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|
(**************************************************************************)
(* *)
(* SMTCoq *)
(* Copyright (C) 2011 - 2016 *)
(* *)
(* Michaël Armand *)
(* Benjamin Grégoire *)
(* Chantal Keller *)
(* *)
(* Inria - École Polytechnique - Université Paris-Sud *)
(* *)
(* This file is distributed under the terms of the CeCILL-C licence *)
(* *)
(**************************************************************************)
open SmtForm
type used = int
type clause_id = int
type 'hform rule =
| ImmFlatten of 'hform clause * 'hform
(* CNF Transformations *)
| True
(* * true : {true}
*)
| False
(* * false : {(not false)}
*)
| BuildDef of 'hform (* the first literal of the clause *)
(* * and_neg : {(and a_1 ... a_n) (not a_1) ... (not a_n)}
* or_pos : {(not (or a_1 ... a_n)) a_1 ... a_n}
* implies_pos : {(not (implies a b)) (not a) b}
* xor_pos1 : {(not (xor a b)) a b}
* xor_neg1 : {(xor a b) a (not b)}
* equiv_pos1 : {(not (iff a b)) a (not b)}
* equiv_neg1 : {(iff a b) (not a) (not b)}
* ite_pos1 : {(not (if_then_else a b c)) a c}
* ite_neg1 : {(if_then_else a b c) a (not c)}
*)
| BuildDef2 of 'hform (* the first literal of the clause *)
(* * xor_pos2 : {(not (xor a b)) (not a) (not b)}
* xor_neg2 : {(xor a b) (not a) b}
* equiv_pos2 : {(not (iff a b)) (not a) b}
* equiv_neg2 : {(iff a b) a b}
* ite_pos2 : {(not (if_then_else a b c)) (not a) b}
* ite_neg2 : {(if_then_else a b c) (not a) (not b)}
*)
| BuildProj of 'hform * int
(* * or_neg : {(or a_1 ... a_n) (not a_i)}
* and_pos : {(not (and a_1 ... a_n)) a_i}
* implies_neg1 : {(implies a b) a}
* implies_neg2 : {(implies a b) (not b)}
*)
(* Immediate CNF transformation : CNF transformation + Reso *)
| ImmBuildDef of 'hform clause
(* * not_and : {(not (and a_1 ... a_n))} --> {(not a_1) ... (not a_n)}
* or : {(or a_1 ... a_n)} --> {a_1 ... a_n}
* implies : {(implies a b)} --> {(not a) b}
* xor1 : {(xor a b)} --> {a b}
* not_xor1 : {(not (xor a b))} --> {a (not b)}
* equiv2 : {(iff a b)} --> {a (not b)}
* not_equiv2 : {(not (iff a b))} --> {(not a) (not b)}
* ite1 : {(if_then_else a b c)} --> {a c}
* not_ite1 : {(not (if_then_else a b c))} --> {a (not c)}
*)
| ImmBuildDef2 of 'hform clause
(* * xor2 : {(xor a b)} --> {(not a) (not b)}
* not_xor2 : {(not (xor a b))} --> {(not a) b}
* equiv1 : {(iff a b)} --> {(not a) b}
* not_equiv1 : {(not (iff a b))} --> {a b}
* ite2 : {(if_then_else a b c)} --> {(not a) b}
* not_ite2 : {(not (if_then_else a b c))} --> {(not a) (not b)}
*)
| ImmBuildProj of 'hform clause * int
(* * and : {(and a_1 ... a_n)} --> {a_i}
* not_or : {(not (or a_1 ... a_n))} --> {(not a_i)}
* not_implies1 : {(not (implies a b))} --> {a}
* not_implies2 : {(not (implies a b))} --> {(not b)}
*)
(* Equality *)
| EqTr of 'hform * 'hform list
(* * eq_reflexive : {(= x x)}
* eq_transitive : {(not (= x_1 x_2)) ... (not (= x_{n-1} x_n)) (= x_1 x_n)}
*)
| EqCgr of 'hform * ('hform option) list
(* * eq_congruent : {(not (= x_1 y_1)) ... (not (= x_n y_n))
(= (f x_1 ... x_n) (f y_1 ... y_n))}
*)
| EqCgrP of 'hform * 'hform * ('hform option) list
(* * eq_congruent_pred : {(not (= x_1 y_1)) ... (not (= x_n y_n))
(not (p x_1 ... x_n)) (p y_1 ... y_n)}
*)
(* Linear arithmetic *)
| LiaMicromega of 'hform list * Structures.Micromega_plugin_Certificate.Mc.zArithProof list
| LiaDiseq of 'hform
(* Arithmetic simplifications *)
| SplArith of 'hform clause * 'hform * Structures.Micromega_plugin_Certificate.Mc.zArithProof list
(* Elimination of operators *)
| SplDistinctElim of 'hform clause * 'hform
(* Possibility to introduce "holes" in proofs (that should be filled in Coq) *)
| Hole of ('hform clause) list * 'hform list
| Forall_inst of 'hform clause * 'hform
| Qf_lemma of 'hform clause * 'hform
and 'hform clause = {
mutable id : clause_id;
mutable kind : 'hform clause_kind;
mutable pos : int option;
mutable used : used;
mutable prev : 'hform clause option;
mutable next : 'hform clause option;
mutable value : 'hform list option
(* This field should be defined for rules which can create atoms :
EqTr, EqCgr, EqCgrP, Lia, Dlde, Lra *)
}
and 'hform clause_kind =
| Root
| Same of 'hform clause
| Res of 'hform resolution
| Other of 'hform rule
and 'hform resolution = {
mutable rc1 : 'hform clause;
mutable rc2 : 'hform clause;
mutable rtail : 'hform clause list}
let used_clauses r =
match r with
| ImmBuildProj (c, _) | ImmBuildDef c | ImmBuildDef2 c
| ImmFlatten (c,_) | SplArith (c,_,_) | SplDistinctElim (c,_)
| Forall_inst (c, _) | Qf_lemma (c, _) -> [c]
| Hole (cs, _) -> cs
| True | False | BuildDef _ | BuildDef2 _ | BuildProj _
| EqTr _ | EqCgr _ | EqCgrP _
| LiaMicromega _ | LiaDiseq _ -> []
(* For debugging certif processing purposes : <add_scertif> <select> <occur> <alloc> *)
let to_string r =
match r with
Root -> "Root"
| Same c -> "Same(" ^ string_of_int (c.id) ^ ")"
| Res r ->
let id1 = string_of_int r.rc1.id in
let id2 = string_of_int r.rc2.id in
let rest_ids = List.fold_left (fun str rc -> str ^ "; " ^ string_of_int rc.id) "" r.rtail in
"Res [" ^ id1 ^ "; " ^ id2 ^ rest_ids ^"]"
| Other x -> "Other(" ^
begin match x with
| True -> "True"
| False -> "False"
| BuildDef _ -> "BuildDef"
| BuildDef2 _ -> "BuildDef2"
| BuildProj _ -> "BuildProj"
| EqTr _ -> "EqTr"
| EqCgr _ -> "EqCgr"
| EqCgrP _ -> "EqCgrP"
| LiaMicromega _ -> "LiaMicromega"
| LiaDiseq _ -> "LiaDiseq"
| Qf_lemma _ -> "Qf_lemma"
| Hole _ -> "Hole"
| ImmFlatten _ -> "ImmFlatten"
| ImmBuildDef _ -> "ImmBuildDef"
| ImmBuildDef2 _ -> "ImmBuildDef2"
| ImmBuildProj _ -> "ImmBuildProj"
| SplArith _ -> "SplArith"
| SplDistinctElim _ -> "SplDistinctElim"
| Forall_inst _ -> "Forall_inst" end ^ ")"
(* To use <print_certif>, pass, as first and second argument, <Form.to_smt> and <Atom.to_string> *)
let print_certif form_to_smt atom_to_string c where=
let rec start c =
match c.prev with
| None -> c
| Some c -> start c in
let r = ref (start c) in
let out_channel = open_out where in
let fmt = Format.formatter_of_out_channel out_channel in
let continue = ref true in
while !continue do
let kind = to_string (!r.kind) in
let id = !r.id in
let pos = match !r.pos with
| None -> "None"
| Some p -> string_of_int p in
let used = !r.used in
Format.fprintf fmt "id:%i kind:%s pos:%s used:%i value:" id kind pos used;
begin match !r.value with
| None -> Format.fprintf fmt "None"
| Some l -> List.iter (fun f -> form_to_smt atom_to_string fmt f;
Format.fprintf fmt " ") l end;
Format.fprintf fmt "\n";
match !r.next with
| None -> continue := false
| Some n -> r := n
done;
Format.fprintf fmt "@."; close_out out_channel
|
