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Definition order_map ( m m' : IntMap.ptrie LForm) : Prop := forall i f, IntMap.get' i m = Some f -> IntMap.get' i m' = Some f. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 424 |
Definition order_dom {A B:Type} (m : IntMap.ptrie A) (m': IntMap.ptrie B) : Prop := forall i, IntMap.get' i m <> None -> IntMap.get' i m' <> None. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 425 |
Definition valid_index (hm : hmap) (i : int) := exists f, has_form hm f /\ f.(id) = i. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 426 |
Definition wf_units_def {A:Type} (u: IntMap.ptrie A) (m: hmap) : Prop := forall i, IntMap.get' i u <> None -> valid_index m i. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 427 |
Record wf_pset (hm: hmap) (ps: LitSet.t) := { wf_map_pset : LitSet.wf ps; wf_index : forall i, LitSet.mem i ps = true -> valid_index hm i }. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 428 |
Definition is_literal_of_pset (d : LitSet.t) (l : literal) := IntMap.get' (id_of_literal l) d = Some None \/ IntMap.get' (id_of_literal l) d = Some (Some (is_positive_literal l)). | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 429 |
Definition is_literal_of_units (u: IntMap.ptrie (Annot.t bool)) (l:literal) := exists b, IntMap.get' (id_of_literal l) u = Some b /\ is_positive_literal l = Annot.elt b. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 430 |
Definition is_literal_of_state (st: state) (l: literal) := is_literal_of_units (units st) l \/ In l (List.map Annot.elt (unit_stack st)). | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 431 |
Definition is_pset_units (u: IntMap.ptrie (Annot.t bool)) (d: LitSet.t) := exists i b, IntMap.get' i u = Some b /\ d = Annot.deps b. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 432 |
Definition is_pset_stack (u: list (Annot.t literal)) (d: LitSet.t) := exists a, In a u /\ d = Annot.deps a. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 433 |
Definition is_pset_state (st: state) (d: LitSet.t) := is_pset_units (units st) d \/ is_pset_stack (unit_stack st) d. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 434 |
Definition is_covered_deps (hm: hmap) (p: LitSet.t) (Q: literal -> Prop) := forall l, has_literal hm l -> is_literal_of_pset p l -> Q l. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 435 |
Definition all_deps_covered (hm: hmap) (P : LitSet.t -> Prop) (Q : literal -> Prop) := forall p, P p -> is_covered_deps hm p Q. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 436 |
Definition only_deps (st: state) := all_deps_covered (hconsmap st) (is_pset_state st) (is_literal_of_state st). | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 437 |
Definition wf_units_lit {A:Type} (u: IntMap.ptrie (Annot.t A)) (m: hmap) : Prop := forall i b, IntMap.get' i u = Some b -> valid_index m i /\ wf_pset m (Annot.deps b). | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 438 |
Record check_annot {A: Type} (C: hmap -> A -> Prop) (h: hmap) (a: Annot.t A) : Prop := { wf_deps : wf_pset h (Annot.deps a); wf_elt : Annot.lift (C h) a; }. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 439 |
Definition has_clauses (m : hmap) (cl : WMap.t) := WMap.Forall (check_annot has_watched_clause m) cl. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 440 |
Record wf_state (st : state) : Prop := { wf_hm : wf (hconsmap st); wf_arrows : List.Forall (has_literal (hconsmap st)) (arrows st) ; wf_wn_m : wf_map (wneg st); wf_wneg : wf_units_def (wneg st) (hconsmap st); wf_units : wf_units_lit (units st) (hconsmap st); wf_stack : List.Forall (check_annot has_literal (hconsmap st)) (unit_stack st); wf_clauses : has_clauses (hconsmap st) (clauses st); wf_units_m : wf_map (units st); wf_clauses_m : WMap.wf (clauses st); }. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 441 |
Definition eval_obool (b:OBool.t) (f : HFormula) := match b with | None => False | Some b => eval_literal (literal_of_bool b f) end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 442 |
Definition eval_pset (m: hmap) (ps: LitSet.t) := forall f b, has_form m f -> OBool.lift_has_bool b (LitSet.get f.(id) ps) -> eval_literal (literal_of_bool b f). | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 443 |
Definition eval_annot {A: Type} (eval : A -> Prop) (m: hmap) (e: Annot.t A) := eval_pset m (Annot.deps e) -> eval (Annot.elt e). | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 444 |
Definition eval_annot_units (u: IntMap.ptrie (Annot.t bool)) (m: hmap) : Prop := forall_units (eval_annot eval_literal m) m u. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 445 |
Definition eval_annot_clauses (m: hmap) (cl : WMap.t) := WMap.Forall (eval_annot eval_watched_clause m) cl. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 446 |
Record eval_annot_state (st: state) : Prop := { ev_an_stack : List.Forall (eval_annot eval_literal (hconsmap st)) (unit_stack st); ev_an_units : eval_annot_units (units st) (hconsmap st); ev_an_clauses : eval_annot_clauses (hconsmap st) (clauses st) }. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 447 |
Record eval_state (st: state) : Prop := { ev_units : eval_units (hconsmap st) (units st) ; ev_stack : eval_stack (unit_stack st) ; ev_clauses : eval_clauses (clauses st) }. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 448 |
Definition has_oform (m: hmap) (o : option HFormula) : Prop := match o with | None => True | Some f => has_form m f end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 449 |
Definition ohold {A: Type} (P: A -> Prop) (o : option A) := match o with | None => True | Some v => P v end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 450 |
Definition has_conflict_clause (m: hmap) (l: list literal) := Forall (has_literal m) l. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 451 |
Definition wf_result_state (st: dresult) := match st with | Progress st => wf_state st | Success (hm,d) => wf_pset hm d | Fail _ => False end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 452 |
Definition eval_result_state (st: dresult) := match st with | Success _ => False | Progress st => eval_state st | Fail _ => True end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 453 |
Definition eval_annot_result_state (st: dresult) := match st with | Success (h,d) => eval_pset h d -> False | Progress st => eval_annot_state st | Fail _ => True end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 454 |
Definition only_result_state (st:state) (r: dresult) := match r with | Progress st => only_deps st | Success (hm,d) => is_covered_deps hm d (is_literal_of_state st) | Fail _ => True end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 455 |
Definition is_fail {A B: Type} (p : result A B) : Prop := match p with | Fail _ => True | _ => False end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 456 |
Definition hconsmap_result (o: dresult) := match o with Fail _ => IntMap.empty _ | Success(h,_) => h | Progress st => hconsmap st end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 457 |
Definition hconsmap_progress_r (F : dresult -> dresult) (st : dresult):= ~ is_fail (F st) -> hconsmap_result (F st) = hconsmap_result st. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 458 |
Definition hconsmap_progress (F: state -> dresult) (st:state) := not (is_fail (F st)) -> hconsmap_result (F st) = hconsmap st. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 459 |
Definition ohold2 {A B:Type} (P : A -> B -> Prop) (o: option A) (b:B) := match o with | None => True | Some a => P a b end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 460 |
Definition hconsmap_eq (F: state ->state) := forall st, hconsmap (F st) = hconsmap st. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 461 |
Definition map_dresult (F : state -> dresult) (d : dresult) := match d with | Fail f => Fail f | Success p => Success p | Progress st => F st end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 462 |
Definition wf_result_state' (st: dresult) := match st with | Progress st => wf_state st | Success (hm,d) => wf_pset hm d | Fail _ => True end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 463 |
Definition eval_oT {A:Type} (P: A -> Prop) (s : option A) := match s with | None => True | Some v => P v end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 464 |
Definition annot_lit (f : HFormula) := annot_hyp (POS f). | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 465 |
Definition is_classic_lit (l:literal) : bool := match l with | POS _ => true | NEG f => f.(is_dec) end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 466 |
Fixpoint check_classic (l : list literal) := match l with | nil => true | e::l => match is_classic_lit e with | true => check_classic l | false => false end end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 467 |
Definition is_empty {A: Type} (m: IntMap.ptrie (key:=int) A) := match m with | IntMap.Leaf _ _ _ => true | _ => false end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 468 |
Definition select_clause (is_bot: bool) (lit: IntMap.ptrie (Annot.t bool)) (k:int) (cl : Annot.t watched_clause) : option (Annot.t (list literal)) := let cl' := Annot.elt cl in let res := reduce_lits lit (Annot.deps cl) (watch1 cl' :: watch2 cl' :: unwatched cl') in match res with | None => None | Some l => if (lazy_or is_bot (fun x => Annot.lift check_classic l)) then Some l else None end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 469 |
Definition select_in_wmap (pos: bool) (lit : IntMap.ptrie (Annot.t bool)) (is_bot: bool) (cl:WMap.t) : option (Annot.t (list literal)) := WMap.search (select_clause is_bot lit) pos cl. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 470 |
Definition find_split (lit : IntMap.ptrie (Annot.t bool)) (is_bot: bool) (cl:WMap.t) : option (Annot.t (list literal)) := match select_in_wmap true lit is_bot cl with | None => select_in_wmap false lit is_bot cl | Some r => Some r end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 471 |
Definition progress_arrow (l:literal) (st:state): bool := match find_lit (POS (form_of_literal l)) (units st) with | None => true | Some b => Annot.lift negb b end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 472 |
Fixpoint find_arrows (st: state) (l : list literal) := match l with | nil => nil | f :: l => if progress_arrow f st then f::(find_arrows st l) else (find_arrows st l) end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 473 |
Fixpoint make_clause (lit: IntMap.ptrie (Annot.t bool)) (ann: LitSet.t) (l: list literal) : Annot.t clause_kind := match l with | nil => Annot.mk EMPTY ann | e::l => match find_lit e lit with | None => reduce lit ann e l | Some b => if Annot.elt b then Annot.mk TRUE LitSet.empty else make_clause lit (LitSet.union (Annot.deps b) ann) l end end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 474 |
Definition augment_with_clause (cl: list literal) (st:state) : dresult := let (fr,st') := get_fresh_clause_id st in insert_normalised_clause fr (make_clause (units st') LitSet.empty cl) st'. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 475 |
Definition augment_clauses (l: list (list literal)) (st: state) := fold_update augment_with_clause l st. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 476 |
Definition set_hmap (hm: hmap) (st:state) : state := {| fresh_clause_id := fresh_clause_id st; hconsmap := hm; wneg := wneg st; arrows := arrows st; defs := defs st; units := units st; unit_stack := unit_stack st; clauses := clauses st |}. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 477 |
Definition conflict_clause := list literal. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 478 |
Definition ProverT := state -> option HFormula -> result state (hmap * list conflict_clause * LitSet.t). | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 479 |
Definition sound_prover (Prover : ProverT) (st: state) := forall (g: option HFormula) (m: hmap) (prf : list conflict_clause) d (WFS : wf_state st) (HASF: has_oform (hconsmap st) g) (PRF : Prover st g = Success (m,prf,d )), (eval_state st -> eval_annot_state st -> eval_ohformula g) /\ (eval_annot_state st -> eval_pset m d -> eval_ohformula g) /\ Forall eval_literal_list prf /\ hmap_order (hconsmap st) m /\ Forall (has_conflict_clause m) prf /\ wf_pset m d. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 480 |
Definition sound_prover_progress (Prover : ProverT) (st st': state) := forall (g: option HFormula) (WFS : wf_state st) (HASF: has_oform (hconsmap st) g) (PRF : Prover st g = Progress st'), ((eval_state st' -> eval_annot_state st' -> eval_ohformula g) -> (eval_state st -> eval_annot_state st -> eval_ohformula g)) /\ (eval_annot_state st -> eval_annot_state st') /\ (wf_state st -> wf_state st') /\ hmap_order (hconsmap st) (hconsmap st'). | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 481 |
Variable ProverT : state -> option HFormula -> result state (hmap * list conflict_clause * LitSet.t). | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 482 |
Definition has_lit (h: literal) (s : LitSet.t) := match LitSet.get (id_of_literal h) s with | Some (Some b) => Bool.eqb b (is_positive_literal h) | _ => false end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 483 |
Definition remove_lit (h:literal) (s: LitSet.t) := LitSet.remove (id_of_literal h) s. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 484 |
Definition annot_holds (u: IntMap.ptrie (key:=int) (Annot.t bool)) (s : LitSet.t) := IntMap.fold' (fun (acc:bool) i b => if acc then match b with | None => false | Some b' => match IntMap.get' i u with | Some b2 => Bool.eqb b' (Annot.elt b2) | _ => false end end else acc) s true. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 485 |
Definition lazy_and (b:bool) (f: unit -> bool) := match b with | true => f tt | false => false end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 486 |
Fixpoint case_split (cl: list literal) (st: state) (g : option HFormula) : result_dis := match cl with | nil => Backjump false (hconsmap st) nil LitSet.empty | f :: cl => match ProverT (insert_unit (annot_hyp f) st) g with | Success (m,prf,ann') => if lazy_and (negb (has_lit f ann')) (fun _ => annot_holds (units st) ann') then Backjump true m prf ann' else match augment_clauses prf (set_hmap m st) with | Success (m,d') => Backjump true m prf d' | Progress st' => match case_split cl st' g with | Failure f => Failure f | Backjump b m' prf' d' => Backjump b m' (prf++prf') (if b then d' else (LitSet.union d' (if (has_lit f ann') then (remove_lit f ann') else ann'))) end | Fail f => Failure f end | Fail f => Failure f | Progress st => Failure OutOfFuel end end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 487 |
Definition case_split_ann (an: LitSet.t) (cl:list literal) (st:state) (g: option HFormula) : result state (hmap * list conflict_clause * LitSet.t) := match case_split cl st g with | Failure f => Fail f | Backjump b hm prf d => Success (hm, prf, if b then d else LitSet.union an d) end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 488 |
Fixpoint eval_or (l:list literal) := match l with | nil => False | l::r => eval_literal l \/ eval_or r end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 489 |
Definition prover_intro (st: state) (g:option HFormula) := match g with | None => Fail HasModel | Some g => match intro_state st g.(elt) g with | Success (h,d) => Success (h,nil,d) | Progress (st',g') => ProverT st' g' | Fail f => Fail f end end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 490 |
Fixpoint prover_arrows (l : list literal) (st: state) (g : option HFormula) : result state (hmap * list conflict_clause * LitSet.t) := match l with | nil => Fail Stuck | e::l => let f := form_of_literal e in match prover_intro (remove_arrow e st) (Some f) with | Success (m,prf,d) => let st'' := insert_unit (annot_lit f) st in match augment_clauses prf (set_hmap m st'') with | Success (h,d) => Success (h,prf,d) | Progress st'' => ProverT st'' g | Fail f => Fail f end | Fail (OutOfFuel|InternalError) as e => e | Fail (HasModel | Stuck) | Progress _ => prover_arrows l st g end end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 491 |
Variable ProverTCorrect : forall st, sound_prover ProverT st. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 492 |
Variable thy_prover: ThyP. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 493 |
Variable thy_prover_sound : Thy thy_prover. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 494 |
Definition get_atom (m: hmap) (k: int) := match IntMap.get' k m with | None => None | Some (d,f) => match f with | LAT a => Some (HCons.mk k d f) | _ => None end end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 495 |
Definition get_literal (m:hmap) (k:int) (b:bool) : option literal := match get_atom m k with | None => None | Some a => Some (literal_of_bool b a) end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 496 |
Definition collect_literal (m:hmap) (acc: list literal * list literal) (k:int) (b:Annot.t bool) := match get_atom m k with | None => acc | Some f => if Annot.elt b then ( (NEG f):: fst acc, snd acc) else (fst acc, (POS f)::snd acc) end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 497 |
Definition get_wneg (m:hmap) (acc: list literal) (k:int) (b : unit) := match get_atom m k with | None => acc | Some f => POS f::acc end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 498 |
Definition collect_all_wneg (m:hmap) (wn : IntMap.ptrie (key:=int) unit) := IntMap.fold' (get_wneg m) wn nil. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 499 |
Definition extract_theory_problem (m : hmap) (u : IntMap.ptrie (key:=int) (Annot.t bool)) : list literal * list literal := IntMap.fold' (collect_literal m) u (nil,nil). | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 500 |
Definition add_conclusion (c : option HFormula) (acc : list literal * list literal) := match c with | None => acc | Some f => match f.(elt) with | LAT a => (fst acc, POS f:: snd acc) | _ => acc end end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 501 |
Definition generate_conflict_clause (st:state) (g: option HFormula) := let (ln,lp) := add_conclusion g (extract_theory_problem (hconsmap st) (units st)) in let wn := collect_all_wneg (hconsmap st) (wneg st) in ln ++ (wn++lp). | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 502 |
Definition deps_of_clause (l : list literal) : LitSet.t := LitSet.empty. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 503 |
Definition run_thy_prover (st: state) (g: option HFormula) := let cl := generate_conflict_clause st g in match thy_prover (hconsmap st) cl with | None => Fail HasModel | Some (h',cl') => match augment_with_clause cl' (set_hmap h' st) with | Success (h',d) => Success (h',cl'::nil,d) | Progress st' => ProverT st' g | Fail f => Fail f end end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 504 |
Definition seq_prover (p : ProverT) (q: ProverT) : ProverT := fun st f => match p st f with | Success(h,l, d) => Success(h,l,d) | Progress st' => q st' f | Fail Stuck => q st f | Fail _ as e => e end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 505 |
Fixpoint seq_provers (l: list ProverT) : ProverT := match l with | nil => fun st f => Fail HasModel | p :: nil => p | p::l => seq_prover p (seq_provers l) end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 506 |
Definition prover_case_split (P: ProverT) (st:state) (g: option HFormula) := match find_split (units st) (is_classic g) (clauses st) with | None => Fail Stuck | Some cl => case_split_ann P (Annot.deps cl) (Annot.elt cl) st g end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 507 |
Definition prover_thy (P: ProverT) (thy: ThyP) (use_prover: bool) (st: state) (g: option HFormula) := if use_prover then run_thy_prover P thy st g else Fail HasModel. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 508 |
Definition prover_unit_propagation (n:nat) (st:state) (g : option HFormula) : result state (hmap * list conflict_clause * LitSet.t) := match unit_propagation n g st with | Success (hm,d) => Success (hm,nil,d) | Progress st' => Progress st' | Fail f => Fail f end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 509 |
Definition prover_impl_arrows (P:ProverT) st g := prover_arrows P (find_arrows st (arrows st)) st g. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 510 |
Fixpoint prover (thy: ThyP) (use_prover: bool) (n:nat) (st:state) (g : option HFormula) : result state (hmap * list conflict_clause * LitSet.t) := match n with | O => Fail OutOfFuel | S n => let ProverTRec := prover thy use_prover n in seq_prover (prover_unit_propagation n) (seq_prover (prover_case_split ProverTRec) (seq_prover (prover_impl_arrows ProverTRec) (prover_thy ProverTRec thy use_prover))) st g end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 511 |
Fixpoint prover_opt (thy: ThyP) (use_prover: bool) (n:nat) (st:state) (g : option HFormula) : result state (hmap * list conflict_clause * LitSet.t) := match n with | O => Fail OutOfFuel | S n => let ProverTRec := prover_opt thy use_prover n in match unit_propagation n g st with | Success (hm,d) => Success(hm,nil,d) | Progress st' => (seq_prover (prover_case_split ProverTRec) (seq_prover (prover_impl_arrows ProverTRec) (prover_thy ProverTRec thy use_prover))) st' g | Fail f => Fail f end end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 512 |
Definition eq_prover (P1 P2: ProverT) := forall st g, P1 st g = P2 st g. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 513 |
Definition never_progress (Prover : ProverT) (st: state) := forall (g: option HFormula) st' (PRF : Prover st g = Progress st'), False. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 514 |
Definition wf_entry (p : LForm -> bool) (v : option (bool * LForm)) := match v with | None => false | Some(b,f) => p f && Bool.eqb b true end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 515 |
Definition wfb (m:hmap) : bool := (wf_entry is_FF (IntMap.get' 0 m)) && (wf_entry is_TT (IntMap.get' 1 m)). | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 516 |
Definition prover_formula thy (up: bool) (m: hmap) (n:nat) (f: HFormula) := if wfb m && chkHc m f.(elt) f.(id) f.(is_dec) then prover_intro (prover_opt thy up n) (insert_unit (annot_lit hTT) (empty_state m)) (Some f) else Fail InternalError. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 517 |
Definition prover_bformula thy (m: hmap) (n:nat) (f: HFormula) := match prover_formula thy false m n f with | Success _ => true | _ => false end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 518 |
Fixpoint hcons (m : hmap) (f : LForm) : hmap := match f with | LAT a => m | LOP o l => List.fold_left (fun m f => IntMap.set' f.(id) (f.(is_dec),f.(elt)) (hcons m f.(elt))) l m | LIMPL l r => List.fold_left (fun m f => IntMap.set' f.(id) (f.(is_dec),f.(elt)) (hcons m f.(elt))) (r::l) m end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 519 |
Definition hmap_empty := IntMap.set' 0 (true, FF) (IntMap.set' 1 (true,TT) (IntMap.empty _)). | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 520 |
Definition hcons_form (f : HFormula) : hmap := IntMap.set' f.(id) (f.(is_dec),f.(elt)) (hcons hmap_empty f.(elt)). | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 521 |
Definition hcons_prover (thy:ThyP) (n:nat) (f:HFormula) := let m := hcons_form f in prover_bformula thy m n f. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 522 |
Definition eval_kind (k:kind) : Type := match k with | IsProp => Prop | IsBool => bool end. | Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause | fbesson-itauto/theories/Formula | fbesson-itauto | 523 |
Subsets and Splits