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fact
string | imports
string | filename
string | symbolic_name
string | __index_level_0__
int64 |
|---|---|---|---|---|
Fixpoint set' {A: Type} (i: key) (x: A) (t: ptrie A) := match t with | Empty => Leaf i x | Leaf j v => if eqb i j then Leaf i x else join i (Leaf i x) j (Leaf j v) | Branch prefix brbit l r => if match_prefix i prefix brbit then if zerobit i brbit then Branch prefix brbit (set' i x l) r else Branch prefix brbit l (set' i x r) else join i (Leaf i x) prefix (Branch prefix brbit l r) end.
|
List Bool ZArith Lia
|
fbesson-itauto/theories/PatriciaR
|
fbesson-itauto
| 224
|
Definition branch {A: Type} (prefix m: key) (t1 t2: ptrie A) := match t1 with | Empty => t2 | _ => match t2 with | Empty => t1 | _ => Branch prefix m t1 t2 end end.
|
List Bool ZArith Lia
|
fbesson-itauto/theories/PatriciaR
|
fbesson-itauto
| 225
|
Fixpoint remove' {A: Type} (i: key) (t: ptrie A) := match t with | Empty => Empty | Leaf k v => if eqb k i then Empty else t | Branch p m l r => if match_prefix i p m then if zerobit i m then branch p m (remove' i l) r else branch p m l (remove' i r) else t end.
|
List Bool ZArith Lia
|
fbesson-itauto/theories/PatriciaR
|
fbesson-itauto
| 226
|
Fixpoint map' {A B: Type} (f: key -> A -> B) (m: ptrie A): ptrie B := match m with | Empty => Empty | Leaf k v => Leaf k (f k v) | Branch p m l r => Branch p m (map' f l) (map' f r) end.
|
List Bool ZArith Lia
|
fbesson-itauto/theories/PatriciaR
|
fbesson-itauto
| 227
|
Fixpoint map1' {A B: Type} (f: A -> B) (m: ptrie A): ptrie B := match m with | Empty => Empty | Leaf k v => Leaf k (f v) | Branch p m l r => Branch p m (map1' f l) (map1' f r) end.
|
List Bool ZArith Lia
|
fbesson-itauto/theories/PatriciaR
|
fbesson-itauto
| 228
|
Fixpoint elements' {A: Type} (m: ptrie A) (acc: list (key * A)): list (key * A) := match m with | Empty => acc | Leaf k v => (k, v)::acc | Branch p m l r => elements' l (elements' r acc) end.
|
List Bool ZArith Lia
|
fbesson-itauto/theories/PatriciaR
|
fbesson-itauto
| 229
|
Definition keys' {A: Type} (m: ptrie A) := List.map (@fst key A) (elements' m nil).
|
List Bool ZArith Lia
|
fbesson-itauto/theories/PatriciaR
|
fbesson-itauto
| 230
|
Fixpoint fold' {A B: Type} (f: B -> key -> A -> B) (m: ptrie A) (acc: B): B := match m with | Empty => acc | Leaf k v => f acc k v | Branch p m l r => fold' f r (fold' f l acc) end.
|
List Bool ZArith Lia
|
fbesson-itauto/theories/PatriciaR
|
fbesson-itauto
| 231
|
Fixpoint fold1' {A B: Type} (f: B -> A -> B) (m: ptrie A) (acc: B): B := match m with | Empty => acc | Leaf k v => f acc v | Branch p m l r => fold1' f r (fold1' f l acc) end.
|
List Bool ZArith Lia
|
fbesson-itauto/theories/PatriciaR
|
fbesson-itauto
| 232
|
Fixpoint search {A B: Type} (f: key -> A -> option B) (m: ptrie A) : option B := match m with | Empty => None | Leaf k v => f k v | Branch p m l r => match search f l with | Some r => Some r | None => search f r end end.
|
List Bool ZArith Lia
|
fbesson-itauto/theories/PatriciaR
|
fbesson-itauto
| 233
|
Fixpoint insert' {A: Type} (c: A -> A -> A) (i: key) (x: A) (m: ptrie A): ptrie A := match m with | Empty => Leaf i x | Leaf j v => if eqb i j then Leaf i (c x v) else join i (Leaf i x) j (Leaf j v) | Branch prefix brbit l r => if match_prefix i prefix brbit then if zerobit i brbit then Branch prefix brbit (insert' c i x l) r else Branch prefix brbit l (insert' c i x r) else join i (Leaf i x) prefix (Branch prefix brbit l r) end.
|
List Bool ZArith Lia
|
fbesson-itauto/theories/PatriciaR
|
fbesson-itauto
| 234
|
Fixpoint update {A: Type} (f : A -> option A ) (i: key) (m: ptrie A) : ptrie A := match m with | Empty => Empty | Leaf j v => if eqb i j then match f v with | None => Empty | Some v' => Leaf i v' end else Leaf j v | Branch prefix brbit l r => if match_prefix i prefix brbit then if zerobit i brbit then branch prefix brbit (update f i l) r else branch prefix brbit l (update f i r) else m end.
|
List Bool ZArith Lia
|
fbesson-itauto/theories/PatriciaR
|
fbesson-itauto
| 235
|
Fixpoint updater {A B: Type} (f : A -> B) (g : B -> option A) (acc:B) (i:key) (m:ptrie A) : ptrie A * B := match m with | Empty => (Empty, acc) | Leaf j v => if eqb i j then let r := f v in match g r with | None => (Empty,r) | Some v' => (Leaf i v',r) end else (Leaf j v,acc) | Branch prefix brbit l r => if match_prefix i prefix brbit then if zerobit i brbit then let (u,v) := updater f g acc i l in (branch prefix brbit u r,v) else let (u,v) := updater f g acc i r in (branch prefix brbit l u,v) else (m,acc) end.
|
List Bool ZArith Lia
|
fbesson-itauto/theories/PatriciaR
|
fbesson-itauto
| 236
|
Fixpoint beq' {A B: Type} (beq_elt: A -> B -> bool) (m1 : ptrie A) (m2: ptrie B): bool := match m1, m2 with | Empty, Empty => true | Leaf k1 v1, Leaf k2 v2 => eqb k1 k2 && beq_elt v1 v2 | Branch p1 brbit1 l1 r1, Branch p2 brbit2 l2 r2 => eqb p1 p2 && eqb brbit1 brbit2 && beq' beq_elt l1 l2 && beq' beq_elt r1 r2 | _, _ => false end.
|
List Bool ZArith Lia
|
fbesson-itauto/theories/PatriciaR
|
fbesson-itauto
| 237
|
Fixpoint xcombine' {A: Type} (c: A -> A -> A) (t1: ptrie A) { struct t1 } := fix combine_aux t2 { struct t2 } := match t1, t2 with | Empty, _ => t2 | _, Empty => t1 | Leaf i x, _ => insert' c i x t2 | _, Leaf i x => insert' (fun a b => c b a) i x t1 | Branch p1 m1 l1 r1, Branch p2 m2 l2 r2 => if eqb p1 p2 && eqb m1 m2 then Branch p1 m1 (xcombine' c l1 l2) (xcombine' c r1 r2) else if ltb m1 m2 && match_prefix p2 p1 m1 then if zerobit p2 m1 then Branch p1 m1 (xcombine' c l1 t2) r1 else Branch p1 m1 l1 (xcombine' c r1 t2) else if ltb m2 m1 && match_prefix p1 p2 m2 then if zerobit p1 m2 then Branch p2 m2 (combine_aux l2) r2 else Branch p2 m2 l2 (combine_aux r2) else join p1 t1 p2 t2 end.
|
List Bool ZArith Lia
|
fbesson-itauto/theories/PatriciaR
|
fbesson-itauto
| 238
|
Fixpoint combine' {A: Type} (c: A -> A -> A) (t1: ptrie A) { struct t1 } := fix combine_aux t2 { struct t2 } := match t1, t2 with | Empty, _ => t2 | _, Empty => t1 | Leaf i x, _ => insert' c i x t2 | _, Leaf i x => insert' (fun a b => c b a) i x t1 | Branch p1 m1 l1 r1, Branch p2 m2 l2 r2 => if lazy_and (eqb p1 p2) (fun _ => eqb m1 m2) then Branch p1 m1 (combine' c l1 l2) (combine' c r1 r2) else if lazy_and (ltb m1 m2) (fun _ => match_prefix p2 p1 m1) then if zerobit p2 m1 then Branch p1 m1 (combine' c l1 t2) r1 else Branch p1 m1 l1 (combine' c r1 t2) else if lazy_and (ltb m2 m1) (fun _ => match_prefix p1 p2 m2) then if zerobit p1 m2 then Branch p2 m2 (combine_aux l2) r2 else Branch p2 m2 l2 (combine_aux r2) else join p1 t1 p2 t2 end.
|
List Bool ZArith Lia
|
fbesson-itauto/theories/PatriciaR
|
fbesson-itauto
| 239
|
Record ZarithThy : Type.
|
Cdcl.Itauto ZifyClasses Lia
|
fbesson-itauto/theories/NOlia
|
fbesson-itauto
| 240
|
Definition wf_map {A: Type} (m : IntMap.ptrie A) := PTrie.wf None 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
| 241
|
Variable Depth : LForm -> nat.
|
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
| 242
|
Definition max_list (l: list (HCons.t LForm)) := List.fold_right (fun e acc => max (Depth e.(elt)) acc) O 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
| 243
|
Fixpoint depth (f:LForm) : nat := match f with | LAT _ => O | LOP _ l => S (max_list depth l) | LIMPL l r => S (max (max_list depth l) (depth r.(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
| 244
|
Variable P : LForm -> Prop.
|
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
| 245
|
Variable PA : forall a, P (LAT 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
| 246
|
Variable PLOP : forall o l, (forall x, In x l -> P (x.(elt))) -> P (LOP o 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
| 247
|
Variable PLIMP : forall l r, (forall x, In x l -> P (x.(elt))) -> (P r.(elt)) -> P (LIMPL l r).
|
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
| 248
|
Definition FF := (LOP LOR 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
| 249
|
Definition TT := (LOP LAND 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
| 250
|
Fixpoint lform_app (o:lop) (acc : list (HCons.t LForm)) (l: list (HCons.t LForm)) := match l with | nil => acc | e :: l => match e.(elt) with | LOP o' l' => if lop_eqb o o' then lform_app o (rev_append l' acc) l else lform_app o (e::acc) l | _ => lform_app o (e::acc) 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
| 251
|
Definition mk_impl (l : list HFormula) (r : HFormula) : LForm := match r.(elt) with | LIMPL l' r' => LIMPL (rev_append l l') r' | _ => LIMPL l 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
| 252
|
Definition hFF := HCons.mk 0 true FF.
|
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
| 253
|
Definition hTT := HCons.mk 1 true TT.
|
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
| 254
|
Definition is_TT (g: LForm) : bool := match g with | LOP LAND nil => 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
| 255
|
Definition mklform (f : HFormula) : HFormula := if is_TT f.(elt) then hTT else 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
| 256
|
Definition nform (F: LForm -> LForm) (f: HFormula) := match F (elt f) with | LOP LAND nil => hTT | LOP LOR nil => hFF | LOP _ (e::nil) => e | LAT i => HCons.mk i (is_dec f) (LAT i) | LOP o l => HCons.mk (id f) (List.forallb is_dec l) (LOP o l) | LIMPL nil r => r | LIMPL l r => HCons.mk (id f) (List.forallb is_dec l && is_dec r) (LIMPL l 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
| 257
|
Fixpoint lform (f : LForm) := match f with | LAT i => LAT i | LOP o l => LOP o (lform_app o nil (List.map (nform lform) l)) | LIMPL l r => mk_impl (lform_app LAND nil (List.map (nform lform) l)) (nform lform 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
| 258
|
Definition op_eqb (o o': op) : bool := match o , o' with | AND , AND => true | OR , OR => true | IMPL , IMPL => 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
| 259
|
Definition hmap := IntMap.ptrie (key:=int) (bool*LForm)%type.
|
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
| 260
|
Definition t := LForm.
|
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
| 261
|
Definition lop_compare (o1 o2:lop) := match o1, o2 with | LAND , LAND | LOR , LOR => Eq | LAND , _ => Lt | _ , LAND => Gt 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
| 262
|
Fixpoint list_compare (l1 l2 : list HFormula) : comparison := match l1 , l2 with | nil , nil => Eq | nil , _ => Lt | _ , nil => Gt | e1::l1 , e2::l2 => match e1.(id) ?= e2.(id) with | Eq => list_compare l1 l2 | x => x 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
| 263
|
Definition compare (f1 f2:LForm) : comparison := match f1, f2 with | LAT i , LAT j => i ?= j | LAT i , _ => Lt | _ , LAT i => Gt | LOP o1 l1 , LOP o2 l2 => match lop_compare o1 o2 with | Eq => list_compare l1 l2 | x => x end | LOP _ _ , _ => Lt | _ , LOP _ _ => Gt | LIMPL l1 f1 , LIMPL l2 f2 => match f1.(id) ?= f2.(id) with | Eq => list_compare l1 l2 | x => x 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
| 264
|
Definition t := option 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
| 265
|
Definition union (o1 o2: option bool) : option bool := match o1 , o2 with | Some b1 , Some b2 => if Bool.eqb b1 b2 then o1 else None | _ , _ => 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
| 266
|
Definition has_boolb (b: bool) (o: option bool) := match o with | None => true | Some b' => Bool.eqb 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
| 267
|
Definition has_bool (b: bool) (o: option bool) := has_boolb b o = 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
| 268
|
Definition lift_has_boolb (b:bool) (o : option (option bool)) := match o with | None => false | Some o' => has_boolb b o' 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
| 269
|
Definition lift_has_bool (b:bool) (o : option (option bool)) := lift_has_boolb b o = 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
| 270
|
Definition order (o o': option bool) := match o , o' with | None , None | Some _ , None => True | Some b , Some b' => b = b' | None , Some b => 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
| 271
|
Definition lift_order (o o' : option (option bool)) := match o , o' with | None , None => True | None , Some _ => True | Some _ , None => False | Some b1 , Some b2 => order b1 b2 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
| 272
|
Definition t := IntMap.ptrie (key:= int) OBool.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
| 273
|
Definition empty : t := IntMap.empty OBool.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
| 274
|
Definition is_empty (x:t) := match x with | IntMap.Empty _ => 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
| 275
|
Definition union (s s':t) : t := IntMap.combine' OBool.union s 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
| 276
|
Definition singleton (i:int) (b:bool) := IntMap.Leaf OBool.t i (Some 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
| 277
|
Definition add (k:int) (b:bool) (s:t) : t := union (singleton k b) 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
| 278
|
Definition fold {A: Type} : forall (f: A -> int -> OBool.t -> A) (s:t) (a:A), A := @IntMap.fold' int OBool.t 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
| 279
|
Definition mem (i:int) (s:t) := IntMap.mem' i 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
| 280
|
Definition get (i:int) (s:t) := IntMap.get' i 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
| 281
|
Definition remove (i:int) (s:t) := IntMap.remove' i 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
| 282
|
Definition has (i:int) (b:bool) (s:t) := OBool.lift_has_boolb b (get i 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
| 283
|
Definition subset (s s':t) := forall k, OBool.lift_order (get k s) (get k 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
| 284
|
Definition wf (s:t) := wf_map 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
| 285
|
Record t (A: Type) : Type := mk { elt : A; deps : 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
| 286
|
Definition set {A B: Type} (a : t A) (e: B) := mk e (deps a).
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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
| 287
|
Definition map {A B: Type} (f : A -> B) (a: t A) : t B := mk (f (elt a)) (deps a).
|
Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause
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fbesson-itauto/theories/Formula
|
fbesson-itauto
| 288
|
Definition mk_elt {A: Type} (e:A) : t A := mk e 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
| 289
|
Definition lift {A B: Type} (f: A -> B) (e : t A): B := f (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
| 290
|
Definition lift_deps {A: Type} (f : LitSet.t -> Prop) (e: t A) := f (deps 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
| 291
|
Definition hmap_order (h h' : hmap) := forall k v, IntMap.get' k h = Some v -> IntMap.get' k h' = Some v.
|
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
| 292
|
Definition isMono {A: Type} (F : hmap -> A -> Prop) := forall m m' (OHM : hmap_order m m') x (Fm: F m x), F m' x.
|
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
| 293
|
Definition IntMapForall {A:Type} (P: A -> Prop) (m: IntMap.ptrie A) := forall k r, IntMap.get' k m = Some r -> P r.
|
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
| 294
|
Definition IntMapForall2 {A: Type} (P: A -> Prop) (m: IntMap.ptrie A* IntMap.ptrie A) := IntMapForall P (fst m) /\ IntMapForall P (snd 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
| 295
|
Record watched_clause : Type := { watch1 : literal; watch2 : literal; unwatched : 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
| 296
|
Definition form_of_literal (l: literal) : HFormula := match l with | POS f => f | NEG f => 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
| 297
|
Definition id_of_literal (l:literal) : int := (form_of_literal l).(id).
|
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
| 298
|
Definition is_positive_literal (l:literal) : bool := match l with | POS _ => true | NEG _ => 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
| 299
|
Definition ForallPair {A: Type} (P : A -> Prop) (x : A * A) := P (fst x) /\ P (snd x).
|
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
| 300
|
Definition t := IntMap.ptrie (key:=int) watch_map_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
| 301
|
Definition empty := IntMap.empty (key:=int) watch_map_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
| 302
|
Definition wf (m: t) := wf_map m /\ IntMapForall (fun x => wf_map (fst x) /\ wf_map (snd x)) 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
| 303
|
Definition find_clauses_p (v: int) (cls: t) := match IntMap.get' v cls with | None => (IntMap.empty (Annot.t watched_clause), IntMap.empty (Annot.t watched_clause)) | Some r => 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
| 304
|
Definition find_clauses (v:literal) (cls : t) := match v with | POS f => match IntMap.get' f.(id) cls with | None => IntMap.empty (Annot.t watched_clause) | Some r => fst r end | NEG f => match IntMap.get' f.(id) cls with | None => IntMap.empty (Annot.t watched_clause) | Some r => snd r 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
| 305
|
Definition add_clause_old (l:literal) (clause_id: int) (cl: Annot.t watched_clause) (cls : WMap.t) := let lid := id_of_literal l in let (ln,lp) := find_clauses_p lid cls in if is_positive_literal l then IntMap.set' lid (ln,IntMap.set' clause_id cl lp) cls else IntMap.set' lid (IntMap.set' clause_id cl ln,lp) cls.
|
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
| 306
|
Definition add_clause (l:literal) (clause_id: int) (cl: Annot.t watched_clause) (cls : WMap.t) := match l with | POS f => IntMap.insert' (fun _ '(ln,lp) => (ln,IntMap.set' clause_id cl lp)) f.(id) (IntMap.empty _, IntMap.Leaf _ clause_id cl) cls | NEG f => IntMap.insert' (fun _ '(ln,lp) => (IntMap.set' clause_id cl ln,lp)) f.(id) (IntMap.Leaf _ clause_id cl, IntMap.empty _) cls 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
| 307
|
Definition remove_watched_id_old (l:literal) (id:int) (cl: WMap.t) := let lid := id_of_literal l in let (ln,lp) := WMap.find_clauses_p lid cl in if is_positive_literal l then IntMap.set' lid (ln, IntMap.remove' id lp) cl else IntMap.set' lid (IntMap.remove' id ln,lp) 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
| 308
|
Definition remove_watched_id (l:literal) (cid:int) (cl: WMap.t) := match l with POS f => IntMap.insert' (fun _ '(ln,lp) => (ln,IntMap.remove' cid lp)) f.(id) (IntMap.empty _, IntMap.empty _) cl | NEG f => IntMap.insert' (fun _ '(ln,lp) => (IntMap.remove' cid ln,lp)) f.(id) (IntMap.empty _, IntMap.empty _) cl 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
| 309
|
Definition Forall (F : Annot.t watched_clause -> Prop) (m : t) := IntMapForall (IntMapForall2 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
| 310
|
Definition fold_watch_map {B:Type} (f : B -> int -> Annot.t watched_clause -> B) (m:watch_map) (acc:B) := IntMap.fold' f m acc.
|
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
| 311
|
Definition elements (m: watch_map) := IntMap.elements' 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
| 312
|
Variable select : forall (k:int) (cl: Annot.t watched_clause), option 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
| 313
|
Definition search_in_map (m : IntMap.ptrie (Annot.t watched_clause)) := IntMap.search select 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
| 314
|
Definition search_in_pair_map (pos : bool) (k:int) (e: IntMap.ptrie (Annot.t watched_clause) * IntMap.ptrie (Annot.t watched_clause)) := if pos then search_in_map (snd e) else search_in_map (fst 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
| 315
|
Definition search (only_pos:bool) (cl:WMap.t) := IntMap.search (search_in_pair_map only_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
| 316
|
Definition Forall_watch_map (P: Annot.t watched_clause -> Prop) (m:watch_map) := IntMapForall P 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
| 317
|
Definition wf_watch_map (m:watch_map) := wf_map 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
| 318
|
Variable AT_is_dec : 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
| 319
|
Definition chkHc_list (l1 l2 : list HFormula) := forall2b HCons.eq_hc l1 l2.
|
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
| 320
|
Fixpoint chkHc (m: hmap) (f:LForm) (i:int) (b:bool) : bool := match f with | LAT a => match IntMap.get' i m with | Some(b',LAT a') => (a =? a') && Bool.eqb b (AT_is_dec a) && Bool.eqb b b' | _ => false end | LOP o l => List.forallb (fun f => chkHc m f.(elt) f.(id) f.(is_dec)) l && match IntMap.get' i m with | Some (b',LOP o' l') => lop_eqb o o' && Bool.eqb b (forallb (fun f => f.(is_dec)) l) && Bool.eqb b b' && chkHc_list l l' | _ => false end | LIMPL l r => List.forallb (fun f => chkHc m f.(elt) f.(id) f.(is_dec)) l && chkHc m r.(elt) r.(id) r.(is_dec) && match IntMap.get' i m with | Some (b',LIMPL l' r') => Bool.eqb b ((forallb is_dec l) && (is_dec r)) && Bool.eqb b b' && chkHc_list l l' && HCons.eq_hc r r' | _ => 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
| 321
|
Record wf (m: IntMap.ptrie (bool * LForm)) : Prop := { wf_false : IntMap.get' 0 m = Some (true,FF); wf_true : IntMap.get' 1 m = Some (true,TT); }.
|
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
| 322
|
Definition eval_op (o: op) (f1 f2 : Prop) : Prop := match o with | AND => f1 /\ f2 | OR => f1 \/ f2 | IMPL => f1 -> f2 | NOT => f1 -> False | IFF _ _ => f1 <-> 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
| 323
|
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