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|
(**************************************************************************)
(* *)
(* SMTCoq *)
(* Copyright (C) 2011 - 2021 *)
(* *)
(* See file "AUTHORS" for the list of authors *)
(* *)
(* This file is distributed under the terms of the CeCILL-C licence *)
(* *)
(**************************************************************************)
open SmtForm
open SmtCertif
open SmtTrace
module MakeCnf (Form:FORM) =
struct
type form_info =
| Immediate of bool (* true if the positive literal is set *)
| Done (* means that the equivalence clauses have been generated *)
| Todo (* nothing has been done, process the cnf transformation *)
let info = Hashtbl.create 17
let init_last =
let last = SmtTrace.mk_scertif Root None in
SmtTrace.clear ();
last
let last = ref init_last
let cnf_todo = ref []
let clear () =
Hashtbl.clear info;
last := init_last;
cnf_todo := []
let push_cnf args = cnf_todo := args :: !cnf_todo
let get_info l =
try Hashtbl.find info (Form.index l)
with Not_found -> Todo
let set_done l =
Hashtbl.add info (Form.index l) Done
let set_immediate l =
Hashtbl.add info (Form.index l) (Immediate (Form.is_pos l))
let test_immediate l =
match get_info l with
| Immediate b -> b = Form.is_pos l
| _ -> false
let check_trivial cl =
List.exists test_immediate cl
let link_Other other cl =
if not (check_trivial cl) then
let c = mkOther other (Some cl) in
link !last c;
last := c
let both_lit l = if Form.is_pos l then Form.neg l,l else l, Form.neg l
let or_of_imp args =
Array.mapi (fun i l ->
if i = Array.length args - 1 then l else Form.neg l) args
let rec cnf l =
match get_info l with
| Immediate _ | Done -> ()
| Todo ->
match Form.pform l with
| Fatom _ | FbbT _ -> ()
| Fapp (op,args) ->
match op with
| Ftrue | Ffalse -> ()
| Fand ->
let nl,pl = both_lit l in
let nargs = Array.map Form.neg args in
link_Other (BuildDef pl) (pl::Array.to_list nargs);
Array.iteri (fun i l' ->
link_Other (BuildProj (nl,i)) [nl;l']) args;
set_done l;
Array.iter cnf args
| For ->
let nl,pl = both_lit l in
link_Other (BuildDef nl) (nl::Array.to_list args);
Array.iteri (fun i l' ->
link_Other (BuildProj(pl,i)) [pl;Form.neg l']) args;
set_done l;
Array.iter cnf args
| Fimp ->
let args = or_of_imp args in
let nl,pl = both_lit l in
link_Other (BuildDef nl) (nl::Array.to_list args);
Array.iteri (fun i l' ->
link_Other (BuildProj(pl,i)) [pl;Form.neg l']) args;
set_done l;
Array.iter cnf args
| Fxor ->
let nl,pl = both_lit l in
let a, b = args.(0), args.(1) in
let na, nb = Form.neg a, Form.neg b in
link_Other (BuildDef nl) [nl;a;b];
link_Other (BuildDef pl) [pl;a;nb];
link_Other (BuildDef2 nl) [nl;na;nb];
link_Other (BuildDef2 pl) [pl;na;b];
set_done l;
cnf a;
cnf b
| Fiff ->
let nl,pl = both_lit l in
let a, b = args.(0), args.(1) in
let na, nb = Form.neg a, Form.neg b in
link_Other (BuildDef nl) [nl;a;nb];
link_Other (BuildDef pl) [pl;na;nb];
link_Other (BuildDef2 nl) [nl;na;b];
link_Other (BuildDef2 pl) [pl;a;b];
set_done l;
cnf a;
cnf b
| Fite ->
let nl,pl = both_lit l in
let a, b, c = args.(0), args.(1), args.(2) in
let na, nb, nc = Form.neg a, Form.neg b, Form.neg c in
link_Other (BuildDef nl) [nl;a;c];
link_Other (BuildDef pl) [pl;a;nc];
link_Other (BuildDef2 nl) [nl;na;b];
link_Other (BuildDef2 pl) [pl;na;nb];
set_done l;
cnf a;
cnf b;
cnf c
| Fnot2 _ -> cnf args.(0)
| Fforall _ -> assert false
exception Cnf_done
let rec imm_link_Other other l =
if not (test_immediate l) then
let c = mkOther other (Some [l]) in
link !last c;
last := c;
imm_cnf c
and imm_cnf c =
let l =
match c.value with
| Some [l] ->
begin match Form.pform l with
| Fapp (Fnot2 _, args) ->
let l' = args.(0) in
if Form.is_pos l then l'
else Form.neg l'
| _ -> l
end
| _ -> assert false in
match get_info l with
| Immediate b -> if b = Form.is_neg l then raise Cnf_done
| Done -> assert false
| Todo ->
set_immediate l;
match Form.pform l with
| Fatom _ | FbbT _ -> ()
| Fapp (op,args) ->
match op with
| Ftrue | Ffalse -> ()
| Fand ->
if Form.is_pos l then
Array.iteri (fun i l' ->
imm_link_Other (ImmBuildProj(c,i)) l') args
else begin
let nargs = Array.map Form.neg args in
link_Other (ImmBuildDef c) (Array.to_list nargs);
push_cnf args
end
| For ->
if Form.is_pos l then begin
link_Other (ImmBuildDef c) (Array.to_list args);
push_cnf args
end else
Array.iteri (fun i l' ->
imm_link_Other (ImmBuildProj(c,i)) (Form.neg l')) args
| Fimp ->
let args = or_of_imp args in
if Form.is_pos l then begin
link_Other (ImmBuildDef c) (Array.to_list args);
push_cnf args
end else
Array.iteri (fun i l' ->
imm_link_Other (ImmBuildProj(c,i)) (Form.neg l')) args
| Fxor ->
let args1 =
if Form.is_pos l then [args.(0);args.(1)]
else [args.(0);Form.neg args.(1)] in
let args2 =
if Form.is_pos l then [Form.neg args.(0);Form.neg args.(1)]
else [Form.neg args.(0); args.(1)] in
link_Other (ImmBuildDef c) args1;
link_Other (ImmBuildDef2 c) args2;
push_cnf args
| Fiff ->
let args1 =
if Form.is_pos l then [args.(0);Form.neg args.(1)]
else [Form.neg args.(0);Form.neg args.(1)] in
let args2 =
if Form.is_pos l then [Form.neg args.(0);args.(1)]
else [args.(0); args.(1)] in
link_Other (ImmBuildDef c) args1;
link_Other (ImmBuildDef2 c) args2;
push_cnf args
| Fite ->
let args1 =
if Form.is_pos l then [args.(0);Form.neg args.(2)]
else [args.(0);Form.neg args.(2)] in
let args2 =
if Form.is_pos l then [Form.neg args.(0);args.(1)]
else [Form.neg args.(0); Form.neg args.(1)] in
link_Other (ImmBuildDef c) args1;
link_Other (ImmBuildDef2 c) args2;
push_cnf args
| Fnot2 _ -> assert false
| Fforall _ -> assert false
let make_cnf reify c =
let ftrue = Form.get reify (Fapp(Ftrue, [||])) in
let ffalse = Form.get reify (Fapp(Ffalse, [||])) in
last := c;
link_Other True [ftrue];
link_Other False [Form.neg ffalse];
(try
imm_cnf c;
List.iter (Array.iter cnf) !cnf_todo
with Cnf_done -> ());
let res = !last in
clear ();
res
end
|
