add a later in texan triples

heap_lang/heap.v

@@ -104,11 +104,11 @@ Section heap.
   Proof. by rewrite heap_mapsto_op_half. Qed.
 
   (** Weakest precondition *)
-  Lemma wp_alloc E e v Φ :
+  Lemma wp_alloc E e v :
     to_val e = Some v → nclose heapN ⊆ E →
-    heap_ctx ★ ▷ (∀ l, l ↦ v ={E}=★ Φ (LitV (LitLoc l))) ⊢ WP Alloc e @ E {{ Φ }}.
+    {{{ heap_ctx }}} Alloc e @ E {{{ l; LitV (LitLoc l), l ↦ v }}}.
   Proof.
-    iIntros (<-%of_to_val ?) "[#Hinv HΦ]". rewrite /heap_ctx.
+    iIntros (<-%of_to_val ? Φ) "[#Hinv HΦ]". rewrite /heap_ctx.
     iMod (auth_empty heap_name) as "Ha".
     iMod (auth_open with "[$Hinv $Ha]") as (σ) "(%&Hσ&Hcl)"; first done.
     iApply wp_alloc_pst. iFrame "Hσ". iNext. iIntros (l) "[% Hσ] !>".
@@ -118,12 +118,12 @@ Section heap.
     iApply "HΦ". by rewrite heap_mapsto_eq /heap_mapsto_def.
   Qed.
 
-  Lemma wp_load E l q v Φ :
+  Lemma wp_load E l q v :
     nclose heapN ⊆ E →
-    heap_ctx ★ ▷ l ↦{q} v ★ ▷ (l ↦{q} v ={E}=★ Φ v)
-    ⊢ WP Load (Lit (LitLoc l)) @ E {{ Φ }}.
+    {{{ heap_ctx ★ ▷ l ↦{q} v }}} Load (Lit (LitLoc l)) @ E
+    {{{; v, l ↦{q} v }}}.
   Proof.
-    iIntros (?) "[#Hinv [>Hl HΦ]]".
+    iIntros (? Φ) "[[#Hinv >Hl] HΦ]".
     rewrite /heap_ctx heap_mapsto_eq /heap_mapsto_def.
     iMod (auth_open with "[$Hinv $Hl]") as (σ) "(%&Hσ&Hcl)"; first done.
     iApply (wp_load_pst _ σ); first eauto using heap_singleton_included.
@@ -131,12 +131,12 @@ Section heap.
     iMod ("Hcl" with "* [Hσ]") as "Ha"; first eauto. by iApply "HΦ".
   Qed.
 
-  Lemma wp_store E l v' e v Φ :
+  Lemma wp_store E l v' e v :
     to_val e = Some v → nclose heapN ⊆ E →
-    heap_ctx ★ ▷ l ↦ v' ★ ▷ (l ↦ v ={E}=★ Φ (LitV LitUnit))
-    ⊢ WP Store (Lit (LitLoc l)) e @ E {{ Φ }}.
+    {{{ heap_ctx ★ ▷ l ↦ v' }}} Store (Lit (LitLoc l)) e @ E
+    {{{; LitV LitUnit, l ↦ v }}}.
   Proof.
-    iIntros (<-%of_to_val ?) "[#Hinv [>Hl HΦ]]".
+    iIntros (<-%of_to_val ? Φ) "[[#Hinv >Hl] HΦ]".
     rewrite /heap_ctx heap_mapsto_eq /heap_mapsto_def.
     iMod (auth_open with "[$Hinv $Hl]") as (σ) "(%&Hσ&Hcl)"; first done.
     iApply (wp_store_pst _ σ); first eauto using heap_singleton_included.
@@ -147,12 +147,12 @@ Section heap.
     by iApply "HΦ".
   Qed.
 
-  Lemma wp_cas_fail E l q v' e1 v1 e2 v2 Φ :
+  Lemma wp_cas_fail E l q v' e1 v1 e2 v2 :
     to_val e1 = Some v1 → to_val e2 = Some v2 → v' ≠ v1 → nclose heapN ⊆ E →
-    heap_ctx ★ ▷ l ↦{q} v' ★ ▷ (l ↦{q} v' ={E}=★ Φ (LitV (LitBool false)))
-    ⊢ WP CAS (Lit (LitLoc l)) e1 e2 @ E {{ Φ }}.
+    {{{ heap_ctx ★ ▷ l ↦{q} v' }}} CAS (Lit (LitLoc l)) e1 e2 @ E
+    {{{; LitV (LitBool false), l ↦{q} v' }}}.
   Proof.
-    iIntros (<-%of_to_val <-%of_to_val ??) "[#Hinv [>Hl HΦ]]".
+    iIntros (<-%of_to_val <-%of_to_val ?? Φ) "[[#Hinv >Hl] HΦ]".
     rewrite /heap_ctx heap_mapsto_eq /heap_mapsto_def.
     iMod (auth_open with "[$Hinv $Hl]") as (σ) "(%&Hσ&Hcl)"; first done.
     iApply (wp_cas_fail_pst _ σ); [eauto using heap_singleton_included|done|].
@@ -160,12 +160,12 @@ Section heap.
     iMod ("Hcl" with "* [Hσ]") as "Ha"; first eauto. by iApply "HΦ".
   Qed.
 
-  Lemma wp_cas_suc E l e1 v1 e2 v2 Φ :
+  Lemma wp_cas_suc E l e1 v1 e2 v2 :
     to_val e1 = Some v1 → to_val e2 = Some v2 → nclose heapN ⊆ E →
-    heap_ctx ★ ▷ l ↦ v1 ★ ▷ (l ↦ v2 ={E}=★ Φ (LitV (LitBool true)))
-    ⊢ WP CAS (Lit (LitLoc l)) e1 e2 @ E {{ Φ }}.
+    {{{ heap_ctx ★ ▷ l ↦ v1 }}} CAS (Lit (LitLoc l)) e1 e2 @ E
+    {{{; LitV (LitBool true), l ↦ v2 }}}.
   Proof.
-    iIntros (<-%of_to_val <-%of_to_val ?) "[#Hinv [>Hl HΦ]]".
+    iIntros (<-%of_to_val <-%of_to_val ? Φ) "[[#Hinv >Hl] HΦ]".
     rewrite /heap_ctx heap_mapsto_eq /heap_mapsto_def.
     iMod (auth_open with "[$Hinv $Hl]") as (σ) "(%&Hσ&Hcl)"; first done.
     iApply (wp_cas_suc_pst _ σ); first eauto using heap_singleton_included.

heap_lang/lib/barrier/proof.v

@@ -147,7 +147,7 @@ Proof.
     iAssert (sts_ownS γ (i_states i) {[Change i]})%I with ">[Hγ]" as "Hγ".
     { iApply (sts_own_weaken with "Hγ"); eauto using i_states_closed. }
     iModIntro. wp_if.
-    iApply ("IH" with "Hγ [HQR] HΦ"). auto.
+    iApply ("IH" with "Hγ [HQR] [HΦ]"); auto.
   - (* a High state: the comparison succeeds, and we perform a transition and
     return to the client *)
     iDestruct "Hr" as (Ψ) "[HΨ Hsp]".

heap_lang/lib/barrier/specification.v

@@ -20,7 +20,8 @@ Proof.
   intros HN.
   exists (λ l, CofeMor (recv N l)), (λ l, CofeMor (send N l)).
   split_and?; simpl.
-  - iIntros (P) "#? !# _". iApply (newbarrier_spec _ P); eauto.
+  - iIntros (P) "#? !# _". iApply (newbarrier_spec _ P); first done.
+    iSplit; first done. iNext. eauto.
   - iIntros (l P) "!# [Hl HP]". iApply signal_spec; iFrame "Hl HP"; by eauto.
   - iIntros (l P) "!# Hl". iApply wait_spec; iFrame "Hl"; eauto.
   - iIntros (l P Q) "!#". by iApply recv_split.

heap_lang/lib/counter.v

@@ -65,7 +65,7 @@ Section mono_proof.
       by apply mnat_included, le_n_S.
     - wp_cas_fail; first (by intros [= ?%Nat2Z.inj]).
       iMod ("Hclose" with "[Hl Hγ]") as "_"; [iNext; iExists c'; by iFrame|].
-      iModIntro. wp_if. iApply ("IH" with "[Hγf] HΦ").
+      iModIntro. wp_if. iApply ("IH" with "[Hγf] [HΦ]"); last by auto.
       rewrite {3}/mcounter; eauto 10.
   Qed.
 
@@ -140,7 +140,7 @@ Section contrib_spec.
       iModIntro. wp_if. by iApply "HΦ".
     - wp_cas_fail; first (by intros [= ?%Nat2Z.inj]).
       iMod ("Hclose" with "[Hl Hγ]") as "_"; [iNext; iExists c'; by iFrame|].
-      iModIntro. wp_if. by iApply ("IH" with "[Hγf] HΦ").
+      iModIntro. wp_if. by iApply ("IH" with "[Hγf] [HΦ]"); auto.
   Qed.
 
   Lemma read_contrib_spec γ l q n :

heap_lang/lib/par.v

@@ -19,15 +19,15 @@ Context `{!heapG Σ, !spawnG Σ}.
 Lemma par_spec (Ψ1 Ψ2 : val → iProp Σ) e (f1 f2 : val) (Φ : val → iProp Σ) :
   to_val e = Some (f1,f2)%V →
   (heap_ctx ★ WP f1 #() {{ Ψ1 }} ★ WP f2 #() {{ Ψ2 }} ★
-   ∀ v1 v2, Ψ1 v1 ★ Ψ2 v2 -★ ▷ Φ (v1,v2)%V)
+   ▷ ∀ v1 v2, Ψ1 v1 ★ Ψ2 v2 -★ ▷ Φ (v1,v2)%V)
   ⊢ WP par e {{ Φ }}.
 Proof.
   iIntros (?) "(#Hh&Hf1&Hf2&HΦ)".
   rewrite /par. wp_value. iModIntro. wp_let. wp_proj.
   wp_apply (spawn_spec parN); try wp_done; try solve_ndisj; iFrame "Hf1 Hh".
-  iIntros (l) "Hl". wp_let. wp_proj. wp_bind (f2 _).
+  iNext. iIntros (l) "Hl". wp_let. wp_proj. wp_bind (f2 _).
   iApply wp_wand_l; iFrame "Hf2"; iIntros (v) "H2". wp_let.
-  wp_apply join_spec; iFrame "Hl". iIntros (w) "H1".
+  wp_apply join_spec; iFrame "Hl". iNext. iIntros (w) "H1".
   iSpecialize ("HΦ" with "* [-]"); first by iSplitL "H1". by wp_let.
 Qed.
 

heap_lang/lib/spawn.v

@@ -70,7 +70,7 @@ Proof.
   iLöb as "IH". wp_rec. wp_bind (! _)%E. iInv N as (v) "[Hl Hinv]" "Hclose".
   wp_load. iDestruct "Hinv" as "[%|Hinv]"; subst.
   - iMod ("Hclose" with "[Hl]"); [iNext; iExists _; iFrame; eauto|].
-    iModIntro. wp_match. iApply ("IH" with "Hγ Hv").
+    iModIntro. wp_match. iApply ("IH" with "Hγ [Hv]"). auto.
   - iDestruct "Hinv" as (v') "[% [HΨ|Hγ']]"; simplify_eq/=.
     + iMod ("Hclose" with "[Hl Hγ]"); [iNext; iExists _; iFrame; eauto|].
       iModIntro. wp_match. by iApply "Hv".

heap_lang/lib/spin_lock.v

@@ -76,7 +76,7 @@ Section proof.
     iIntros (Φ) "[#Hl HΦ]". iLöb as "IH". wp_rec. wp_bind (try_acquire _).
     iApply try_acquire_spec. iFrame "#". iSplit.
     - iIntros "Hlked HR". wp_if. iModIntro. iApply "HΦ"; iFrame.
-    - wp_if. iApply ("IH" with "HΦ").
+    - wp_if. iApply ("IH" with "[HΦ]"). auto.
   Qed.
 
   Lemma release_spec γ lk R :

heap_lang/lib/ticket_lock.v

@@ -136,7 +136,7 @@ Section proof.
     - wp_cas_fail.
       iMod ("Hclose" with "[Hlo' Hln' Hauth Haown]") as "_".
       { iNext. iExists o', n'. by iFrame. }
-      iModIntro. wp_if. by iApply "IH".
+      iModIntro. wp_if. by iApply "IH"; auto.
   Qed.
 
   Lemma release_spec γ lk R :

heap_lang/proofmode.v

@@ -25,7 +25,7 @@ Lemma tac_wp_alloc Δ Δ' E j e v Φ :
     (Δ'' ⊢ |={E}=> Φ (LitV (LitLoc l)))) →
   Δ ⊢ WP Alloc e @ E {{ Φ }}.
 Proof.
-  intros ???? HΔ. rewrite -wp_alloc // -always_and_sep_l.
+  intros ???? HΔ. rewrite -wp_fupd -wp_alloc // -always_and_sep_l.
   apply and_intro; first done.
   rewrite into_later_env_sound; apply later_mono, forall_intro=> l.
   destruct (HΔ l) as (Δ''&?&HΔ'). rewrite envs_app_sound //; simpl.
@@ -39,7 +39,8 @@ Lemma tac_wp_load Δ Δ' E i l q v Φ :
   (Δ' ⊢ |={E}=> Φ v) →
   Δ ⊢ WP Load (Lit (LitLoc l)) @ E {{ Φ }}.
 Proof.
-  intros. rewrite -wp_load // -always_and_sep_l. apply and_intro; first done.
+  intros. rewrite -wp_fupd -wp_load // -assoc -always_and_sep_l.
+  apply and_intro; first done.
   rewrite into_later_env_sound -later_sep envs_lookup_split //; simpl.
   by apply later_mono, sep_mono_r, wand_mono.
 Qed.
@@ -53,7 +54,8 @@ Lemma tac_wp_store Δ Δ' Δ'' E i l v e v' Φ :
   (Δ'' ⊢ |={E}=> Φ (LitV LitUnit)) →
   Δ ⊢ WP Store (Lit (LitLoc l)) e @ E {{ Φ }}.
 Proof.
-  intros. rewrite -wp_store // -always_and_sep_l. apply and_intro; first done.
+  intros. rewrite -wp_fupd -wp_store // -assoc -always_and_sep_l.
+  apply and_intro; first done.
   rewrite into_later_env_sound -later_sep envs_simple_replace_sound //; simpl.
   rewrite right_id. by apply later_mono, sep_mono_r, wand_mono.
 Qed.
@@ -66,7 +68,8 @@ Lemma tac_wp_cas_fail Δ Δ' E i l q v e1 v1 e2 v2 Φ :
   (Δ' ⊢ |={E}=> Φ (LitV (LitBool false))) →
   Δ ⊢ WP CAS (Lit (LitLoc l)) e1 e2 @ E {{ Φ }}.
 Proof.
-  intros. rewrite -wp_cas_fail // -always_and_sep_l. apply and_intro; first done.
+  intros. rewrite -wp_fupd -wp_cas_fail // -assoc -always_and_sep_l.
+  apply and_intro; first done.
   rewrite into_later_env_sound -later_sep envs_lookup_split //; simpl.
   by apply later_mono, sep_mono_r, wand_mono.
 Qed.
@@ -80,8 +83,8 @@ Lemma tac_wp_cas_suc Δ Δ' Δ'' E i l v e1 v1 e2 v2 Φ :
   (Δ'' ⊢ |={E}=> Φ (LitV (LitBool true))) →
   Δ ⊢ WP CAS (Lit (LitLoc l)) e1 e2 @ E {{ Φ }}.
 Proof.
-  intros; subst.
-  rewrite -wp_cas_suc // -always_and_sep_l. apply and_intro; first done.
+  intros; subst. rewrite -wp_fupd -wp_cas_suc // -assoc -always_and_sep_l.
+  apply and_intro; first done.
   rewrite into_later_env_sound -later_sep envs_simple_replace_sound //; simpl.
   rewrite right_id. by apply later_mono, sep_mono_r, wand_mono.
 Qed.

program_logic/weakestpre.v

@@ -50,16 +50,27 @@ Notation "'WP' e {{ v , Q } }" := (wp ⊤ e%E (λ v, Q))
   (at level 20, e, Q at level 200,
    format "'WP'  e  {{  v ,  Q  } }") : uPred_scope.
 
+(* Texan triples *)
 Notation "'{{{' pre } } } e {{{ x .. y ; pat , post } } }" :=
   (∀ (ψ : _ → uPred _),
-      (pre ★ (∀ x, .. (∀ y, post -★ ψ (pat)%V) .. )%I) ⊢ WP e {{ ψ }})
+      (pre ★ ▷ (∀ x, .. (∀ y, post -★ ψ (pat)%V) .. )%I) ⊢ WP e {{ ψ }})
     (at level 20, x closed binder, y closed binder,
      format "{{{  pre  } } }  e  {{{ x .. y ;  pat ,  post } } }") : C_scope.
+Notation "'{{{' pre } } } e @ E {{{ x .. y ; pat , post } } }" :=
+  (∀ (ψ : _ → uPred _),
+      (pre ★ ▷ (∀ x, .. (∀ y, post -★ ψ (pat)%V) .. )%I) ⊢ WP e @ E {{ ψ }})
+    (at level 20, x closed binder, y closed binder,
+     format "{{{  pre  } } }  e  @  E  {{{ x .. y ;  pat ,  post } } }") : C_scope.
 Notation "'{{{' pre } } } e {{{ ; pat , post } } }" :=
   (∀ (ψ : _ → uPred _),
-      (pre ★ (post -★ ψ (pat)%V)%I) ⊢ WP e {{ ψ }})
+      (pre ★ ▷ (post -★ ψ (pat)%V)%I) ⊢ WP e {{ ψ }})
     (at level 20,
      format "{{{  pre  } } }  e  {{{ ; pat ,  post } } }") : C_scope.
+Notation "'{{{' pre } } } e @ E {{{ ; pat , post } } }" :=
+  (∀ (ψ : _ → uPred _),
+      (pre ★ ▷ (post -★ ψ (pat)%V)%I) ⊢ WP e @ E {{ ψ }})
+    (at level 20,
+     format "{{{  pre  } } }  e  @  E  {{{ ; pat ,  post } } }") : C_scope.
 
 Section wp.
 Context `{irisG Λ Σ}.

tests/barrier_client.v

@@ -30,7 +30,7 @@ Section client.
   Proof.
     iIntros "[#Hh Hrecv]". wp_lam. wp_let.
     wp_apply wait_spec; iFrame "Hrecv".
-    iDestruct 1 as (f) "[Hy #Hf]".
+    iNext. iDestruct 1 as (f) "[Hy #Hf]".
     wp_seq. wp_load.
     iApply wp_wand_r; iSplitR; [iApply "Hf"|by iIntros (v) "_"].
   Qed.
@@ -39,7 +39,7 @@ Section client.
   Proof.
     iIntros (?) "#Hh"; rewrite /client. wp_alloc y as "Hy". wp_let.
     wp_apply (newbarrier_spec N (y_inv 1 y)); first done.
-    iFrame "Hh". iIntros (l) "[Hr Hs]". wp_let.
+    iFrame "Hh". iNext. iIntros (l) "[Hr Hs]". wp_let.
     iApply (wp_par (λ _, True%I) (λ _, True%I)). iFrame "Hh".
     iSplitL "Hy Hs".
     - (* The original thread, the sender. *)

tests/joining_existentials.v

@@ -36,7 +36,7 @@ Lemma worker_spec e γ l (Φ Ψ : X → iProp Σ) `{!Closed [] e} :
   ⊢ WP wait #l ;; e {{ _, barrier_res γ Ψ }}.
 Proof.
   iIntros "[Hl #He]". wp_apply wait_spec; simpl; iFrame "Hl".
-  iDestruct 1 as (x) "[#Hγ Hx]".
+  iNext. iDestruct 1 as (x) "[#Hγ Hx]".
   wp_seq. iApply wp_wand_l. iSplitR; [|by iApply "He"].
   iIntros (v) "?"; iExists x; by iSplit.
 Qed.
@@ -77,7 +77,7 @@ Proof.
   iIntros (HN) "/= (#Hh&HP&#He&#He1&#He2)"; rewrite /client.
   iMod (own_alloc (Pending : one_shotR Σ F)) as (γ) "Hγ"; first done.
   wp_apply (newbarrier_spec N (barrier_res γ Φ)); auto.
-  iFrame "Hh". iIntros (l) "[Hr Hs]".
+  iFrame "Hh". iNext. iIntros (l) "[Hr Hs]".
   set (workers_post (v : val) := (barrier_res γ Ψ1 ★ barrier_res γ Ψ2)%I).
   wp_let. wp_apply (wp_par  (λ _, True)%I workers_post); iFrame "Hh".
   iSplitL "HP Hs Hγ"; [|iSplitL "Hr"].