912 lines
25 KiB
OCaml
912 lines
25 KiB
OCaml
(***********************************************************************)
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(* *)
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(* Objective Caml *)
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(* *)
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(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *)
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(* *)
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(* Copyright 1996 Institut National de Recherche en Informatique et *)
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(* en Automatique. All rights reserved. This file is distributed *)
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(* under the terms of the Q Public License version 1.0. *)
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(* *)
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(***********************************************************************)
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(* $Id$ *)
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(* Manipulations over terms *)
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type term =
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Var of int
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| Prop of head * term list
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and head =
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{ name: string;
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mutable props: (term * term) list }
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let rec print_term = function
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Var v ->
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print_string "v"; print_int v
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| Prop (head,argl) ->
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print_string "(";
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print_string head.name;
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List.iter (fun t -> print_string " "; print_term t) argl;
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print_string ")"
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let lemmas = ref ([] : head list)
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(* Replacement for property lists *)
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let get name =
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let rec get_rec = function
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hd1::hdl ->
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if hd1.name = name then hd1 else get_rec hdl
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| [] ->
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let entry = {name = name; props = []} in
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lemmas := entry :: !lemmas;
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entry
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in get_rec !lemmas
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let add_lemma = function
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| Prop(_, [(Prop(headl,_) as left); right]) ->
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headl.props <- (left, right) :: headl.props
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| _ -> assert false
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(* Substitutions *)
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type subst = Bind of int * term
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let get_binding v list =
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let rec get_rec = function
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[] -> failwith "unbound"
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| Bind(w,t)::rest -> if v = w then t else get_rec rest
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in get_rec list
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let apply_subst alist term =
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let rec as_rec = function
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Var v -> begin try get_binding v alist with Failure _ -> term end
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| Prop (head,argl) -> Prop (head, List.map as_rec argl)
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in as_rec term
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exception Unify
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let rec unify term1 term2 =
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unify1 term1 term2 []
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and unify1 term1 term2 unify_subst =
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match term2 with
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Var v ->
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begin try
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if get_binding v unify_subst = term1
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then unify_subst
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else raise Unify
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with Failure _ ->
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Bind(v,term1) :: unify_subst
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end
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| Prop (head2, argl2) ->
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match term1 with
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Var _ -> raise Unify
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| Prop (head1,argl1) ->
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if head1 == head2
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then unify1_lst argl1 argl2 unify_subst
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else raise Unify
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and unify1_lst l1 l2 unify_subst =
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match (l1, l2) with
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([], []) -> unify_subst
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| (h1::r1, h2::r2) -> unify1_lst r1 r2 (unify1 h1 h2 unify_subst)
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| _ -> raise Unify
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let rec rewrite = function
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Var _ as term -> term
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| Prop (head, argl) ->
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rewrite_with_lemmas (Prop (head, List.map rewrite argl)) head.props
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and rewrite_with_lemmas term lemmas =
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match lemmas with
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[] ->
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term
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| (t1,t2)::rest ->
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try
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rewrite (apply_subst (unify term t1) t2)
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with Unify ->
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rewrite_with_lemmas term rest
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type cterm = CVar of int | CProp of string * cterm list
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let rec cterm_to_term = function
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CVar v -> Var v
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| CProp(p, l) -> Prop(get p, List.map cterm_to_term l)
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let add t = add_lemma (cterm_to_term t)
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let _ =
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add (CProp
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("equal",
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[CProp ("compile",[CVar 5]);
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CProp
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("reverse",
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[CProp ("codegen",[CProp ("optimize",[CVar 5]); CProp ("nil",[])])])]));
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add (CProp
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("equal",
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[CProp ("eqp",[CVar 23; CVar 24]);
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CProp ("equal",[CProp ("fix",[CVar 23]); CProp ("fix",[CVar 24])])]));
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add (CProp
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("equal",
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[CProp ("gt",[CVar 23; CVar 24]); CProp ("lt",[CVar 24; CVar 23])]));
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add (CProp
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("equal",
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[CProp ("le",[CVar 23; CVar 24]); CProp ("ge",[CVar 24; CVar 23])]));
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add (CProp
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("equal",
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[CProp ("ge",[CVar 23; CVar 24]); CProp ("le",[CVar 24; CVar 23])]));
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add (CProp
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("equal",
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[CProp ("boolean",[CVar 23]);
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CProp
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("or",
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[CProp ("equal",[CVar 23; CProp ("true",[])]);
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CProp ("equal",[CVar 23; CProp ("false",[])])])]));
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add (CProp
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("equal",
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[CProp ("iff",[CVar 23; CVar 24]);
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CProp
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("and",
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[CProp ("implies",[CVar 23; CVar 24]);
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CProp ("implies",[CVar 24; CVar 23])])]));
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add (CProp
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("equal",
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[CProp ("even1",[CVar 23]);
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CProp
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("if",
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[CProp ("zerop",[CVar 23]); CProp ("true",[]);
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CProp ("odd",[CProp ("sub1",[CVar 23])])])]));
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add (CProp
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("equal",
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[CProp ("countps_",[CVar 11; CVar 15]);
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CProp ("countps_loop",[CVar 11; CVar 15; CProp ("zero",[])])]));
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add (CProp
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("equal",
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[CProp ("fact_",[CVar 8]);
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CProp ("fact_loop",[CVar 8; CProp ("one",[])])]));
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add (CProp
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("equal",
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[CProp ("reverse_",[CVar 23]);
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CProp ("reverse_loop",[CVar 23; CProp ("nil",[])])]));
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add (CProp
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("equal",
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[CProp ("divides",[CVar 23; CVar 24]);
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CProp ("zerop",[CProp ("remainder",[CVar 24; CVar 23])])]));
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add (CProp
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("equal",
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[CProp ("assume_true",[CVar 21; CVar 0]);
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CProp ("cons",[CProp ("cons",[CVar 21; CProp ("true",[])]); CVar 0])]));
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add (CProp
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("equal",
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[CProp ("assume_false",[CVar 21; CVar 0]);
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CProp ("cons",[CProp ("cons",[CVar 21; CProp ("false",[])]); CVar 0])]));
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add (CProp
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("equal",
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[CProp ("tautology_checker",[CVar 23]);
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CProp ("tautologyp",[CProp ("normalize",[CVar 23]); CProp ("nil",[])])]));
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add (CProp
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("equal",
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[CProp ("falsify",[CVar 23]);
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CProp ("falsify1",[CProp ("normalize",[CVar 23]); CProp ("nil",[])])]));
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add (CProp
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("equal",
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[CProp ("prime",[CVar 23]);
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CProp
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("and",
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[CProp ("not",[CProp ("zerop",[CVar 23])]);
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CProp
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("not",
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[CProp ("equal",[CVar 23; CProp ("add1",[CProp ("zero",[])])])]);
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CProp ("prime1",[CVar 23; CProp ("sub1",[CVar 23])])])]));
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add (CProp
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("equal",
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[CProp ("and",[CVar 15; CVar 16]);
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CProp
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("if",
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[CVar 15;
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CProp ("if",[CVar 16; CProp ("true",[]); CProp ("false",[])]);
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CProp ("false",[])])]));
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add (CProp
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("equal",
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[CProp ("or",[CVar 15; CVar 16]);
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CProp
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("if",
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[CVar 15; CProp ("true",[]);
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CProp ("if",[CVar 16; CProp ("true",[]); CProp ("false",[])]);
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CProp ("false",[])])]));
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add (CProp
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("equal",
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[CProp ("not",[CVar 15]);
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CProp ("if",[CVar 15; CProp ("false",[]); CProp ("true",[])])]));
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add (CProp
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("equal",
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[CProp ("implies",[CVar 15; CVar 16]);
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CProp
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("if",
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[CVar 15;
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CProp ("if",[CVar 16; CProp ("true",[]); CProp ("false",[])]);
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CProp ("true",[])])]));
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add (CProp
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("equal",
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[CProp ("fix",[CVar 23]);
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CProp ("if",[CProp ("numberp",[CVar 23]); CVar 23; CProp ("zero",[])])]));
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add (CProp
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("equal",
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[CProp ("if",[CProp ("if",[CVar 0; CVar 1; CVar 2]); CVar 3; CVar 4]);
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CProp
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("if",
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[CVar 0; CProp ("if",[CVar 1; CVar 3; CVar 4]);
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CProp ("if",[CVar 2; CVar 3; CVar 4])])]));
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add (CProp
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("equal",
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[CProp ("zerop",[CVar 23]);
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CProp
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("or",
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[CProp ("equal",[CVar 23; CProp ("zero",[])]);
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CProp ("not",[CProp ("numberp",[CVar 23])])])]));
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add (CProp
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("equal",
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[CProp ("plus",[CProp ("plus",[CVar 23; CVar 24]); CVar 25]);
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CProp ("plus",[CVar 23; CProp ("plus",[CVar 24; CVar 25])])]));
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add (CProp
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("equal",
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[CProp ("equal",[CProp ("plus",[CVar 0; CVar 1]); CProp ("zero",[])]);
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CProp ("and",[CProp ("zerop",[CVar 0]); CProp ("zerop",[CVar 1])])]));
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add (CProp
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("equal",[CProp ("difference",[CVar 23; CVar 23]); CProp ("zero",[])]));
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add (CProp
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("equal",
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[CProp
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("equal",
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[CProp ("plus",[CVar 0; CVar 1]); CProp ("plus",[CVar 0; CVar 2])]);
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CProp ("equal",[CProp ("fix",[CVar 1]); CProp ("fix",[CVar 2])])]));
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add (CProp
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("equal",
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[CProp
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("equal",[CProp ("zero",[]); CProp ("difference",[CVar 23; CVar 24])]);
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CProp ("not",[CProp ("gt",[CVar 24; CVar 23])])]));
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add (CProp
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("equal",
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[CProp ("equal",[CVar 23; CProp ("difference",[CVar 23; CVar 24])]);
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CProp
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("and",
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[CProp ("numberp",[CVar 23]);
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CProp
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("or",
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[CProp ("equal",[CVar 23; CProp ("zero",[])]);
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CProp ("zerop",[CVar 24])])])]));
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add (CProp
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("equal",
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[CProp
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("meaning",
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[CProp ("plus_tree",[CProp ("append",[CVar 23; CVar 24])]); CVar 0]);
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CProp
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("plus",
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[CProp ("meaning",[CProp ("plus_tree",[CVar 23]); CVar 0]);
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CProp ("meaning",[CProp ("plus_tree",[CVar 24]); CVar 0])])]));
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add (CProp
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("equal",
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[CProp
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("meaning",
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[CProp ("plus_tree",[CProp ("plus_fringe",[CVar 23])]); CVar 0]);
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CProp ("fix",[CProp ("meaning",[CVar 23; CVar 0])])]));
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add (CProp
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("equal",
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[CProp ("append",[CProp ("append",[CVar 23; CVar 24]); CVar 25]);
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CProp ("append",[CVar 23; CProp ("append",[CVar 24; CVar 25])])]));
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add (CProp
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("equal",
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[CProp ("reverse",[CProp ("append",[CVar 0; CVar 1])]);
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CProp
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("append",[CProp ("reverse",[CVar 1]); CProp ("reverse",[CVar 0])])]));
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add (CProp
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("equal",
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[CProp ("times",[CVar 23; CProp ("plus",[CVar 24; CVar 25])]);
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CProp
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("plus",
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[CProp ("times",[CVar 23; CVar 24]);
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CProp ("times",[CVar 23; CVar 25])])]));
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add (CProp
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("equal",
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[CProp ("times",[CProp ("times",[CVar 23; CVar 24]); CVar 25]);
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CProp ("times",[CVar 23; CProp ("times",[CVar 24; CVar 25])])]));
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add (CProp
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("equal",
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[CProp
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("equal",[CProp ("times",[CVar 23; CVar 24]); CProp ("zero",[])]);
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CProp ("or",[CProp ("zerop",[CVar 23]); CProp ("zerop",[CVar 24])])]));
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add (CProp
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("equal",
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[CProp ("exec",[CProp ("append",[CVar 23; CVar 24]); CVar 15; CVar 4]);
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CProp
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("exec",[CVar 24; CProp ("exec",[CVar 23; CVar 15; CVar 4]); CVar 4])]));
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add (CProp
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("equal",
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[CProp ("mc_flatten",[CVar 23; CVar 24]);
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CProp ("append",[CProp ("flatten",[CVar 23]); CVar 24])]));
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add (CProp
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("equal",
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[CProp ("member",[CVar 23; CProp ("append",[CVar 0; CVar 1])]);
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CProp
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("or",
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[CProp ("member",[CVar 23; CVar 0]);
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CProp ("member",[CVar 23; CVar 1])])]));
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add (CProp
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("equal",
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[CProp ("member",[CVar 23; CProp ("reverse",[CVar 24])]);
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CProp ("member",[CVar 23; CVar 24])]));
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add (CProp
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("equal",
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[CProp ("length",[CProp ("reverse",[CVar 23])]);
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CProp ("length",[CVar 23])]));
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add (CProp
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("equal",
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[CProp ("member",[CVar 0; CProp ("intersect",[CVar 1; CVar 2])]);
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CProp
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("and",
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[CProp ("member",[CVar 0; CVar 1]); CProp ("member",[CVar 0; CVar 2])])]));
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add (CProp
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("equal",[CProp ("nth",[CProp ("zero",[]); CVar 8]); CProp ("zero",[])]));
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add (CProp
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("equal",
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[CProp ("exp",[CVar 8; CProp ("plus",[CVar 9; CVar 10])]);
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CProp
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("times",
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[CProp ("exp",[CVar 8; CVar 9]); CProp ("exp",[CVar 8; CVar 10])])]));
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add (CProp
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("equal",
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[CProp ("exp",[CVar 8; CProp ("times",[CVar 9; CVar 10])]);
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CProp ("exp",[CProp ("exp",[CVar 8; CVar 9]); CVar 10])]));
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add (CProp
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("equal",
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[CProp ("reverse_loop",[CVar 23; CVar 24]);
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CProp ("append",[CProp ("reverse",[CVar 23]); CVar 24])]));
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add (CProp
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("equal",
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[CProp ("reverse_loop",[CVar 23; CProp ("nil",[])]);
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CProp ("reverse",[CVar 23])]));
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add (CProp
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("equal",
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[CProp ("count_list",[CVar 25; CProp ("sort_lp",[CVar 23; CVar 24])]);
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CProp
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("plus",
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[CProp ("count_list",[CVar 25; CVar 23]);
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CProp ("count_list",[CVar 25; CVar 24])])]));
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add (CProp
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("equal",
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[CProp
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("equal",
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[CProp ("append",[CVar 0; CVar 1]); CProp ("append",[CVar 0; CVar 2])]);
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CProp ("equal",[CVar 1; CVar 2])]));
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add (CProp
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("equal",
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[CProp
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("plus",
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[CProp ("remainder",[CVar 23; CVar 24]);
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CProp ("times",[CVar 24; CProp ("quotient",[CVar 23; CVar 24])])]);
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CProp ("fix",[CVar 23])]));
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add (CProp
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("equal",
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[CProp
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("power_eval",[CProp ("big_plus",[CVar 11; CVar 8; CVar 1]); CVar 1]);
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CProp ("plus",[CProp ("power_eval",[CVar 11; CVar 1]); CVar 8])]));
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add (CProp
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("equal",
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[CProp
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("power_eval",
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[CProp ("big_plus",[CVar 23; CVar 24; CVar 8; CVar 1]); CVar 1]);
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CProp
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("plus",
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[CVar 8;
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CProp
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("plus",
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[CProp ("power_eval",[CVar 23; CVar 1]);
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CProp ("power_eval",[CVar 24; CVar 1])])])]));
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add (CProp
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("equal",
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[CProp ("remainder",[CVar 24; CProp ("one",[])]); CProp ("zero",[])]));
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add (CProp
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("equal",
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[CProp ("lt",[CProp ("remainder",[CVar 23; CVar 24]); CVar 24]);
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CProp ("not",[CProp ("zerop",[CVar 24])])]));
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add (CProp
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("equal",[CProp ("remainder",[CVar 23; CVar 23]); CProp ("zero",[])]));
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add (CProp
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("equal",
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[CProp ("lt",[CProp ("quotient",[CVar 8; CVar 9]); CVar 8]);
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CProp
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("and",
|
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[CProp ("not",[CProp ("zerop",[CVar 8])]);
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CProp
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("or",
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[CProp ("zerop",[CVar 9]);
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CProp ("not",[CProp ("equal",[CVar 9; CProp ("one",[])])])])])]));
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add (CProp
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("equal",
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[CProp ("lt",[CProp ("remainder",[CVar 23; CVar 24]); CVar 23]);
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CProp
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("and",
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[CProp ("not",[CProp ("zerop",[CVar 24])]);
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CProp ("not",[CProp ("zerop",[CVar 23])]);
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CProp ("not",[CProp ("lt",[CVar 23; CVar 24])])])]));
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add (CProp
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("equal",
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[CProp ("power_eval",[CProp ("power_rep",[CVar 8; CVar 1]); CVar 1]);
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CProp ("fix",[CVar 8])]));
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add (CProp
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("equal",
|
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[CProp
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("power_eval",
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[CProp
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("big_plus",
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[CProp ("power_rep",[CVar 8; CVar 1]);
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CProp ("power_rep",[CVar 9; CVar 1]); CProp ("zero",[]);
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CVar 1]);
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CVar 1]);
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CProp ("plus",[CVar 8; CVar 9])]));
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add (CProp
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("equal",
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[CProp ("gcd",[CVar 23; CVar 24]); CProp ("gcd",[CVar 24; CVar 23])]));
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add (CProp
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("equal",
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[CProp ("nth",[CProp ("append",[CVar 0; CVar 1]); CVar 8]);
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CProp
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("append",
|
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[CProp ("nth",[CVar 0; CVar 8]);
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CProp
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("nth",
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[CVar 1; CProp ("difference",[CVar 8; CProp ("length",[CVar 0])])])])]));
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add (CProp
|
|
("equal",
|
|
[CProp ("difference",[CProp ("plus",[CVar 23; CVar 24]); CVar 23]);
|
|
CProp ("fix",[CVar 24])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("difference",[CProp ("plus",[CVar 24; CVar 23]); CVar 23]);
|
|
CProp ("fix",[CVar 24])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp
|
|
("difference",
|
|
[CProp ("plus",[CVar 23; CVar 24]); CProp ("plus",[CVar 23; CVar 25])]);
|
|
CProp ("difference",[CVar 24; CVar 25])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("times",[CVar 23; CProp ("difference",[CVar 2; CVar 22])]);
|
|
CProp
|
|
("difference",
|
|
[CProp ("times",[CVar 2; CVar 23]);
|
|
CProp ("times",[CVar 22; CVar 23])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("remainder",[CProp ("times",[CVar 23; CVar 25]); CVar 25]);
|
|
CProp ("zero",[])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp
|
|
("difference",
|
|
[CProp ("plus",[CVar 1; CProp ("plus",[CVar 0; CVar 2])]); CVar 0]);
|
|
CProp ("plus",[CVar 1; CVar 2])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp
|
|
("difference",
|
|
[CProp ("add1",[CProp ("plus",[CVar 24; CVar 25])]); CVar 25]);
|
|
CProp ("add1",[CVar 24])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp
|
|
("lt",
|
|
[CProp ("plus",[CVar 23; CVar 24]); CProp ("plus",[CVar 23; CVar 25])]);
|
|
CProp ("lt",[CVar 24; CVar 25])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp
|
|
("lt",
|
|
[CProp ("times",[CVar 23; CVar 25]);
|
|
CProp ("times",[CVar 24; CVar 25])]);
|
|
CProp
|
|
("and",
|
|
[CProp ("not",[CProp ("zerop",[CVar 25])]);
|
|
CProp ("lt",[CVar 23; CVar 24])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("lt",[CVar 24; CProp ("plus",[CVar 23; CVar 24])]);
|
|
CProp ("not",[CProp ("zerop",[CVar 23])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp
|
|
("gcd",
|
|
[CProp ("times",[CVar 23; CVar 25]);
|
|
CProp ("times",[CVar 24; CVar 25])]);
|
|
CProp ("times",[CVar 25; CProp ("gcd",[CVar 23; CVar 24])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("value",[CProp ("normalize",[CVar 23]); CVar 0]);
|
|
CProp ("value",[CVar 23; CVar 0])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp
|
|
("equal",
|
|
[CProp ("flatten",[CVar 23]);
|
|
CProp ("cons",[CVar 24; CProp ("nil",[])])]);
|
|
CProp
|
|
("and",
|
|
[CProp ("nlistp",[CVar 23]); CProp ("equal",[CVar 23; CVar 24])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("listp",[CProp ("gother",[CVar 23])]);
|
|
CProp ("listp",[CVar 23])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("samefringe",[CVar 23; CVar 24]);
|
|
CProp
|
|
("equal",[CProp ("flatten",[CVar 23]); CProp ("flatten",[CVar 24])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp
|
|
("equal",
|
|
[CProp ("greatest_factor",[CVar 23; CVar 24]); CProp ("zero",[])]);
|
|
CProp
|
|
("and",
|
|
[CProp
|
|
("or",
|
|
[CProp ("zerop",[CVar 24]);
|
|
CProp ("equal",[CVar 24; CProp ("one",[])])]);
|
|
CProp ("equal",[CVar 23; CProp ("zero",[])])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp
|
|
("equal",
|
|
[CProp ("greatest_factor",[CVar 23; CVar 24]); CProp ("one",[])]);
|
|
CProp ("equal",[CVar 23; CProp ("one",[])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("numberp",[CProp ("greatest_factor",[CVar 23; CVar 24])]);
|
|
CProp
|
|
("not",
|
|
[CProp
|
|
("and",
|
|
[CProp
|
|
("or",
|
|
[CProp ("zerop",[CVar 24]);
|
|
CProp ("equal",[CVar 24; CProp ("one",[])])]);
|
|
CProp ("not",[CProp ("numberp",[CVar 23])])])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("times_list",[CProp ("append",[CVar 23; CVar 24])]);
|
|
CProp
|
|
("times",
|
|
[CProp ("times_list",[CVar 23]); CProp ("times_list",[CVar 24])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("prime_list",[CProp ("append",[CVar 23; CVar 24])]);
|
|
CProp
|
|
("and",
|
|
[CProp ("prime_list",[CVar 23]); CProp ("prime_list",[CVar 24])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("equal",[CVar 25; CProp ("times",[CVar 22; CVar 25])]);
|
|
CProp
|
|
("and",
|
|
[CProp ("numberp",[CVar 25]);
|
|
CProp
|
|
("or",
|
|
[CProp ("equal",[CVar 25; CProp ("zero",[])]);
|
|
CProp ("equal",[CVar 22; CProp ("one",[])])])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("ge",[CVar 23; CVar 24]);
|
|
CProp ("not",[CProp ("lt",[CVar 23; CVar 24])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("equal",[CVar 23; CProp ("times",[CVar 23; CVar 24])]);
|
|
CProp
|
|
("or",
|
|
[CProp ("equal",[CVar 23; CProp ("zero",[])]);
|
|
CProp
|
|
("and",
|
|
[CProp ("numberp",[CVar 23]);
|
|
CProp ("equal",[CVar 24; CProp ("one",[])])])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("remainder",[CProp ("times",[CVar 24; CVar 23]); CVar 24]);
|
|
CProp ("zero",[])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("equal",[CProp ("times",[CVar 0; CVar 1]); CProp ("one",[])]);
|
|
CProp
|
|
("and",
|
|
[CProp ("not",[CProp ("equal",[CVar 0; CProp ("zero",[])])]);
|
|
CProp ("not",[CProp ("equal",[CVar 1; CProp ("zero",[])])]);
|
|
CProp ("numberp",[CVar 0]); CProp ("numberp",[CVar 1]);
|
|
CProp ("equal",[CProp ("sub1",[CVar 0]); CProp ("zero",[])]);
|
|
CProp ("equal",[CProp ("sub1",[CVar 1]); CProp ("zero",[])])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp
|
|
("lt",
|
|
[CProp ("length",[CProp ("delete",[CVar 23; CVar 11])]);
|
|
CProp ("length",[CVar 11])]);
|
|
CProp ("member",[CVar 23; CVar 11])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("sort2",[CProp ("delete",[CVar 23; CVar 11])]);
|
|
CProp ("delete",[CVar 23; CProp ("sort2",[CVar 11])])]));
|
|
add (CProp ("equal",[CProp ("dsort",[CVar 23]); CProp ("sort2",[CVar 23])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp
|
|
("length",
|
|
[CProp
|
|
("cons",
|
|
[CVar 0;
|
|
CProp
|
|
("cons",
|
|
[CVar 1;
|
|
CProp
|
|
("cons",
|
|
[CVar 2;
|
|
CProp
|
|
("cons",
|
|
[CVar 3;
|
|
CProp ("cons",[CVar 4; CProp ("cons",[CVar 5; CVar 6])])])])])])])
|
|
; CProp ("plus",[CProp ("six",[]); CProp ("length",[CVar 6])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp
|
|
("difference",
|
|
[CProp ("add1",[CProp ("add1",[CVar 23])]); CProp ("two",[])]);
|
|
CProp ("fix",[CVar 23])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp
|
|
("quotient",
|
|
[CProp ("plus",[CVar 23; CProp ("plus",[CVar 23; CVar 24])]);
|
|
CProp ("two",[])]);
|
|
CProp
|
|
("plus",[CVar 23; CProp ("quotient",[CVar 24; CProp ("two",[])])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("sigma",[CProp ("zero",[]); CVar 8]);
|
|
CProp
|
|
("quotient",
|
|
[CProp ("times",[CVar 8; CProp ("add1",[CVar 8])]); CProp ("two",[])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("plus",[CVar 23; CProp ("add1",[CVar 24])]);
|
|
CProp
|
|
("if",
|
|
[CProp ("numberp",[CVar 24]);
|
|
CProp ("add1",[CProp ("plus",[CVar 23; CVar 24])]);
|
|
CProp ("add1",[CVar 23])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp
|
|
("equal",
|
|
[CProp ("difference",[CVar 23; CVar 24]);
|
|
CProp ("difference",[CVar 25; CVar 24])]);
|
|
CProp
|
|
("if",
|
|
[CProp ("lt",[CVar 23; CVar 24]);
|
|
CProp ("not",[CProp ("lt",[CVar 24; CVar 25])]);
|
|
CProp
|
|
("if",
|
|
[CProp ("lt",[CVar 25; CVar 24]);
|
|
CProp ("not",[CProp ("lt",[CVar 24; CVar 23])]);
|
|
CProp ("equal",[CProp ("fix",[CVar 23]); CProp ("fix",[CVar 25])])])])])
|
|
);
|
|
add (CProp
|
|
("equal",
|
|
[CProp
|
|
("meaning",
|
|
[CProp ("plus_tree",[CProp ("delete",[CVar 23; CVar 24])]); CVar 0]);
|
|
CProp
|
|
("if",
|
|
[CProp ("member",[CVar 23; CVar 24]);
|
|
CProp
|
|
("difference",
|
|
[CProp ("meaning",[CProp ("plus_tree",[CVar 24]); CVar 0]);
|
|
CProp ("meaning",[CVar 23; CVar 0])]);
|
|
CProp ("meaning",[CProp ("plus_tree",[CVar 24]); CVar 0])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("times",[CVar 23; CProp ("add1",[CVar 24])]);
|
|
CProp
|
|
("if",
|
|
[CProp ("numberp",[CVar 24]);
|
|
CProp
|
|
("plus",
|
|
[CVar 23; CProp ("times",[CVar 23; CVar 24]);
|
|
CProp ("fix",[CVar 23])])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("nth",[CProp ("nil",[]); CVar 8]);
|
|
CProp
|
|
("if",[CProp ("zerop",[CVar 8]); CProp ("nil",[]); CProp ("zero",[])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("last",[CProp ("append",[CVar 0; CVar 1])]);
|
|
CProp
|
|
("if",
|
|
[CProp ("listp",[CVar 1]); CProp ("last",[CVar 1]);
|
|
CProp
|
|
("if",
|
|
[CProp ("listp",[CVar 0]);
|
|
CProp ("cons",[CProp ("car",[CProp ("last",[CVar 0])]); CVar 1]);
|
|
CVar 1])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("equal",[CProp ("lt",[CVar 23; CVar 24]); CVar 25]);
|
|
CProp
|
|
("if",
|
|
[CProp ("lt",[CVar 23; CVar 24]);
|
|
CProp ("equal",[CProp ("true",[]); CVar 25]);
|
|
CProp ("equal",[CProp ("false",[]); CVar 25])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("assignment",[CVar 23; CProp ("append",[CVar 0; CVar 1])]);
|
|
CProp
|
|
("if",
|
|
[CProp ("assignedp",[CVar 23; CVar 0]);
|
|
CProp ("assignment",[CVar 23; CVar 0]);
|
|
CProp ("assignment",[CVar 23; CVar 1])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("car",[CProp ("gother",[CVar 23])]);
|
|
CProp
|
|
("if",
|
|
[CProp ("listp",[CVar 23]);
|
|
CProp ("car",[CProp ("flatten",[CVar 23])]); CProp ("zero",[])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("flatten",[CProp ("cdr",[CProp ("gother",[CVar 23])])]);
|
|
CProp
|
|
("if",
|
|
[CProp ("listp",[CVar 23]);
|
|
CProp ("cdr",[CProp ("flatten",[CVar 23])]);
|
|
CProp ("cons",[CProp ("zero",[]); CProp ("nil",[])])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("quotient",[CProp ("times",[CVar 24; CVar 23]); CVar 24]);
|
|
CProp
|
|
("if",
|
|
[CProp ("zerop",[CVar 24]); CProp ("zero",[]);
|
|
CProp ("fix",[CVar 23])])]));
|
|
add (CProp
|
|
("equal",
|
|
[CProp ("get",[CVar 9; CProp ("set",[CVar 8; CVar 21; CVar 12])]);
|
|
CProp
|
|
("if",
|
|
[CProp ("eqp",[CVar 9; CVar 8]); CVar 21;
|
|
CProp ("get",[CVar 9; CVar 12])])]))
|
|
|
|
(* Tautology checker *)
|
|
|
|
let truep x lst =
|
|
match x with
|
|
Prop(head, _) ->
|
|
head.name = "true" || List.mem x lst
|
|
| _ ->
|
|
List.mem x lst
|
|
|
|
and falsep x lst =
|
|
match x with
|
|
Prop(head, _) ->
|
|
head.name = "false" || List.mem x lst
|
|
| _ ->
|
|
List.mem x lst
|
|
|
|
|
|
let rec tautologyp x true_lst false_lst =
|
|
if truep x true_lst then true else
|
|
if falsep x false_lst then false else begin
|
|
(*
|
|
print_term x; print_newline();
|
|
*)
|
|
match x with
|
|
Var _ -> false
|
|
| Prop (head,[test; yes; no]) as p ->
|
|
if head.name = "if" then
|
|
if truep test true_lst then
|
|
tautologyp yes true_lst false_lst
|
|
else if falsep test false_lst then
|
|
tautologyp no true_lst false_lst
|
|
else tautologyp yes (test::true_lst) false_lst &&
|
|
tautologyp no true_lst (test::false_lst)
|
|
else
|
|
false
|
|
| _ -> assert false
|
|
end
|
|
|
|
|
|
let tautp x =
|
|
(* print_term x; print_string"\n"; *)
|
|
let y = rewrite x in
|
|
(* print_term y; print_string "\n"; *)
|
|
tautologyp y [] []
|
|
|
|
(* the benchmark *)
|
|
|
|
let subst =
|
|
[Bind(23, cterm_to_term(
|
|
CProp
|
|
("f",
|
|
[CProp
|
|
("plus",
|
|
[CProp ("plus",[CVar 0; CVar 1]);
|
|
CProp ("plus",[CVar 2; CProp ("zero",[])])])])));
|
|
Bind(24, cterm_to_term(
|
|
CProp
|
|
("f",
|
|
[CProp
|
|
("times",
|
|
[CProp ("times",[CVar 0; CVar 1]);
|
|
CProp ("plus",[CVar 2; CVar 3])])])));
|
|
Bind(25, cterm_to_term(
|
|
CProp
|
|
("f",
|
|
[CProp
|
|
("reverse",
|
|
[CProp
|
|
("append",
|
|
[CProp ("append",[CVar 0; CVar 1]);
|
|
CProp ("nil",[])])])])));
|
|
Bind(20, cterm_to_term(
|
|
CProp
|
|
("equal",
|
|
[CProp ("plus",[CVar 0; CVar 1]);
|
|
CProp ("difference",[CVar 23; CVar 24])])));
|
|
Bind(22, cterm_to_term(
|
|
CProp
|
|
("lt",
|
|
[CProp ("remainder",[CVar 0; CVar 1]);
|
|
CProp ("member",[CVar 0; CProp ("length",[CVar 1])])])))]
|
|
|
|
let term = cterm_to_term(
|
|
CProp
|
|
("implies",
|
|
[CProp
|
|
("and",
|
|
[CProp ("implies",[CVar 23; CVar 24]);
|
|
CProp
|
|
("and",
|
|
[CProp ("implies",[CVar 24; CVar 25]);
|
|
CProp
|
|
("and",
|
|
[CProp ("implies",[CVar 25; CVar 20]);
|
|
CProp ("implies",[CVar 20; CVar 22])])])]);
|
|
CProp ("implies",[CVar 23; CVar 22])]))
|
|
|
|
let _ =
|
|
let ok = ref true in
|
|
for i = 1 to 50 do
|
|
if not (tautp (apply_subst subst term)) then ok := false
|
|
done;
|
|
if !ok then
|
|
print_string "Proved!\n"
|
|
else
|
|
print_string "Cannot prove!\n";
|
|
exit 0
|
|
|
|
(*********
|
|
with
|
|
failure s ->
|
|
print_string "Exception failure("; print_string s; print_string ")\n"
|
|
| Unify ->
|
|
print_string "Exception Unify\n"
|
|
| match_failure(file,start,stop) ->
|
|
print_string "Exception match_failure(";
|
|
print_string file;
|
|
print_string ",";
|
|
print_int start;
|
|
print_string ",";
|
|
print_int stop;
|
|
print_string ")\n"
|
|
| _ ->
|
|
print_string "Exception ?\n"
|
|
|
|
**********)
|