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Axiom lopp_spec_low: forall k m, (forall p, (p < m)%nat -> testbit k p = false) -> testbit k m = true -> forall p, (p < m)%nat -> testbit (lopp k) p = false. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 103 |
Axiom lopp_spec_eq: forall k m, (forall p, (p < m)%nat -> testbit k p = false) -> testbit k m = true -> testbit (lopp k) m = true. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 104 |
Axiom lopp_spec_high: forall k m, (forall p, (p < m)%nat -> testbit k p = false) -> testbit k m = true -> forall p, (p > m)%nat -> testbit (lopp k) p = negb (testbit k p). | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 105 |
Axiom ltb_spec: forall m1 n1 m2 n2, is_mask m1 n1 -> is_mask m2 n2 -> (ltb m1 m2 = true <-> (n1 < n2)%nat). | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 106 |
Axiom LPO : forall (k:t), k <> zero -> exists p, testbit k p = true. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 107 |
Axiom zerobit: t -> t -> bool. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 118 |
Axiom mask: t -> t -> t. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 119 |
Axiom lowest_bit: t -> t. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 120 |
Axiom branching_bit: t -> t -> t. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 121 |
Axiom match_prefix: t -> t -> t -> bool. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 122 |
Axiom eqb_false : forall (k1 k2:t), eqb k1 k2 = false <-> k1 <> k2. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 124 |
Axiom zerobit_spec: forall k m n, is_mask m n -> zerobit k m = negb (testbit k n). | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 134 |
Axiom mask_spec: forall k m n, is_mask m n -> (forall p, (p < n)%nat -> testbit (mask k m) p = testbit k p) /\ (forall p, (p >= n)%nat -> testbit (mask k m) p = false). | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 135 |
Axiom mask_spec': forall k m n, is_mask m n -> mask (mask k m) m = mask k m. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 136 |
Axiom lowest_bit_spec: forall k, k <> zero -> exists n, is_mask (lowest_bit k) n /\ (forall p, (p < n)%nat -> testbit k p = false). | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 137 |
Axiom branching_bit_spec: forall k1 k2, k1 <> k2 -> exists n, is_mask (branching_bit k1 k2) n /\ (forall p, (p < n)%nat -> testbit k1 p = testbit k2 p) /\ (testbit k1 n <> testbit k2 n). | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 138 |
Axiom branching_bit_sym: forall k1 k2, branching_bit k1 k2 = branching_bit k2 k1. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 139 |
Axiom match_prefix_spec: forall k p m n, is_mask m n -> mask p m = p -> (match_prefix k p m = true <-> forall q, (q < n)%nat -> testbit k q = testbit p q). | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 140 |
Axiom match_prefix_spec': forall k p m n, is_mask m n -> mask p m = p -> (match_prefix k p m = false <-> k <> p /\ exists n', (n' < n)%nat /\ testbit (branching_bit k p) n' = true). | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 141 |
Definition t := K.t. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 142 |
Definition zero := K.zero. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 143 |
Definition eqb := K.eqb. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 144 |
Definition testbit := K.testbit. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 145 |
Definition interp := K.interp. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 146 |
Definition land := K.land. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 147 |
Definition lxor := K.lxor. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 148 |
Definition lopp := K.lopp. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 149 |
Definition ltb := K.ltb. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 150 |
Definition zero_spec := K.zero_spec. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 151 |
Definition testbit_spec := K.testbit_spec. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 152 |
Definition interp_spec := K.interp_spec. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 153 |
Definition land_spec := K.land_spec. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 154 |
Definition lxor_spec := K.lxor_spec. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 155 |
Definition lopp_spec_low := K.lopp_spec_low. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 156 |
Definition lopp_spec_eq := K.lopp_spec_eq. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 157 |
Definition lopp_spec_high := K.lopp_spec_high. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 158 |
Definition ltb_spec := K.ltb_spec. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 159 |
Definition is_mask (m: t) (n: nat) := K.is_mask m n. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 160 |
Definition zerobit (k m: t) := eqb (land k m) zero. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 161 |
Definition mask (k m: t) := land k (interp m). | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 162 |
Definition lowest_bit (x: t) := land x (lopp x). | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 163 |
Definition branching_bit (p p': t) := lowest_bit (lxor p p'). | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 164 |
Definition match_prefix (k p m: t) := eqb (mask k m) p. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 165 |
Definition eqb_spec := K.eqb_spec. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 166 |
Fixpoint find_lowest (n: nat) (k: t) (p: nat) := match p with | O => n | S q => if testbit k (n - p)%nat then (n - p)%nat else find_lowest n k q end. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 167 |
Definition elt := Key.t. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 168 |
Definition elt_eqb:= Key.eqb. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 169 |
Definition t := fun (A:Type) => ptrie A. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 170 |
Definition empty (A: Type): ptrie A := Empty. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 171 |
Fixpoint get' (A: Type) (i: elt) (t: ptrie A) := match t with | Empty => None | Leaf k v => if elt_eqb i k then Some v else None | Branch prefix brbit l r => if Key.zerobit i brbit then get' i l else get' i r end. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 172 |
Definition join (A: Type) (k1: Key.t) (t1: ptrie A) (k2: Key.t) (t2: ptrie A) := let m := Key.branching_bit k1 k2 in if Key.zerobit k1 m then Branch (Key.mask k1 m) m t1 t2 else Branch (Key.mask k1 m) m t2 t1. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 173 |
Fixpoint set' (A: Type) (i: elt) (x: A) (t: ptrie A) := match t with | Empty => Leaf i x | Leaf j v => if elt_eqb i j then Leaf i x else join i (Leaf i x) j (Leaf j v) | Branch prefix brbit l r => if Key.match_prefix i prefix brbit then if Key.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. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 174 |
Definition branch (A: Type) (prefix m: Key.t) (t1 t2: ptrie A) := match t1 with | Empty => t2 | _ => match t2 with | Empty => t1 | _ => Branch prefix m t1 t2 end end. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 175 |
Fixpoint remove' (A: Type) (i: elt) (t: ptrie A) := match t with | Empty => Empty | Leaf k v => if elt_eqb k i then Empty else t | Branch p m l r => if Key.match_prefix i p m then if Key.zerobit i m then branch p m (remove' i l) r else branch p m l (remove' i r) else t end. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 176 |
Fixpoint map' (A B: Type) (f: elt -> 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. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 177 |
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. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 178 |
Fixpoint elements' (A: Type) (m: ptrie A) (acc: list (elt * A)): list (elt * A) := match m with | Empty => acc | Leaf k v => (k, v)::acc | Branch p m l r => elements' l (elements' r acc) end. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 179 |
Definition keys' (A: Type) (m: ptrie A) := List.map (@fst elt A) (elements' m nil). | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 180 |
Fixpoint fold' (A B: Type) (f: B -> elt -> 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. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 181 |
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. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 182 |
Fixpoint insert' (A: Type) (c: A -> A -> A) (i: elt) (x: A) (m: ptrie A): ptrie A := match m with | Empty => Leaf i x | Leaf j v => if elt_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 Key.match_prefix i prefix brbit then if Key.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. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 183 |
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 elt_eqb p1 p2 && elt_eqb m1 m2 then Branch p1 m1 (combine' c l1 l2) (combine' c r1 r2) else if Key.ltb m1 m2 && Key.match_prefix p2 p1 m1 then if Key.zerobit p2 m1 then Branch p1 m1 (combine' c l1 t2) r1 else Branch p1 m1 l1 (combine' c r1 t2) else if Key.ltb m2 m1 && Key.match_prefix p1 p2 m2 then if Key.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. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 184 |
Fixpoint beq' (A: Type) (beqA: A -> A -> bool) (m1 m2: ptrie A): bool := match m1, m2 with | Empty, Empty => true | Leaf k1 v1, Leaf k2 v2 => elt_eq k1 k2 && beqA v1 v2 | Branch p1 brbit1 l1 r1, Branch p2 brbit2 l2 r2 => elt_eq p1 p2 && elt_eq brbit1 brbit2 && beq' beqA l1 l2 && beq' beqA r1 r2 | _, _ => false end. | Lia Cdcl.Coqlib | fbesson-itauto/theories/Patricia | fbesson-itauto | 185 |
Variable A: Type. | Bool Uint63 | fbesson-itauto/theories/Syntax | fbesson-itauto | 186 |
Record t : Type := mk { id : int; is_dec: bool; elt: A }. | Bool Uint63 | fbesson-itauto/theories/Syntax | fbesson-itauto | 187 |
Definition eq_hc (f1 f2 : t) := (id f1 =? id f2)%uint63 && Bool.eqb (is_dec f1) (is_dec f2). | Bool Uint63 | fbesson-itauto/theories/Syntax | fbesson-itauto | 188 |
Definition map [A B] (f: A -> B) (e: t A) : t B := mk _ (id _ e) (is_dec _ e) (f (elt _ e)). | Bool Uint63 | fbesson-itauto/theories/Syntax | fbesson-itauto | 189 |
Definition HFormula : Type := HCons.t LForm. | Bool Uint63 | fbesson-itauto/theories/Syntax | fbesson-itauto | 190 |
Definition lop_eqb (o o': lop) : bool := match o , o' with | LAND , LAND => true | LOR , LOR => true | _ , _ => false end. | Bool Uint63 | fbesson-itauto/theories/Syntax | fbesson-itauto | 191 |
Variable F : A -> B -> bool. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List | fbesson-itauto/theories/Lib | fbesson-itauto | 192 |
Fixpoint forall2b (l1 : list A) (l2 : list B) : bool := match l1 , l2 with | nil , nil => true | e1::l1', e2::l2' => F e1 e2 && forall2b l1' l2' | _ , _ => false end. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List | fbesson-itauto/theories/Lib | fbesson-itauto | 193 |
Variable eval : A -> Prop. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Cdcl.Lib Cdcl.Syntax Cdcl.Lit | fbesson-itauto/theories/Clause | fbesson-itauto | 194 |
Fixpoint eval_and_list (l : list A) := match l with | nil => True | e :: nil => eval e | e1 ::l => eval e1 /\ eval_and_list l end. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Cdcl.Lib Cdcl.Syntax Cdcl.Lit | fbesson-itauto/theories/Clause | fbesson-itauto | 195 |
Fixpoint eval_and_list' (l : list A) := match l with | nil => True | e1 ::l => eval e1 /\ eval_and_list' l end. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Cdcl.Lib Cdcl.Syntax Cdcl.Lit | fbesson-itauto/theories/Clause | fbesson-itauto | 196 |
Fixpoint eval_or_list (l : list A) := match l with | nil => False | e :: nil => eval e | e1 ::l => eval e1 \/ eval_or_list l end. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Cdcl.Lib Cdcl.Syntax Cdcl.Lit | fbesson-itauto/theories/Clause | fbesson-itauto | 197 |
Fixpoint eval_or_list' (l : list A) := match l with | nil => False | e1 ::l => eval e1 \/ eval_or_list' l end. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Cdcl.Lib Cdcl.Syntax Cdcl.Lit | fbesson-itauto/theories/Clause | fbesson-itauto | 198 |
Definition eval_op_list (o:lop) (l : list A) := match o with | LAND => eval_and_list l | LOR => eval_or_list l end. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Cdcl.Lib Cdcl.Syntax Cdcl.Lit | fbesson-itauto/theories/Clause | fbesson-itauto | 199 |
Fixpoint eval_impl_list (l : list A) (r: Prop) := match l with | nil => r | e::l => eval e -> eval_impl_list l r end. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Cdcl.Lib Cdcl.Syntax Cdcl.Lit | fbesson-itauto/theories/Clause | fbesson-itauto | 200 |
Definition eval_lop (o: lop) := match o with | LAND => and | LOR => or end. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Cdcl.Lib Cdcl.Syntax Cdcl.Lit | fbesson-itauto/theories/Clause | fbesson-itauto | 201 |
Definition clause := list Lit.t. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Cdcl.Lib Cdcl.Syntax Cdcl.Lit | fbesson-itauto/theories/Clause | fbesson-itauto | 202 |
Definition wf (l : clause) := exists l1 l2, l=(List.map NEG l1) ++ (List.map POS l2). | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Cdcl.Lib Cdcl.Syntax Cdcl.Lit | fbesson-itauto/theories/Clause | fbesson-itauto | 203 |
Fixpoint eval_clause (env : HFormula -> Prop) (cl : clause) := match cl with | nil => False | e::cl' => eval_lit env e (eval_clause env cl') end. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Cdcl.Lib Cdcl.Syntax Cdcl.Lit | fbesson-itauto/theories/Clause | fbesson-itauto | 204 |
Fixpoint beval_clause (env : HFormula -> bool) (cl : clause) := match cl with | nil => false | e::cl' => beval_lit env e || beval_clause env cl' end. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Cdcl.Lib Cdcl.Syntax Cdcl.Lit | fbesson-itauto/theories/Clause | fbesson-itauto | 205 |
Definition cnf := list clause. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Cdcl.Lib Cdcl.Syntax Cdcl.Lit | fbesson-itauto/theories/Clause | fbesson-itauto | 206 |
Definition penv (env : HFormula -> bool) := fun x => is_true (env x). | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Cdcl.Lib Cdcl.Syntax Cdcl.Lit | fbesson-itauto/theories/Clause | fbesson-itauto | 207 |
Definition beval_cnf (env :HFormula -> bool) (l: cnf) := List.fold_right (fun e acc => beval_clause env e && acc) true l. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Cdcl.Lib Cdcl.Syntax Cdcl.Lit | fbesson-itauto/theories/Clause | fbesson-itauto | 208 |
Definition eval_cnf (env :HFormula -> Prop) (l: cnf) := List.fold_right (fun e acc => eval_clause env e /\ acc) True l. | Bool ZifyBool ZArith ZifyUint63 Uint63 Lia List Cdcl.Lib Cdcl.Syntax Cdcl.Lit | fbesson-itauto/theories/Clause | fbesson-itauto | 209 |
Definition lazy_and (b:bool) (f: unit -> bool) := match b with | false => false | true => f tt end. | List Bool ZArith Lia | fbesson-itauto/theories/PatriciaR | fbesson-itauto | 210 |
Definition lazy_or (b:bool) (f: unit -> bool) := match b with | true => true | false => f tt end. | List Bool ZArith Lia | fbesson-itauto/theories/PatriciaR | fbesson-itauto | 211 |
Definition le_o (o : option nat) (n:nat) := match o with | None => True | Some n' => (n' <= n)%nat end. | List Bool ZArith Lia | fbesson-itauto/theories/PatriciaR | fbesson-itauto | 212 |
Definition zerobit (k m: key) := eqb (land k m) zero. | List Bool ZArith Lia | fbesson-itauto/theories/PatriciaR | fbesson-itauto | 213 |
Definition mask (k m: key) := land k (interp m). | List Bool ZArith Lia | fbesson-itauto/theories/PatriciaR | fbesson-itauto | 214 |
Definition lowest_bit (x: key) := land x (lopp x). | List Bool ZArith Lia | fbesson-itauto/theories/PatriciaR | fbesson-itauto | 215 |
Definition branching_bit (p p': key) := lowest_bit (lxor p p'). | List Bool ZArith Lia | fbesson-itauto/theories/PatriciaR | fbesson-itauto | 216 |
Definition match_prefix (k p m: key) := eqb (mask k m) p. | List Bool ZArith Lia | fbesson-itauto/theories/PatriciaR | fbesson-itauto | 217 |
Fixpoint find_lowest (n: nat) (k: key) (p: nat) := match p with | O => n | S q => if testbit k (n - p)%nat then (n - p)%nat else find_lowest n k q end. | List Bool ZArith Lia | fbesson-itauto/theories/PatriciaR | fbesson-itauto | 218 |
Fixpoint get' {A: Type} (i: key) (t: ptrie A) := match t with | Empty => None | Leaf k v => if eqb i k then Some v else None | Branch prefix brbit l r => if zerobit i brbit then get' i l else get' i r end. | List Bool ZArith Lia | fbesson-itauto/theories/PatriciaR | fbesson-itauto | 220 |
Fixpoint mem' {A: Type} (i: key) (t: ptrie A) := match t with | Empty => false | Leaf k v => eqb i k | Branch prefix brbit l r => if zerobit i brbit then mem' i l else mem' i r end. | List Bool ZArith Lia | fbesson-itauto/theories/PatriciaR | fbesson-itauto | 221 |
Definition is_Some {A: Type} (e: option A) : bool := match e with | Some _ => true | None => false end. | List Bool ZArith Lia | fbesson-itauto/theories/PatriciaR | fbesson-itauto | 222 |
Definition join {A: Type} (k1: key) (t1: ptrie A) (k2: key) (t2: ptrie A) := let m := branching_bit k1 k2 in if zerobit k1 m then Branch (mask k1 m) m t1 t2 else Branch (mask k1 m) m t2 t1. | List Bool ZArith Lia | fbesson-itauto/theories/PatriciaR | fbesson-itauto | 223 |