z)
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(plus x (plus y z)))
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(equal (equal (plus a b)
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(zero))
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(and (zerop a)
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(zerop b)))
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(equal (difference x x)
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(zero))
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(equal (equal (plus a b)
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(plus a c))
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(equal (fix b)
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(fix c)))
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(equal (equal (zero)
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(difference x y))
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(not (lessp y x)))
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(equal (equal x (difference x y))
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(and (numberp x)
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(or (equal x (zero))
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(zerop y))))
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(equal (meaning (plus-tree (append x y))
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a)
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(plus (meaning (plus-tree x)
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a)
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(meaning (plus-tree y)
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a)))
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(equal (meaning (plus-tree (plus-fringe x))
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a)
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(fix (meaning x a)))
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(equal (append (append x y)
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z)
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(append x (append y z)))
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(equal (reverse (append a b))
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(append (reverse b)
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(reverse a)))
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(equal (times x (plus y z))
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(plus (times x y)
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(times x z)))
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(equal (times (times x y)
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z)
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(times x (times y z)))
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(equal (equal (times x y)
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(zero))
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(or (zerop x)
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(zerop y)))
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(equal (exec (append x y)
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pds envrn)
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(exec y (exec x pds envrn)
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envrn))
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(equal (mc-flatten x y)
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(append (flatten x)
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y))
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(equal (member x (append a b))
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(or (member x a)
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(member x b)))
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(equal (member x (reverse y))
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(member x y))
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(equal (length (reverse x))
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(length x))
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(equal (member a (intersect b c))
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(and (member a b)
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(member a c)))
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(equal (nth (zero)
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i)
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(zero))
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(equal (exp i (plus j k))
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(times (exp i j)
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(exp i k)))
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(equal (exp i (times j k))
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(exp (exp i j)
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k))
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(equal (reverse-loop x y)
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(append (reverse x)
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y))
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(equal (reverse-loop x (nil))
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(reverse x))
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(equal (count-list z (sort-lp x y))
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(plus (count-list z x)
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(count-list z y)))
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(equal (equal (append a b)
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(append a c))
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(equal b c))
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(equal (plus (remainder x y)
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(times y (quotient x y)))
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(fix x))
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(equal (power-eval (big-plus1 l i base)
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base)
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(plus (power-eval l base)
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i))
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(equal (power-eval (big-plus x y i base)
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base)
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(plus i (plus (power-eval x base)
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(power-eval y base))))
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(equal (remainder y 1)
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(zero))
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(equal (lessp (remainder x y)
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y)
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(not (zerop y)))
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(equal (remainder x x)
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(zero))
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(equal (lessp (quotient i j)
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i)
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(and (not (zerop i))
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(or (zerop j)
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(not (equal j 1)))))
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(equal (lessp (remainder x y)
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x)
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(and (not (zerop y))
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(not (zerop x))
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(not (lessp x y))))
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(equal (power-eval (power-rep i base)
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base)
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(fix i))
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(equal (power-eval (big-plus (power-rep i base)
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(power-rep j base)
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(zero)
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base)
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base)
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(plus i j))
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(equal (gcd x y)
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(gcd y x))
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(equal (nth (append a b)
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i)
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(append (nth a i)
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(nth b (difference i (length a)))))
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(equal (difference (plus x y)
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x)
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(fix y))
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(equal (difference (plus y x)
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x)
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(fix y))
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(equal (difference (plus x y)
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(plus x z))
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(difference y z))
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(equal (times x (difference c w))
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(difference (times c x)
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(times w x)))
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(equal (remainder (times x z)
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z)
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(zero))
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(equal (difference (plus b (plus a c))
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a)
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(plus b c))
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(equal (difference (add1 (plus y z))
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z)
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(add1 y))
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(equal (lessp (plus x y)
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(plus x z))
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(lessp y z))
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(equal (lessp (times x z)
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(times y z))
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(and (not (zerop z))
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(lessp x y)))
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(equal (lessp y (plus x y))
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(not (zerop x)))
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(equal (gcd (times x z)
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(times y z))
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(times z (gcd x y)))
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(equal (value (normalize x)
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a)
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(value x a))
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(equal (equal (flatten x)
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(cons y (nil)))
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(and (nlistp x)
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(equal x y)))
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(equal (listp (gopher x))
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(listp x))
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(equal (samefringe x y)
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(equal (flatten x)
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(flatten y)))
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(equal (equal (greatest-factor x y)
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(zero))
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(and (or (zerop y)
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(equal y 1))
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(equal x (zero))))
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(equal (equal (greatest-factor x y)
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1)
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(equal x 1))
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(equal (numberp (greatest-factor x y))
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(not (and (or (zerop y)
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(equal y 1))
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(not (numberp x)))))
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(equal (times-list (append x y))
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(times (times-list x)
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(times-list y)))
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(equal (prime-list (append x y))
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(and (prime-list x)
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(prime-list y)))
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||
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(equal (equal z (times w z))
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(and (numberp z)
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(or (equal z (zero))
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(equal w 1))))
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(equal (greatereqpr x y)
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(not (lessp x y)))
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||
|
|
(equal (equal x (times x y))
|
||
|
|
(or (equal x (zero))
|
||
|
|
(and (numberp x)
|
||
|
|
(equal y 1))))
|
||
|
|
(equal (remainder (times y x)
|
||
|
|
y)
|
||
|
|
(zero))
|
||
|
|
(equal (equal (times a b)
|
||
|
|
1)
|
||
|
|
(and (not (equal a (zero)))
|
||
|
|
(not (equal b (zero)))
|
||
|
|
(numberp a)
|
||
|
|
(numberp b)
|
||
|
|
(equal (_1- a)
|
||
|
|
(zero))
|
||
|
|
(equal (_1- b)
|
||
|
|
(zero))))
|
||
|
|
(equal (lessp (length (delete x l))
|
||
|
|
(length l))
|
||
|
|
(member x l))
|
||
|
|
(equal (sort2 (delete x l))
|
||
|
|
(delete x (sort2 l)))
|
||
|
|
(equal (dsort x)
|
||
|
|
(sort2 x))
|
||
|
|
(equal (length (cons x1
|
||
|
|
(cons x2
|
||
|
|
(cons x3 (cons x4
|
||
|
|
(cons x5
|
||
|
|
(cons x6 x7)))))))
|
||
|
|
(plus 6 (length x7)))
|
||
|
|
(equal (difference (add1 (add1 x))
|
||
|
|
2)
|
||
|
|
(fix x))
|
||
|
|
(equal (quotient (plus x (plus x y))
|
||
|
|
2)
|
||
|
|
(plus x (quotient y 2)))
|
||
|
|
(equal (sigma (zero)
|
||
|
|
i)
|
||
|
|
(quotient (times i (add1 i))
|
||
|
|
2))
|
||
|
|
(equal (plus x (add1 y))
|
||
|
|
(if (numberp y)
|
||
|
|
(add1 (plus x y))
|
||
|
|
(add1 x)))
|
||
|
|
(equal (equal (difference x y)
|
||
|
|
(difference z y))
|
||
|
|
(if (lessp x y)
|
||
|
|
(not (lessp y z))
|
||
|
|
(if (lessp z y)
|
||
|
|
(not (lessp y x))
|
||
|
|
(equal (fix x)
|
||
|
|
(fix z)))))
|
||
|
|
(equal (meaning (plus-tree (delete x y))
|
||
|
|
a)
|
||
|
|
(if (member x y)
|
||
|
|
(difference (meaning (plus-tree y)
|
||
|
|
a)
|
||
|
|
(meaning x a))
|
||
|
|
(meaning (plus-tree y)
|
||
|
|
a)))
|
||
|
|
(equal (times x (add1 y))
|
||
|
|
(if (numberp y)
|
||
|
|
(plus x (times x y))
|
||
|
|
(fix x)))
|
||
|
|
(equal (nth (nil)
|
||
|
|
i)
|
||
|
|
(if (zerop i)
|
||
|
|
(nil)
|
||
|
|
(zero)))
|
||
|
|
(equal (last (append a b))
|
||
|
|
(if (listp b)
|
||
|
|
(last b)
|
||
|
|
(if (listp a)
|
||
|
|
(cons (car (last a))
|
||
|
|
b)
|
||
|
|
b)))
|
||
|
|
(equal (equal (lessp x y)
|
||
|
|
z)
|
||
|
|
(if (lessp x y)
|
||
|
|
(equal t z)
|
||
|
|
(equal f z)))
|
||
|
|
(equal (assignment x (append a b))
|
||
|
|
(if (assignedp x a)
|
||
|
|
(assignment x a)
|
||
|
|
(assignment x b)))
|
||
|
|
(equal (car (gopher x))
|
||
|
|
(if (listp x)
|
||
|
|
(car (flatten x))
|
||
|
|
(zero)))
|
||
|
|
(equal (flatten (cdr (gopher x)))
|
||
|
|
(if (listp x)
|
||
|
|
(cdr (flatten x))
|
||
|
|
(cons (zero)
|
||
|
|
(nil))))
|
||
|
|
(equal (quotient (times y x)
|
||
|
|
y)
|
||
|
|
(if (zerop y)
|
||
|
|
(zero)
|
||
|
|
(fix x)))
|
||
|
|
(equal (get j (set i val mem))
|
||
|
|
(if (eqp j i)
|
||
|
|
val
|
||
|
|
(get j mem)))))))
|
||
|
|
|
||
|
|
(define (tautologyp x true-lst false-lst)
|
||
|
|
(cond ((truep x true-lst)
|
||
|
|
#t)
|
||
|
|
((falsep x false-lst)
|
||
|
|
#f)
|
||
|
|
((not (pair? x))
|
||
|
|
#f)
|
||
|
|
((eq? (car x)
|
||
|
|
(quote if))
|
||
|
|
(cond ((truep (cadr x)
|
||
|
|
true-lst)
|
||
|
|
(tautologyp (caddr x)
|
||
|
|
true-lst false-lst))
|
||
|
|
((falsep (cadr x)
|
||
|
|
false-lst)
|
||
|
|
(tautologyp (cadddr x)
|
||
|
|
true-lst false-lst))
|
||
|
|
(else (and (tautologyp (caddr x)
|
||
|
|
(cons (cadr x)
|
||
|
|
true-lst)
|
||
|
|
false-lst)
|
||
|
|
(tautologyp (cadddr x)
|
||
|
|
true-lst
|
||
|
|
(cons (cadr x)
|
||
|
|
false-lst))))))
|
||
|
|
(else #f)))
|
||
|
|
|
||
|
|
(define (tautp x)
|
||
|
|
(tautologyp (rewrite x)
|
||
|
|
'() '()))
|
||
|
|
|
||
|
|
(define (test alist term)
|
||
|
|
(tautp
|
||
|
|
(apply-subst alist term)))
|
||
|
|
|
||
|
|
(define (trans-of-implies n)
|
||
|
|
(list (quote implies)
|
||
|
|
(trans-of-implies1 n)
|
||
|
|
(list (quote implies)
|
||
|
|
0 n)))
|
||
|
|
|
||
|
|
(define (trans-of-implies1 n)
|
||
|
|
(cond ((equal? n 1)
|
||
|
|
(list (quote implies)
|
||
|
|
0 1))
|
||
|
|
(else (list (quote and)
|
||
|
|
(list (quote implies)
|
||
|
|
(- n 1)
|
||
|
|
n)
|
||
|
|
(trans-of-implies1 (- n 1))))))
|
||
|
|
|
||
|
|
(define (truep x lst)
|
||
|
|
(or (equal? x (quote (t)))
|
||
|
|
(member x lst)))
|
||
|
|
|
||
|
|
(setup)
|
||
|
|
|
||
|
|
(define (main . args)
|
||
|
|
(run-benchmark
|
||
|
|
"boyer"
|
||
|
|
boyer-iters
|
||
|
|
(lambda (result) (equal? result #t))
|
||
|
|
(lambda (alist term) (lambda () (test alist term)))
|
||
|
|
(quote ((x f (plus (plus a b)
|
||
|
|
(plus c (zero))))
|
||
|
|
(y f (times (times a b)
|
||
|
|
(plus c d)))
|
||
|
|
(z f (reverse (append (append a b)
|
||
|
|
(nil))))
|
||
|
|
(u equal (plus a b)
|
||
|
|
(difference x y))
|
||
|
|
(w lessp (remainder a b)
|
||
|
|
(member a (length b)))))
|
||
|
|
(quote (implies (and (implies x y)
|
||
|
|
(and (implies y z)
|
||
|
|
(and (implies z u)
|
||
|
|
(implies u w))))
|
||
|
|
(implies x w)))))
|