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From iris . algebra Require Import auth .
From iris . proofmode Require Import proofmode .
From semantics . pl . program_logic Require Export sequential_wp adequacy .
From iris . heap_lang Require Import notation .
From semantics . pl . heap_lang Require Export proofmode .
From iris . prelude Require Import options .
Class heapGpreS Σ := HeapGpreS {
heapGpreS_iris : invGpreS Σ ;
heapGpreS_heap : gen_heapGpreS loc ( option val ) Σ ;
} .
# [ export ] Existing Instance heapGpreS_iris .
# [ export ] Existing Instance heapGpreS_heap .
Definition heap Σ : gFunctors :=
# [ inv Σ ; gen_heap Σ loc ( option val ) ] .
Global Instance subG_heapGpreS { Σ } : subG heap Σ Σ → heapGpreS Σ .
Proof . solve_inG . Qed .
Definition heap_adequacy Σ ` { ! heapGpreS Σ } s e σ φ :
( ∀ ` { ! heapGS Σ } , ⊢ WP e @ s ; ⊤ { { v , ⌜ φ v ⌝ } } ) →
adequate s e σ ( λ v _ , φ v ) .
Proof .
intros Hwp ; eapply ( wp_adequacy _ _ ) ; iIntros ( ? ) .
iMod ( gen_heap_init σ . ( heap ) ) as ( ? ) " [Hh _] " .
iModIntro . iExists
( λ σ , ( gen_heap_interp σ . ( heap ) ) % I ) .
iFrame . iApply ( Hwp ( HeapGS _ _ _ ) ) .
Qed .