1021 lines
22 KiB
Scheme
1021 lines
22 KiB
Scheme
;;; Translated from the SML version of the Boyer benchmark.
|
|
|
|
;;; From 1terms.sch
|
|
|
|
; terms.sch
|
|
;
|
|
; Translated from smlbench/boyer/terms.sml by William D Clinger
|
|
; Last modified: 25 October 1996
|
|
|
|
; The SML types for this, whose spirit I have attempted to preserve,
|
|
; are just awful:
|
|
|
|
; signature TERMS =
|
|
; sig
|
|
; type head;
|
|
; datatype term =
|
|
; Var of int
|
|
; | Prop of head * term list;
|
|
; datatype binding = Bind of int * term;
|
|
; val get: string -> head
|
|
; and headname: head -> string
|
|
; and add_lemma: term -> unit
|
|
; and apply_subst: binding list -> term -> term
|
|
; and rewrite: term -> term
|
|
; end;
|
|
|
|
; In the Scheme version, a term has one of two forms:
|
|
; * an integer
|
|
; * a list of the form (<head> <terms>)
|
|
; where <head> is a head and <terms> is a list of terms.
|
|
|
|
(define (Var i) i)
|
|
(define (Prop head terms) (cons head terms))
|
|
|
|
(define (Var? x) (not (pair? x)))
|
|
(define (Prop? x) (pair? x))
|
|
|
|
(define (Var.i x) x)
|
|
(define (Prop.head x) (car x))
|
|
(define (Prop.terms x) (cdr x))
|
|
|
|
(define Bind cons)
|
|
(define Bind.i car)
|
|
(define Bind.term cdr)
|
|
|
|
(define get)
|
|
(define headname)
|
|
(define add_lemma)
|
|
(define apply_subst)
|
|
(define rewrite)
|
|
|
|
;(let ()
|
|
|
|
; datatype term
|
|
; = Var of int
|
|
; | Prop of { name: string, props: (term * term) list ref } * term list
|
|
;
|
|
; type head = { name: string, props: (term * term) list ref }
|
|
;
|
|
; A head has the form (<name> . <props>),
|
|
; where <name> is a string and <props> is a list of pairs of terms.
|
|
; The <props> field can be updated destructively.
|
|
|
|
(define (head name props) (cons name props))
|
|
|
|
(define (head.name x) (car x))
|
|
(define (head.props x) (cdr x))
|
|
(define (head.props! x newprops) (set-cdr! x newprops))
|
|
|
|
(define lemmas '())
|
|
|
|
(set! headname car)
|
|
|
|
(set! get
|
|
(lambda (name)
|
|
(define (get_rec ls)
|
|
(cond ((null? ls)
|
|
(let ((entry (head name '())))
|
|
(set! lemmas (cons entry lemmas))
|
|
entry))
|
|
((string=? name (head.name (car ls)))
|
|
(car ls))
|
|
(else
|
|
(get_rec (cdr ls)))))
|
|
(get_rec lemmas)))
|
|
|
|
(set! add_lemma
|
|
(lambda (lemma)
|
|
(let* ((terms (Prop.terms lemma))
|
|
(left (car terms))
|
|
(right (cadr terms))
|
|
(h (Prop.head left))
|
|
(r (head.props h)))
|
|
(head.props! h (cons (cons left right) r)))))
|
|
|
|
; Given an int v, returns a procedure that, given a list
|
|
; of bindings, returns the value associated with v or #f.
|
|
; This won't work if #f is associated with v, but that
|
|
; won't ever happen in this benchmark.
|
|
|
|
(define (get_binding v)
|
|
(define (get_rec bindings)
|
|
(cond ((null? bindings)
|
|
#f)
|
|
((eqv? (Bind.i (car bindings)) v)
|
|
(Bind.term (car bindings)))
|
|
(else
|
|
(get_rec (cdr bindings)))))
|
|
get_rec)
|
|
|
|
(set! apply_subst
|
|
(lambda (alist)
|
|
(define (as_rec term)
|
|
(if (Var? term)
|
|
(or ((get_binding (Var.i term)) alist)
|
|
term)
|
|
(Prop (Prop.head term)
|
|
(map as_rec (Prop.terms term)))))
|
|
as_rec))
|
|
|
|
; Given two terms, returns a list of bindings that unify
|
|
; them, or returns #f if they are not unifiable.
|
|
|
|
(define (unify term1 term2)
|
|
(unify1 term1 term2 '()))
|
|
|
|
(define (unify1 term1 term2 unify_subst)
|
|
(if (Var? term2)
|
|
(let* ((v (Var.i term2))
|
|
(value ((get_binding v) unify_subst)))
|
|
(if value
|
|
(if (equal? value term1)
|
|
unify_subst
|
|
#f)
|
|
(cons (cons v term1) unify_subst)))
|
|
(if (Var? term1)
|
|
#f
|
|
(if (equal? (Prop.head term1)
|
|
(Prop.head term2))
|
|
(unify1_lst (Prop.terms term1)
|
|
(Prop.terms term2)
|
|
unify_subst)
|
|
#f))))
|
|
|
|
(define (unify1_lst ls1 ls2 unify_subst)
|
|
(cond ((and (null? ls1) (null? ls2))
|
|
unify_subst)
|
|
((and (pair? ls1) (pair? ls2))
|
|
(let ((unify_subst
|
|
(unify1 (car ls1) (car ls2) unify_subst)))
|
|
(if unify_subst
|
|
(unify1_lst (cdr ls1) (cdr ls2) unify_subst)
|
|
#f)))
|
|
(else
|
|
#f)))
|
|
|
|
(set! rewrite
|
|
(lambda (term)
|
|
(if (Var? term)
|
|
term
|
|
(let ((head (Prop.head term)))
|
|
(rewrite_with_lemmas
|
|
(Prop head
|
|
(map rewrite (Prop.terms term)))
|
|
(head.props head))))))
|
|
|
|
(define (rewrite_with_lemmas term lemmas)
|
|
(if (null? lemmas)
|
|
term
|
|
(let* ((lemma (car lemmas))
|
|
(t1 (car lemma))
|
|
(t2 (cdr lemma))
|
|
(u (unify term t1)))
|
|
(if u
|
|
(rewrite ((apply_subst u) t2))
|
|
(rewrite_with_lemmas term (cdr lemmas))))))
|
|
|
|
;;; From 1rules.sch
|
|
|
|
; rules.sch
|
|
;
|
|
; Translated from smlbench/boyer/rules.sml by William D Clinger
|
|
; Last modified: 22 October 1996
|
|
|
|
; requires terms.sch
|
|
|
|
; datatype cterm = CVar of int | CProp of string * cterm list;
|
|
|
|
(let ()
|
|
|
|
(define (CVar i) i)
|
|
(define (CProp s terms) (list s terms))
|
|
|
|
(define (CVar? x) (not (pair? x)))
|
|
(define (CProp? x) (pair? x))
|
|
|
|
(define (CVar.i x) x)
|
|
(define (CProp.name x) (car x))
|
|
(define (CProp.terms x) (cadr x))
|
|
|
|
(define (cterm_to_term x)
|
|
(if (Cvar? x)
|
|
(Var (Cvar.i x))
|
|
(Prop (get (CProp.name x))
|
|
(map cterm_to_term (CProp.terms x)))))
|
|
|
|
(define (add t) (add_lemma (cterm_to_term t)))
|
|
|
|
; The following code was obtained from rules.sml by using a text editor to
|
|
; * delete all occurrences of "CVar"
|
|
; * delete all occurrences of "CProp"
|
|
; * replace all commas by spaces
|
|
; * replace all left and right square brackets by parentheses
|
|
; * replace all occurrences of "add (" by "(add '".
|
|
|
|
|
|
(add '
|
|
("equal"
|
|
( ("compile" (5))
|
|
|
|
("reverse"
|
|
( ("codegen" ( ("optimize" (5)) ("nil" ()))))))));
|
|
(add '
|
|
("equal"
|
|
( ("eqp" (23 24))
|
|
("equal" ( ("fix" (23)) ("fix" (24)))))));
|
|
(add '
|
|
("equal"
|
|
( ("gt" (23 24)) ("lt" (24 23)))));
|
|
(add '
|
|
("equal"
|
|
( ("le" (23 24)) ("ge" (24 23)))));
|
|
(add '
|
|
("equal"
|
|
( ("ge" (23 24)) ("le" (24 23)))));
|
|
(add '
|
|
("equal"
|
|
( ("boolean" (23))
|
|
|
|
("or"
|
|
( ("equal" (23 ("true" ())))
|
|
("equal" (23 ("false" ()))))))));
|
|
(add '
|
|
("equal"
|
|
( ("iff" (23 24))
|
|
|
|
("and"
|
|
( ("implies" (23 24))
|
|
("implies" (24 23)))))));
|
|
(add '
|
|
("equal"
|
|
( ("even1" (23))
|
|
|
|
("if"
|
|
( ("zerop" (23)) ("true" ())
|
|
("odd" ( ("sub1" (23)))))))));
|
|
(add '
|
|
("equal"
|
|
( ("countps_" (11 15))
|
|
("countps_loop" (11 15 ("zero" ()))))));
|
|
(add '
|
|
("equal"
|
|
( ("fact_" (8))
|
|
("fact_loop" (8 ("one" ()))))));
|
|
(add '
|
|
("equal"
|
|
( ("reverse_" (23))
|
|
("reverse_loop" (23 ("nil" ()))))));
|
|
(add '
|
|
("equal"
|
|
( ("divides" (23 24))
|
|
("zerop" ( ("remainder" (24 23)))))));
|
|
(add '
|
|
("equal"
|
|
( ("assume_true" (21 0))
|
|
("cons" ( ("cons" (21 ("true" ()))) 0)))));
|
|
(add '
|
|
("equal"
|
|
( ("assume_false" (21 0))
|
|
("cons" ( ("cons" (21 ("false" ()))) 0)))));
|
|
(add '
|
|
("equal"
|
|
( ("tautology_checker" (23))
|
|
("tautologyp" ( ("normalize" (23)) ("nil" ()))))));
|
|
(add '
|
|
("equal"
|
|
( ("falsify" (23))
|
|
("falsify1" ( ("normalize" (23)) ("nil" ()))))));
|
|
(add '
|
|
("equal"
|
|
( ("prime" (23))
|
|
|
|
("and"
|
|
( ("not" ( ("zerop" (23))))
|
|
|
|
("not"
|
|
( ("equal" (23 ("add1" ( ("zero" ())))))))
|
|
("prime1" (23 ("sub1" (23)))))))));
|
|
(add '
|
|
("equal"
|
|
( ("and" (15 16))
|
|
|
|
("if"
|
|
(15
|
|
("if" (16 ("true" ()) ("false" ())))
|
|
("false" ()))))));
|
|
(add '
|
|
("equal"
|
|
( ("or" (15 16))
|
|
|
|
("if"
|
|
(15 ("true" ())
|
|
("if" (16 ("true" ()) ("false" ())))
|
|
("false" ()))))));
|
|
(add '
|
|
("equal"
|
|
( ("not" (15))
|
|
("if" (15 ("false" ()) ("true" ()))))));
|
|
(add '
|
|
("equal"
|
|
( ("implies" (15 16))
|
|
|
|
("if"
|
|
(15
|
|
("if" (16 ("true" ()) ("false" ())))
|
|
("true" ()))))));
|
|
(add '
|
|
("equal"
|
|
( ("fix" (23))
|
|
("if" ( ("numberp" (23)) 23 ("zero" ()))))));
|
|
(add '
|
|
("equal"
|
|
( ("if" ( ("if" (0 1 2)) 3 4))
|
|
|
|
("if"
|
|
(0 ("if" (1 3 4))
|
|
("if" (2 3 4)))))));
|
|
(add '
|
|
("equal"
|
|
( ("zerop" (23))
|
|
|
|
("or"
|
|
( ("equal" (23 ("zero" ())))
|
|
("not" ( ("numberp" (23)))))))));
|
|
(add '
|
|
("equal"
|
|
( ("plus" ( ("plus" (23 24)) 25))
|
|
("plus" (23 ("plus" (24 25)))))));
|
|
(add '
|
|
("equal"
|
|
( ("equal" ( ("plus" (0 1)) ("zero" ())))
|
|
("and" ( ("zerop" (0)) ("zerop" (1)))))));
|
|
(add '
|
|
("equal" ( ("difference" (23 23)) ("zero" ()))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("equal"
|
|
( ("plus" (0 1)) ("plus" (0 2))))
|
|
("equal" ( ("fix" (1)) ("fix" (2)))))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("equal" ( ("zero" ()) ("difference" (23 24))))
|
|
("not" ( ("gt" (24 23)))))));
|
|
(add '
|
|
("equal"
|
|
( ("equal" (23 ("difference" (23 24))))
|
|
|
|
("and"
|
|
( ("numberp" (23))
|
|
|
|
("or"
|
|
( ("equal" (23 ("zero" ())))
|
|
("zerop" (24)))))))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("meaning"
|
|
( ("plus_tree" ( ("append" (23 24)))) 0))
|
|
|
|
("plus"
|
|
( ("meaning" ( ("plus_tree" (23)) 0))
|
|
("meaning" ( ("plus_tree" (24)) 0)))))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("meaning"
|
|
( ("plus_tree" ( ("plus_fringe" (23)))) 0))
|
|
("fix" ( ("meaning" (23 0)))))));
|
|
(add '
|
|
("equal"
|
|
( ("append" ( ("append" (23 24)) 25))
|
|
("append" (23 ("append" (24 25)))))));
|
|
(add '
|
|
("equal"
|
|
( ("reverse" ( ("append" (0 1))))
|
|
|
|
("append" ( ("reverse" (1)) ("reverse" (0)))))));
|
|
(add '
|
|
("equal"
|
|
( ("times" (23 ("plus" (24 25))))
|
|
|
|
("plus"
|
|
( ("times" (23 24))
|
|
("times" (23 25)))))));
|
|
(add '
|
|
("equal"
|
|
( ("times" ( ("times" (23 24)) 25))
|
|
("times" (23 ("times" (24 25)))))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("equal" ( ("times" (23 24)) ("zero" ())))
|
|
("or" ( ("zerop" (23)) ("zerop" (24)))))));
|
|
(add '
|
|
("equal"
|
|
( ("exec" ( ("append" (23 24)) 15 4))
|
|
|
|
("exec" (24 ("exec" (23 15 4)) 4)))));
|
|
(add '
|
|
("equal"
|
|
( ("mc_flatten" (23 24))
|
|
("append" ( ("flatten" (23)) 24)))));
|
|
(add '
|
|
("equal"
|
|
( ("member" (23 ("append" (0 1))))
|
|
|
|
("or"
|
|
( ("member" (23 0))
|
|
("member" (23 1)))))));
|
|
(add '
|
|
("equal"
|
|
( ("member" (23 ("reverse" (24))))
|
|
("member" (23 24)))));
|
|
(add '
|
|
("equal"
|
|
( ("length" ( ("reverse" (23))))
|
|
("length" (23)))));
|
|
(add '
|
|
("equal"
|
|
( ("member" (0 ("intersect" (1 2))))
|
|
|
|
("and"
|
|
( ("member" (0 1)) ("member" (0 2)))))));
|
|
(add '
|
|
("equal" ( ("nth" ( ("zero" ()) 8)) ("zero" ()))));
|
|
(add '
|
|
("equal"
|
|
( ("exp" (8 ("plus" (9 10))))
|
|
|
|
("times"
|
|
( ("exp" (8 9)) ("exp" (8 10)))))));
|
|
(add '
|
|
("equal"
|
|
( ("exp" (8 ("times" (9 10))))
|
|
("exp" ( ("exp" (8 9)) 10)))));
|
|
(add '
|
|
("equal"
|
|
( ("reverse_loop" (23 24))
|
|
("append" ( ("reverse" (23)) 24)))));
|
|
(add '
|
|
("equal"
|
|
( ("reverse_loop" (23 ("nil" ())))
|
|
("reverse" (23)))));
|
|
(add '
|
|
("equal"
|
|
( ("count_list" (25 ("sort_lp" (23 24))))
|
|
|
|
("plus"
|
|
( ("count_list" (25 23))
|
|
("count_list" (25 24)))))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("equal"
|
|
( ("append" (0 1)) ("append" (0 2))))
|
|
("equal" (1 2)))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("plus"
|
|
( ("remainder" (23 24))
|
|
("times" (24 ("quotient" (23 24))))))
|
|
("fix" (23)))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("power_eval" ( ("big_plus" (11 8 1)) 1))
|
|
("plus" ( ("power_eval" (11 1)) 8)))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("power_eval"
|
|
( ("big_plus" (23 24 8 1)) 1))
|
|
|
|
("plus"
|
|
(8
|
|
|
|
("plus"
|
|
( ("power_eval" (23 1))
|
|
("power_eval" (24 1)))))))));
|
|
(add '
|
|
("equal"
|
|
( ("remainder" (24 ("one" ()))) ("zero" ()))));
|
|
(add '
|
|
("equal"
|
|
( ("lt" ( ("remainder" (23 24)) 24))
|
|
("not" ( ("zerop" (24)))))));
|
|
(add '
|
|
("equal" ( ("remainder" (23 23)) ("zero" ()))));
|
|
(add '
|
|
("equal"
|
|
( ("lt" ( ("quotient" (8 9)) 8))
|
|
|
|
("and"
|
|
( ("not" ( ("zerop" (8))))
|
|
|
|
("or"
|
|
( ("zerop" (9))
|
|
("not" ( ("equal" (9 ("one" ()))))))))))));
|
|
(add '
|
|
("equal"
|
|
( ("lt" ( ("remainder" (23 24)) 23))
|
|
|
|
("and"
|
|
( ("not" ( ("zerop" (24))))
|
|
("not" ( ("zerop" (23))))
|
|
("not" ( ("lt" (23 24)))))))));
|
|
(add '
|
|
("equal"
|
|
( ("power_eval" ( ("power_rep" (8 1)) 1))
|
|
("fix" (8)))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("power_eval"
|
|
(
|
|
("big_plus"
|
|
( ("power_rep" (8 1))
|
|
("power_rep" (9 1)) ("zero" ())
|
|
1))
|
|
1))
|
|
("plus" (8 9)))));
|
|
(add '
|
|
("equal"
|
|
( ("gcd" (23 24)) ("gcd" (24 23)))));
|
|
(add '
|
|
("equal"
|
|
( ("nth" ( ("append" (0 1)) 8))
|
|
|
|
("append"
|
|
( ("nth" (0 8))
|
|
|
|
("nth"
|
|
(1 ("difference" (8 ("length" (0)))))))))));
|
|
(add '
|
|
("equal"
|
|
( ("difference" ( ("plus" (23 24)) 23))
|
|
("fix" (24)))));
|
|
(add '
|
|
("equal"
|
|
( ("difference" ( ("plus" (24 23)) 23))
|
|
("fix" (24)))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("difference"
|
|
( ("plus" (23 24)) ("plus" (23 25))))
|
|
("difference" (24 25)))));
|
|
(add '
|
|
("equal"
|
|
( ("times" (23 ("difference" (2 22))))
|
|
|
|
("difference"
|
|
( ("times" (2 23))
|
|
("times" (22 23)))))));
|
|
(add '
|
|
("equal"
|
|
( ("remainder" ( ("times" (23 25)) 25))
|
|
("zero" ()))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("difference"
|
|
( ("plus" (1 ("plus" (0 2)))) 0))
|
|
("plus" (1 2)))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("difference"
|
|
( ("add1" ( ("plus" (24 25)))) 25))
|
|
("add1" (24)))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("lt"
|
|
( ("plus" (23 24)) ("plus" (23 25))))
|
|
("lt" (24 25)))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("lt"
|
|
( ("times" (23 25))
|
|
("times" (24 25))))
|
|
|
|
("and"
|
|
( ("not" ( ("zerop" (25))))
|
|
("lt" (23 24)))))));
|
|
(add '
|
|
("equal"
|
|
( ("lt" (24 ("plus" (23 24))))
|
|
("not" ( ("zerop" (23)))))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("gcd"
|
|
( ("times" (23 25))
|
|
("times" (24 25))))
|
|
("times" (25 ("gcd" (23 24)))))));
|
|
(add '
|
|
("equal"
|
|
( ("value" ( ("normalize" (23)) 0))
|
|
("value" (23 0)))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("equal"
|
|
( ("flatten" (23))
|
|
("cons" (24 ("nil" ())))))
|
|
|
|
("and"
|
|
( ("nlistp" (23)) ("equal" (23 24)))))));
|
|
(add '
|
|
("equal"
|
|
( ("listp" ( ("gother" (23))))
|
|
("listp" (23)))));
|
|
(add '
|
|
("equal"
|
|
( ("samefringe" (23 24))
|
|
|
|
("equal" ( ("flatten" (23)) ("flatten" (24)))))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("equal"
|
|
( ("greatest_factor" (23 24)) ("zero" ())))
|
|
|
|
("and"
|
|
(
|
|
("or"
|
|
( ("zerop" (24))
|
|
("equal" (24 ("one" ())))))
|
|
("equal" (23 ("zero" ()))))))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("equal"
|
|
( ("greatest_factor" (23 24)) ("one" ())))
|
|
("equal" (23 ("one" ()))))));
|
|
(add '
|
|
("equal"
|
|
( ("numberp" ( ("greatest_factor" (23 24))))
|
|
|
|
("not"
|
|
(
|
|
("and"
|
|
(
|
|
("or"
|
|
( ("zerop" (24))
|
|
("equal" (24 ("one" ())))))
|
|
("not" ( ("numberp" (23)))))))))));
|
|
(add '
|
|
("equal"
|
|
( ("times_list" ( ("append" (23 24))))
|
|
|
|
("times"
|
|
( ("times_list" (23)) ("times_list" (24)))))));
|
|
(add '
|
|
("equal"
|
|
( ("prime_list" ( ("append" (23 24))))
|
|
|
|
("and"
|
|
( ("prime_list" (23)) ("prime_list" (24)))))));
|
|
(add '
|
|
("equal"
|
|
( ("equal" (25 ("times" (22 25))))
|
|
|
|
("and"
|
|
( ("numberp" (25))
|
|
|
|
("or"
|
|
( ("equal" (25 ("zero" ())))
|
|
("equal" (22 ("one" ()))))))))));
|
|
(add '
|
|
("equal"
|
|
( ("ge" (23 24))
|
|
("not" ( ("lt" (23 24)))))));
|
|
(add '
|
|
("equal"
|
|
( ("equal" (23 ("times" (23 24))))
|
|
|
|
("or"
|
|
( ("equal" (23 ("zero" ())))
|
|
|
|
("and"
|
|
( ("numberp" (23))
|
|
("equal" (24 ("one" ()))))))))));
|
|
(add '
|
|
("equal"
|
|
( ("remainder" ( ("times" (24 23)) 24))
|
|
("zero" ()))));
|
|
(add '
|
|
("equal"
|
|
( ("equal" ( ("times" (0 1)) ("one" ())))
|
|
|
|
("and"
|
|
( ("not" ( ("equal" (0 ("zero" ())))))
|
|
("not" ( ("equal" (1 ("zero" ())))))
|
|
("numberp" (0)) ("numberp" (1))
|
|
("equal" ( ("sub1" (0)) ("zero" ())))
|
|
("equal" ( ("sub1" (1)) ("zero" ()))))))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("lt"
|
|
( ("length" ( ("delete" (23 11))))
|
|
("length" (11))))
|
|
("member" (23 11)))));
|
|
(add '
|
|
("equal"
|
|
( ("sort2" ( ("delete" (23 11))))
|
|
("delete" (23 ("sort2" (11)))))));
|
|
(add ' ("equal" ( ("dsort" (23)) ("sort2" (23)))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("length"
|
|
(
|
|
("cons"
|
|
(0
|
|
|
|
("cons"
|
|
(1
|
|
|
|
("cons"
|
|
(2
|
|
|
|
("cons"
|
|
(3
|
|
("cons" (4 ("cons" (5 6))))))))))))))
|
|
("plus" ( ("six" ()) ("length" (6)))))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("difference"
|
|
( ("add1" ( ("add1" (23)))) ("two" ())))
|
|
("fix" (23)))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("quotient"
|
|
( ("plus" (23 ("plus" (23 24))))
|
|
("two" ())))
|
|
|
|
("plus" (23 ("quotient" (24 ("two" ()))))))));
|
|
(add '
|
|
("equal"
|
|
( ("sigma" ( ("zero" ()) 8))
|
|
|
|
("quotient"
|
|
( ("times" (8 ("add1" (8)))) ("two" ()))))));
|
|
(add '
|
|
("equal"
|
|
( ("plus" (23 ("add1" (24))))
|
|
|
|
("if"
|
|
( ("numberp" (24))
|
|
("add1" ( ("plus" (23 24))))
|
|
("add1" (23)))))));
|
|
(add '
|
|
("equal"
|
|
(
|
|
("equal"
|
|
( ("difference" (23 24))
|
|
("difference" (25 24))))
|
|
|
|
("if"
|
|
( ("lt" (23 24))
|
|
("not" ( ("lt" (24 25))))
|
|
|
|
("if"
|
|
( ("lt" (25 24))
|
|
("not" ( ("lt" (24 23))))
|
|
("equal" ( ("fix" (23)) ("fix" (25))))))))))
|
|
);
|
|
(add '
|
|
("equal"
|
|
(
|
|
("meaning"
|
|
( ("plus_tree" ( ("delete" (23 24)))) 0))
|
|
|
|
("if"
|
|
( ("member" (23 24))
|
|
|
|
("difference"
|
|
( ("meaning" ( ("plus_tree" (24)) 0))
|
|
("meaning" (23 0))))
|
|
("meaning" ( ("plus_tree" (24)) 0)))))));
|
|
(add '
|
|
("equal"
|
|
( ("times" (23 ("add1" (24))))
|
|
|
|
("if"
|
|
( ("numberp" (24))
|
|
|
|
("plus"
|
|
(23 ("times" (23 24))
|
|
("fix" (23)))))))));
|
|
(add '
|
|
("equal"
|
|
( ("nth" ( ("nil" ()) 8))
|
|
|
|
("if" ( ("zerop" (8)) ("nil" ()) ("zero" ()))))));
|
|
(add '
|
|
("equal"
|
|
( ("last" ( ("append" (0 1))))
|
|
|
|
("if"
|
|
( ("listp" (1)) ("last" (1))
|
|
|
|
("if"
|
|
( ("listp" (0))
|
|
("cons" ( ("car" ( ("last" (0)))) 1))
|
|
1)))))));
|
|
(add '
|
|
("equal"
|
|
( ("equal" ( ("lt" (23 24)) 25))
|
|
|
|
("if"
|
|
( ("lt" (23 24))
|
|
("equal" ( ("true" ()) 25))
|
|
("equal" ( ("false" ()) 25)))))));
|
|
(add '
|
|
("equal"
|
|
( ("assignment" (23 ("append" (0 1))))
|
|
|
|
("if"
|
|
( ("assignedp" (23 0))
|
|
("assignment" (23 0))
|
|
("assignment" (23 1)))))));
|
|
(add '
|
|
("equal"
|
|
( ("car" ( ("gother" (23))))
|
|
|
|
("if"
|
|
( ("listp" (23))
|
|
("car" ( ("flatten" (23)))) ("zero" ()))))));
|
|
(add '
|
|
("equal"
|
|
( ("flatten" ( ("cdr" ( ("gother" (23))))))
|
|
|
|
("if"
|
|
( ("listp" (23))
|
|
("cdr" ( ("flatten" (23))))
|
|
("cons" ( ("zero" ()) ("nil" ()))))))));
|
|
(add '
|
|
("equal"
|
|
( ("quotient" ( ("times" (24 23)) 24))
|
|
|
|
("if"
|
|
( ("zerop" (24)) ("zero" ())
|
|
("fix" (23)))))));
|
|
(add '
|
|
("equal"
|
|
( ("get" (9 ("set" (8 21 12))))
|
|
|
|
("if"
|
|
( ("eqp" (9 8)) 21
|
|
("get" (9 12))))))))
|
|
|
|
;;; From 1boyer.sch
|
|
|
|
; mlboyer.sch
|
|
;
|
|
; Translated from smlbench/boyer/boyer.sml by William D Clinger
|
|
; Last modified: 25 October 1996
|
|
|
|
; requires mlterms.sch
|
|
|
|
; structure Boyer: BOYER
|
|
|
|
(define tautp)
|
|
|
|
; structure Main: BMARK
|
|
|
|
(define doit)
|
|
(define testit)
|
|
|
|
;(let ()
|
|
|
|
(define (mem x z)
|
|
(if (null? z)
|
|
#f
|
|
(or (equal? x (car z))
|
|
(mem x (cdr z)))))
|
|
|
|
(define (truep x lst)
|
|
(if (Prop? x)
|
|
(or (string=? (headname (Prop.head x)) "true")
|
|
(mem x lst))
|
|
(mem x lst)))
|
|
|
|
(define (falsep x lst)
|
|
(if (Prop? x)
|
|
(or (string=? (headname (Prop.head x)) "false")
|
|
(mem x lst))
|
|
(mem x lst)))
|
|
|
|
(define (tautologyp x true_lst false_lst)
|
|
(cond ((truep x true_lst)
|
|
#t)
|
|
((falsep x false_lst)
|
|
#f)
|
|
((Var? x)
|
|
#f)
|
|
((string=? (headname (Prop.head x)) "if")
|
|
(let* ((terms (Prop.terms x))
|
|
(test (car terms))
|
|
(yes (cadr terms))
|
|
(no (caddr terms)))
|
|
(cond ((truep test true_lst)
|
|
(tautologyp yes true_lst false_lst))
|
|
((falsep test false_lst)
|
|
(tautologyp no true_lst false_lst))
|
|
(else (and (tautologyp yes
|
|
(cons test true_lst)
|
|
false_lst)
|
|
(tautologyp no
|
|
true_lst
|
|
(cons test false_lst)))))))
|
|
(else #f)))
|
|
|
|
(set! tautp
|
|
(lambda (x)
|
|
(tautologyp (rewrite x) '() '())))
|
|
|
|
;)
|
|
|
|
(let ((subst (list
|
|
|
|
(Bind 23
|
|
(Prop
|
|
(get "f")
|
|
(list (Prop
|
|
(get "plus")
|
|
(list (Prop (get "plus") (list (Var 0) (Var 1)))
|
|
(Prop (get "plus") (list (Var 2) (Prop (get "zero") '()))))))))
|
|
(Bind 24
|
|
(Prop
|
|
(get "f")
|
|
(list (Prop
|
|
(get "times")
|
|
(list (Prop (get "times") (list (Var 0) (Var 1)))
|
|
(Prop (get "plus") (list (Var 2) (Var 3))))))))
|
|
(Bind 25
|
|
(Prop
|
|
(get "f")
|
|
(list (Prop
|
|
(get "reverse")
|
|
(list (Prop
|
|
(get "append")
|
|
(list (Prop (get "append") (list (Var 0) (Var 1)))
|
|
(Prop (get "nil") '()))))))))
|
|
(Bind 20
|
|
(Prop
|
|
(get "equal")
|
|
(list (Prop (get "plus") (list (Var 0) (Var 1)))
|
|
(Prop (get "difference") (list (Var 23) (Var 24))))))
|
|
(Bind 22
|
|
(Prop
|
|
(get "lt")
|
|
(list (Prop (get "remainder") (list (Var 0) (Var 1)))
|
|
(Prop (get "member")
|
|
(list (Var 0)
|
|
(Prop (get "length") (list (Var 1))))))))))
|
|
|
|
(term
|
|
(Prop
|
|
(get "implies")
|
|
(list (Prop
|
|
(get "and")
|
|
(list (Prop (get "implies") (list (Var 23) (Var 24)))
|
|
(Prop
|
|
(get "and")
|
|
(list (Prop (get "implies") (list (Var 24) (Var 25)))
|
|
(Prop
|
|
(get "and")
|
|
(list (Prop (get "implies") (list (Var 25) (Var 20)))
|
|
(Prop (get "implies") (list (Var 20) (Var 22)))))))))
|
|
(Prop (get "implies") (list (Var 23) (Var 22)))))))
|
|
|
|
(set! testit
|
|
(lambda (outstrm)
|
|
(if (tautp ((apply_subst subst) term))
|
|
(display "Proved!" outstrm)
|
|
(display "Cannot prove!" outstrm))
|
|
(newline outstrm)))
|
|
|
|
(set! doit
|
|
(lambda ()
|
|
(tautp ((apply_subst subst) term))))
|
|
)
|
|
|
|
(define (main . args)
|
|
(run-benchmark
|
|
"smlboyer"
|
|
smlboyer-iters
|
|
doit
|
|
(lambda (result) result)))
|