Commit 466710ad authored by Ralf Jung's avatar Ralf Jung Committed by Robbert Krebbers

saved_prop: provide convenience definitions for common instances

parent c9707f98
From iris.base_logic Require Export own.
From iris.algebra Require Import agree.
From stdpp Require Import gmap.
From iris.proofmode Require Import tactics.
Set Default Proof Using "Type".
Import uPred.
Class savedPropG (Σ : gFunctors) (F : cFunctor) :=
saved_prop_inG :> inG Σ (agreeR (F (iPreProp Σ))).
Definition savedPropΣ (F : cFunctor) `{!cFunctorContractive F} : gFunctors :=
(* "Saved anything" -- this can give you saved propositions, saved predicates,
saved whatever-you-like. *)
Class savedAnythingG (Σ : gFunctors) (F : cFunctor) :=
saved_anything_inG :> inG Σ (agreeR (F (iPreProp Σ))).
Definition savedAnythingΣ (F : cFunctor) `{!cFunctorContractive F} : gFunctors :=
#[ GFunctor (agreeRF F) ].
Instance subG_savedPropΣ {Σ F} `{!cFunctorContractive F} :
subG (savedPropΣ F) Σ savedPropG Σ F.
Instance subG_savedAnythingΣ {Σ F} `{!cFunctorContractive F} :
subG (savedAnythingΣ F) Σ savedAnythingG Σ F.
Proof. solve_inG. Qed.
Definition saved_prop_own `{savedPropG Σ F}
Definition saved_anything_own `{savedAnythingG Σ F}
(γ : gname) (x : F (iProp Σ)) : iProp Σ :=
own γ (to_agree $ (cFunctor_map F (iProp_fold, iProp_unfold) x)).
Typeclasses Opaque saved_prop_own.
Instance: Params (@saved_prop_own) 3.
Typeclasses Opaque saved_anything_own.
Instance: Params (@saved_anything_own) 3.
Section saved_prop.
Context `{savedPropG Σ F}.
Section saved_anything.
Context `{savedAnythingG Σ F}.
Implicit Types x y : F (iProp Σ).
Implicit Types γ : gname.
Global Instance saved_prop_persistent γ x : Persistent (saved_prop_own γ x).
Proof. rewrite /saved_prop_own; apply _. Qed.
Global Instance saved_prop_persistent γ x : Persistent (saved_anything_own γ x).
Proof. rewrite /saved_anything_own; apply _. Qed.
Lemma saved_prop_alloc_strong x (G : gset gname) :
(|==> γ, ⌜γ G saved_prop_own γ x)%I.
Lemma saved_anything_alloc_strong x (G : gset gname) :
(|==> γ, ⌜γ G saved_anything_own γ x)%I.
Proof. by apply own_alloc_strong. Qed.
Lemma saved_prop_alloc x : (|==> γ, saved_prop_own γ x)%I.
Lemma saved_anything_alloc x : (|==> γ, saved_anything_own γ x)%I.
Proof. by apply own_alloc. Qed.
Lemma saved_prop_agree γ x y :
saved_prop_own γ x - saved_prop_own γ y - x y.
Lemma saved_anything_agree γ x y :
saved_anything_own γ x - saved_anything_own γ y - x y.
Proof.
(* TODO: Use the proof mode. *)
apply wand_intro_r.
rewrite -own_op own_valid agree_validI agree_equivI.
set (G1 := cFunctor_map F (iProp_fold, iProp_unfold)).
......@@ -46,4 +51,43 @@ Section saved_prop.
apply (ne_proper (cFunctor_map F)); split=>?; apply iProp_fold_unfold. }
rewrite -{2}[x]help -{2}[y]help. apply f_equiv, _.
Qed.
End saved_prop.
End saved_anything.
(** Provide specialized versions of this for convenience. **)
(* Saved propositions. *)
Notation savedPropG Σ := (savedAnythingG Σ ( )).
Notation savedPropΣ := (savedAnythingΣ ( )).
Definition saved_prop_own `{savedPropG Σ} (γ : gname) (P: iProp Σ) :=
saved_anything_own (F := ) γ (Next P).
Lemma saved_prop_alloc `{savedPropG Σ} (P: iProp Σ) :
(|==> γ, saved_prop_own γ P)%I.
Proof. iApply saved_anything_alloc. Qed.
Lemma saved_prop_agree `{savedPropG Σ} γ P Q :
saved_prop_own γ P - saved_prop_own γ Q - (P Q).
Proof.
iIntros "HP HQ". iApply later_equivI. iApply (saved_anything_agree with "HP HQ").
Qed.
(* Saved predicates. *)
Notation savedPredG Σ A := (savedAnythingG Σ (constCF A -n> )).
Notation savedPredΣ A := (savedAnythingΣ (constCF A -n> )).
Definition saved_pred_own `{savedPredG Σ A} (γ : gname) (f: A -n> iProp Σ) :=
saved_anything_own (F := A -n> ) γ (CofeMor Next f).
Lemma saved_pred_alloc `{savedPredG Σ A} (f: A -n> iProp Σ) :
(|==> γ, saved_pred_own γ f)%I.
Proof. iApply saved_anything_alloc. Qed.
Lemma saved_pred_agree `{savedPredG Σ A} γ f g :
saved_pred_own γ f - saved_pred_own γ g - x, (f x g x).
Proof.
iIntros "Hx Hy *". unfold saved_pred_own. iApply later_equivI.
iDestruct (ofe_morC_equivI (CofeMor Next f) (CofeMor Next g)) as "[FE _]".
simpl. iApply ("FE" with "[-]").
iApply (saved_anything_agree with "Hx Hy").
Qed.
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