Commit fe8930b6 by Robbert Krebbers

### Merge branch 'gmap_filter'

parents 2175e39f 20f1b822
 ... ... @@ -19,6 +19,13 @@ Class FinMapDom K M D `{∀ A, Dom (M A) D, FMap M, Section fin_map_dom. Context `{FinMapDom K M D}. Lemma dom_map_filter {A} (P : K * A → Prop) `{!∀ x, Decision (P x)} (m : M A): dom D (filter P m) ⊆ dom D m. Proof. intros ?. rewrite 2!elem_of_dom. destruct 1 as [?[Eq _]%map_filter_lookup_Some]. by eexists. Qed. Lemma elem_of_dom_2 {A} (m : M A) i x : m !! i = Some x → i ∈ dom D m. Proof. rewrite elem_of_dom; eauto. Qed. Lemma not_elem_of_dom {A} (m : M A) i : i ∉ dom D m ↔ m !! i = None. ... ...
 ... ... @@ -130,6 +130,9 @@ is unspecified. *) Definition map_fold `{FinMapToList K A M} {B} (f : K → A → B → B) (b : B) : M → B := foldr (curry f) b ∘ map_to_list. Instance map_filter `{FinMapToList K A M, Insert K A M, Empty M} : Filter (K * A) M := λ P _, map_fold (λ k v m, if decide (P (k,v)) then <[k := v]>m else m) ∅. (** * Theorems *) Section theorems. Context `{FinMap K M}. ... ... @@ -1002,6 +1005,53 @@ Proof. assert (m !! j = Some y) by (apply Hm; by right). naive_solver. Qed. (** ** The filter operation *) Section map_Filter. Context {A} (P : K * A → Prop) `{!∀ x, Decision (P x)}. Implicit Types m : M A. Lemma map_filter_lookup_Some m i x : filter P m !! i = Some x ↔ m !! i = Some x ∧ P (i,x). Proof. revert m i x. apply (map_fold_ind (λ m1 m2, ∀ i x, m1 !! i = Some x ↔ m2 !! i = Some x ∧ P _)); intros i x. - rewrite lookup_empty. naive_solver. - intros m m' Hm Eq j y. case_decide; case (decide (j = i))as [->|?]. + rewrite 2!lookup_insert. naive_solver. + rewrite !lookup_insert_ne by done. by apply Eq. + rewrite Eq, Hm, lookup_insert. naive_solver. + by rewrite lookup_insert_ne. Qed. Lemma map_filter_lookup_None m i : filter P m !! i = None ↔ m !! i = None ∨ ∀ x, m !! i = Some x → ¬ P (i,x). Proof. rewrite eq_None_not_Some. unfold is_Some. setoid_rewrite map_filter_lookup_Some. naive_solver. Qed. Lemma map_filter_lookup_eq m1 m2 : (∀ k x, P (k,x) → m1 !! k = Some x ↔ m2 !! k = Some x) → filter P m1 = filter P m2. Proof. intros HP. apply map_eq. intros i. apply option_eq; intros x. rewrite !map_filter_lookup_Some. naive_solver. Qed. Lemma map_filter_lookup_insert m i x : P (i,x) → <[i:=x]> (filter P m) = filter P (<[i:=x]> m). Proof. intros HP. apply map_eq. intros j. apply option_eq; intros y. destruct (decide (j = i)) as [->|?]. - rewrite map_filter_lookup_Some, !lookup_insert. naive_solver. - rewrite lookup_insert_ne, !map_filter_lookup_Some, lookup_insert_ne by done. naive_solver. Qed. Lemma map_filter_empty : filter P (∅ : M A) = ∅. Proof. apply map_fold_empty. Qed. End map_Filter. (** ** Properties of the [map_Forall] predicate *) Section map_Forall. Context {A} (P : K → A → Prop). ... ...
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