100 lines
3.4 KiB
OCaml
100 lines
3.4 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: orderings.ml 2553 1999-11-17 18:59:06Z xleroy $ *)
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(*********************** Recursive Path Ordering ****************************)
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open Terms
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type ordering =
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Greater
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| Equal
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| NotGE
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let ge_ord order pair = match order pair with NotGE -> false | _ -> true
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and gt_ord order pair = match order pair with Greater -> true | _ -> false
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and eq_ord order pair = match order pair with Equal -> true | _ -> false
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let rec rem_eq equiv x = function
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[] -> failwith "rem_eq"
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| y::l -> if equiv (x,y) then l else y :: rem_eq equiv x l
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let diff_eq equiv (x,y) =
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let rec diffrec = function
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([],_) as p -> p
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| (h::t, y) -> try
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diffrec (t, rem_eq equiv h y)
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with Failure _ ->
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let (x',y') = diffrec (t,y) in (h::x',y') in
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if List.length x > List.length y then diffrec(y,x) else diffrec(x,y)
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(* Multiset extension of order *)
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let mult_ext order = function
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Term(_,sons1), Term(_,sons2) ->
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begin match diff_eq (eq_ord order) (sons1,sons2) with
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([],[]) -> Equal
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| (l1,l2) ->
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if List.for_all
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(fun n -> List.exists (fun m -> gt_ord order (m,n)) l1) l2
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then Greater else NotGE
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end
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| _ -> failwith "mult_ext"
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(* Lexicographic extension of order *)
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let lex_ext order = function
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(Term(_,sons1) as m), (Term(_,sons2) as n) ->
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let rec lexrec = function
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([] , []) -> Equal
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| ([] , _ ) -> NotGE
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| ( _ , []) -> Greater
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| (x1::l1, x2::l2) ->
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match order (x1,x2) with
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Greater -> if List.for_all (fun n' -> gt_ord order (m,n')) l2
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then Greater else NotGE
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| Equal -> lexrec (l1,l2)
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| NotGE -> if List.exists (fun m' -> ge_ord order (m',n)) l1
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then Greater else NotGE in
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lexrec (sons1, sons2)
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| _ -> failwith "lex_ext"
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(* Recursive path ordering *)
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let rpo op_order ext =
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let rec rporec (m,n) =
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if m = n then Equal else
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match m with
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Var vm -> NotGE
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| Term(op1,sons1) ->
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match n with
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Var vn ->
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if occurs vn m then Greater else NotGE
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| Term(op2,sons2) ->
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match (op_order op1 op2) with
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Greater ->
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if List.for_all (fun n' -> gt_ord rporec (m,n')) sons2
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then Greater else NotGE
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| Equal ->
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ext rporec (m,n)
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| NotGE ->
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if List.exists (fun m' -> ge_ord rporec (m',n)) sons1
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then Greater else NotGE
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in rporec
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