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Commit 76e5e029 authored by Robbert Krebbers's avatar Robbert Krebbers
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Write `wp_strong_mono` in a curried way.

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theories/program_logic/weakestpre.v
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...@@ -213,9 +213,9 @@ Proof. by rewrite wp_unfold /wp_pre to_of_val. Qed. ...@@ -213,9 +213,9 @@ Proof. by rewrite wp_unfold /wp_pre to_of_val. Qed.
Lemma wp_strong_mono s1 s2 E1 E2 e Φ Ψ : Lemma wp_strong_mono s1 s2 E1 E2 e Φ Ψ :
s1 ⊑ s2 → E1 ⊆ E2 → s1 ⊑ s2 → E1 ⊆ E2 →
(∀ v, Φ v ={E2}=∗ Ψ v) ∗ WP e @ s1; E1 {{ Φ }} ⊢ WP e @ s2; E2 {{ Ψ }}. WP e @ s1; E1 {{ Φ }} -∗ (∀ v, Φ v ={E2}=∗ Ψ v) -∗ WP e @ s2; E2 {{ Ψ }}.
Proof. Proof.
iIntros (? HE) "[HΦ H]". iLöb as "IH" forall (e E1 E2 HE Φ Ψ). iIntros (? HE) "H HΦ". iLöb as "IH" forall (e E1 E2 HE Φ Ψ).
rewrite !wp_unfold /wp_pre. rewrite !wp_unfold /wp_pre.
destruct (to_val e) as [v|] eqn:?. destruct (to_val e) as [v|] eqn:?.
{ iApply ("HΦ" with "[> -]"). by iApply (fupd_mask_mono E1 _). } { iApply ("HΦ" with "[> -]"). by iApply (fupd_mask_mono E1 _). }
...@@ -224,9 +224,9 @@ Proof. ...@@ -224,9 +224,9 @@ Proof.
iModIntro. iSplit; [by destruct s1, s2|]. iNext. iIntros (e2 σ2 efs Hstep). iModIntro. iSplit; [by destruct s1, s2|]. iNext. iIntros (e2 σ2 efs Hstep).
iMod ("H" with "[//]") as "($ & H & Hefs)". iMod ("H" with "[//]") as "($ & H & Hefs)".
iMod "Hclose" as "_". iModIntro. iSplitR "Hefs". iMod "Hclose" as "_". iModIntro. iSplitR "Hefs".
- by iApply ("IH" with "[] HΦ"). - iApply ("IH" with "[//] H HΦ").
- iApply (big_sepL_impl with "[$Hefs]"); iIntros "!#" (k ef _) "H". - iApply (big_sepL_impl with "[$Hefs]"); iIntros "!#" (k ef _) "H".
by iApply ("IH" with "[] [] H"). by iApply ("IH" with "[] H").
Qed. Qed.
Lemma fupd_wp s E e Φ : (|={E}=> WP e @ s; E {{ Φ }}) ⊢ WP e @ s; E {{ Φ }}. Lemma fupd_wp s E e Φ : (|={E}=> WP e @ s; E {{ Φ }}) ⊢ WP e @ s; E {{ Φ }}.
...@@ -236,7 +236,7 @@ Proof. ...@@ -236,7 +236,7 @@ Proof.
iIntros (σ1) "Hσ1". iMod "H". by iApply "H". iIntros (σ1) "Hσ1". iMod "H". by iApply "H".
Qed. Qed.
Lemma wp_fupd s E e Φ : WP e @ s; E {{ v, |={E}=> Φ v }} ⊢ WP e @ s; E {{ Φ }}. Lemma wp_fupd s E e Φ : WP e @ s; E {{ v, |={E}=> Φ v }} ⊢ WP e @ s; E {{ Φ }}.
Proof. iIntros "H". iApply (wp_strong_mono s s E); try iFrame; auto. Qed. Proof. iIntros "H". iApply (wp_strong_mono s s E with "H"); auto. Qed.
Lemma wp_atomic s E1 E2 e Φ `{!Atomic (stuckness_to_atomicity s) e} : Lemma wp_atomic s E1 E2 e Φ `{!Atomic (stuckness_to_atomicity s) e} :
(|={E1,E2}=> WP e @ s; E2 {{ v, |={E2,E1}=> Φ v }}) ⊢ WP e @ s; E1 {{ Φ }}. (|={E1,E2}=> WP e @ s; E2 {{ v, |={E2,E1}=> Φ v }}) ⊢ WP e @ s; E1 {{ Φ }}.
...@@ -263,8 +263,8 @@ Proof. ...@@ -263,8 +263,8 @@ Proof.
iIntros (σ1) "Hσ". iMod "HR". iMod ("H" with "[$]") as "[$ H]". iIntros (σ1) "Hσ". iMod "HR". iMod ("H" with "[$]") as "[$ H]".
iModIntro; iNext; iIntros (e2 σ2 efs Hstep). iModIntro; iNext; iIntros (e2 σ2 efs Hstep).
iMod ("H" $! e2 σ2 efs with "[% //]") as "($ & H & $)". iMod ("H" $! e2 σ2 efs with "[% //]") as "($ & H & $)".
iMod "HR". iModIntro. iApply (wp_strong_mono s s E2); [done..|]. iMod "HR". iModIntro. iApply (wp_strong_mono s s E2 with "H"); [done..|].
iSplitR "H"; last iExact "H". iIntros (v) "H". by iApply "H". iIntros (v) "H". by iApply "H".
Qed. Qed.
Lemma wp_bind K `{!LanguageCtx K} s E e Φ : Lemma wp_bind K `{!LanguageCtx K} s E e Φ :
...@@ -300,17 +300,17 @@ Qed. ...@@ -300,17 +300,17 @@ Qed.
(** * Derived rules *) (** * Derived rules *)
Lemma wp_mono s E e Φ Ψ : (∀ v, Φ v ⊢ Ψ v) → WP e @ s; E {{ Φ }} ⊢ WP e @ s; E {{ Ψ }}. Lemma wp_mono s E e Φ Ψ : (∀ v, Φ v ⊢ Ψ v) → WP e @ s; E {{ Φ }} ⊢ WP e @ s; E {{ Ψ }}.
Proof. Proof.
iIntros (HΦ) "H"; iApply (wp_strong_mono s s E E); auto. iIntros (HΦ) "H"; iApply (wp_strong_mono with "H"); auto.
iIntros "{$H}" (v) "?". by iApply HΦ. iIntros (v) "?". by iApply HΦ.
Qed. Qed.
Lemma wp_stuck_mono s1 s2 E e Φ : Lemma wp_stuck_mono s1 s2 E e Φ :
s1 ⊑ s2 → WP e @ s1; E {{ Φ }} ⊢ WP e @ s2; E {{ Φ }}. s1 ⊑ s2 → WP e @ s1; E {{ Φ }} ⊢ WP e @ s2; E {{ Φ }}.
Proof. iIntros (?) "H". iApply (wp_strong_mono s1 s2); auto with iFrame. Qed. Proof. iIntros (?) "H". iApply (wp_strong_mono with "H"); auto. Qed.
Lemma wp_stuck_weaken s E e Φ : Lemma wp_stuck_weaken s E e Φ :
WP e @ s; E {{ Φ }} ⊢ WP e @ E ?{{ Φ }}. WP e @ s; E {{ Φ }} ⊢ WP e @ E ?{{ Φ }}.
Proof. apply wp_stuck_mono. by destruct s. Qed. Proof. apply wp_stuck_mono. by destruct s. Qed.
Lemma wp_mask_mono s E1 E2 e Φ : E1 ⊆ E2 → WP e @ s; E1 {{ Φ }} ⊢ WP e @ s; E2 {{ Φ }}. Lemma wp_mask_mono s E1 E2 e Φ : E1 ⊆ E2 → WP e @ s; E1 {{ Φ }} ⊢ WP e @ s; E2 {{ Φ }}.
Proof. iIntros (?) "H"; iApply (wp_strong_mono s s E1 E2); auto. iFrame; eauto. Qed. Proof. iIntros (?) "H"; iApply (wp_strong_mono with "H"); auto. Qed.
Global Instance wp_mono' s E e : Global Instance wp_mono' s E e :
Proper (pointwise_relation _ (⊢) ==> (⊢)) (@wp Λ Σ _ s E e). Proper (pointwise_relation _ (⊢) ==> (⊢)) (@wp Λ Σ _ s E e).
Proof. by intros Φ Φ' ?; apply wp_mono. Qed. Proof. by intros Φ Φ' ?; apply wp_mono. Qed.
...@@ -324,9 +324,9 @@ Lemma wp_value_fupd s E Φ e v `{!IntoVal e v} : ...@@ -324,9 +324,9 @@ Lemma wp_value_fupd s E Φ e v `{!IntoVal e v} :
Proof. intros. rewrite -wp_fupd -wp_value //. Qed. Proof. intros. rewrite -wp_fupd -wp_value //. Qed.
Lemma wp_frame_l s E e Φ R : R ∗ WP e @ s; E {{ Φ }} ⊢ WP e @ s; E {{ v, R ∗ Φ v }}. Lemma wp_frame_l s E e Φ R : R ∗ WP e @ s; E {{ Φ }} ⊢ WP e @ s; E {{ v, R ∗ Φ v }}.
Proof. iIntros "[??]". iApply (wp_strong_mono s s E E _ Φ); try iFrame; eauto. Qed. Proof. iIntros "[? H]". iApply (wp_strong_mono with "H"); auto with iFrame. Qed.
Lemma wp_frame_r s E e Φ R : WP e @ s; E {{ Φ }} ∗ R ⊢ WP e @ s; E {{ v, Φ v ∗ R }}. Lemma wp_frame_r s E e Φ R : WP e @ s; E {{ Φ }} ∗ R ⊢ WP e @ s; E {{ v, Φ v ∗ R }}.
Proof. iIntros "[??]". iApply (wp_strong_mono s s E E _ Φ); try iFrame; eauto. Qed. Proof. iIntros "[H ?]". iApply (wp_strong_mono with "H"); auto with iFrame. Qed.
Lemma wp_frame_step_l s E1 E2 e Φ R : Lemma wp_frame_step_l s E1 E2 e Φ R :
to_val e = None → E2 ⊆ E1 → to_val e = None → E2 ⊆ E1 →
...@@ -352,8 +352,8 @@ Proof. iIntros (?) "[??]". iApply (wp_frame_step_r s E E); try iFrame; eauto. Qe ...@@ -352,8 +352,8 @@ Proof. iIntros (?) "[??]". iApply (wp_frame_step_r s E E); try iFrame; eauto. Qe
Lemma wp_wand s E e Φ Ψ : Lemma wp_wand s E e Φ Ψ :
WP e @ s; E {{ Φ }} -∗ (∀ v, Φ v -∗ Ψ v) -∗ WP e @ s; E {{ Ψ }}. WP e @ s; E {{ Φ }} -∗ (∀ v, Φ v -∗ Ψ v) -∗ WP e @ s; E {{ Ψ }}.
Proof. Proof.
iIntros "Hwp H". iApply (wp_strong_mono s s E); auto. iIntros "Hwp H". iApply (wp_strong_mono with "Hwp"); auto.
iIntros "{$Hwp}" (?) "?". by iApply "H". iIntros (?) "?". by iApply "H".
Qed. Qed.
Lemma wp_wand_l s E e Φ Ψ : Lemma wp_wand_l s E e Φ Ψ :
(∀ v, Φ v -∗ Ψ v) ∗ WP e @ s; E {{ Φ }} ⊢ WP e @ s; E {{ Ψ }}. (∀ v, Φ v -∗ Ψ v) ∗ WP e @ s; E {{ Φ }} ⊢ WP e @ s; E {{ Ψ }}.
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