Commit 4fc67339 authored by Robbert Krebbers's avatar Robbert Krebbers
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Merge branch 'robbert/set_unfold_dom' into 'master'

Add `set_solver` support for `dom`

Closes #53

See merge request iris/stdpp!116
parents 268507ec 5f26f6cd
......@@ -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)
......
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 ## {[ i := x ]} m2 m2 ## <[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.
......@@ -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.
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