113 lines
3.2 KiB
OCaml
113 lines
3.2 KiB
OCaml
(***********************************************************************)
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(* *)
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(* OCaml *)
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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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(****************** Equation manipulations *************)
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open Terms
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type rule =
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{ number: int;
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numvars: int;
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lhs: term;
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rhs: term }
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(* standardizes an equation so its variables are 1,2,... *)
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let mk_rule num m n =
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let all_vars = union (vars m) (vars n) in
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let counter = ref 0 in
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let subst =
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List.map (fun v -> incr counter; (v, Var !counter)) (List.rev all_vars) in
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{ number = num;
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numvars = !counter;
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lhs = substitute subst m;
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rhs = substitute subst n }
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(* checks that rules are numbered in sequence and returns their number *)
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let check_rules rules =
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let counter = ref 0 in
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List.iter (fun r -> incr counter;
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if r.number <> !counter
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then failwith "Rule numbers not in sequence")
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rules;
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!counter
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let pretty_rule rule =
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print_int rule.number; print_string " : ";
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pretty_term rule.lhs; print_string " = "; pretty_term rule.rhs;
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print_newline()
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let pretty_rules rules = List.iter pretty_rule rules
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(****************** Rewriting **************************)
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(* Top-level rewriting. Let eq:L=R be an equation, M be a term such that L<=M.
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With sigma = matching L M, we define the image of M by eq as sigma(R) *)
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let reduce l m r =
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substitute (matching l m) r
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(* Test whether m can be reduced by l, i.e. m contains an instance of l. *)
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let can_match l m =
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try let _ = matching l m in true
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with Failure _ -> false
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let rec reducible l m =
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can_match l m ||
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(match m with
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| Term(_,sons) -> List.exists (reducible l) sons
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| _ -> false)
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(* Top-level rewriting with multiple rules. *)
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let rec mreduce rules m =
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match rules with
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[] -> failwith "mreduce"
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| rule::rest ->
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try
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reduce rule.lhs m rule.rhs
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with Failure _ ->
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mreduce rest m
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(* One step of rewriting in leftmost-outermost strategy,
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with multiple rules. Fails if no redex is found *)
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let rec mrewrite1 rules m =
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try
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mreduce rules m
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with Failure _ ->
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match m with
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Var n -> failwith "mrewrite1"
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| Term(f, sons) -> Term(f, mrewrite1_sons rules sons)
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and mrewrite1_sons rules = function
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[] -> failwith "mrewrite1"
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| son::rest ->
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try
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mrewrite1 rules son :: rest
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with Failure _ ->
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son :: mrewrite1_sons rules rest
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(* Iterating rewrite1. Returns a normal form. May loop forever *)
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let rec mrewrite_all rules m =
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try
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mrewrite_all rules (mrewrite1 rules m)
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with Failure _ ->
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m
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