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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). | 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 | 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 |