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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 *)
(* *)
(**************************************************************************)
type used = int
type clause_id = int
type 'hform rule =
(* Weakening *)
| Weaken of 'hform clause * 'hform list
(* * weaken : {a_1 ... a_n} --> {a_1 ... a_n b_1 ... b_n} *)
(* Simplification *)
| 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 * CoqInterface.Micromega_plugin_Certificate.Mc.zArithProof list
| LiaDiseq of 'hform
(* Arithmetic simplifications *)
| SplArith of 'hform clause * 'hform * CoqInterface.Micromega_plugin_Certificate.Mc.zArithProof list
(* Elimination of operators *)
| SplDistinctElim of 'hform clause * 'hform
(* Bit-blasting *)
| BBVar of 'hform
(* Bit-blasting a variable:
----------------------- bbVar
bbT(x, [x0; ...; xn])
*)
| BBConst of 'hform
(* Bit-blasting a constant:
----------------------- bbConst
bbT(#0100, [0; 0; 1; 0])
*)
| BBOp of 'hform clause * 'hform clause * 'hform
(* Bit-blasting bitwise operations: bbAnd, bbOr, ...
bbT(a, [a0; ...; an]) bbT(b, [b0; ...; bn])
-------------------------------------------------- bbAnd
bbT(a&b, [a0 /\ b0; ...; an /\ bn])
*)
| BBNot of 'hform clause * 'hform
(* Bit-blasting bitvector not
bbT(a, [a0; ...; an])
------------------------------ bbNot
bbT(not a, [~a0 ; ...; ~an])
*)
| BBNeg of 'hform clause * 'hform
(* Bit-blasting bitvector negation
bbT(a, [a0; ...; an])
------------------------------ bbNot
bbT(-a, [...])
*)
| BBAdd of 'hform clause * 'hform clause * 'hform
(* Bit-blasting bitvector addition
bbT(a, [a0; ...; an]) bbT(b, [b0; ...; bn])
-------------------------------------------------- bbAnd
bbT(a+b, [...])
*)
| BBMul of 'hform clause * 'hform clause * 'hform
(* Bit-blasting bitvector multiplication
bbT(a, [a0; ...; an]) bbT(b, [b0; ...; bn])
-------------------------------------------------- bbAnd
bbT(a*b, [...])
*)
| BBUlt of 'hform clause * 'hform clause * 'hform
(* Bit-blasting bitvector unsigned comparison
bbT(a, [a0; ...; an]) bbT(b, [b0; ...; bn])
-------------------------------------------------- bbAnd
bvult a b <-> ...
*)
| BBSlt of 'hform clause * 'hform clause * 'hform
(* Bit-blasting bitvector signed comparison
bbT(a, [a0; ...; an]) bbT(b, [b0; ...; bn])
-------------------------------------------------- bbAnd
bvslt a b <-> ...
*)
| BBConc of 'hform clause * 'hform clause * 'hform
(* Bit-blasting bitvector concatenation
bbT(a, [a0; ...; an]) bbT(b, [b0; ...; bn])
-------------------------------------------------- bbConc
bbT(concat a b, [a0; ...; an; b0; ...; bn])
*)
| BBExtr of 'hform clause * 'hform
(* Bit-blasting bitvector extraction
bbT(a, [a0; ...; an])
----------------------------------- bbExtr
bbT(extract i j a, [ai; ...; aj])
*)
| BBZextn of 'hform clause * 'hform
| BBSextn of 'hform clause * 'hform
(* Bit-blasting bitvector extensions
*)
| BBShl of 'hform clause * 'hform clause * 'hform
(* Bit-blasting bitvector shift left *)
| BBShr of 'hform clause * 'hform clause * 'hform
(* Bit-blasting bitvector shift right *)
| BBEq of 'hform clause * 'hform clause * 'hform
(* Bit-blasting equality
bbT(a, [a0; ...; an]) bbT(b, [b0; ...; bn])
-------------------------------------------------- bbEq
(a = b) <-> [(a0 <-> b0) /\ ... /\ (an <-> bn)]
*)
| BBDiseq of 'hform
(* disequality over constant bitvectors
----------------------------- bbDiseq
#b000010101 <> #b00000000
*)
| RowEq of 'hform
(* Read over write same index
------------------------------- roweq
select (store a i v) i = v
*)
| RowNeq of 'hform list
(* Read over write other index
------------------------------------------------- rowneq
i <> j -> select (store a i v) j = select a j
*)
| Ext of 'hform
(* Extensionality over arrays
------------------------------------------------------- ext
a = b \/ select a (diff a b) <> select b (diff a b)
*)
(* 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;
}
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;
}
val used_clauses : 'a rule -> 'a clause list
val to_string : 'a clause_kind -> string
val print_certif : ('a -> Format.formatter -> 'b -> unit) -> 'a -> 'b clause -> string -> unit
|
