Base stringmap on gmap.

theories/stringmap.v → theories/strings.v

@@ -5,7 +5,7 @@ range over Coq's data type of strings [string]. The implementation uses radix-2
 search trees (uncompressed Patricia trees) as implemented in the file [pmap]
 and guarantees logarithmic-time operations. *)
 Require Export prelude.fin_maps prelude.pretty.
-Require Import Ascii String prelude.list prelude.pmap prelude.mapset.
+Require Import Ascii String prelude.gmap.
 
 (** * Encoding and decoding *)
 (** In order to reuse or existing implementation of radix-2 search trees over
@@ -47,120 +47,16 @@ Definition string_of_pos (p : positive) : string :=
   string_of_digits (digits_of_pos p).
 Lemma string_of_to_pos s : string_of_pos (string_to_pos s) = s.
 Proof.
-  unfold string_of_pos.
-  by induction s as [|[[] [] [] [] [] [] [] []]]; simpl; f_equal.
-Qed.
-Instance: Injective (=) (=) string_to_pos.
-Proof.
-  intros s1 s2 Hs. by rewrite <-(string_of_to_pos s1), Hs, string_of_to_pos.
-Qed.
-
-(** * The data structure *)
-(** We pack a [Pmap] together with a proof that ensures that all keys correspond
-to actual strings. *)
-Definition stringmap_wf {A} : Pmap A → Prop :=
-  map_Forall (λ p _, string_to_pos (string_of_pos p) = p).
-Record stringmap A := StringMap {
-  stringmap_car : Pmap A;
-  stringmap_prf : bool_decide (stringmap_wf stringmap_car)
-}.
-Arguments StringMap {_} _ _.
-Arguments stringmap_car {_} _.
-Lemma stringmap_eq {A} (m1 m2 : stringmap A) :
-  m1 = m2 ↔ stringmap_car m1 = stringmap_car m2.
-Proof.
-  split; [by intros ->|intros]. destruct m1, m2; simplify_equality'.
-  f_equal; apply proof_irrel.
-Qed.
-Instance stringmap_eq_eq {A} `{∀ x y : A, Decision (x = y)}
-  (m1 m2 : stringmap A) : Decision (m1 = m2).
-Proof.
- refine (cast_if (decide (stringmap_car m1 = stringmap_car m2)));
-  abstract (by rewrite stringmap_eq).
-Defined.
-
-(** * Operations on the data structure *)
-Instance stringmap_lookup {A} : Lookup string A (stringmap A) := λ s m,
-  let (m,_) := m in m !! string_to_pos s.
-Instance stringmap_empty {A} : Empty (stringmap A) := StringMap ∅ I.
-Lemma stringmap_partial_alter_wf {A} (f : option A → option A) m s :
-  stringmap_wf m → stringmap_wf (partial_alter f (string_to_pos s) m).
-Proof.
-  intros Hm p x. destruct (decide (string_to_pos s = p)) as [<-|?].
-  * by rewrite string_of_to_pos.
-  * rewrite lookup_partial_alter_ne by done. by apply Hm.
-Qed.
-Instance stringmap_partial_alter {A} :
-    PartialAlter string A (stringmap A) := λ f s m,
-  let (m,Hm) := m in StringMap (partial_alter f (string_to_pos s) m)
-    (bool_decide_pack _ (stringmap_partial_alter_wf f m s
-    (bool_decide_unpack _ Hm))).
-Lemma stringmap_fmap_wf {A B} (f : A → B) m :
-  stringmap_wf m → stringmap_wf (f <$> m).
-Proof. intros ? p x. rewrite lookup_fmap, fmap_Some; intros (?&?&?); eauto. Qed.
-Instance stringmap_fmap : FMap stringmap := λ A B f m,
-  let (m,Hm) := m in StringMap (f <$> m)
-    (bool_decide_pack _ (stringmap_fmap_wf f m (bool_decide_unpack _ Hm))).
-Lemma stringmap_omap_wf {A B} (f : A → option B) m :
-  stringmap_wf m → stringmap_wf (omap f m).
-Proof. intros ? p x; rewrite lookup_omap, bind_Some; intros (?&?&?); eauto. Qed.
-Instance stringmap_omap : OMap stringmap := λ A B f m,
-  let (m,Hm) := m in StringMap (omap f m)
-    (bool_decide_pack _ (stringmap_omap_wf f m (bool_decide_unpack _ Hm))).
-Lemma stringmap_merge_wf {A B C} (f : option A → option B → option C) m1 m2 :
-  let f' o1 o2 := match o1, o2 with None, None => None | _, _ => f o1 o2 end in
-  stringmap_wf m1 → stringmap_wf m2 → stringmap_wf (merge f' m1 m2).
-Proof.
-  intros f' Hm1 Hm2 p z; rewrite lookup_merge by done; intros.
-  destruct (m1 !! _) eqn:?, (m2 !! _) eqn:?; naive_solver.
-Qed.
-Instance stringmap_merge : Merge stringmap := λ A B C f m1 m2,
-  let (m1,Hm1) := m1 in let (m2,Hm2) := m2 in
-  let f' o1 o2 := match o1, o2 with None, None => None | _, _ => f o1 o2 end in
-  StringMap (merge f' m1 m2) (bool_decide_pack _ (stringmap_merge_wf f _ _
-    (bool_decide_unpack _ Hm1) (bool_decide_unpack _ Hm2))).
-Instance stringmap_to_list {A} : FinMapToList string A (stringmap A) := λ m,
-  let (m,_) := m in prod_map string_of_pos id <$> map_to_list m.
-
-(** * Instantiation of the finite map interface *)
-Instance: FinMap string stringmap.
-Proof.
-  split.
-  * unfold lookup; intros A [m1 Hm1] [m2 Hm2] H.
-    apply stringmap_eq, map_eq; intros i; simpl in *.
-    apply bool_decide_unpack in Hm1; apply bool_decide_unpack in Hm2.
-    apply option_eq; intros x; split; intros Hi.
-    + generalize Hi. rewrite <-(Hm1 i x) by done; eauto using option_eq_1.
-    + generalize Hi. rewrite <-(Hm2 i x) by done; eauto using option_eq_1.
-  * done.
-  * intros A f [m Hm] s; apply (lookup_partial_alter f m).
-  * intros A f [m Hm] s s' Hs; apply (lookup_partial_alter_ne f m).
-    by contradict Hs; apply (injective string_to_pos).
-  * intros A B f [m Hm] s; apply (lookup_fmap f m).
-  * intros A [m Hm]; unfold map_to_list; simpl.
-    apply bool_decide_unpack, map_Forall_to_list in Hm; revert Hm.
-    induction (NoDup_map_to_list m) as [|[p x] l Hpx];
-      inversion 1 as [|??? Hm']; simplify_equality'; constructor; eauto.
-    rewrite elem_of_list_fmap; intros ([p' x']&?&?); simplify_equality'.
-    cut (string_to_pos (string_of_pos p') = p'); [congruence|].
-    rewrite Forall_forall in Hm'. eapply (Hm' (_,_)); eauto.
-  * intros A [m Hm] s x; unfold map_to_list, lookup; simpl.
-    apply bool_decide_unpack in Hm; rewrite elem_of_list_fmap; split.
-    + intros ([p' x']&?&Hp'); simplify_equality'.
-      apply elem_of_map_to_list in Hp'. by rewrite (Hm p' x').
-    + intros. exists (string_to_pos s,x); simpl.
-      by rewrite elem_of_map_to_list, string_of_to_pos.
-  * intros A B f [m Hm] s; apply (lookup_omap f m).
-  * intros A B C f ? [m1 Hm1] [m2 Hm2] s; unfold merge, lookup; simpl.
-    set (f' o1 o2 := match o1, o2 with None, None => None | _, _ => f o1 o2 end).
-    rewrite lookup_merge by done. by destruct (m1 !! _), (m2 !! _).
+  unfold string_of_pos. by induction s as [|[[][][][][][][][]]]; f_equal'.
 Qed.
+Program Instance string_countable : Countable string := {|
+  encode := string_to_pos; decode p := Some (string_of_pos p)
+|}.
+Solve Obligations with naive_solver eauto using string_of_to_pos with f_equal.
 
-(** * Finite sets *)
-(** We construct sets of [strings]s satisfying extensional equality. *)
-Notation stringset := (mapset stringmap).
-Instance stringmap_dom {A} : Dom (stringmap A) stringset := mapset_dom.
-Instance: FinMapDom positive Pmap Pset := mapset_dom_spec.
+(** * Maps and sets *)
+Notation stringmap := (gmap string).
+Notation stringset := (gset string).
 
 (** * Generating fresh strings *)
 Local Open Scope N_scope.