Commit 6b5ee4fa authored by Jacques-Henri Jourdan's avatar Jacques-Henri Jourdan

Lifting lemmas : get rid of \phi when it has became useless

parent 76a7d9a2
Pipeline #1890 skipped
......@@ -18,19 +18,17 @@ Lemma wp_ectx_bind {E e} K Φ :
WP e @ E {{ v, WP fill K (of_val v) @ E {{ Φ }} }} WP fill K e @ E {{ Φ }}.
Proof. apply: weakestpre.wp_bind. Qed.
Lemma wp_lift_head_step E1 E2
(φ : expr state option expr Prop) Φ e1 :
Lemma wp_lift_head_step E1 E2 Φ e1 :
E2 E1 to_val e1 = None
(|={E1,E2}=> σ1,
head_reducible e1 σ1
( e2 σ2 ef, head_step e1 σ1 e2 σ2 ef φ e2 σ2 ef)
ownP σ1 e2 σ2 ef,
( φ e2 σ2 ef ownP σ2) ={E2,E1}= WP e2 @ E1 {{ Φ }} wp_fork ef)
(|={E1,E2}=> σ1, head_reducible e1 σ1
ownP σ1 e2 σ2 ef, ( head_step e1 σ1 e2 σ2 ef ownP σ2)
={E2,E1}= WP e2 @ E1 {{ Φ }} wp_fork ef)
WP e1 @ E1 {{ Φ }}.
Proof.
iIntros {??} "H". iApply (wp_lift_step E1 E2 φ); try done.
iPvs "H" as {σ1} "(%&%&Hσ1&?)". set_solver. iPvsIntro. iExists σ1.
repeat iSplit; eauto. by iFrame.
iIntros {??} "H". iApply (wp_lift_step E1 E2); try done.
iPvs "H" as {σ1} "(%&Hσ1&Hwp)". set_solver. iPvsIntro. iExists σ1.
iSplit; first by eauto. iFrame. iNext. iIntros {e2 σ2 ef} "[% ?]".
iApply "Hwp". by eauto.
Qed.
Lemma wp_lift_pure_head_step E (φ : expr option expr Prop) Φ e1 :
......
......@@ -18,24 +18,22 @@ Implicit Types e : expr Λ.
Implicit Types P Q R : iProp Λ Σ.
Implicit Types Ψ : val Λ iProp Λ Σ.
Lemma ht_lift_step E1 E2
(φ : expr Λ state Λ option (expr Λ) Prop) P P' Φ1 Φ2 Ψ e1 :
Lemma ht_lift_step E1 E2 P Pσ1 Φ1 Φ2 Ψ e1 :
E2 E1 to_val e1 = None
(P ={E1,E2}=> σ1,
reducible e1 σ1
( e2 σ2 ef, prim_step e1 σ1 e2 σ2 ef φ e2 σ2 ef)
ownP σ1 P')
( e2 σ2 ef, φ e2 σ2 ef ownP σ2 P' ={E2,E1}=> Φ1 e2 σ2 ef Φ2 e2 σ2 ef)
(P ={E1,E2}=> σ1, reducible e1 σ1
ownP σ1 Pσ1 σ1)
( σ1 e2 σ2 ef, prim_step e1 σ1 e2 σ2 ef ownP σ2 Pσ1 σ1
={E2,E1}=> Φ1 e2 σ2 ef Φ2 e2 σ2 ef)
( e2 σ2 ef, {{ Φ1 e2 σ2 ef }} e2 @ E1 {{ Ψ }})
( e2 σ2 ef, {{ Φ2 e2 σ2 ef }} ef ?@ {{ _, True }})
{{ P }} e1 @ E1 {{ Ψ }}.
Proof.
iIntros {??} "#(#Hvs&HΦ&He2&Hef) ! HP".
iApply (wp_lift_step E1 E2 φ _ e1); auto.
iPvs ("Hvs" with "HP") as {σ1} "(%&%&Hσ&HP)"; first set_solver.
iPvsIntro. iExists σ1. repeat iSplit; eauto. iFrame.
iApply (wp_lift_step E1 E2 _ e1); auto.
iPvs ("Hvs" with "HP") as {σ1} "(%&Hσ&HP)"; first set_solver.
iPvsIntro. iExists σ1. repeat iSplit. by eauto. iFrame.
iNext. iIntros {e2 σ2 ef} "[#Hφ Hown]".
iSpecialize ("HΦ" $! e2 σ2 ef with "[-]"). by iFrame "Hφ HP Hown".
iSpecialize ("HΦ" $! σ1 e2 σ2 ef with "[-]"). by iFrame "Hφ HP Hown".
iPvs "HΦ" as "[H1 H2]"; first by set_solver. iPvsIntro. iSplitL "H1".
- by iApply "He2".
- destruct ef as [e|]; last done. by iApply ("Hef" $! _ _ (Some e)).
......@@ -50,15 +48,15 @@ Lemma ht_lift_atomic_step
{{ ownP σ1 P }} e1 @ E {{ v, σ2 ef, ownP σ2 φ (of_val v) σ2 ef }}.
Proof.
iIntros {? Hsafe Hstep} "#Hef".
set (φ' e σ ef := is_Some (to_val e) φ e σ ef).
iApply (ht_lift_step E E φ' _ P
(λ e2 σ2 ef, ownP σ2 (φ' e2 σ2 ef))%I (λ e2 σ2 ef, φ e2 σ2 ef P)%I);
set (φ' (_:state Λ) e σ ef := is_Some (to_val e) φ e σ ef).
iApply (ht_lift_step E E _ (λ σ1', P σ1 = σ1')%I
(λ e2 σ2 ef, ownP σ2 (φ' σ1 e2 σ2 ef))%I (λ e2 σ2 ef, φ e2 σ2 ef P)%I);
try by (eauto using atomic_not_val).
repeat iSplit.
- iIntros "![Hσ1 HP]". iExists σ1. iPvsIntro. unfold φ'.
repeat iSplit; eauto using atomic_step. by iFrame.
- iIntros {e2 σ2 ef} "! (#Hφ&Hown&HP)"; iPvsIntro.
iSplitL "Hown". by iSplit. iSplit. by iDestruct "Hφ" as %[_ ?]. done.
- iIntros "![Hσ1 HP]". iExists σ1. iPvsIntro.
iSplit. by eauto using atomic_step. iFrame. by auto.
- iIntros {? e2 σ2 ef} "! (%&Hown&HP&%)". iPvsIntro. subst.
iFrame. iSplit; iPureIntro; auto. split; eauto using atomic_step.
- iIntros {e2 σ2 ef} "! [Hown #Hφ]"; iDestruct "Hφ" as %[[v2 <-%of_to_val] ?].
iApply wp_value'. iExists σ2, ef. by iSplit.
- done.
......
......@@ -18,19 +18,16 @@ Implicit Types Φ : val Λ → iProp Λ Σ.
Notation wp_fork ef := (default True ef (flip (wp ) (λ _, True)))%I.
Lemma wp_lift_step E1 E2
(φ : expr Λ state Λ option (expr Λ) Prop) Φ e1 :
Lemma wp_lift_step E1 E2 Φ e1 :
E2 E1 to_val e1 = None
(|={E1,E2}=> σ1,
reducible e1 σ1
( e2 σ2 ef, prim_step e1 σ1 e2 σ2 ef φ e2 σ2 ef)
ownP σ1 e2 σ2 ef,
( φ e2 σ2 ef ownP σ2) ={E2,E1}= WP e2 @ E1 {{ Φ }} wp_fork ef)
(|={E1,E2}=> σ1, reducible e1 σ1 ownP σ1
e2 σ2 ef, ( prim_step e1 σ1 e2 σ2 ef ownP σ2)
={E2,E1}= WP e2 @ E1 {{ Φ }} wp_fork ef)
WP e1 @ E1 {{ Φ }}.
Proof.
intros ? He. rewrite pvs_eq wp_eq.
uPred.unseal; split=> n r ? Hvs; constructor; auto. intros k Ef σ1' rf ???.
destruct (Hvs (S k) Ef σ1' rf) as (r'&(σ1&Hsafe&Hstep&r1&r2&?&?&Hwp)&Hws);
destruct (Hvs (S k) Ef σ1' rf) as (r'&(σ1&Hsafe&r1&r2&?&?&Hwp)&Hws);
auto; clear Hvs; cofe_subst r'.
destruct (wsat_update_pst k (E2 Ef) σ1 σ1' r1 (r2 rf)) as [-> Hws'].
{ apply equiv_dist. rewrite -(ownP_spec k); auto. }
......@@ -38,7 +35,7 @@ Proof.
constructor; [done|intros e2 σ2 ef ?; specialize (Hws' σ2)].
destruct (λ H1 H2 H3, Hwp e2 σ2 ef k (update_pst σ2 r1) H1 H2 H3 k Ef σ2 rf)
as (r'&(r1'&r2'&?&?&?)&?); auto; cofe_subst r'.
{ split. by eapply Hstep. apply ownP_spec; auto. }
{ split. done. apply ownP_spec; auto. }
{ rewrite (comm _ r2) -assoc; eauto using wsat_le. }
exists r1', r2'; split_and?; try done. by uPred.unseal; intros ? ->.
Qed.
......@@ -71,11 +68,10 @@ Lemma wp_lift_atomic_step {E Φ} e1
φ (of_val v2) σ2 ef ownP σ2 - (|={E}=> Φ v2) wp_fork ef)
WP e1 @ E {{ Φ }}.
Proof.
iIntros {???} "[Hσ1 Hwp]". iApply (wp_lift_step E E (λ e2 σ2 ef,
is_Some (to_val e2) φ e2 σ2 ef) _ e1); auto using atomic_not_val.
iApply pvs_intro. iExists σ1. repeat iSplit; eauto using atomic_step.
iFrame. iNext. iIntros {e2 σ2 ef} "[#He2 Hσ2]".
iDestruct "He2" as %[[v2 Hv%of_to_val]?]. subst e2.
iIntros {???} "[Hσ1 Hwp]". iApply (wp_lift_step E E _ e1); auto using atomic_not_val.
iPvsIntro. iExists σ1. repeat iSplit; eauto 10 using atomic_step.
iFrame. iNext. iIntros {e2 σ2 ef} "[% Hσ2]".
edestruct @atomic_step as [v2 Hv%of_to_val]; eauto. subst e2.
iDestruct ("Hwp" $! v2 σ2 ef with "[Hσ2]") as "[HΦ ?]". by eauto.
iFrame. iPvs "HΦ". iPvsIntro. iApply wp_value; auto using to_of_val.
Qed.
......
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