100 lines
3.4 KiB
OCaml
100 lines
3.4 KiB
OCaml
(***********************************************************************)
|
|
(* *)
|
|
(* Objective Caml *)
|
|
(* *)
|
|
(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *)
|
|
(* *)
|
|
(* Copyright 1996 Institut National de Recherche en Informatique et *)
|
|
(* en Automatique. All rights reserved. This file is distributed *)
|
|
(* under the terms of the Q Public License version 1.0. *)
|
|
(* *)
|
|
(***********************************************************************)
|
|
|
|
(* $Id$ *)
|
|
|
|
(*********************** Recursive Path Ordering ****************************)
|
|
|
|
open Terms
|
|
|
|
type ordering =
|
|
Greater
|
|
| Equal
|
|
| NotGE
|
|
|
|
let ge_ord order pair = match order pair with NotGE -> false | _ -> true
|
|
and gt_ord order pair = match order pair with Greater -> true | _ -> false
|
|
and eq_ord order pair = match order pair with Equal -> true | _ -> false
|
|
|
|
|
|
let rec rem_eq equiv x = function
|
|
[] -> failwith "rem_eq"
|
|
| y::l -> if equiv (x,y) then l else y :: rem_eq equiv x l
|
|
|
|
|
|
let diff_eq equiv (x,y) =
|
|
let rec diffrec = function
|
|
([],_) as p -> p
|
|
| (h::t, y) -> try
|
|
diffrec (t, rem_eq equiv h y)
|
|
with Failure _ ->
|
|
let (x',y') = diffrec (t,y) in (h::x',y') in
|
|
if List.length x > List.length y then diffrec(y,x) else diffrec(x,y)
|
|
|
|
|
|
(* Multiset extension of order *)
|
|
|
|
let mult_ext order = function
|
|
Term(_,sons1), Term(_,sons2) ->
|
|
begin match diff_eq (eq_ord order) (sons1,sons2) with
|
|
([],[]) -> Equal
|
|
| (l1,l2) ->
|
|
if List.for_all
|
|
(fun n -> List.exists (fun m -> gt_ord order (m,n)) l1) l2
|
|
then Greater else NotGE
|
|
end
|
|
| _ -> failwith "mult_ext"
|
|
|
|
|
|
(* Lexicographic extension of order *)
|
|
|
|
let lex_ext order = function
|
|
(Term(_,sons1) as m), (Term(_,sons2) as n) ->
|
|
let rec lexrec = function
|
|
([] , []) -> Equal
|
|
| ([] , _ ) -> NotGE
|
|
| ( _ , []) -> Greater
|
|
| (x1::l1, x2::l2) ->
|
|
match order (x1,x2) with
|
|
Greater -> if List.for_all (fun n' -> gt_ord order (m,n')) l2
|
|
then Greater else NotGE
|
|
| Equal -> lexrec (l1,l2)
|
|
| NotGE -> if List.exists (fun m' -> ge_ord order (m',n)) l1
|
|
then Greater else NotGE in
|
|
lexrec (sons1, sons2)
|
|
| _ -> failwith "lex_ext"
|
|
|
|
|
|
(* Recursive path ordering *)
|
|
|
|
let rpo op_order ext =
|
|
let rec rporec (m,n) =
|
|
if m = n then Equal else
|
|
match m with
|
|
Var vm -> NotGE
|
|
| Term(op1,sons1) ->
|
|
match n with
|
|
Var vn ->
|
|
if occurs vn m then Greater else NotGE
|
|
| Term(op2,sons2) ->
|
|
match (op_order op1 op2) with
|
|
Greater ->
|
|
if List.for_all (fun n' -> gt_ord rporec (m,n')) sons2
|
|
then Greater else NotGE
|
|
| Equal ->
|
|
ext rporec (m,n)
|
|
| NotGE ->
|
|
if List.exists (fun m' -> ge_ord rporec (m',n)) sons1
|
|
then Greater else NotGE
|
|
in rporec
|
|
|