Get rid of `ρ` argument of `spec_ctx`.

theories/logrel/F_mu_ref_conc/examples/counter.v

@@ -60,21 +60,21 @@ Section CG_Counter.
 
   Hint Rewrite CG_increment_subst : autosubst.
 
-  Lemma steps_CG_increment E ρ j K x n:
+  Lemma steps_CG_increment E j K x n:
     nclose specN ⊆ E →
-    spec_ctx ρ ∗ x ↦ₛ (#nv n) ∗ j ⤇ fill K (App (CG_increment (Loc x)) Unit)
+    spec_ctx ∗ x ↦ₛ (#nv n) ∗ j ⤇ fill K (App (CG_increment (Loc x)) Unit)
       ⊢ |={E}=> j ⤇ fill K (Unit) ∗ x ↦ₛ (#nv (S n)).
   Proof.
     iIntros (HNE) "[#Hspec [Hx Hj]]". unfold CG_increment.
     iMod (do_step_pure with "[$Hj]") as "Hj"; eauto.
-    iMod (step_load _ _ j ((BinOpRCtx _ (#nv _) :: StoreRCtx (LocV _) :: K))
+    iMod (step_load _ j ((BinOpRCtx _ (#nv _) :: StoreRCtx (LocV _) :: K))
                     _ _ _ with "[Hj Hx]") as "[Hj Hx]"; eauto.
     { iFrame "Hspec Hj"; trivial. }
     simpl.
-    iMod (do_step_pure _ _ _ ((StoreRCtx (LocV _)) :: K)  with "[$Hj]") as "Hj";
+    iMod (do_step_pure _ _ ((StoreRCtx (LocV _)) :: K)  with "[$Hj]") as "Hj";
       eauto.
     simpl.
-    iMod (step_store _ _ j K with "[$Hj $Hx]") as "[Hj Hx]"; eauto.
+    iMod (step_store _ j K with "[$Hj $Hx]") as "[Hj Hx]"; eauto.
     iModIntro; iFrame.
   Qed.
 
@@ -108,15 +108,15 @@ Section CG_Counter.
 
   Hint Rewrite CG_locked_increment_subst : autosubst.
 
-  Lemma steps_CG_locked_increment E ρ j K x n l :
+  Lemma steps_CG_locked_increment E j K x n l :
     nclose specN ⊆ E →
-    spec_ctx ρ ∗ x ↦ₛ (#nv n) ∗ l ↦ₛ (#♭v false)
+    spec_ctx ∗ x ↦ₛ (#nv n) ∗ l ↦ₛ (#♭v false)
       ∗ j ⤇ fill K (App (CG_locked_increment (Loc x) (Loc l)) Unit)
     ={E}=∗ j ⤇ fill K Unit ∗ x ↦ₛ (#nv S n) ∗ l ↦ₛ (#♭v false).
   Proof.
     iIntros (HNE) "[#Hspec [Hx [Hl Hj]]]".
     iMod (steps_with_lock
-            _ _ j K _ _ _ _ UnitV UnitV with "[$Hj Hx $Hl]") as "Hj"; eauto.
+            _ j K _ _ _ _ UnitV UnitV with "[$Hj Hx $Hl]") as "Hj"; eauto.
     - iIntros (K') "[#Hspec Hxj]".
       iApply steps_CG_increment; by try iFrame.
     - by iFrame.
@@ -151,16 +151,16 @@ Section CG_Counter.
 
   Hint Rewrite counter_read_subst : autosubst.
 
-  Lemma steps_counter_read E ρ j K x n :
+  Lemma steps_counter_read E j K x n :
     nclose specN ⊆ E →
-    spec_ctx ρ ∗ x ↦ₛ (#nv n)
+    spec_ctx ∗ x ↦ₛ (#nv n)
                ∗ j ⤇ fill K (App (counter_read (Loc x)) Unit)
     ={E}=∗ j ⤇ fill K (#n n) ∗ x ↦ₛ (#nv n).
   Proof.
     intros HNE. iIntros "[#Hspec [Hx Hj]]". unfold counter_read.
     iMod (do_step_pure with "[$Hj]") as "Hj"; eauto.
     iAsimpl.
-    iMod (step_load _ _ j K with "[$Hj Hx]") as "[Hj Hx]"; eauto.
+    iMod (step_load _ j K with "[$Hj Hx]") as "[Hj Hx]"; eauto.
     by iFrame.
   Qed.
 
@@ -247,17 +247,17 @@ Section CG_Counter.
   Lemma FG_CG_counter_refinement :
     [] ⊨ FG_counter ≤log≤ CG_counter : TProd (TArrow TUnit TUnit) (TArrow TUnit TNat).
   Proof.
-    iIntros (Δ [|??] ρ ?) "#(Hspec & HΓ)"; iIntros (j K) "Hj"; last first.
+    iIntros (Δ [|??] ?) "#(Hspec & HΓ)"; iIntros (j K) "Hj"; last first.
     { iDestruct (interp_env_length with "HΓ") as %[=]. }
     iClear "HΓ". cbn -[FG_counter CG_counter].
     rewrite ?empty_env_subst /CG_counter /FG_counter.
     iApply fupd_wp.
-    iMod (steps_newlock _ _ j (LetInCtx _ :: K) with "[$Hj]")
+    iMod (steps_newlock _ j (LetInCtx _ :: K) with "[$Hj]")
       as (l) "[Hj Hl]"; eauto.
     simpl.
     iMod (do_step_pure with "[$Hj]") as "Hj"; eauto.
     iAsimpl.
-    iMod (step_alloc _ _ j (LetInCtx _ :: K) with "[$Hj]")
+    iMod (step_alloc _ j (LetInCtx _ :: K) with "[$Hj]")
       as (cnt') "[Hj Hcnt']"; eauto.
     simpl.
     iMod (do_step_pure with "[$Hj]") as "Hj"; eauto.
@@ -308,7 +308,7 @@ Section CG_Counter.
       + (* CAS succeeds *)
         (* In this case, we perform increment in the coarse-grained one *)
         iMod (steps_CG_locked_increment
-                _ _ _ _ _ _ _ _ with "[Hj Hl Hcnt']") as "[Hj [Hcnt' Hl]]".
+                _ _ _ _ _ _ _ with "[Hj Hl Hcnt']") as "[Hj [Hcnt' Hl]]".
         { iFrame "Hspec Hcnt' Hl Hj"; trivial. }
         iApply (wp_cas_suc with "[Hcnt]"); auto.
         iModIntro. iNext. iIntros "Hcnt".

theories/logrel/F_mu_ref_conc/examples/fact.v

@@ -68,7 +68,7 @@ Section fact_equiv.
   Lemma fact_fact_acc_refinement :
     [] ⊨ fact ≤log≤ fact_acc : (TArrow TNat TNat).
   Proof.
-    iIntros (? vs ρ _) "[#HE HΔ]".
+    iIntros (? vs _) "[#HE HΔ]".
     iDestruct (interp_env_length with "HΔ") as %?; destruct vs; simplify_eq.
     iClear "HΔ". simpl.
     iIntros (j K) "Hj"; simpl.
@@ -87,7 +87,7 @@ Section fact_equiv.
     - iApply wp_pure_step_later; auto.
       iNext; simpl; asimpl.
       rewrite fact_acc_body_unfold.
-      iMod (do_step_pure _ _ _ (AppLCtx _ :: _) with "[$Hj]") as "Hj"; auto.
+      iMod (do_step_pure _ _ (AppLCtx _ :: _) with "[$Hj]") as "Hj"; auto.
       rewrite -fact_acc_body_unfold.
       simpl; asimpl.
       iMod (do_step_pure with "[$Hj]") as "Hj"; auto.
@@ -95,7 +95,7 @@ Section fact_equiv.
       iApply wp_pure_step_later; auto.
       iNext; simpl.
       iApply wp_value. simpl.
-      iMod (do_step_pure _ _ _ (IfCtx _ _ :: _) with "[$Hj]") as "Hj"; auto.
+      iMod (do_step_pure _ _ (IfCtx _ _ :: _) with "[$Hj]") as "Hj"; auto.
       simpl.
       iApply wp_pure_step_later; auto.
       iNext; simpl.
@@ -106,7 +106,7 @@ Section fact_equiv.
     - iApply wp_pure_step_later; auto.
       iNext; simpl; asimpl.
       rewrite fact_acc_body_unfold.
-      iMod (do_step_pure _ _ _ (AppLCtx _ :: _) with "[$Hj]") as "Hj"; auto.
+      iMod (do_step_pure _ _ (AppLCtx _ :: _) with "[$Hj]") as "Hj"; auto.
       rewrite -fact_acc_body_unfold.
       simpl; asimpl.
       iMod (do_step_pure with "[$Hj]") as "Hj"; auto.
@@ -114,7 +114,7 @@ Section fact_equiv.
       iApply wp_pure_step_later; auto.
       iNext; simpl.
       iApply wp_value. simpl.
-      iMod (do_step_pure _ _ _ (IfCtx _ _ :: _) with "[$Hj]") as "Hj"; auto.
+      iMod (do_step_pure _ _ (IfCtx _ _ :: _) with "[$Hj]") as "Hj"; auto.
       simpl.
       iApply wp_pure_step_later; auto.
       iNext; simpl.
@@ -124,11 +124,11 @@ Section fact_equiv.
       iApply (wp_bind (fill [AppRCtx (RecV _)])).
       iApply wp_pure_step_later; auto.
       iNext; simpl; iApply wp_value; simpl.
-      iMod (do_step_pure _ _ _ (LetInCtx _ :: _) with "[$Hj]") as "Hj"; auto.
+      iMod (do_step_pure _ _ (LetInCtx _ :: _) with "[$Hj]") as "Hj"; auto.
       simpl.
       iMod (do_step_pure with "[$Hj]") as "Hj"; auto.
       asimpl.
-      iMod (do_step_pure _ _ _ (LetInCtx _ :: _) with "[$Hj]") as "Hj"; auto.
+      iMod (do_step_pure _ _ (LetInCtx _ :: _) with "[$Hj]") as "Hj"; auto.
       simpl.
       iMod (do_step_pure with "[$Hj]") as "Hj"; auto.
       asimpl.
@@ -146,7 +146,7 @@ Section fact_equiv.
   Lemma fact_acc_fact_refinement :
     [] ⊨ fact_acc ≤log≤ fact : (TArrow TNat TNat).
   Proof.
-    iIntros (? vs ρ _) "[#HE HΔ]".
+    iIntros (? vs _) "[#HE HΔ]".
     iDestruct (interp_env_length with "HΔ") as %?; destruct vs; simplify_eq.
     iClear "HΔ". simpl.
     iIntros (j K) "Hj"; simpl.
@@ -173,7 +173,7 @@ Section fact_equiv.
       iNext; simpl; asimpl.
       iMod (do_step_pure with "[$Hj]") as "Hj"; auto.
       simpl; asimpl.
-      iMod (do_step_pure _ _ _ (IfCtx _ _ :: _) with "[$Hj]") as "Hj"; auto.
+      iMod (do_step_pure _ _ (IfCtx _ _ :: _) with "[$Hj]") as "Hj"; auto.
       iApply (wp_bind (fill [IfCtx _ _])).
       iApply wp_pure_step_later; auto.
       iNext; simpl.
@@ -198,12 +198,12 @@ Section fact_equiv.
       iApply wp_pure_step_later; auto.
       iNext; simpl.
       iApply wp_value. simpl.
-      iMod (do_step_pure _ _ _ (IfCtx _ _ :: _) with "[$Hj]") as "Hj"; auto.
+      iMod (do_step_pure _ _ (IfCtx _ _ :: _) with "[$Hj]") as "Hj"; auto.
       simpl.
       iApply wp_pure_step_later; auto.
       iNext; simpl.
       iMod (do_step_pure with "[$Hj]") as "Hj"; auto.
-      iMod (do_step_pure _ _ _ (AppRCtx (RecV _):: BinOpRCtx _ (#nv _) :: _)
+      iMod (do_step_pure _ _ (AppRCtx (RecV _):: BinOpRCtx _ (#nv _) :: _)
               with "[$Hj]") as "Hj"; eauto.
       simpl.
       iApply (wp_bind (fill [LetInCtx _])).

theories/logrel/F_mu_ref_conc/examples/lock.v

@@ -84,29 +84,29 @@ Section proof.
   Context `{cfgSG Σ}.
   Context `{heapIG Σ}.
 
-  Lemma steps_newlock E ρ j K :
+  Lemma steps_newlock E j K :
     nclose specN ⊆ E →
-    spec_ctx ρ ∗ j ⤇ fill K newlock
+    spec_ctx ∗ j ⤇ fill K newlock
       ⊢ |={E}=> ∃ l, j ⤇ fill K (Loc l) ∗ l ↦ₛ (#♭v false).
   Proof.
     iIntros (HNE) "[#Hspec Hj]".
-    by iMod (step_alloc _ _ j K with "[Hj]") as "Hj"; eauto.
+    by iMod (step_alloc _ j K with "[Hj]") as "Hj"; eauto.
   Qed.
 
   Typeclasses Opaque newlock.
   Global Opaque newlock.
 
-  Lemma steps_acquire E ρ j K l :
+  Lemma steps_acquire E j K l :
     nclose specN ⊆ E →
-    spec_ctx ρ ∗ l ↦ₛ (#♭v false) ∗ j ⤇ fill K (App acquire (Loc l))
+    spec_ctx ∗ l ↦ₛ (#♭v false) ∗ j ⤇ fill K (App acquire (Loc l))
       ⊢ |={E}=> j ⤇ fill K Unit ∗ l ↦ₛ (#♭v true).
   Proof.
     iIntros (HNE) "[#Hspec [Hl Hj]]". unfold acquire.
-    iMod (step_rec _ _ j K with "[Hj]") as "Hj"; eauto. done.
-    iMod (step_cas_suc _ _ j ((IfCtx _ _) :: K)
+    iMod (step_rec _ j K with "[Hj]") as "Hj"; eauto. done.
+    iMod (step_cas_suc _ j ((IfCtx _ _) :: K)
                        _ _ _ _ _ _ _ _ _ with "[Hj Hl]") as "[Hj Hl]"; trivial.
     { simpl. iFrame "Hspec Hj Hl"; eauto. }
-    iMod (step_if_true _ _ j K _ _ _ with "[Hj]") as "Hj"; trivial.
+    iMod (step_if_true _ j K _ _ _ with "[Hj]") as "Hj"; trivial.
     { by iFrame. }
     by iIntros "!> {$Hj $Hl}".
     Unshelve. all:trivial.
@@ -115,9 +115,9 @@ Section proof.
   Typeclasses Opaque acquire.
   Global Opaque acquire.
 
-  Lemma steps_release E ρ j K l b:
+  Lemma steps_release E j K l b:
     nclose specN ⊆ E →
-    spec_ctx ρ ∗ l ↦ₛ (#♭v b) ∗ j ⤇ fill K (App release (Loc l))
+    spec_ctx ∗ l ↦ₛ (#♭v b) ∗ j ⤇ fill K (App release (Loc l))
       ⊢ |={E}=> j ⤇ fill K Unit ∗ l ↦ₛ (#♭v false).
   Proof.
     iIntros (HNE) "[#Hspec [Hl Hj]]". unfold release.
@@ -129,26 +129,26 @@ Section proof.
   Typeclasses Opaque release.
   Global Opaque release.
 
-  Lemma steps_with_lock E ρ j K e l P Q v w:
+  Lemma steps_with_lock E j K e l P Q v w:
     nclose specN ⊆ E →
     (* (∀ f, e.[f] = e) (* e is a closed term *) → *)
-    (∀ K', spec_ctx ρ ∗ P ∗ j ⤇ fill K' (App e (of_val w))
+    (∀ K', spec_ctx ∗ P ∗ j ⤇ fill K' (App e (of_val w))
             ⊢ |={E}=> j ⤇ fill K' (of_val v) ∗ Q) →
-    spec_ctx ρ ∗ P ∗ l ↦ₛ (#♭v false)
+    spec_ctx ∗ P ∗ l ↦ₛ (#♭v false)
                 ∗ j ⤇ fill K (App (with_lock e (Loc l)) (of_val w))
       ⊢ |={E}=> j ⤇ fill K (of_val v) ∗ Q ∗ l ↦ₛ (#♭v false).
   Proof.
     iIntros (HNE He) "[#Hspec [HP [Hl Hj]]]".
     iMod (do_step_pure with "[$Hj]") as "Hj"; eauto.
     iAsimpl.
-    iMod (steps_acquire _ _ j (SeqCtx _ :: K) with "[$Hj Hl]") as "[Hj Hl]";
+    iMod (steps_acquire _ j (SeqCtx _ :: K) with "[$Hj Hl]") as "[Hj Hl]";
       auto. simpl.
     iMod (do_step_pure with "[$Hj]") as "Hj"; eauto.
     iMod (He (LetInCtx _ :: K) with "[$Hj HP]") as "[Hj HQ]"; eauto.
     simpl.
     iMod (do_step_pure with "[$Hj]") as "Hj"; eauto.
     iAsimpl.
-    iMod (steps_release _ _ j (SeqCtx _ :: K) _ _ with "[$Hj $Hl]")
+    iMod (steps_release _ j (SeqCtx _ :: K) _ _ with "[$Hj $Hl]")
       as "[Hj Hl]"; eauto.
     simpl.
     iMod (do_step_pure with "[$Hj]") as "Hj"; eauto.

theories/logrel/F_mu_ref_conc/examples/stack/CG_stack.v

@@ -81,18 +81,18 @@ Section CG_Stack.
 
   Hint Rewrite CG_push_subst : autosubst.
 
-  Lemma steps_CG_push E ρ j K st v w :
+  Lemma steps_CG_push E j K st v w :
     nclose specN ⊆ E →
-    spec_ctx ρ ∗ st ↦ₛ v ∗ j ⤇ fill K (App (CG_push (Loc st)) (of_val w))
+    spec_ctx ∗ st ↦ₛ v ∗ j ⤇ fill K (App (CG_push (Loc st)) (of_val w))
     ⊢ |={E}=> j ⤇ fill K Unit ∗ st ↦ₛ FoldV (InjRV (PairV w v)).
   Proof.
     intros HNE. iIntros "[#Hspec [Hx Hj]]". unfold CG_push.
     iMod (do_step_pure with "[$Hj]") as "Hj"; eauto.
     iAsimpl.
-    iMod (step_load _ _ j (PairRCtx _ :: InjRCtx :: FoldCtx :: StoreRCtx (LocV _) :: K)
+    iMod (step_load _ j (PairRCtx _ :: InjRCtx :: FoldCtx :: StoreRCtx (LocV _) :: K)
             with "[$Hj $Hx]") as "[Hj Hx]"; eauto.
     simpl.
-    iMod (step_store _ _ j K with "[$Hj $Hx]") as "[Hj Hx]"; eauto.
+    iMod (step_store _ j K with "[$Hj $Hx]") as "[Hj Hx]"; eauto.
     { rewrite /= !to_of_val //. }
     iModIntro. by iFrame.
   Qed.
@@ -124,14 +124,14 @@ Section CG_Stack.
 
   Hint Rewrite CG_locked_push_subst : autosubst.
 
-  Lemma steps_CG_locked_push E ρ j K st w v l :
+  Lemma steps_CG_locked_push E j K st w v l :
     nclose specN ⊆ E →
-    spec_ctx ρ ∗ st ↦ₛ v ∗ l ↦ₛ (#♭v false)
+    spec_ctx ∗ st ↦ₛ v ∗ l ↦ₛ (#♭v false)
       ∗ j ⤇ fill K (App (CG_locked_push (Loc st) (Loc l)) (of_val w))
     ⊢ |={E}=> j ⤇ fill K Unit ∗ st ↦ₛ FoldV (InjRV (PairV w v)) ∗ l ↦ₛ (#♭v false).
   Proof.
     intros HNE. iIntros "[#Hspec [Hx [Hl Hj]]]". unfold CG_locked_push.
-    iMod (steps_with_lock _ _ _ _ _ _ (st ↦ₛ v)%I _ UnitV with "[$Hj $Hx $Hl]")
+    iMod (steps_with_lock _ _ _ _ _ (st ↦ₛ v)%I _ UnitV with "[$Hj $Hx $Hl]")
       as "Hj"; auto.
     iIntros (K') "[#Hspec Hxj]".
     iApply steps_CG_push; first done. by iFrame.
@@ -164,46 +164,46 @@ Section CG_Stack.
 
   Hint Rewrite CG_pop_subst : autosubst.
 
-  Lemma steps_CG_pop_suc E ρ j K st v w :
+  Lemma steps_CG_pop_suc E j K st v w :
     nclose specN ⊆ E →
-    spec_ctx ρ ∗ st ↦ₛ FoldV (InjRV (PairV w v)) ∗
+    spec_ctx ∗ st ↦ₛ FoldV (InjRV (PairV w v)) ∗
                j ⤇ fill K (App (CG_pop (Loc st)) Unit)
       ⊢ |={E}=> j ⤇ fill K (InjR (of_val w)) ∗ st ↦ₛ v.
   Proof.
     intros HNE. iIntros "[#Hspec [Hx Hj]]". unfold CG_pop.
     iMod (do_step_pure with "[$Hj]") as "Hj"; eauto.
     iAsimpl.
-    iMod (step_load _ _ _ (UnfoldCtx :: CaseCtx _ _ :: K)  with "[$Hj $Hx]")
+    iMod (step_load _ _ (UnfoldCtx :: CaseCtx _ _ :: K)  with "[$Hj $Hx]")
       as "[Hj Hx]"; eauto.
     simpl.
-    iMod (do_step_pure  _ _ _ (CaseCtx _ _ :: K) with "[$Hj]") as "Hj"; eauto.
+    iMod (do_step_pure _ _ (CaseCtx _ _ :: K) with "[$Hj]") as "Hj"; eauto.
     simpl.
     iMod (do_step_pure with "[$Hj]") as "Hj"; eauto.
     iAsimpl.
-    iMod (do_step_pure _ _ _ (StoreRCtx (LocV _) :: SeqCtx _ :: K)
+    iMod (do_step_pure _ _ (StoreRCtx (LocV _) :: SeqCtx _ :: K)
             with "[$Hj]") as "Hj"; eauto.
     simpl.
-    iMod (step_store _ _ j (SeqCtx _ :: K) with "[$Hj $Hx]") as "[Hj Hx]";
+    iMod (step_store _ j (SeqCtx _ :: K) with "[$Hj $Hx]") as "[Hj Hx]";
       eauto using to_of_val.
     simpl.
     iMod (do_step_pure with "[$Hj]") as "Hj"; eauto.
-    iMod (do_step_pure _ _ _ (InjRCtx :: K) with "[$Hj]") as "Hj"; eauto.
+    iMod (do_step_pure _ _ (InjRCtx :: K) with "[$Hj]") as "Hj"; eauto.
     simpl.
     by iFrame "Hj Hx".
   Qed.
 
-  Lemma steps_CG_pop_fail E ρ j K st :
+  Lemma steps_CG_pop_fail E j K st :
     nclose specN ⊆ E →
-    spec_ctx ρ ∗ st ↦ₛ FoldV (InjLV UnitV) ∗
+    spec_ctx ∗ st ↦ₛ FoldV (InjLV UnitV) ∗
                j ⤇ fill K (App (CG_pop (Loc st)) Unit)
       ⊢ |={E}=> j ⤇ fill K (InjL Unit) ∗ st ↦ₛ FoldV (InjLV UnitV).
   Proof.
     iIntros (HNE) "[#Hspec [Hx Hj]]". unfold CG_pop.
     iMod (do_step_pure with "[$Hj]") as "Hj"; eauto.
     iAsimpl.
-    iMod (step_load _ _ j (UnfoldCtx :: CaseCtx _ _ :: K)
+    iMod (step_load _ j (UnfoldCtx :: CaseCtx _ _ :: K)
                     _ _ _ with "[$Hj $Hx]") as "[Hj Hx]"; eauto.
-    iMod (do_step_pure _ _ _ (CaseCtx _ _ :: K) with "[$Hj]") as "Hj"; eauto.
+    iMod (do_step_pure _ _ (CaseCtx _ _ :: K) with "[$Hj]") as "Hj"; eauto.
     simpl.
     iMod (do_step_pure with "[$Hj]") as "Hj"; eauto.
     by iFrame "Hj Hx"; trivial.
@@ -237,28 +237,28 @@ Section CG_Stack.