Commit 453d2b16 authored by Ralf Jung's avatar Ralf Jung

heap: start to use proof mode

parent 04e8c944
Pipeline #516 failed with stage
......@@ -2,6 +2,7 @@ From iris.heap_lang Require Export lifting.
From iris.algebra Require Import upred_big_op frac dec_agree.
From iris.program_logic Require Export invariants ghost_ownership.
From iris.program_logic Require Import ownership auth.
From iris.proofmode Require Import weakestpre.
Import uPred.
(* TODO: The entire construction could be generalized to arbitrary languages that have
a finmap as their state. Or maybe even beyond "as their state", i.e. arbitrary
......@@ -140,29 +141,25 @@ Section heap.
(** Weakest precondition *)
Lemma wp_alloc N E e v P Φ :
to_val e = Some v
P heap_ctx N nclose N E
P ( l, l v - Φ (LitV (LitLoc l)))
P WP Alloc e @ E {{ Φ }}.
to_val e = Some v nclose N E
(heap_ctx N l, l v - Φ (LitV $ LitLoc l)) WP Alloc e @ E {{ Φ }}.
Proof.
rewrite /heap_ctx /heap_inv=> ??? HP.
trans (|={E}=> auth_own heap_name P)%I.
{ by rewrite -pvs_frame_r -(auth_empty _ E) left_id. }
apply wp_strip_pvs, (auth_fsa heap_inv (wp_fsa (Alloc e)))
iIntros {??} "[#Hinv HΦ]". rewrite /heap_ctx.
iPvs (auth_empty heap_name) as "Hheap".
(* TODO: use an iTactic *)
apply (auth_fsa heap_inv (wp_fsa (Alloc e)))
with N heap_name ; simpl; eauto with I.
rewrite -later_intro. apply sep_mono_r,forall_intro=> h; apply wand_intro_l.
rewrite -assoc left_id; apply const_elim_sep_l=> ?.
rewrite -(wp_alloc_pst _ (of_heap h)) //.
apply sep_mono_r; rewrite HP; apply later_mono.
apply forall_mono=> l; apply wand_intro_l.
rewrite always_and_sep_l -assoc; apply const_elim_sep_l=> ?.
rewrite -(exist_intro (op {[ l := Frac 1 (DecAgree v) ]})).
repeat erewrite <-exist_intro by apply _; simpl.
rewrite -of_heap_insert left_id right_id.
rewrite /heap_mapsto. ecancel [_ - Φ _]%I.
rewrite -(insert_singleton_op h); last by apply of_heap_None.
rewrite const_equiv; last by apply (insert_valid h).
by rewrite left_id -later_intro.
iFrame "Hheap". iIntros {h}. rewrite [ h]left_id.
iIntros "[% Hheap]". rewrite /heap_inv.
iApply wp_alloc_pst; first done. iFrame "Hheap". iNext.
iIntros {l} "[% Hheap]". iExists (op {[ l := Frac 1 (DecAgree v) ]}), _, _.
rewrite [{[ _ := _ ]} ]right_id.
rewrite -of_heap_insert -(insert_singleton_op h); last by apply of_heap_None.
iFrame "Hheap". iSplit.
{ (* FIXME iTactic for introduction of constant assertions? *)
rewrite const_equiv; first done. split; first done.
by apply (insert_valid h). }
iIntros "Hheap". iApply "HΦ". rewrite /heap_mapsto. done.
Qed.
Lemma wp_load N E l q v P Φ :
......
......@@ -25,7 +25,8 @@ Lemma tac_wp_alloc Δ Δ' N E j e v Φ :
Δ'' Φ (LitV (LitLoc l)))
Δ WP Alloc e @ E {{ Φ }}.
Proof.
intros ???? HΔ; eapply wp_alloc; eauto.
intros ???? HΔ. etrans; last apply: wp_alloc; eauto.
rewrite -always_and_sep_l. iSplit; first done.
rewrite strip_later_env_sound; apply later_mono, forall_intro=> l.
destruct (HΔ l) as (Δ''&?&HΔ'). rewrite envs_app_sound //; simpl.
by rewrite right_id HΔ'.
......
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