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Definition HBForm := HCons.t (BForm IsProp). | 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 | 524 |
Variable eval_atom : forall (k:kind), int -> eval_kind k. | 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 | 525 |
Definition eval_TT (k:kind) : eval_kind k := match k with | IsProp => True | IsBool => 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 | 526 |
Definition eval_FF (k:kind) : eval_kind k := match k with | IsProp => False | IsBool => 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 | 527 |
Definition eval_binop (fp : Prop -> Prop -> Prop) (fb : bool -> bool -> bool) (k:kind) : eval_kind k -> eval_kind k -> eval_kind k := match k with | IsProp => fp | IsBool => fb 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 | 528 |
Definition eval_op (o:op) (k:kind) : eval_kind k -> eval_kind k -> eval_kind k := match o with | AND => eval_binop and andb k | OR => eval_binop or orb k | IMPL => eval_binop (fun x y => x -> y) implb k | IFF _ _ => eval_binop (fun x y => x <-> y) Bool.eqb k | NOT => eval_binop (fun x y => not x) (fun x y => negb x) k 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 | 529 |
Definition eval_bprop (o:bprop) := @eq bool. | 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 | 530 |
Definition eval_ite (k:kind) (o:ite) : bool -> eval_kind k -> eval_kind k -> eval_kind k := fun (b:bool) e1 e2 => if b then e1 else e2. | 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 | 531 |
Fixpoint eval_bformula (k:kind) (f: BForm k) : eval_kind k := match f with | BTT k => eval_TT k | BFF k => eval_FF k | BAT k i => eval_atom k i | BOP k o f1 f2 => eval_op o k (eval_bformula k (elt f1)) (eval_bformula k (elt f2)) | BITE k o c f1 f2 => eval_ite k o (eval_bformula IsBool (elt c)) (eval_bformula k (elt f1)) (eval_bformula k (elt f2)) | BPROP o f1 f2 => eval_bprop o (eval_bformula _ (elt f1)) (eval_bformula _ (elt f2)) 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 | 532 |
Variable has_bool : int -> bool. | 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 | 533 |
Definition map_hcons {A B:Type} (f: A -> B) (e : HCons.t A) : HCons.t B := HCons.mk e.(id) e.(is_dec) (f e.(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 | 534 |
Definition keep_atom (k:kind) (i:int) := match k with | IsProp => true | IsBool => has_bool i 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 | 535 |
Fixpoint keep_all (k:kind) (f: BForm k) : bool := match f with | BTT k => true | BFF k => true | BAT k i => keep_atom k i | BOP k o f1 f2 => keep_all k f1.(elt) && keep_all k f2.(elt) | BPROP _ f1 f2 => keep_all IsBool f1.(elt) && keep_all IsBool f2.(elt) | BITE k _ c f1 f2 => keep_all _ c.(elt) && keep_all k f1.(elt) && keep_all k f2.(elt) 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 | 536 |
Fixpoint to_formula (pol:bool) (k:kind) (f:BForm k) : LForm:= match f with | BTT k => TT | BFF k => FF | BAT k i => if keep_atom k i then LAT i else if pol then FF else TT | BOP k o f1 f2 => match o with | NOT => LIMPL (map_hcons (to_formula (negb pol) k) f1::nil) hFF | AND => LOP LAND ((map_hcons (to_formula pol k) f1):: (map_hcons (to_formula pol k) f2)::nil) | OR => LOP LOR ((map_hcons (to_formula pol k) f1):: (map_hcons (to_formula pol k) f2)::nil) | IMPL => LIMPL ((map_hcons (to_formula (negb pol) k) f1):: nil) (map_hcons (to_formula pol k) f2) | IFF i1 i2 => let f1' := LIMPL ((map_hcons (to_formula (negb pol) k) f1):: nil) (map_hcons (to_formula pol k) f2) in let f2' := LIMPL ((map_hcons (to_formula (negb pol) k) f2):: nil) (map_hcons (to_formula pol k) f1) in let dec := f1.(is_dec) && f2.(is_dec) in LOP LAND (HCons.mk i1 dec f1' :: HCons.mk i2 dec f2' :: nil) end | BPROP (EQB i1 i2) f1 f2 => let f1' := LIMPL ((map_hcons (to_formula (negb pol) IsBool) f1):: nil) (map_hcons (to_formula pol IsBool) f2) in let f2' := LIMPL ((map_hcons (to_formula (negb pol) IsBool) f2):: nil) (map_hcons (to_formula pol IsBool) f1) in let dec := f1.(is_dec) && f2.(is_dec) in LOP LAND (HCons.mk i1 dec f1' :: HCons.mk i2 dec f2' :: nil) | BITE k (ITE i1 i2) c f1 f2 => let f1' := LIMPL ((map_hcons (to_formula (negb pol) IsBool) c):: nil) (map_hcons (to_formula pol k) f1) in let f2' := LOP LOR ((map_hcons (to_formula pol IsBool) c):: map_hcons (to_formula pol k) f2::nil) in let dec := f1.(is_dec) && f2.(is_dec) in LOP LAND (HCons.mk i1 dec f1' :: HCons.mk i2 dec f2' :: nil) 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 | 537 |
Definition hold (k:kind) : eval_kind k -> Prop := match k with | IsBool => fun v => is_true v | IsProp => fun v => 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 | 538 |
Definition impl_pol (pol : bool) (p1 p2: Prop) := if pol then p1 -> p2 else p2 -> p1. | 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 | 539 |
Variable has_bool_correct : forall i : int, has_bool i = true -> eval_atom IsProp i <-> is_true (eval_atom IsBool 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 | 540 |
Fixpoint aux_to_formula_correct (pol:bool) (k:kind) (f:BForm k) {struct f} : if pol then eval_formula (eval_atom IsProp) (to_formula pol k f) -> hold k (eval_bformula k f) else hold k (eval_bformula k f) -> eval_formula (eval_atom IsProp) (to_formula pol k 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 | 541 |
Definition to_hformula (f : HBForm) := map_hcons (to_formula true IsProp) 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 | 542 |
Definition eval_hbformula (f: HBForm) := eval_bformula IsProp 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 | 543 |
Definition empty (A:Type) : @IntMap.ptrie int A := IntMap.empty 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 | 544 |
Definition set (A:Type) (i:int) (v:A) (m : IntMap.ptrie A) := IntMap.set' i v 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 | 545 |
Definition mkAtom (p:Prop) := NBool p 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 | 546 |
Definition mkAtomDec (p:Prop) (H:p\/ ~p) := NBool p (Some H). | 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 | 547 |
Definition hold_prop (p:Prop) (k: kind) : eval_kind k := match k with | IsProp => p | IsBool => 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 | 548 |
Definition hold_bool (b:bool) (k: kind) : eval_kind k := match k with | IsProp => False | IsBool => 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 | 549 |
Definition eval_prop (m: IntMap.ptrie atomT) (k:kind) (i:int) : eval_kind k := match IntMap.get' i m with | None => BForm.eval_FF k | Some v => match v with | NBool p _ => hold_prop p k | TBool b p _ => match k with | IsBool => b | IsProp => p end 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 | 550 |
Definition bool_of_ptrie {A:Type} (f : A -> bool) (m:IntMap.ptrie A) (i:int) : bool := match IntMap.get' i m with | None => false | Some v => f 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 | 551 |
Definition map_bool_of_ptrie {A: Type} (f: A -> bool) (m: IntMap.ptrie (key:=int) A) : IntMap.ptrie bool := IntMap.map1' f 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 | 552 |
Definition bool_of_ptrie_bool (m : IntMap.ptrie (key:=int) bool) (i:int) : bool := match IntMap.get' i m with | None => false | Some b => 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 | 553 |
Definition has_bool_atomT (a:atomT) := match a with | NBool _ _ => false | TBool _ _ _ => 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 | 554 |
Definition has_bool (m:IntMap.ptrie atomT) (i:int) : bool := bool_of_ptrie has_bool_atomT 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 | 555 |
Definition is_dec_atomT (a: atomT) := match a with | NBool _ o => match o with | None => false | Some _ => true end | TBool _ _ _ => 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 | 556 |
Definition eval_is_dec (m: IntMap.ptrie atomT) (i:int) := bool_of_ptrie is_dec_atomT 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 | 557 |
Definition empty_thy_prover (hm:hmap ) (l:list literal) : option (hmap * list (literal)) := 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 | 558 |
Definition hlform (hf : HFormula) := nform lform hf. | 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 | 559 |
Definition hcons_bprover (m : IntMap.ptrie atomT) (thy:ThyP) (n:nat) (f: BForm.HBForm) := hcons_prover (eval_is_dec m) thy n (hlform (BForm.to_hformula (has_bool m) 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 | 560 |
Definition eqb_map {A: Type} (f : A -> bool) (m: IntMap.ptrie bool) (m': IntMap.ptrie A) : bool := IntMap.beq' (fun x y => Bool.eqb x (f y)) m 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 | 561 |
Definition hcons_tauto_prover (eval_is_dec : int -> bool) (has_bool : int -> bool) (n:nat) (f: BForm.HBForm) := hcons_prover eval_is_dec empty_thy_prover n (hlform (BForm.to_hformula has_bool 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 | 562 |
Variable eqb : LForm -> LForm -> bool. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 563 |
Definition xhformula_eqb (f1 f2: HFormula) := HCons.eq_hc f1 f2 && eqb f1.(HCons.elt) f2.(HCons.elt). | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 564 |
Fixpoint formula_eqb (f1 f2 : LForm) {struct f1}: bool := match f1 , f2 with | LAT i , LAT j => Uint63.eqb i j | LOP o1 l1, LOP o2 l2 => lop_eqb o1 o2 && forall2b (xhformula_eqb formula_eqb) l1 l2 | LIMPL l1 r1, LIMPL l2 r2 => forall2b (xhformula_eqb formula_eqb) l1 l2 && xhformula_eqb formula_eqb r1 r2 | _ , _ => false end. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 565 |
Definition hformula_eqb (x y: HFormula) := xhformula_eqb formula_eqb x y. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 566 |
Fixpoint formula_eqb_true (f1 f2: LForm) : formula_eqb f1 f2 = true -> f1 = f2. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 567 |
Fixpoint formula_eqb_refl (f1: LForm) : formula_eqb f1 f1 = true. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 568 |
Definition hformula_eqb_true (f1 f2: HFormula) : hformula_eqb f1 f2 = true -> f1 = f2. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 569 |
Definition t := literal. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 570 |
Definition pol (x:t) := match x with | POS _ => true | NEG _ => false end. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 571 |
Definition isPOS (x:t) := pol x = true. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 572 |
Definition var (x:t) := match x with | POS p => p | NEG p => p end. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 573 |
Definition neg (x:t) := match x with | POS x => NEG x | NEG x => POS x end. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 574 |
Definition beval_lit (env : HFormula -> bool) (l:t) := if pol l then env (var l) else negb (env (var l)). | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 575 |
Definition eval_lit (env: HFormula -> Prop) (l:t) (X:Prop) := if pol l then env (var l) \/ X else env (var l) -> X. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 576 |
Definition get_pol (p:HFormula) (l : Lit.t) : option bool := if hformula_eqb p (var l) then Some (pol l) else None. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 577 |
Definition eq_dec (l1 l2:t) : {l1 = l2} + {l1 <> l2}. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 578 |
Definition make (b:bool) (v:HFormula) := if b then POS v else NEG v. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Morphisms Cdcl.Lib Cdcl.Syntax | fbesson-itauto/theories/Lit | fbesson-itauto | 579 |
Fixpoint cons_lit (l:Lit.t) (cl:clause) := match cl with | nil => l::nil | l1::cl' => if pol l1 || negb (pol l) then l::cl else l1 ::(cons_lit l cl') end. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 580 |
Definition vars_of_clause (cl:clause) := List.map Lit.var cl. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 581 |
Definition vars_of_cnf (cls : cnf) := List.fold_right (fun e acc => vars_of_clause e ++ acc) nil cls. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 582 |
Definition is_clause_of (p:HFormula) (cl: list Lit.t) := forall l, In l cl -> var l = p. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 583 |
Definition boeval (env : HFormula -> bool) (o: option HFormula) := match o with | None => false | Some i => env i end. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 584 |
Definition oeval (env: HFormula -> Prop) (o: option HFormula) := match o with | None => False | Some i => env i end. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 585 |
Fixpoint map_filter {A B: Type} (F: A -> option B ) (l: list A) : list B := match l with | nil => nil | e::l => match F e with | None => map_filter F l | Some e' => e' :: map_filter F l end end. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 586 |
Fixpoint get_polarity_rec (p:HFormula) (l : clause) := match l with | nil => None | li :: l => match Lit.get_pol p li with | None => match get_polarity_rec p l with | None => None | Some (b,l) => Some (b,li::l) end | Some b => Some (b,l) end end. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 587 |
Fixpoint normalise (cl: clause): option clause := match cl with | nil => Some nil | l::cl' => match normalise cl' with | None => None | Some cl' => match get_polarity_rec (Lit.var l) cl' with | None => Some (l::cl') | Some(b,_) => if Lit.eq_dec (Lit.make (negb b) (Lit.var l)) l then None else Some cl' end end end. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 588 |
Fixpoint split_clause (l1: clause) : clause * clause := match l1 with | nil => (nil,nil) | POS p::l => (nil,l1) | NEG p::l => let (ln,lp):= split_clause l in (NEG p::ln,lp) end. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 589 |
Definition merge_clause (cl1 cl2 : clause) : clause := let (cln1,clp1) := split_clause cl1 in let (cln2,clp2) := split_clause cl2 in cln1 ++ cln2 ++ clp1 ++ clp2. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 590 |
Fixpoint resolve_all (l1:cnf) (l2:cnf) := match l1 with | nil => nil | cl::l1 => map_filter normalise (List.map (merge_clause cl) l2) ++ (resolve_all l1 l2) end. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 591 |
Fixpoint split_polarity (p: HFormula) (l: cnf) : cnf * cnf * cnf:= match l with | nil => (nil,nil,nil) | cl::l => let '(lp,ln,lo) := split_polarity p l in match normalise cl with | None => split_polarity p l | Some cl' => match get_polarity_rec p cl' with | None => (lp,ln,cl'::lo) | Some(b,cl') => (if b then cl'::lp else lp ,if b then ln else cl'::ln,lo) end end end. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 592 |
Definition elim (p:HFormula) (l: cnf) := let '(lp,ln,lo) := split_polarity p l in resolve_all lp ln ++ lo. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 593 |
Definition is_var_of_clause (v:HFormula) (cl: clause) := exists l, In l cl /\ var l = v. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 594 |
Definition is_var_of_cnf (v:HFormula) (cls: cnf) := exists cl, In cl cls /\ is_var_of_clause v cl. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 595 |
Definition match_option (p:HFormula) (o:option HFormula) := match o with | None => False | Some q => p = q end. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 596 |
Definition beval_option {A: Type} (eA: A -> bool) (v: option A) := match v with | None => true | Some v => eA v end. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 597 |
Definition eval_option {A: Type} (eA: A -> Prop) (v: option A) := match v with | None => True | Some v => eA v end. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 598 |
Definition set_env {A: Type}(env: HFormula -> A) (x': HFormula) (v: A) := fun x => if hformula_eq_dec x x' then v else env x. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 599 |
Definition clause_of_opt (o:option HFormula) := match o with | None => nil | Some i => (NEG i :: nil) ::nil end. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 600 |
Definition eval_or {A: Type} (F : A -> Prop) (l : list A) := List.fold_right (fun e acc => F e \/ acc) False l. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 601 |
Definition eval_and {A: Type} (F : A -> Prop) (l : list A) := List.fold_right (fun e acc => F e /\ acc) True l. | ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause | fbesson-itauto/theories/CnfSolver | fbesson-itauto | 602 |
Definition iter_lcmn (n : nat) := \big[lcmn/1%N]_(1 <= i < n.+1) i. | mathcomp(all_ssreflect all_algebra) | coq-community-apery/arithmetics | coq-community-apery | 603 |
Variable v : int -> int -> rat. | coq-community-apery/ops_for_b | coq-community-apery | 604 |
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Variable v_ann : v.Ann v. | coq-community-apery/ops_for_b | coq-community-apery | 605 |
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Definition ba_casoratian (k : int) : rat := (b (int.shift 1 k) * a k) - b k * a (int.shift 1 k). | mathcomp(all_ssreflect all_algebra) extra_mathcomp tactics shift rat_of_Z seq_defs initial_conds algo_closures reduce_order a_props | coq-community-apery/b_over_a_props | coq-community-apery | 606 |
Definition b_over_a_seq (k : int) := b k / a k. | mathcomp(all_ssreflect all_algebra) extra_mathcomp tactics shift rat_of_Z seq_defs initial_conds algo_closures reduce_order a_props | coq-community-apery/b_over_a_props | coq-community-apery | 607 |
Variable F : realFieldType. | mathcomp(all_ssreflect all_algebra) mathcomp(bigenough cauchyreals) | coq-community-apery/extra_cauchyreals | coq-community-apery | 608 |
Record posnum_def (R : numDomainType) := PosNumDef { num_of_pos :> R; posnum_gt0 : num_of_pos > 0 }. | mathcomp(all_ssreflect all_algebra all_field) | coq-community-apery/posnum | coq-community-apery | 609 |
Definition posnum_of (R : numDomainType) (phR : phant R) := posnum_def R. | mathcomp(all_ssreflect all_algebra all_field) | coq-community-apery/posnum | coq-community-apery | 610 |
Definition PosNum (R : numDomainType) x x_gt0 : {posnum R} := @PosNumDef _ x x_gt0. | mathcomp(all_ssreflect all_algebra all_field) | coq-community-apery/posnum | coq-community-apery | 611 |
Definition pos_of_num (R : numDomainType) (x : {posnum R}) (phx : phantom R x) := x. | mathcomp(all_ssreflect all_algebra all_field) | coq-community-apery/posnum | coq-community-apery | 612 |
Definition posnum_gt0_def x (phx : phantom R x) := posnum_gt0 x. | mathcomp(all_ssreflect all_algebra all_field) mathcomp(algC) | coq-community-apery/posnum | coq-community-apery | 613 |
Variable c : int -> int -> rat. | annotated_recs_v | coq-community-apery/ops_for_v | coq-community-apery | 614 |
Variable u : int -> int -> rat. | annotated_recs_v | coq-community-apery/ops_for_v | coq-community-apery | 615 |
Variable c_ann : c.Ann c. | annotated_recs_v | coq-community-apery/ops_for_v | coq-community-apery | 616 |
Variable u_ann : u.Ann u. | annotated_recs_v | coq-community-apery/ops_for_v | coq-community-apery | 617 |
Definition Rint : int -> Z -> Type := fun_hrel int_of_Z. | BinInt mathcomp(all_ssreflect all_algebra) CoqEAL(hrel param refinements) CoqEAL(pos binnat rational) tactics rat_of_Z | coq-community-apery/rho_computations | coq-community-apery | 618 |
Definition generic_beta (i : AQ) : AQ := ((i + cast 1%coqZ) %/ (i + cast 2%coqZ)) ^ 3%N. | BinInt mathcomp(all_ssreflect all_algebra) CoqEAL(hrel param refinements) CoqEAL(pos binnat rational) tactics rat_of_Z | coq-community-apery/rho_computations | coq-community-apery | 619 |
Definition generic_alpha (i : AQ) : AQ := (cast 17%coqZ * i ^ 2%N + cast 51%coqZ * i + cast 39%coqZ) * (cast 2%coqZ * i + cast 3%coqZ) %/ (i + cast 2%coqZ) ^ 3%N. | BinInt mathcomp(all_ssreflect all_algebra) CoqEAL(hrel param refinements) CoqEAL(pos binnat rational) tactics rat_of_Z | coq-community-apery/rho_computations | coq-community-apery | 620 |
Definition generic_h (i : AQ) (x : AQ) := generic_alpha i - generic_beta i %/ x. | BinInt mathcomp(all_ssreflect all_algebra) CoqEAL(hrel param refinements) CoqEAL(pos binnat rational) tactics rat_of_Z | coq-community-apery/rho_computations | coq-community-apery | 621 |
Fixpoint generic_h_iter (n : nat) : AQ := match n with | 0 => 0%C | 1 => 0%C | 2 => cast 1445%coqZ %/ cast 73%coqZ | m.+1 => let mz := cast m in let res_m := generic_h_iter m in generic_h mz res_m end. | BinInt mathcomp(all_ssreflect all_algebra) CoqEAL(hrel param refinements) CoqEAL(pos binnat rational) tactics rat_of_Z | coq-community-apery/rho_computations | coq-community-apery | 622 |
Definition subr {R : zmodType} (x y : R) : R := x - y. | BinInt mathcomp(all_ssreflect all_algebra) CoqEAL(hrel param refinements) CoqEAL(pos binnat rational) tactics rat_of_Z | coq-community-apery/rho_computations | coq-community-apery | 623 |
Subsets and Splits