diff --git a/README.md b/README.md index 3950fdafa95f1978b6435d84cce44d64a5668ada..9453e1e25df4b8c2713e8ee0524fad9248b23154 100644 --- a/README.md +++ b/README.md @@ -10,6 +10,11 @@ This version is known to compile with: - Coq 8.7.1 / 8.7.2 / 8.8.0 - A development version of [std++](https://gitlab.mpi-sws.org/robbertkrebbers/coq-stdpp) +For a version compatible with Coq 8.6, have a look at the +[iris-3.1 branch](https://gitlab.mpi-sws.org/FP/iris-coq/tree/iris-3.1). +If you need to work with Coq 8.5, please check out the +[iris-3.0 branch](https://gitlab.mpi-sws.org/FP/iris-coq/tree/iris-3.0). + ## Installing via opam To obtain the latest stable release via opam (1.2.2 or newer), you have to add diff --git a/_CoqProject b/_CoqProject index 86c783a15c58f8a092d97d4f40458bcafa12f1fe..ef9ce69e3574f0f9b6b5e265c949f4fae273eae3 100644 --- a/_CoqProject +++ b/_CoqProject @@ -22,6 +22,7 @@ theories/algebra/vector.v theories/algebra/updates.v theories/algebra/local_updates.v theories/algebra/gset.v +theories/algebra/gmultiset.v theories/algebra/coPset.v theories/algebra/deprecated.v theories/algebra/proofmode_classes.v diff --git a/opam b/opam index 33b35c14ba4d785a1e043724f7bf04e52fc304f5..c39ba665638b613d6206f7f9ef8233ca22e59bef 100644 --- a/opam +++ b/opam @@ -10,6 +10,6 @@ build: [make "-j%{jobs}%"] install: [make "install"] remove: ["rm" "-rf" "%{lib}%/coq/user-contrib/iris"] depends: [ - "coq" { >= "8.7.1" & < "8.9~" | (= "dev") } + "coq" { (>= "8.7.1" & < "8.9~") | (= "dev") } "coq-stdpp" { (= "dev.2018-04-06.0") | (= "dev") } ] diff --git a/theories/algebra/gmultiset.v b/theories/algebra/gmultiset.v new file mode 100644 index 0000000000000000000000000000000000000000..86a1fc0c8b8f11a41db9907f57a170008942323a --- /dev/null +++ b/theories/algebra/gmultiset.v @@ -0,0 +1,79 @@ +From iris.algebra Require Export cmra. +From iris.algebra Require Import updates local_updates. +From stdpp Require Export collections gmultiset countable. +Set Default Proof Using "Type". + +(* The multiset union CMRA *) +Section gmultiset. + Context `{Countable K}. + Implicit Types X Y : gmultiset K. + + Canonical Structure gmultisetC := discreteC (gmultiset K). + + Instance gmultiset_valid : Valid (gmultiset K) := λ _, True. + Instance gmultiset_validN : ValidN (gmultiset K) := λ _ _, True. + Instance gmultiset_unit : Unit (gmultiset K) := (∅ : gmultiset K). + Instance gmultiset_op : Op (gmultiset K) := union. + Instance gmultiset_pcore : PCore (gmultiset K) := λ X, Some ∅. + + Lemma gmultiset_op_union X Y : X ⋅ Y = X ∪ Y. + Proof. done. Qed. + Lemma gmultiset_core_empty X : core X = ∅. + Proof. done. Qed. + Lemma gmultiset_included X Y : X ≼ Y ↔ X ⊆ Y. + Proof. + split. + - intros [Z ->%leibniz_equiv]. + rewrite gmultiset_op_union. apply gmultiset_union_subseteq_l. + - intros ->%gmultiset_union_difference. by exists (Y ∖ X). + Qed. + + Lemma gmultiset_ra_mixin : RAMixin (gmultiset K). + Proof. + apply ra_total_mixin; eauto. + - by intros X Y Z ->%leibniz_equiv. + - by intros X Y ->%leibniz_equiv. + - solve_proper. + - intros X1 X2 X3. by rewrite !gmultiset_op_union assoc_L. + - intros X1 X2. by rewrite !gmultiset_op_union comm_L. + - intros X. by rewrite gmultiset_core_empty left_id. + - intros X1 X2 HX. rewrite !gmultiset_core_empty. exists ∅. + by rewrite left_id. + Qed. + + Canonical Structure gmultisetR := discreteR (gmultiset K) gmultiset_ra_mixin. + + Global Instance gmultiset_cmra_discrete : CmraDiscrete gmultisetR. + Proof. apply discrete_cmra_discrete. Qed. + + Lemma gmultiset_ucmra_mixin : UcmraMixin (gmultiset K). + Proof. split. done. intros X. by rewrite gmultiset_op_union left_id_L. done. Qed. + Canonical Structure gmultisetUR := UcmraT (gmultiset K) gmultiset_ucmra_mixin. + + Lemma gmultiset_opM X mY : X ⋅? mY = X ∪ from_option id ∅ mY. + Proof. destruct mY; by rewrite /= ?right_id_L. Qed. + + Lemma gmultiset_update X Y : X ~~> Y. + Proof. done. Qed. + + Lemma gmultiset_local_update_alloc X Y X' : (X,Y) ~l~> (X ∪ X', Y ∪ X'). + Proof. + rewrite local_update_unital_discrete=> Z' _ /leibniz_equiv_iff->. + split. done. rewrite !gmultiset_op_union. + by rewrite -!assoc (comm _ Z' X'). + Qed. + + Lemma gmultiset_local_update_dealloc X Y X' : X' ⊆ X → X' ⊆ Y → (X,Y) ~l~> (X ∖ X', Y ∖ X'). + Proof. + intros ->%gmultiset_union_difference ->%gmultiset_union_difference. + rewrite local_update_unital_discrete=> Z' _ /leibniz_equiv_iff->. + split. done. rewrite !gmultiset_op_union=> x. + repeat (rewrite multiplicity_difference || rewrite multiplicity_union). + omega. + Qed. + +End gmultiset. + +Arguments gmultisetC _ {_ _}. +Arguments gmultisetR _ {_ _}. +Arguments gmultisetUR _ {_ _}.