Get rid of `irisG'`.

theories/program_logic/adequacy.v

@@ -179,7 +179,7 @@ Theorem wp_strong_adequacy Σ Λ `{invPreG Σ} s e σ φ :
      (|={⊤}=> ∃
          (stateI : state Λ → list (observation Λ) → nat → iProp Σ)
          (fork_post : iProp Σ),
-       let _ : irisG Λ Σ := IrisG _ _ _ Hinv stateI fork_post in
+       let _ : irisG Λ Σ := IrisG _ _ Hinv stateI fork_post in
        (* This could be strengthened so that φ also talks about the number 
        of forked-off threads *)
        stateI σ κs 0 ∗ WP e @ s; ⊤ {{ v, ∀ σ m, stateI σ [] m ={⊤,∅}=∗ ⌜φ v σ⌝ }})%I) →
@@ -190,19 +190,19 @@ Proof.
     eapply (step_fupdN_soundness' _ (S (S n)))=> Hinv. rewrite Nat_iter_S.
     iMod (Hwp _ (κs ++ [])) as (stateI fork_post) "[Hσ Hwp]".
     iApply step_fupd_intro; first done. iModIntro.
-    iApply (@wptp_result _ _ (IrisG _ _ _ Hinv stateI fork_post) with "[Hσ] [Hwp]"); eauto.
+    iApply (@wptp_result _ _ (IrisG _ _ Hinv stateI fork_post) with "[Hσ] [Hwp]"); eauto.
     iApply (wp_wand with "Hwp"). iIntros (v) "H"; iIntros (σ'). iApply "H".
   - destruct s; last done. intros t2 σ2 e2 _ [n [κs ?]]%erased_steps_nsteps ?.
     eapply (step_fupdN_soundness' _ (S (S n)))=> Hinv. rewrite Nat_iter_S.
     iMod (Hwp _ (κs ++ [])) as (stateI fork_post) "[Hσ Hwp]".
     iApply step_fupd_intro; first done. iModIntro.
-    iApply (@wptp_safe _ _ (IrisG _ _ _ Hinv stateI fork_post) with "[Hσ] Hwp"); eauto.
+    iApply (@wptp_safe _ _ (IrisG _ _ Hinv stateI fork_post) with "[Hσ] Hwp"); eauto.
 Qed.
 
 Theorem wp_adequacy Σ Λ `{invPreG Σ} s e σ φ :
   (∀ `{Hinv : invG Σ} κs,
      (|={⊤}=> ∃ stateI : state Λ → list (observation Λ) → iProp Σ,
-       let _ : irisG Λ Σ := IrisG _ _ _ Hinv (λ σ κs _, stateI σ κs) True%I in
+       let _ : irisG Λ Σ := IrisG _ _ Hinv (λ σ κs _, stateI σ κs) True%I in
        stateI σ κs ∗ WP e @ s; ⊤ {{ v, ⌜φ v⌝ }})%I) →
   adequate s e σ (λ v _, φ v).
 Proof.
@@ -218,7 +218,7 @@ Theorem wp_strong_all_adequacy Σ Λ `{invPreG Σ} s e σ1 v vs σ2 φ :
      (|={⊤}=> ∃
          (stateI : state Λ → list (observation Λ) → nat → iProp Σ)
          (fork_post : iProp Σ),
-       let _ : irisG Λ Σ := IrisG _ _ _ Hinv stateI fork_post in
+       let _ : irisG Λ Σ := IrisG _ _ Hinv stateI fork_post in
        stateI σ1 κs 0 ∗ WP e @ s; ⊤ {{ v,
          let m := length vs in
          stateI σ2 [] m -∗ [∗] replicate m fork_post ={⊤,∅}=∗ ⌜ φ v ⌝ }})%I) →
@@ -229,7 +229,7 @@ Proof.
   eapply (step_fupdN_soundness' _ (S (S n)))=> Hinv. rewrite Nat_iter_S.
   iMod Hwp as (stateI fork_post) "[Hσ Hwp]".
   iApply step_fupd_intro; first done. iModIntro.
-  iApply (@wptp_all_result _ _ (IrisG _ _ _ Hinv stateI fork_post)
+  iApply (@wptp_all_result _ _ (IrisG _ _ Hinv stateI fork_post)
     with "[Hσ] [Hwp]"); eauto. by rewrite right_id_L.
 Qed.
 
@@ -238,7 +238,7 @@ Theorem wp_invariance Σ Λ `{invPreG Σ} s e σ1 t2 σ2 φ :
      (|={⊤}=> ∃
          (stateI : state Λ → list (observation Λ) → nat → iProp Σ)
          (fork_post : iProp Σ),
-       let _ : irisG Λ Σ := IrisG _ _ _ Hinv stateI fork_post in
+       let _ : irisG Λ Σ := IrisG _ _ Hinv stateI fork_post in
        stateI σ1 (κs ++ κs') 0 ∗ WP e @ s; ⊤ {{ _, True }} ∗
        (stateI σ2 κs' (pred (length t2)) ={⊤,∅}=∗ ⌜φ⌝))%I) →
   rtc erased_step ([e], σ1) (t2, σ2) →
@@ -248,7 +248,7 @@ Proof.
   apply (step_fupdN_soundness' _ (S (S n)))=> Hinv. rewrite Nat_iter_S.
   iMod (Hwp Hinv κs []) as (Istate fork_post) "(Hσ & Hwp & Hclose)".
   iApply step_fupd_intro; first done.
-  iApply (@wptp_invariance _ _ (IrisG _ _ _ Hinv Istate fork_post)
+  iApply (@wptp_invariance _ _ (IrisG _ _ Hinv Istate fork_post)
     with "Hclose [Hσ] [Hwp]"); eauto.
 Qed.
 
@@ -259,7 +259,7 @@ Corollary wp_invariance' Σ Λ `{invPreG Σ} s e σ1 t2 σ2 φ :
      (|={⊤}=> ∃
          (stateI : state Λ → list (observation Λ) → nat → iProp Σ)
          (fork_post : iProp Σ),
-       let _ : irisG Λ Σ := IrisG _ _ _ Hinv stateI fork_post in
+       let _ : irisG Λ Σ := IrisG _ _ Hinv stateI fork_post in
        stateI σ1 κs 0 ∗ WP e @ s; ⊤ {{ _, True }} ∗
        (stateI σ2 κs' (pred (length t2)) -∗ ∃ E, |={⊤,E}=> ⌜φ⌝))%I) →
   rtc erased_step ([e], σ1) (t2, σ2) →

theories/program_logic/ownp.v

@@ -5,36 +5,34 @@ From iris.algebra Require Import auth.
 From iris.proofmode Require Import tactics classes.
 Set Default Proof Using "Type".
 
-Class ownPG' (Λstate Λobservation : Type) (Σ : gFunctors) := OwnPG {
+Class ownPG (Λ : language) (Σ : gFunctors) := OwnPG {
   ownP_invG : invG Σ;
-  ownP_inG :> inG Σ (authR (optionUR (exclR (leibnizC Λstate))));
+  ownP_inG :> inG Σ (authR (optionUR (exclR (stateC Λ))));
   ownP_name : gname;
 }.
-Notation ownPG Λ Σ := (ownPG' (state Λ) (observation Λ) Σ).
 
-Instance ownPG_irisG `{ownPG' Λstate Λobservation Σ} : irisG' Λstate Λobservation Σ := {
+Instance ownPG_irisG `{ownPG Λ Σ} : irisG Λ Σ := {
   iris_invG := ownP_invG;
-  state_interp σ κs _ := (own ownP_name (● (Excl' (σ:leibnizC Λstate))))%I;
+  state_interp σ κs _ := own ownP_name (● (Excl' σ))%I;
   fork_post := True%I;
 }.
 Global Opaque iris_invG.
 
-Definition ownPΣ (Λstate : Type) : gFunctors :=
+Definition ownPΣ (Λ : language) : gFunctors :=
   #[invΣ;
-    GFunctor (authR (optionUR (exclR (leibnizC Λstate))))].
+    GFunctor (authR (optionUR (exclR (stateC Λ))))].
 
-Class ownPPreG' (Λstate : Type) (Σ : gFunctors) : Set := IrisPreG {
+Class ownPPreG (Λ : language) (Σ : gFunctors) : Set := IrisPreG {
   ownPPre_invG :> invPreG Σ;
-  ownPPre_state_inG :> inG Σ (authR (optionUR (exclR (leibnizC Λstate))))
+  ownPPre_state_inG :> inG Σ (authR (optionUR (exclR (stateC Λ))))
 }.
-Notation ownPPreG Λ Σ := (ownPPreG' (state Λ) Σ).
 
-Instance subG_ownPΣ {Λstate Σ} : subG (ownPΣ Λstate) Σ → ownPPreG' Λstate Σ.
+Instance subG_ownPΣ {Λ Σ} : subG (ownPΣ Λ) Σ → ownPPreG Λ Σ.
 Proof. solve_inG. Qed.
 
 (** Ownership *)
-Definition ownP `{ownPG' Λstate Λobservation Σ} (σ : Λstate) : iProp Σ :=
-  own ownP_name (◯ (Excl' (σ:leibnizC Λstate))).
+Definition ownP `{ownPG Λ Σ} (σ : state Λ) : iProp Σ :=
+  own ownP_name (◯ (Excl' σ)).
 
 Typeclasses Opaque ownP.
 Instance: Params (@ownP) 3.
@@ -46,12 +44,10 @@ Theorem ownP_adequacy Σ `{ownPPreG Λ Σ} s e σ φ :
 Proof.
   intros Hwp. apply (wp_adequacy Σ _).
   iIntros (? κs).
-  iMod (own_alloc (● (Excl' (σ : leibnizC _)) ⋅ ◯ (Excl' σ)))
-    as (γσ) "[Hσ Hσf]"; first done.
-  iModIntro. iExists (λ σ κs,
-                      own γσ (● (Excl' (σ:leibnizC _))))%I.
+  iMod (own_alloc (● (Excl' σ) ⋅ ◯ (Excl' σ))) as (γσ) "[Hσ Hσf]"; first done.
+  iModIntro. iExists (λ σ κs, own γσ (● (Excl' σ)))%I.
   iFrame "Hσ".
-  iApply (Hwp (OwnPG _ _ _ _ _ γσ)). rewrite /ownP. iFrame.
+  iApply (Hwp (OwnPG _ _ _ _ γσ)). rewrite /ownP. iFrame.
 Qed.
 
 Theorem ownP_invariance Σ `{ownPPreG Λ Σ} s e σ1 t2 σ2 φ :
@@ -63,11 +59,10 @@ Theorem ownP_invariance Σ `{ownPPreG Λ Σ} s e σ1 t2 σ2 φ :
 Proof.
   intros Hwp Hsteps. eapply (wp_invariance Σ Λ s e σ1 t2 σ2 _)=> //.
   iIntros (? κs κs').
-  iMod (own_alloc (● (Excl' (σ1 : leibnizC _)) ⋅ ◯ (Excl' σ1)))
-    as (γσ) "[Hσ Hσf]"; first done.
-  iExists (λ σ κs' _, own γσ (● (Excl' (σ:leibnizC _))))%I, True%I.
+  iMod (own_alloc (● (Excl' σ1) ⋅ ◯ (Excl' σ1))) as (γσ) "[Hσ Hσf]"; first done.
+  iExists (λ σ κs' _, own γσ (● (Excl' σ)))%I, True%I.
   iFrame "Hσ".
-  iMod (Hwp (OwnPG _ _ _ _ _ γσ) with "[Hσf]") as "[$ H]";
+  iMod (Hwp (OwnPG _ _ _ _ γσ) with "[Hσf]") as "[$ H]";
     first by rewrite /ownP; iFrame.
   iIntros "!> Hσ". iMod "H" as (σ2') "[Hσf %]". rewrite /ownP.
   iDestruct (own_valid_2 with "Hσ Hσf")
@@ -90,7 +85,7 @@ Section lifting.
   Qed.
   Lemma ownP_state_twice σ1 σ2 : ownP σ1 ∗ ownP σ2 ⊢ False.
   Proof. rewrite /ownP -own_op own_valid. by iIntros (?). Qed.
-  Global Instance ownP_timeless σ : Timeless (@ownP (state Λ) (observation Λ) Σ _ σ).
+  Global Instance ownP_timeless σ : Timeless (@ownP Λ Σ _ σ).
   Proof. rewrite /ownP; apply _. Qed.
 
   Lemma ownP_lift_step s E Φ e1 :

theories/program_logic/total_adequacy.v

@@ -63,8 +63,8 @@ Proof.
   iRevert (t1) "IH1"; iRevert (t2) "H2".
   iApply twptp_ind; iIntros "!#" (t2) "IH2". iIntros (t1) "IH1".
   rewrite twptp_unfold /twptp_pre. iIntros (t1'' σ1 κ κs σ2 n Hstep) "Hσ1".
-  destruct Hstep as [e1 σ1' e2 σ2' efs' t1' t2' ?? Hstep]; simplify_eq/=.
-  apply app_eq_inv in H as [(t&?&?)|(t&?&?)]; subst.
+  destruct Hstep as [e1 σ1' e2 σ2' efs' t1' t2' [=Ht ?] ? Hstep]; simplify_eq/=.
+  apply app_eq_inv in Ht as [(t&?&?)|(t&?&?)]; subst.
   - destruct t as [|e1' ?]; simplify_eq/=.
     + iMod ("IH2" with "[%] Hσ1") as (n2) "($ & Hσ & IH2 & _)".
       { by eapply step_atomic with (t1:=[]). }
@@ -119,13 +119,13 @@ Theorem twp_total Σ Λ `{invPreG Σ} s e σ Φ :
      (|={⊤}=> ∃
          (stateI : state Λ → list (observation Λ) → nat → iProp Σ)
          (fork_post : iProp Σ),
-       let _ : irisG Λ Σ := IrisG _ _ _ Hinv stateI fork_post in
+       let _ : irisG Λ Σ := IrisG _ _ Hinv stateI fork_post in
        stateI σ [] 0 ∗ WP e @ s; ⊤ [{ Φ }])%I) →
   sn erased_step ([e], σ). (* i.e. ([e], σ) is strongly normalizing *)
 Proof.
   intros Hwp. apply (soundness (M:=iResUR Σ) _  2); simpl.
   apply (fupd_plain_soundness ⊤ _)=> Hinv.
   iMod (Hwp) as (stateI fork_post) "[Hσ H]".
-  iApply (@twptp_total _ _ (IrisG _ _ _ Hinv stateI fork_post) with "Hσ").
-  by iApply (@twp_twptp _ _ (IrisG _ _ _ Hinv stateI fork_post)).
+  iApply (@twptp_total _ _ (IrisG _ _ Hinv stateI fork_post) with "Hσ").
+  by iApply (@twp_twptp _ _ (IrisG _ _ Hinv stateI fork_post)).
 Qed.

theories/program_logic/weakestpre.v

@@ -5,7 +5,7 @@ From iris.proofmode Require Import base tactics classes.
 Set Default Proof Using "Type".
 Import uPred.
 
-Class irisG' (Λstate Λobservation : Type) (Σ : gFunctors) := IrisG {
+Class irisG (Λ : language) (Σ : gFunctors) := IrisG {
   iris_invG :> invG Σ;
 
   (** The state interpretation is an invariant that should hold in between each
@@ -13,14 +13,13 @@ Class irisG' (Λstate Λobservation : Type) (Σ : gFunctors) := IrisG {
   the remaining observations, and [nat] is the number of forked-off threads
   (not the total number of threads, which is one higher because there is always
   a main thread). *)
-  state_interp : Λstate → list Λobservation → nat → iProp Σ;
+  state_interp : state Λ → list (observation Λ) → nat → iProp Σ;
 
   (** A fixed postcondition for any forked-off thread. For most languages, e.g.
   heap_lang, this will simply be [True]. However, it is useful if one wants to
   keep track of resources precisely, as in e.g. Iron. *)
   fork_post : iProp Σ;
 }.
-Notation irisG Λ Σ := (irisG' (state Λ) (observation Λ) Σ).
 Global Opaque iris_invG.
 
 Definition wp_pre `{irisG Λ Σ} (s : stuckness)