diff --git a/CHANGELOG.md b/CHANGELOG.md index 571ee447f1b490af02778bb405db7f8640083284..277da4886f4cc651699c3df4ac0ec45b1ac4d221 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -13,6 +13,8 @@ API-breaking change is listed. https://gitlab.mpi-sws.org/iris/stdpp/merge_requests/93 - Add type class `TopSet` for sets with a `⊤` element. Provide instances for `boolset`, `propset`, and `coPset`. +- Add `set_solver` support for `dom`. + ## std++ 1.2.1 (released 2019-08-29) diff --git a/tests/fin_maps.v b/tests/fin_maps.v index 842c20a80d908673e12a5e5e11a4460ce2f77db6..b81d06aeb5b249326e07af3130c6d2a8c058dd02 100644 --- a/tests/fin_maps.v +++ b/tests/fin_maps.v @@ -1,4 +1,4 @@ -From stdpp Require Import fin_maps. +From stdpp Require Import fin_maps fin_map_dom. Section map_disjoint. Context `{FinMap K M}. @@ -11,3 +11,14 @@ Section map_disjoint. m2 !! i = None → m1 ##ₘ {[ i := x ]} ∪ m2 → m2 ##ₘ <[i:=x]> m1 ∧ m1 !! i = None. Proof. intros. solve_map_disjoint. Qed. End map_disjoint. + +Section map_dom. + Context `{FinMapDom K M D}. + + Lemma set_solver_dom_subseteq {A} (i j : K) (x y : A) : + {[i; j]} ⊆ dom D (<[i:=x]> (<[j:=y]> (∅ : M A))). + Proof. set_solver. Qed. + + Lemma set_solver_dom_disjoint {A} (X : D) : dom D (∅ : M A) ## X. + Proof. set_solver. Qed. +End map_dom. diff --git a/theories/fin_map_dom.v b/theories/fin_map_dom.v index 0674cbfd600338bd99a853918aba57f9907a1f7b..5ba8bb788b4ee5ddcd9ba095e5759a7766d3358e 100644 --- a/theories/fin_map_dom.v +++ b/theories/fin_map_dom.v @@ -142,32 +142,84 @@ Global Instance dom_proper_L `{!Equiv A, !LeibnizEquiv D} : Proper ((≡@{M A}) ==> (=)) (dom D) | 0. Proof. intros ???. unfold_leibniz. by apply dom_proper. Qed. -Context `{!LeibnizEquiv D}. -Lemma dom_map_filter_L {A} (P : K * A → Prop) `{!∀ x, Decision (P x)} (m : M A) X : - (∀ i, i ∈ X ↔ ∃ x, m !! i = Some x ∧ P (i, x)) → - dom D (filter P m) = X. -Proof. unfold_leibniz. apply dom_map_filter. Qed. -Lemma dom_empty_L {A} : dom D (@empty (M A) _) = ∅. -Proof. unfold_leibniz; apply dom_empty. Qed. -Lemma dom_empty_inv_L {A} (m : M A) : dom D m = ∅ → m = ∅. -Proof. by intros; apply dom_empty_inv; unfold_leibniz. Qed. -Lemma dom_alter_L {A} f (m : M A) i : dom D (alter f i m) = dom D m. -Proof. unfold_leibniz; apply dom_alter. Qed. -Lemma dom_insert_L {A} (m : M A) i x : dom D (<[i:=x]>m) = {[ i ]} ∪ dom D m. -Proof. unfold_leibniz; apply dom_insert. Qed. -Lemma dom_singleton_L {A} (i : K) (x : A) : dom D ({[i := x]} : M A) = {[ i ]}. -Proof. unfold_leibniz; apply dom_singleton. Qed. -Lemma dom_delete_L {A} (m : M A) i : dom D (delete i m) = dom D m ∖ {[ i ]}. -Proof. unfold_leibniz; apply dom_delete. Qed. -Lemma dom_union_L {A} (m1 m2 : M A) : dom D (m1 ∪ m2) = dom D m1 ∪ dom D m2. -Proof. unfold_leibniz; apply dom_union. Qed. -Lemma dom_intersection_L {A} (m1 m2 : M A) : - dom D (m1 ∩ m2) = dom D m1 ∩ dom D m2. -Proof. unfold_leibniz; apply dom_intersection. Qed. -Lemma dom_difference_L {A} (m1 m2 : M A) : dom D (m1 ∖ m2) = dom D m1 ∖ dom D m2. -Proof. unfold_leibniz; apply dom_difference. Qed. -Lemma dom_fmap_L {A B} (f : A → B) (m : M A) : dom D (f <$> m) = dom D m. -Proof. unfold_leibniz; apply dom_fmap. Qed. +Section leibniz. + Context `{!LeibnizEquiv D}. + Lemma dom_map_filter_L {A} (P : K * A → Prop) `{!∀ x, Decision (P x)} (m : M A) X : + (∀ i, i ∈ X ↔ ∃ x, m !! i = Some x ∧ P (i, x)) → + dom D (filter P m) = X. + Proof. unfold_leibniz. apply dom_map_filter. Qed. + Lemma dom_empty_L {A} : dom D (@empty (M A) _) = ∅. + Proof. unfold_leibniz; apply dom_empty. Qed. + Lemma dom_empty_inv_L {A} (m : M A) : dom D m = ∅ → m = ∅. + Proof. by intros; apply dom_empty_inv; unfold_leibniz. Qed. + Lemma dom_alter_L {A} f (m : M A) i : dom D (alter f i m) = dom D m. + Proof. unfold_leibniz; apply dom_alter. Qed. + Lemma dom_insert_L {A} (m : M A) i x : dom D (<[i:=x]>m) = {[ i ]} ∪ dom D m. + Proof. unfold_leibniz; apply dom_insert. Qed. + Lemma dom_singleton_L {A} (i : K) (x : A) : dom D ({[i := x]} : M A) = {[ i ]}. + Proof. unfold_leibniz; apply dom_singleton. Qed. + Lemma dom_delete_L {A} (m : M A) i : dom D (delete i m) = dom D m ∖ {[ i ]}. + Proof. unfold_leibniz; apply dom_delete. Qed. + Lemma dom_union_L {A} (m1 m2 : M A) : dom D (m1 ∪ m2) = dom D m1 ∪ dom D m2. + Proof. unfold_leibniz; apply dom_union. Qed. + Lemma dom_intersection_L {A} (m1 m2 : M A) : + dom D (m1 ∩ m2) = dom D m1 ∩ dom D m2. + Proof. unfold_leibniz; apply dom_intersection. Qed. + Lemma dom_difference_L {A} (m1 m2 : M A) : dom D (m1 ∖ m2) = dom D m1 ∖ dom D m2. + Proof. unfold_leibniz; apply dom_difference. Qed. + Lemma dom_fmap_L {A B} (f : A → B) (m : M A) : dom D (f <$> m) = dom D m. + Proof. unfold_leibniz; apply dom_fmap. Qed. +End leibniz. + +(** * Set solver instances *) +Global Instance set_unfold_dom_empty {A} i : SetUnfoldElemOf i (dom D (∅:M A)) False. +Proof. constructor. by rewrite dom_empty, elem_of_empty. Qed. +Global Instance set_unfold_dom_alter {A} f i j (m : M A) Q : + SetUnfoldElemOf i (dom D m) Q → + SetUnfoldElemOf i (dom D (alter f j m)) Q. +Proof. constructor. by rewrite dom_alter, (set_unfold_elem_of _ (dom _ _) _). Qed. +Global Instance set_unfold_dom_insert {A} i j x (m : M A) Q : + SetUnfoldElemOf i (dom D m) Q → + SetUnfoldElemOf i (dom D (<[j:=x]> m)) (i = j ∨ Q). +Proof. + constructor. by rewrite dom_insert, elem_of_union, + (set_unfold_elem_of _ (dom _ _) _), elem_of_singleton. +Qed. +Global Instance set_unfold_dom_delete {A} i j (m : M A) Q : + SetUnfoldElemOf i (dom D m) Q → + SetUnfoldElemOf i (dom D (delete j m)) (Q ∧ i ≠j). +Proof. + constructor. by rewrite dom_delete, elem_of_difference, + (set_unfold_elem_of _ (dom _ _) _), elem_of_singleton. +Qed. +Global Instance set_unfold_dom_singleton {A} i j : + SetUnfoldElemOf i (dom D ({[ j := x ]} : M A)) (i = j). +Proof. constructor. by rewrite dom_singleton, elem_of_singleton. Qed. +Global Instance set_unfold_dom_union {A} i (m1 m2 : M A) Q1 Q2 : + SetUnfoldElemOf i (dom D m1) Q1 → SetUnfoldElemOf i (dom D m2) Q2 → + SetUnfoldElemOf i (dom D (m1 ∪ m2)) (Q1 ∨ Q2). +Proof. + constructor. by rewrite dom_union, elem_of_union, + !(set_unfold_elem_of _ (dom _ _) _). +Qed. +Global Instance set_unfold_dom_intersection {A} i (m1 m2 : M A) Q1 Q2 : + SetUnfoldElemOf i (dom D m1) Q1 → SetUnfoldElemOf i (dom D m2) Q2 → + SetUnfoldElemOf i (dom D (m1 ∩ m2)) (Q1 ∧ Q2). +Proof. + constructor. by rewrite dom_intersection, elem_of_intersection, + !(set_unfold_elem_of _ (dom _ _) _). +Qed. +Global Instance set_unfold_dom_difference {A} i (m1 m2 : M A) Q1 Q2 : + SetUnfoldElemOf i (dom D m1) Q1 → SetUnfoldElemOf i (dom D m2) Q2 → + SetUnfoldElemOf i (dom D (m1 ∖ m2)) (Q1 ∧ ¬Q2). +Proof. + constructor. by rewrite dom_difference, elem_of_difference, + !(set_unfold_elem_of _ (dom _ _) _). +Qed. +Global Instance set_unfold_dom_fmap {A B} (f : A → B) i (m : M A) Q : + SetUnfoldElemOf i (dom D m) Q → + SetUnfoldElemOf i (dom D (f <$> m)) Q. +Proof. constructor. by rewrite dom_fmap, (set_unfold_elem_of _ (dom _ _) _). Qed. End fin_map_dom. Lemma dom_seq `{FinMapDom nat M D} {A} start (xs : list A) : @@ -180,3 +232,7 @@ Qed. Lemma dom_seq_L `{FinMapDom nat M D, !LeibnizEquiv D} {A} start (xs : list A) : dom D (map_seq (M:=M A) start xs) = set_seq start (length xs). Proof. unfold_leibniz. apply dom_seq. Qed. + +Instance set_unfold_dom_seq `{FinMapDom nat M D} {A} start (xs : list A) : + SetUnfoldElemOf i (dom D (map_seq start (M:=M A) xs)) (start ≤ i < start + length xs). +Proof. constructor. by rewrite dom_seq, elem_of_set_seq. Qed.