Commit 71788212 authored by Robbert Krebbers's avatar Robbert Krebbers

Seal off definition of iProp using a Module.

parent 2f9e4910
......@@ -6,6 +6,26 @@ From algebra Require Import cofe_solver.
COFEs to the category of CMRAs, which is instantiated with [laterC iProp]. The
[laterC iProp] can be used to construct impredicate CMRAs, such as the stored
propositions using the agreement CMRA. *)
Module Type iProp_solution_sig.
Parameter iPreProp : language rFunctor cofeT.
Definition iGst (Λ : language) (Σ : rFunctor) : cmraT :=
Σ (laterC (iPreProp Λ Σ)).
Definition iRes Λ Σ := res Λ (laterC (iPreProp Λ Σ)) (iGst Λ Σ).
Definition iResR Λ Σ := resR Λ (laterC (iPreProp Λ Σ)) (iGst Λ Σ).
Definition iWld Λ Σ := gmap positive (agree (laterC (iPreProp Λ Σ))).
Definition iPst Λ := excl (state Λ).
Definition iProp (Λ : language) (Σ : rFunctor) : cofeT := uPredC (iResR Λ Σ).
Parameter iProp_unfold: {Λ Σ}, iProp Λ Σ -n> iPreProp Λ Σ.
Parameter iProp_fold: {Λ Σ}, iPreProp Λ Σ -n> iProp Λ Σ.
Parameter iProp_fold_unfold: {Λ Σ} (P : iProp Λ Σ),
iProp_fold (iProp_unfold P) P.
Parameter iProp_unfold_fold: {Λ Σ} (P : iPreProp Λ Σ),
iProp_unfold (iProp_fold P) P.
End iProp_solution_sig.
Module Export iProp_solution : iProp_solution_sig.
Definition iProp_result (Λ : language) (Σ : rFunctor) :
solution (uPredCF (resRF Λ laterCF (laterRF Σ))).
......@@ -17,7 +37,6 @@ Proof.
- apply rFunctor_ne; split; apply laterC_map_contractive=> i ?; by apply Hf.
(* Solution *)
Definition iPreProp (Λ : language) (Σ : rFunctor) : cofeT := iProp_result Λ Σ.
Definition iGst (Λ : language) (Σ : rFunctor) : cmraT :=
Σ (laterC (iPreProp Λ Σ)).
......@@ -35,6 +54,8 @@ Proof. apply solution_unfold_fold. Qed.
Lemma iProp_unfold_fold {Λ Σ} (P : iPreProp Λ Σ) :
iProp_unfold (iProp_fold P) P.
Proof. apply solution_fold_unfold. Qed.
End iProp_solution.
Bind Scope uPred_scope with iProp.
Instance iProp_fold_inj n Λ Σ : Inj (dist n) (dist n) (@iProp_fold Λ Σ).
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