Commit d609ac7e by Jacques-Henri Jourdan

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

parents 06cbdda6 20de7e7c
 ... ... @@ -114,7 +114,7 @@ introduction patterns: - `# ipat` : move the hypothesis to the persistent context. - `%` : move the hypothesis to the pure Coq context (anonymously). - `[ipat ipat]` : (separating) conjunction elimination. - `|ipat|ipat]` : disjunction elimination. - `[ipat|ipat]` : disjunction elimination. - `[]` : false elimination. Apart from this, there are the following introduction patterns that can only ... ... @@ -186,7 +186,7 @@ Many of the proof mode tactics (such as `iDestruct`, `iApply`, `iRewrite`) can take both hypotheses and lemmas, and allow one to instantiate universal quantifiers and implications/wands of these hypotheses/lemmas on the fly. The syntax for the arguments, called _proof mode terms_ of these tactics is: The syntax for the arguments, called _proof mode terms_, of these tactics is: (H \$! t1 ... tn with "spat1 .. spatn") ... ...
 ... ... @@ -205,15 +205,12 @@ Qed. Lemma singleton_valid i x : ✓ ({[ i := x ]} : gmap K A) ↔ ✓ x. Proof. rewrite !cmra_valid_validN. by setoid_rewrite singleton_validN. Qed. Lemma insert_singleton_opN n m i x : m !! i = None → <[i:=x]> m ≡{n}≡ {[ i := x ]} ⋅ m. Lemma insert_singleton_op m i x : m !! i = None → <[i:=x]> m = {[ i := x ]} ⋅ m. Proof. intros Hi j; destruct (decide (i = j)) as [->|]. - by rewrite lookup_op lookup_insert lookup_singleton Hi right_id. - by rewrite lookup_op lookup_insert_ne // lookup_singleton_ne // left_id. intros Hi; apply map_eq=> j; destruct (decide (i = j)) as [->|]. - by rewrite lookup_op lookup_insert lookup_singleton Hi right_id_L. - by rewrite lookup_op lookup_insert_ne // lookup_singleton_ne // left_id_L. Qed. Lemma insert_singleton_op m i x : m !! i = None → <[i:=x]> m ≡ {[ i := x ]} ⋅ m. Proof. rewrite !equiv_dist; naive_solver eauto using insert_singleton_opN. Qed. Lemma core_singleton (i : K) (x : A) cx : pcore x = Some cx → core ({[ i := x ]} : gmap K A) = {[ i := cx ]}. ... ... @@ -252,9 +249,9 @@ 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. Lemma dom_op m1 m2 : dom (gset K) (m1 ⋅ m2) = dom _ m1 ∪ dom _ m2. Proof. apply elem_of_equiv; intros i; rewrite elem_of_union !elem_of_dom. 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. ... ... @@ -303,8 +300,8 @@ Section freshness. { rewrite -not_elem_of_union -dom_op -not_elem_of_union; apply is_fresh. } exists (<[i:=x]>m); split. { by apply HQ; last done; apply not_elem_of_dom. } rewrite insert_singleton_opN; last by apply not_elem_of_dom. rewrite -assoc -insert_singleton_opN; rewrite insert_singleton_op; last by apply not_elem_of_dom. rewrite -assoc -insert_singleton_op; last by apply not_elem_of_dom; rewrite dom_op not_elem_of_union. by apply insert_validN; [apply cmra_valid_validN|]. Qed. ... ...
 ... ... @@ -56,23 +56,23 @@ Lemma spawn_spec (Ψ : val → iProp) e (f : val) (Φ : val → iProp) : heap_ctx heapN ★ WP f #() {{ Ψ }} ★ (∀ l, join_handle l Ψ -★ Φ #l) ⊢ WP spawn e {{ Φ }}. Proof. iIntros {<-%of_to_val ?} "(#Hh&Hf&HΦ)". rewrite /spawn. iIntros {<-%of_to_val ?} "(#Hh & Hf & HΦ)". rewrite /spawn. wp_let. wp_alloc l as "Hl". wp_let. iPvs (own_alloc (Excl ())) as {γ} "Hγ"; first done. iPvs (inv_alloc N _ (spawn_inv γ l Ψ) with "[Hl]") as "#?"; first done. { iNext. iExists (InjLV #0). iFrame; eauto. } wp_apply wp_fork. iSplitR "Hf". - iPvsIntro. wp_seq. iPvsIntro. iApply "HΦ"; rewrite /join_handle. eauto. - wp_focus (f _). iApply wp_wand_l; iFrame "Hf"; iIntros {v} "Hv". - iPvsIntro. wp_seq. iPvsIntro. iApply "HΦ". rewrite /join_handle. eauto. - wp_focus (f _). iApply wp_wand_l. iFrame "Hf"; iIntros {v} "Hv". iInv N as {v'} "[Hl _]"; first wp_done. wp_store. iPvsIntro; iSplit; [iNext|done]. iExists (InjRV v); iFrame; eauto. wp_store. iPvsIntro. iSplit; [iNext|done]. iExists (InjRV v). iFrame. eauto. Qed. Lemma join_spec (Ψ : val → iProp) l (Φ : val → iProp) : join_handle l Ψ ★ (∀ v, Ψ v -★ Φ v) ⊢ WP join #l {{ Φ }}. Proof. rewrite /join_handle; iIntros "[[% H] Hv]"; iDestruct "H" as {γ} "(#?&Hγ&#?)". rewrite /join_handle; iIntros "[[% H] Hv]". iDestruct "H" as {γ} "(#?&Hγ&#?)". iLöb as "IH". wp_rec. wp_focus (! _)%E. iInv N as {v} "[Hl Hinv]". wp_load. iDestruct "Hinv" as "[%|Hinv]"; subst. - iPvsIntro; iSplitL "Hl"; [iNext; iExists _; iFrame; eauto|]. ... ...
 ... ... @@ -393,6 +393,8 @@ Proof. now intros -> ?. Qed. Instance unit_equiv : Equiv unit := λ _ _, True. Instance unit_equivalence : Equivalence (@equiv unit _). Proof. repeat split. Qed. Instance unit_leibniz : LeibnizEquiv unit. Proof. intros [] []; reflexivity. Qed. Instance unit_inhabited: Inhabited unit := populate (). (** ** Products *) ... ... @@ -908,13 +910,6 @@ Class Collection A C `{ElemOf A C, Empty C, Singleton A C, elem_of_intersection X Y (x : A) : x ∈ X ∩ Y ↔ x ∈ X ∧ x ∈ Y; elem_of_difference X Y (x : A) : x ∈ X ∖ Y ↔ x ∈ X ∧ x ∉ Y }. Class CollectionOps A C `{ElemOf A C, Empty C, Singleton A C, Union C, Intersection C, Difference C, IntersectionWith A C, Filter A C} : Prop := { collection_ops :>> Collection A C; elem_of_intersection_with (f : A → A → option A) X Y (x : A) : x ∈ intersection_with f X Y ↔ ∃ x1 x2, x1 ∈ X ∧ x2 ∈ Y ∧ f x1 x2 = Some x; elem_of_filter X P `{∀ x, Decision (P x)} x : x ∈ filter P X ↔ P x ∧ x ∈ X }. (** We axiomative a finite collection as a collection whose elements can be enumerated as a list. These elements, given by the [elements] function, may be ... ...
 ... ... @@ -467,35 +467,6 @@ Section collection. End dec. End collection. Section collection_ops. Context `{CollectionOps A C}. Lemma elem_of_intersection_with_list (f : A → A → option A) Xs Y x : x ∈ intersection_with_list f Y Xs ↔ ∃ xs y, Forall2 (∈) xs Xs ∧ y ∈ Y ∧ foldr (λ x, (≫= f x)) (Some y) xs = Some x. Proof. split. - revert x. induction Xs; simpl; intros x HXs; [eexists [], x; intuition|]. rewrite elem_of_intersection_with in HXs; destruct HXs as (x1&x2&?&?&?). destruct (IHXs x2) as (xs & y & hy & ? & ?); trivial. eexists (x1 :: xs), y. intuition (simplify_option_eq; auto). - intros (xs & y & Hxs & ? & Hx). revert x Hx. induction Hxs; intros; simplify_option_eq; [done |]. rewrite elem_of_intersection_with. naive_solver. Qed. Lemma intersection_with_list_ind (P Q : A → Prop) f Xs Y : (∀ y, y ∈ Y → P y) → Forall (λ X, ∀ x, x ∈ X → Q x) Xs → (∀ x y z, Q x → P y → f x y = Some z → P z) → ∀ x, x ∈ intersection_with_list f Y Xs → P x. Proof. intros HY HXs Hf. induction Xs; simplify_option_eq; [done |]. intros x Hx. rewrite elem_of_intersection_with in Hx. decompose_Forall. destruct Hx as (? & ? & ? & ? & ?). eauto. Qed. End collection_ops. (** * Sets without duplicates up to an equivalence *) Section NoDup. Context `{SimpleCollection A B} (R : relation A) `{!Equivalence R}. ... ...
 ... ... @@ -42,10 +42,6 @@ Instance listset_intersection: Intersection (listset A) := λ l k, let (l') := l in let (k') := k in Listset (list_intersection l' k'). Instance listset_difference: Difference (listset A) := λ l k, let (l') := l in let (k') := k in Listset (list_difference l' k'). Instance listset_intersection_with: IntersectionWith A (listset A) := λ f l k, let (l') := l in let (k') := k in Listset (list_intersection_with f l' k'). Instance listset_filter: Filter A (listset A) := λ P _ l, let (l') := l in Listset (filter P l'). Instance: Collection A (listset A). Proof. ... ... @@ -62,13 +58,6 @@ Proof. - intros. apply elem_of_remove_dups. - intros. apply NoDup_remove_dups. Qed. Global Instance: CollectionOps A (listset A). Proof. split. - apply _. - intros ? [?] [?]. apply elem_of_list_intersection_with. - intros [?] ??. apply elem_of_list_filter. Qed. End listset. (** These instances are declared using [Hint Extern] to avoid too ... ... @@ -83,14 +72,10 @@ Hint Extern 1 (Union (listset _)) => eapply @listset_union : typeclass_instances. Hint Extern 1 (Intersection (listset _)) => eapply @listset_intersection : typeclass_instances. Hint Extern 1 (IntersectionWith _ (listset _)) => eapply @listset_intersection_with : typeclass_instances. Hint Extern 1 (Difference (listset _)) => eapply @listset_difference : typeclass_instances. Hint Extern 1 (Elements _ (listset _)) => eapply @listset_elems : typeclass_instances. Hint Extern 1 (Filter _ (listset _)) => eapply @listset_filter : typeclass_instances. Instance listset_ret: MRet listset := λ A x, {[ x ]}. Instance listset_fmap: FMap listset := λ A B f l, ... ...
 ... ... @@ -29,12 +29,6 @@ Instance listset_nodup_intersection: Intersection C := λ l k, Instance listset_nodup_difference: Difference C := λ l k, let (l',Hl) := l in let (k',Hk) := k in ListsetNoDup _ (NoDup_list_difference _ k' Hl). Instance listset_nodup_intersection_with: IntersectionWith A C := λ f l k, let (l',Hl) := l in let (k',Hk) := k in ListsetNoDup (remove_dups (list_intersection_with f l' k')) (NoDup_remove_dups _). Instance listset_nodup_filter: Filter A C := λ P _ l, let (l',Hl) := l in ListsetNoDup _ (NoDup_filter P _ Hl). Instance: Collection A C. Proof. ... ... @@ -49,15 +43,6 @@ Qed. Global Instance listset_nodup_elems: Elements A C := listset_nodup_car. Global Instance: FinCollection A C. Proof. split. apply _. done. by intros [??]. Qed. Global Instance: CollectionOps A C. Proof. split. - apply _. - intros ? [??] [??] ?. unfold intersection_with, elem_of, listset_nodup_intersection_with, listset_nodup_elem_of; simpl. rewrite elem_of_remove_dups. by apply elem_of_list_intersection_with. - intros [??] ???. apply elem_of_list_filter. Qed. End list_collection. Hint Extern 1 (ElemOf _ (listset_nodup _)) => ... ... @@ -74,5 +59,3 @@ Hint Extern 1 (Difference (listset_nodup _)) => eapply @listset_nodup_difference : typeclass_instances. Hint Extern 1 (Elements _ (listset_nodup _)) => eapply @listset_nodup_elems : typeclass_instances. Hint Extern 1 (Filter _ (listset_nodup _)) => eapply @listset_nodup_filter : typeclass_instances.
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