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|
(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(* $Id$ *)
(* This file implements the basic congruence-closure algorithm by *)
(* Downey,Sethi and Tarjan. *)
open Names
open Term
let init_size=251
type term=Symb of constr|Appli of term*term
(* Basic Union-Find algo w/o path compression *)
module UF = struct
type tag=Congr|Ax of identifier
type cl=Rep of int*(int list)|Eqto of int*(int*int*tag)
type vertex=Leaf|Node of (int*int)
type t=(int ref)*((int,(cl*vertex*term)) Hashtbl.t)
let empty ()=(((ref 0),(Hashtbl.create init_size)):t)
let add_lst i t ((a,m):t)=
match Hashtbl.find m i with
((Rep(l,lst)),v,trm)->Hashtbl.replace m i ((Rep((l+1),(t::lst))),v,trm)
| _ ->failwith "add_lst: not a representative"
let rec find ((a,m):t) i=
let (cl,_,_)=Hashtbl.find m i in
match cl with
Rep(_,_) -> i
| Eqto(j,_) ->find (a,m) j
let list ((a,m):t) i=
match Hashtbl.find m i with
((Rep(_,lst)),_,_)-> lst
| _ ->failwith "list: not a class"
let size ((a,m):t) i=
match Hashtbl.find m i with
((Rep (l,_)),_,_) -> l
| _ ->failwith "size: not a class"
let signature ((a,m):t) i=
let (_,v,_)=Hashtbl.find m i in
match v with
Node(j,k)->(find (a,m) j,find (a,m) k)
| _ ->failwith "signature: not a node"
let nodes ((a,m):t)= (* cherche les noeuds binaires *)
Hashtbl.fold (fun i (_,v,_) l->match v with Node (_,_)->i::l|_->l) m []
let rec add t (a,m) syms =
try Hashtbl.find syms t with Not_found ->
match t with
Symb s ->
let b= !a in incr a;
Hashtbl.add m b ((Rep (0,[])),Leaf,t);
Hashtbl.add syms t b;
b
| Appli (t1,t2) ->
let i1=add t1 (a,m) syms and i2=add t2 (a,m) syms in
let b= !a in incr a;
add_lst (find (a,m) i1) b (a,m);
add_lst (find (a,m) i2) b (a,m);
Hashtbl.add m b ((Rep (0,[])),(Node(i1,i2)),t);
Hashtbl.add syms t b;
b
let union ((a,m):t) i1 i2 t=
let (cl1,v1,t1)=(Hashtbl.find m i1) and
(cl2,v2,t2)=(Hashtbl.find m i2) in
match cl1,cl1 with
((Rep (l1,lst1)),(Rep (l2,lst2))) ->
Hashtbl.replace m i2 ((Eqto (i1,t)),v2,t2);
Hashtbl.replace m i1 ((Rep((l2+l1),(lst2@lst1))),v1,t1)
| _ ->failwith "union: not classes"
end
(* Signature table *)
module ST=struct
(* l: sign -> term r: term -> sign *)
type t = ((int*int,int) Hashtbl.t) * ((int,int*int) Hashtbl.t)
let empty ()=((Hashtbl.create init_size),(Hashtbl.create init_size))
let enter t sign ((l,r) as st:t)=
if Hashtbl.mem l sign then
failwith "enter: signature already entered"
else
Hashtbl.replace l sign t;
Hashtbl.replace r t sign
let query sign ((l,r):t)=Hashtbl.find l sign
let delete t ((l,r) as st:t)=
try let sign=Hashtbl.find r t in
Hashtbl.remove l sign;
Hashtbl.remove r t
with
Not_found -> ()
let rec delete_list l st=
match l with
[]->()
| t::q -> delete t st;delete_list q st
end
let rec combine_rec uf st=function
[]->[]
| v::pending->
let combine=(combine_rec uf st pending) in
let s=UF.signature uf v in
try (v,(ST.query s st))::combine with
Not_found->
ST.enter v s st;combine
let rec process_rec uf st=function
[]->[]
| (v,w)::combine->
let pending=process_rec uf st combine in
let i=UF.find uf v
and j=UF.find uf w in
if (i==j)|| ((Hashtbl.hash i)=(Hashtbl.hash j) && (i=j)) then
pending
else
if (UF.size uf i)<(UF.size uf j) then
let l=UF.list uf i in
UF.union uf j i (v,w,UF.Congr);
ST.delete_list l st;
l@pending
else
let l=UF.list uf j in
UF.union uf i j (w,v,UF.Congr);
ST.delete_list l st;
l@pending
let rec cc_rec uf st=function
[]->()
| pending->
let combine=combine_rec uf st pending in
let pending0=process_rec uf st combine in
(cc_rec uf st pending0)
let cc uf=(cc_rec uf (ST.empty ()) (UF.nodes uf))
let rec make_uf syms=function
[]->(UF.empty ())
| (ax,(v,w))::q->
let uf=make_uf syms q in
let i1=UF.add v uf syms in
let i2=UF.add w uf syms in
UF.union uf (UF.find uf i2) (UF.find uf i1) (i1,i2,(UF.Ax ax));
uf
let decide_prb (axioms,(v,w))=
let syms=Hashtbl.create init_size in
let uf=make_uf syms axioms in
let i1=UF.add v uf syms in
let i2=UF.add w uf syms in
cc uf;
(UF.find uf i1)=(UF.find uf i2)
|
