Commit aa733429 authored by Amin Timany's avatar Amin Timany
Browse files

Merge branch 'master' of https://gitlab.mpi-sws.org/FP/iris-coq

parents e42f5897 c3c39389
......@@ -3,7 +3,7 @@ From iris.algebra Require Import upred updates.
Local Arguments valid _ _ !_ /.
Local Arguments validN _ _ _ !_ /.
Record auth (A : Type) := Auth { authoritative : option (excl A); auth_own : A }.
Record auth (A : Type) := Auth { authoritative : excl' A; auth_own : A }.
Add Printing Constructor auth.
Arguments Auth {_} _ _.
Arguments authoritative {_} _.
......@@ -14,7 +14,7 @@ Notation "● a" := (Auth (Excl' a) ∅) (at level 20).
(* COFE *)
Section cofe.
Context {A : cofeT}.
Implicit Types a : option (excl A).
Implicit Types a : excl' A.
Implicit Types b : A.
Implicit Types x y : auth A.
......
......@@ -520,6 +520,64 @@ Section ucmra.
End ucmra.
Hint Immediate cmra_unit_total.
(** * Properties about CMRAs with Leibniz equality *)
Section cmra_leibniz.
Context {A : cmraT} `{!LeibnizEquiv A}.
Implicit Types x y : A.
Global Instance cmra_assoc_L : Assoc (=) (@op A _).
Proof. intros x y z. unfold_leibniz. by rewrite assoc. Qed.
Global Instance cmra_comm_L : Comm (=) (@op A _).
Proof. intros x y. unfold_leibniz. by rewrite comm. Qed.
Lemma cmra_pcore_l_L x cx : pcore x = Some cx cx x = x.
Proof. unfold_leibniz. apply cmra_pcore_l'. Qed.
Lemma cmra_pcore_idemp_L x cx : pcore x = Some cx pcore cx = Some cx.
Proof. unfold_leibniz. apply cmra_pcore_idemp'. Qed.
Lemma cmra_opM_assoc_L x y mz : (x y) ? mz = x (y ? mz).
Proof. unfold_leibniz. apply cmra_opM_assoc. Qed.
(** ** Core *)
Lemma cmra_pcore_r_L x cx : pcore x = Some cx x cx = x.
Proof. unfold_leibniz. apply cmra_pcore_r'. Qed.
Lemma cmra_pcore_dup_L x cx : pcore x = Some cx cx = cx cx.
Proof. unfold_leibniz. apply cmra_pcore_dup'. Qed.
(** ** Persistent elements *)
Lemma persistent_dup_L x `{!Persistent x} : x x x.
Proof. unfold_leibniz. by apply persistent_dup. Qed.
(** ** Total core *)
Section total_core.
Context `{CMRATotal A}.
Lemma cmra_core_r_L x : x core x = x.
Proof. unfold_leibniz. apply cmra_core_r. Qed.
Lemma cmra_core_l_L x : core x x = x.
Proof. unfold_leibniz. apply cmra_core_l. Qed.
Lemma cmra_core_idemp_L x : core (core x) = core x.
Proof. unfold_leibniz. apply cmra_core_idemp. Qed.
Lemma cmra_core_dup_L x : core x = core x core x.
Proof. unfold_leibniz. apply cmra_core_dup. Qed.
Lemma persistent_total_L x : Persistent x core x = x.
Proof. unfold_leibniz. apply persistent_total. Qed.
Lemma persistent_core_L x `{!Persistent x} : core x = x.
Proof. by apply persistent_total_L. Qed.
End total_core.
End cmra_leibniz.
Section ucmra_leibniz.
Context {A : ucmraT} `{!LeibnizEquiv A}.
Implicit Types x y z : A.
Global Instance ucmra_unit_left_id_L : LeftId (=) (@op A _).
Proof. intros x. unfold_leibniz. by rewrite left_id. Qed.
Global Instance ucmra_unit_right_id_L : RightId (=) (@op A _).
Proof. intros x. unfold_leibniz. by rewrite right_id. Qed.
End ucmra_leibniz.
(** * Constructing a CMRA with total core *)
Section cmra_total.
Context A `{Dist A, Equiv A, PCore A, Op A, Valid A, ValidN A}.
......@@ -1005,7 +1063,7 @@ Section option.
Proof. by destruct my. Qed.
Lemma option_included (mx my : option A) :
mx my mx = None x y, mx = Some x my = Some y (x y x y).
mx my mx = None x y, mx = Some x my = Some y (x y x y).
Proof.
split.
- intros [mz Hmz].
......@@ -1013,10 +1071,10 @@ Section option.
destruct my as [y|]; [exists x, y|destruct mz; inversion_clear Hmz].
destruct mz as [z|]; inversion_clear Hmz; split_and?; auto;
setoid_subst; eauto using cmra_included_l.
- intros [->|(x&y&->&->&[[z Hz]|Hz])].
- intros [->|(x&y&->&->&[Hz|[z Hz]])].
+ exists my. by destruct my.
+ exists (Some z); by constructor.
+ exists None; by constructor.
+ exists (Some z); by constructor.
Qed.
Lemma option_cmra_mixin : CMRAMixin (option A).
......@@ -1036,10 +1094,10 @@ Section option.
destruct (pcore x) as [cx|] eqn:?; simpl; eauto using cmra_pcore_idemp.
- intros mx my; setoid_rewrite option_included.
intros [->|(x&y&->&->&[?|?])]; simpl; eauto.
+ destruct (pcore x) as [cx|] eqn:?; eauto.
destruct (cmra_pcore_mono x y cx) as (?&?&?); eauto 10.
+ destruct (pcore x) as [cx|] eqn:?; eauto.
destruct (cmra_pcore_proper x y cx) as (?&?&?); eauto 10.
+ destruct (pcore x) as [cx|] eqn:?; eauto.
destruct (cmra_pcore_mono x y cx) as (?&?&?); eauto 10.
- intros n [x|] [y|]; rewrite /validN /option_validN /=;
eauto using cmra_validN_op_l.
- intros n mx my1 my2.
......@@ -1084,6 +1142,13 @@ Section option.
Lemma exclusiveN_Some_r n x `{!Exclusive x} my :
{n} (my Some x) my = None.
Proof. rewrite comm. by apply exclusiveN_Some_l. Qed.
Lemma Some_included x y : Some x Some y x y x y.
Proof. rewrite option_included; naive_solver. Qed.
Lemma Some_included' `{CMRATotal A} x y : Some x Some y x y x y.
Proof. rewrite Some_included; naive_solver. Qed.
Lemma is_Some_included mx my : mx my is_Some mx is_Some my.
Proof. rewrite -!not_eq_None_Some option_included. naive_solver. Qed.
End option.
Arguments optionR : clear implicits.
......@@ -1095,8 +1160,8 @@ Proof.
split; first apply _.
- intros n [x|] ?; rewrite /cmra_validN //=. by apply (validN_preserving f).
- intros mx my; rewrite !option_included.
intros [->|(x&y&->&->&[?|Hxy])]; simpl; eauto 10 using @cmra_monotone.
right; exists (f x), (f y). by rewrite {4}Hxy; eauto.
intros [->|(x&y&->&->&[Hxy|?])]; simpl; eauto 10 using @cmra_monotone.
right; exists (f x), (f y). by rewrite {3}Hxy; eauto.
Qed.
Program Definition optionURF (F : rFunctor) : urFunctor := {|
urFunctor_car A B := optionUR (rFunctor_car F A B);
......
......@@ -27,6 +27,13 @@ Section coPset.
repeat (simpl || case_decide);
first [apply (f_equal CoPset)|done|exfalso]; set_solver by eauto.
Lemma coPset_included X Y : CoPset X CoPset Y X Y.
Proof.
split.
- move=> [[Z|]]; simpl; try case_decide; set_solver.
- intros (Z&->&?)%subseteq_disjoint_union_L.
exists (CoPset Z). coPset_disj_solve.
Qed.
Lemma coPset_disj_valid_inv_l X Y :
(CoPset X Y) Y', Y = CoPset Y' X Y'.
Proof. destruct Y; repeat (simpl || case_decide); by eauto. Qed.
......
......@@ -9,6 +9,7 @@ Inductive excl (A : Type) :=
Arguments Excl {_} _.
Arguments ExclBot {_}.
Notation excl' A := (option (excl A)).
Notation Excl' x := (Some (Excl x)).
Notation ExclBot' := (Some ExclBot).
......
......@@ -258,12 +258,6 @@ Proof.
* by rewrite Hi lookup_op lookup_singleton lookup_delete.
* by rewrite lookup_op lookup_singleton_ne // lookup_delete_ne // left_id.
Qed.
Lemma dom_op m1 m2 : dom (gset K) (m1 m2) = dom _ m1 dom _ m2.
Proof.
apply elem_of_equiv_L=> i; rewrite elem_of_union !elem_of_dom.
unfold is_Some; setoid_rewrite lookup_op.
destruct (m1 !! i), (m2 !! i); naive_solver.
Qed.
Lemma insert_updateP (P : A Prop) (Q : gmap K A Prop) m i x :
x ~~>: P ( y, P y Q (<[i:=y]>m)) <[i:=x]>m ~~>: Q.
......@@ -298,6 +292,17 @@ Proof.
- move: (Hm j). by rewrite !lookup_op lookup_delete_ne.
Qed.
Lemma dom_op m1 m2 : dom (gset K) (m1 m2) = dom _ m1 dom _ m2.
Proof.
apply elem_of_equiv_L=> i; rewrite elem_of_union !elem_of_dom.
unfold is_Some; setoid_rewrite lookup_op.
destruct (m1 !! i), (m2 !! i); naive_solver.
Qed.
Lemma dom_included m1 m2 : m1 m2 dom (gset K) m1 dom _ m2.
Proof.
rewrite lookup_included=>? i; rewrite !elem_of_dom. by apply is_Some_included.
Qed.
Section freshness.
Context `{Fresh K (gset K), !FreshSpec K (gset K)}.
Lemma alloc_updateP_strong (Q : gmap K A Prop) (I : gset K) m x :
......
......@@ -28,6 +28,13 @@ Section gset.
repeat (simpl || case_decide);
first [apply (f_equal GSet)|done|exfalso]; set_solver by eauto.
Lemma coPset_included X Y : GSet X GSet Y X Y.
Proof.
split.
- move=> [[Z|]]; simpl; try case_decide; set_solver.
- intros (Z&->&?)%subseteq_disjoint_union_L.
exists (GSet Z). gset_disj_solve.
Qed.
Lemma gset_disj_valid_inv_l X Y : (GSet X Y) Y', Y = GSet Y' X Y'.
Proof. destruct Y; repeat (simpl || case_decide); by eauto. Qed.
Lemma gset_disj_union X Y : X Y GSet X GSet Y = GSet (X Y).
......
......@@ -142,7 +142,7 @@ Section heap.
iIntros (<-%of_to_val ?) "[#Hinv HΦ]". rewrite /heap_ctx.
iVs (auth_empty heap_name) as "Hh".
iVs (auth_open with "[Hh]") as (h) "[Hv [Hh Hclose]]"; eauto.
rewrite left_id /heap_inv. iDestruct "Hv" as %?.
rewrite left_id_L /heap_inv. iDestruct "Hv" as %?.
iApply wp_alloc_pst. iFrame "Hh". iNext.
iIntros (l) "[% Hh] !==>".
iVs ("Hclose" $! {[ l := (1%Qp, DecAgree v) ]} with "[Hh]").
......
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