Make some names more consistent.

F_mu_ref_par/context_refinement.v

 From iris_logrel.F_mu_ref_par Require Export fundamental_binary.
 
 Inductive ctx_item :=
-  | CTX_Lam
+  | CTX_Rec
   | CTX_AppL (e2 : expr)
   | CTX_AppR (e1 : expr)
   (* Products *)
@@ -42,7 +42,7 @@ Inductive ctx_item :=
 
 Fixpoint fill_ctx_item (ctx : ctx_item) (e : expr) : expr :=
   match ctx with
-  | CTX_Lam => Lam e
+  | CTX_Rec => Rec e
   | CTX_AppL e2 => App e e2
   | CTX_AppR e1 => App e1 e
   | CTX_PairL e2 => Pair e e2
@@ -80,8 +80,8 @@ Definition fill_ctx (K : ctx) (e : expr) : expr := foldr fill_ctx_item e K.
 (** typed ctx *)
 Inductive typed_ctx_item :
     ctx_item → list type → type → list type → type → Prop :=
-  | TP_CTX_Lam Γ τ τ' :
-     typed_ctx_item CTX_Lam (TArrow τ τ' :: τ :: Γ) τ' Γ (TArrow τ τ')
+  | TP_CTX_Rec Γ τ τ' :
+     typed_ctx_item CTX_Rec (TArrow τ τ' :: τ :: Γ) τ' Γ (TArrow τ τ')
   | TP_CTX_AppL Γ e2 τ τ' :
      typed Γ e2 τ →
      typed_ctx_item (CTX_AppL e2) Γ (TArrow τ τ') Γ τ'
@@ -211,22 +211,22 @@ Section bin_log_related_under_typed_ctx.
     - inversion_clear 1 as [|? ? ? ? ? ? ? ? Hx1 Hx2]. intros H3 Δ HΔ.
       specialize (IHK _ _ _ _ e e' H1 H2 Hx2 H3).
       inversion Hx1; subst; simpl.
-      + eapply bin_log_related_Lam; eauto;
+      + eapply bin_log_related_rec; eauto;
           match goal with
             H : _ |- _ => eapply (typed_ctx_n_closed _ _ _ _ _ _ _ H)
           end.
-      + eapply bin_log_related_App; eauto using binary_fundamental.
-      + eapply bin_log_related_App; eauto using binary_fundamental.
-      + eapply bin_log_related_Pair; eauto using binary_fundamental.
-      + eapply bin_log_related_Pair; eauto using binary_fundamental.
-      + eapply bin_log_related_Fst; eauto.
-      + eapply bin_log_related_Snd; eauto.
-      + eapply bin_log_related_InjL; eauto.
-      + eapply bin_log_related_InjR; eauto.
+      + eapply bin_log_related_app; eauto using binary_fundamental.
+      + eapply bin_log_related_app; eauto using binary_fundamental.
+      + eapply bin_log_related_pair; eauto using binary_fundamental.
+      + eapply bin_log_related_pair; eauto using binary_fundamental.
+      + eapply bin_log_related_fst; eauto.
+      + eapply bin_log_related_snd; eauto.
+      + eapply bin_log_related_injl; eauto.
+      + eapply bin_log_related_injr; eauto.
       + match goal with
           H : typed_ctx_item _ _ _ _ _ |- _ => inversion H; subst
         end.
-        eapply bin_log_related_Case;
+        eapply bin_log_related_case;
           eauto using binary_fundamental;
           match goal with
             H : _ |- _ => eapply (typed_n_closed _ _ _ H)
@@ -234,7 +234,7 @@ Section bin_log_related_under_typed_ctx.
       + match goal with
           H : typed_ctx_item _ _ _ _ _ |- _ => inversion H; subst
         end.
-        eapply bin_log_related_Case;
+        eapply bin_log_related_case;
           eauto using binary_fundamental;
           try match goal with
                 H : _ |- _ => eapply (typed_n_closed _ _ _ H)
@@ -245,7 +245,7 @@ Section bin_log_related_under_typed_ctx.
       + match goal with
           H : typed_ctx_item _ _ _ _ _ |- _ => inversion H; subst
         end.
-        eapply bin_log_related_Case;
+        eapply bin_log_related_case;
           eauto using binary_fundamental;
           try match goal with
                 H : _ |- _ => eapply (typed_n_closed _ _ _ H)
@@ -253,22 +253,22 @@ Section bin_log_related_under_typed_ctx.
           match goal with
             H : _ |- _ => eapply (typed_ctx_n_closed _ _ _ _ _ _ _ H)
           end.
-      + eapply bin_log_related_If; eauto using typed_ctx_typed, binary_fundamental.
-      + eapply bin_log_related_If; eauto using typed_ctx_typed, binary_fundamental.
-      + eapply bin_log_related_If; eauto using typed_ctx_typed, binary_fundamental.
-      + eapply bin_log_related_nat_bin_op;
+      + eapply bin_log_related_if; eauto using typed_ctx_typed, binary_fundamental.
+      + eapply bin_log_related_if; eauto using typed_ctx_typed, binary_fundamental.
+      + eapply bin_log_related_if; eauto using typed_ctx_typed, binary_fundamental.
+      + eapply bin_log_related_nat_binop;
           eauto using typed_ctx_typed, binary_fundamental.
-      + eapply bin_log_related_nat_bin_op;
+      + eapply bin_log_related_nat_binop;
           eauto using typed_ctx_typed, binary_fundamental.
-      + eapply bin_log_related_Fold; eauto.
-      + eapply bin_log_related_Unfold; eauto.
-      + eapply bin_log_related_TLam; eauto with typeclass_instances.
-      + eapply bin_log_related_TApp; eauto.
-      + eapply bin_log_related_Fork; eauto.
-      + eapply bin_log_related_Alloc; eauto.
-      + eapply bin_log_related_Load; eauto.
-      + eapply bin_log_related_Store; eauto using binary_fundamental.
-      + eapply bin_log_related_Store; eauto using binary_fundamental.
+      + eapply bin_log_related_fold; eauto.
+      + eapply bin_log_related_unfold; eauto.
+      + eapply bin_log_related_tlam; eauto with typeclass_instances.
+      + eapply bin_log_related_tapp; eauto.
+      + eapply bin_log_related_fork; eauto.
+      + eapply bin_log_related_alloc; eauto.
+      + eapply bin_log_related_load; eauto.
+      + eapply bin_log_related_store; eauto using binary_fundamental.
+      + eapply bin_log_related_store; eauto using binary_fundamental.
       + eapply bin_log_related_CAS; eauto using binary_fundamental.
       + eapply bin_log_related_CAS; eauto using binary_fundamental.
       + eapply bin_log_related_CAS; eauto using binary_fundamental.

F_mu_ref_par/examples/counter.v

@@ -3,27 +3,27 @@ From iris_logrel.F_mu_ref_par Require Export examples.lock.
 From iris_logrel.F_mu_ref_par Require Import soundness_binary.
 
 Definition CG_increment (x : expr) : expr :=
-  Lam (Store x.[ren (+ 2)] (BinOp Add (♯ 1) (Load x.[ren (+ 2)]))).
+  Rec (Store x.[ren (+ 2)] (BinOp Add (♯ 1) (Load x.[ren (+ 2)]))).
 
 Definition CG_locked_increment (x l : expr) : expr :=
   with_lock (CG_increment x) l.
 Definition CG_locked_incrementV (x l : expr) : val :=
   with_lockV (CG_increment x) l.
 
-Definition counter_read (x : expr) : expr := Lam (Load x.[ren (+2)]).
-Definition counter_readV (x : expr) : val := LamV (Load x.[ren (+2)]).
+Definition counter_read (x : expr) : expr := Rec (Load x.[ren (+2)]).
+Definition counter_readV (x : expr) : val := RecV (Load x.[ren (+2)]).
 
 Definition CG_counter_body (x l : expr) : expr :=
   Pair (CG_locked_increment x l) (counter_read x).
 Definition CG_counter : expr :=
   App
-    (Lam $ App (Lam (CG_counter_body (Var 1) (Var 3)))
+    (Rec $ App (Rec (CG_counter_body (Var 1) (Var 3)))
                (Alloc (♯ 0)))
     newlock.
 
 Definition FG_increment (x : expr) : expr :=
-  Lam $ App
-    (Lam $
+  Rec $ App
+    (Rec $
       (* try increment *)
       If (CAS x.[ren (+4)] (Var 1) (BinOp Add (♯ 1) (Var 1)))
           Unit (* increment succeeds we return unit *)
@@ -32,7 +32,7 @@ Definition FG_increment (x : expr) : expr :=
 Definition FG_counter_body (x : expr) : expr :=
   Pair (FG_increment x) (counter_read x).
 Definition FG_counter : expr :=
-  App (Lam (FG_counter_body (Var 1))) (Alloc (♯ 0)).
+  App (Rec (FG_counter_body (Var 1))) (Alloc (♯ 0)).
 
 Section CG_Counter.
   Context `{cfgSG Σ, heapIG Σ}.
@@ -63,13 +63,13 @@ Section CG_Counter.
       ={E}=> j ⤇ fill K (Unit) ★ x ↦ₛ (♯v (S n)).
   Proof.
     iIntros {HNE} "[#Hspec [Hx Hj]]". unfold CG_increment.
-    iPvs (step_lam _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iPvs (step_rec _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
     iPvs (step_load _ _ j (K ++ [StoreRCtx (LocV _); BinOpRCtx _ (♯v _)])
                     _ _ _ with "[Hj Hx]") as "[Hj Hx]"; eauto.
     rewrite ?fill_app. simpl.
     iFrame "Hspec Hj"; trivial.
     rewrite ?fill_app. simpl.
-    iPvs (step_nat_bin_op _ _ j (K ++ [StoreRCtx (LocV _)])
+    iPvs (step_nat_binop _ _ j (K ++ [StoreRCtx (LocV _)])
                           _ _ _  with "[Hj]") as "Hj"; eauto.
     rewrite ?fill_app. simpl.
     iFrame "Hspec Hj"; trivial. simpl.
@@ -164,7 +164,7 @@ Section CG_Counter.
     ={E}=> j ⤇ fill K (♯ n) ★ x ↦ₛ (♯v n).
   Proof.
     intros HNE. iIntros "[#Hspec [Hx Hj]]". unfold counter_read.
-    iPvs (step_lam _ _ j K _ Unit with "[Hj]") as "Hj"; eauto.
+    iPvs (step_rec _ _ j K _ Unit with "[Hj]") as "Hj"; eauto.
     asimpl.
     iPvs (step_load _ _ j K with "[Hj Hx]") as "[Hj Hx]"; eauto.
     { by iFrame "Hspec Hj". }
@@ -260,24 +260,24 @@ Section CG_Counter.
     { iDestruct (interp_env_length with "HΓ") as %[=]. }
     iClear "HΓ". cbn -[FG_counter CG_counter].
     rewrite ?empty_env_subst /CG_counter /FG_counter.
-    iPvs (steps_newlock _ _ j (K ++ [AppRCtx (LamV _)]) _ with "[Hj]")
+    iPvs (steps_newlock _ _ j (K ++ [AppRCtx (RecV _)]) _ with "[Hj]")
       as {l} "[Hj Hl]"; eauto.
     { rewrite fill_app /=. by iFrame. }
     rewrite fill_app /=.
-    iPvs (step_lam _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iPvs (step_rec _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
     asimpl. rewrite CG_locked_increment_subst /=.
     rewrite counter_read_subst /=.
-    iPvs (step_alloc _ _ j (K ++ [AppRCtx (LamV _)]) _ _ _ _ with "[Hj]")
+    iPvs (step_alloc _ _ j (K ++ [AppRCtx (RecV _)]) _ _ _ _ with "[Hj]")
       as {cnt'} "[Hj Hcnt']"; eauto.
     { rewrite fill_app; simpl. by iFrame. }
     rewrite fill_app; simpl.
-    iPvs (step_lam _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iPvs (step_rec _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
     asimpl. rewrite CG_locked_increment_subst /=.
     rewrite counter_read_subst /=.
     Unshelve.
     all: try match goal with |- to_val _ = _ => auto using to_of_val end.
     all: trivial.
-    iApply (@wp_bind _ _ _ [AppRCtx (LamV _)]);
+    iApply (@wp_bind _ _ _ [AppRCtx (RecV _)]);
       iApply wp_wand_l; iSplitR; [iIntros {v} "Hv"; iExact "Hv"|].
     iApply wp_alloc; trivial; iFrame "Hheap"; iNext; iIntros {cnt} "Hcnt /=".
     iPvsIntro.
@@ -288,7 +288,7 @@ Section CG_Counter.
     iPvs (inv_alloc counterN with "[Hinv]") as "#Hinv"; trivial.
     { iNext; iExact "Hinv". }
     (* splitting increment and read *)
-    iApply wp_lam; trivial. iNext. asimpl.
+    iApply wp_rec; trivial. iNext. asimpl.
     rewrite counter_read_subst /=.
     iApply wp_value; simpl.
     { by rewrite counter_read_to_val. }
@@ -301,19 +301,19 @@ Section CG_Counter.
       rewrite CG_locked_increment_of_val /=.
       destruct v; iDestruct "Heq" as "[% %]"; simplify_eq/=.
       iLöb as "Hlat".
-      iApply wp_lam; trivial. asimpl. iNext.
+      iApply wp_rec; trivial. asimpl. iNext.
       (* fine-grained reads the counter *)
-      iApply (@wp_bind _ _ _ [AppRCtx (LamV _)]);
+      iApply (@wp_bind _ _ _ [AppRCtx (RecV _)]);
         iApply wp_wand_l; iSplitR; [iIntros {v} "Hv"; iExact "Hv"|].
       iInv> counterN as {n} "[Hl [Hcnt Hcnt']]".
       iApply wp_load; [|iFrame "Hheap"]. solve_ndisj.
       iIntros "> {$Hcnt} Hcnt". iPvsIntro.
       iSplitL "Hl Hcnt Hcnt'"; [iExists _; iFrame "Hl Hcnt Hcnt'"; trivial|].
-      iApply wp_lam; trivial. asimpl. iNext.
+      iApply wp_rec; trivial. asimpl. iNext.
       (* fine-grained performs increment *)
       iApply (@wp_bind _ _ _ [IfCtx _ _; CasRCtx (LocV _) (NatV _)]);
         iApply wp_wand_l; iSplitR; [iIntros {v} "Hv"; iExact "Hv"|].
-      iApply wp_nat_bin_op; simpl.
+      iApply wp_nat_binop; simpl.
       iNext. iPvsIntro.
       iApply (@wp_bind _ _ _ [IfCtx _ _]);
         iApply wp_wand_l; iSplitR; [iIntros {v} "Hv"; iExact "Hv"|].
@@ -343,7 +343,7 @@ Section CG_Counter.
       iDestruct "Heq" as "[% %]"; destruct v; simplify_eq/=.
       Transparent counter_read.
       unfold counter_read at 2.
-      iApply wp_lam; trivial. simpl.
+      iApply wp_rec; trivial. simpl.
       iNext. iInv> counterN as {n} "[Hl [Hcnt Hcnt']]".
       iPvs (steps_counter_read with "[Hj Hcnt']") as "[Hj Hcnt']".
       { solve_ndisj. }

F_mu_ref_par/examples/lock.v

@@ -3,19 +3,19 @@ From iris_logrel.F_mu_ref_par Require Export rules_binary typing.
 
 Definition newlock : expr := Alloc (♭ false).
 Definition acquire : expr :=
-  Lam (If (CAS (Var 1) (♭ false) (♭ true)) (Unit) (App (Var 0) (Var 1))).
-Definition release : expr := Lam (Store (Var 1) (♭ false)).
+  Rec (If (CAS (Var 1) (♭ false) (♭ true)) (Unit) (App (Var 0) (Var 1))).
+Definition release : expr := Rec (Store (Var 1) (♭ false)).
 
 Definition with_lock (e : expr) (l : expr) : expr :=
-  Lam
-    (App (Lam (App (Lam (App (Lam (Var 3)) (App release l.[ren (+6)])))
+  Rec
+    (App (Rec (App (Rec (App (Rec (Var 3)) (App release l.[ren (+6)])))
                    (App e.[ren (+4)] (Var 3))))
          (App acquire l.[ren (+2)])
     ).
 
 Definition with_lockV (e l : expr) : val :=
-  LamV
-    (App (Lam (App (Lam (App (Lam (Var 3)) (App release l.[ren (+6)])))
+  RecV
+    (App (Rec (App (Rec (App (Rec (Var 3)) (App release l.[ren (+6)])))
                    (App e.[ren (+4)] (Var 3))))
          (App acquire l.[ren (+2)])
     ).
@@ -93,7 +93,7 @@ Section proof.
       ={E}=> j ⤇ fill K Unit ★ l ↦ₛ (♭v true).
   Proof.
     iIntros {HNE} "[#Hspec [Hl Hj]]". unfold acquire.
-    iPvs (step_lam _ _ j K with "[Hj]") as "Hj"; eauto. done.
+    iPvs (step_rec _ _ j K with "[Hj]") as "Hj"; eauto. done.
     iPvs (step_cas_suc _ _ j (K ++ [IfCtx _ _])
                        _ _ _ _ _ _ _ _ _ with "[Hj Hl]") as "[Hj Hl]"; trivial.
     rewrite ?fill_app. simpl.
@@ -114,7 +114,7 @@ Section proof.
       ={E}=> j ⤇ fill K Unit ★ l ↦ₛ (♭v false).
   Proof.
     iIntros {HNE} "[#Hspec [Hl Hj]]". unfold release.
-    iPvs (step_lam _ _ j K with "[Hj]") as "Hj"; eauto; try done.
+    iPvs (step_rec _ _ j K with "[Hj]") as "Hj"; eauto; try done.
     iPvs (step_store _ _ j K _ _ _ _ _ with "[Hj Hl]") as "[Hj Hl]"; eauto.
     iFrame "Hspec Hj"; trivial.
     iPvsIntro. iFrame "Hj Hl"; trivial.
@@ -133,26 +133,26 @@ Section proof.
       ={E}=> j ⤇ fill K (# v) ★ Q ★ l ↦ₛ (♭v false).
   Proof.
     iIntros {HNE H1 H2} "[#Hspec [HP [Hl Hj]]]".
-    iPvs (step_lam _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iPvs (step_rec _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
     asimpl. rewrite H1.
-    iPvs (steps_acquire _ _ j (K ++ [AppRCtx (LamV _)])
+    iPvs (steps_acquire _ _ j (K ++ [AppRCtx (RecV _)])
                    _ _ with "[Hj Hl]") as "[Hj Hl]"; eauto.
     rewrite fill_app; simpl.
     iFrame "Hspec Hj"; trivial.
     rewrite fill_app; simpl.
-    iPvs (step_lam _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iPvs (step_rec _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
     asimpl. rewrite H1.
-    iPvs (H2 (K ++ [AppRCtx (LamV _)]) with "[Hj HP]") as "[Hj HQ]"; eauto.
+    iPvs (H2 (K ++ [AppRCtx (RecV _)]) with "[Hj HP]") as "[Hj HQ]"; eauto.
     rewrite ?fill_app /=.
     iFrame "Hspec HP"; trivial.
     rewrite ?fill_app /=.
-    iPvs (step_lam _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iPvs (step_rec _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
     asimpl.
-    iPvs (steps_release _ _ j (K ++ [AppRCtx (LamV _)]) _ _ with "[Hj Hl]")
+    iPvs (steps_release _ _ j (K ++ [AppRCtx (RecV _)]) _ _ with "[Hj Hl]")
       as "[Hj Hl]"; eauto.
     rewrite ?fill_app /=. by iFrame.
     rewrite ?fill_app /=.
-    iPvs (step_lam _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iPvs (step_rec _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
     asimpl. iPvsIntro; by iFrame.
     Unshelve.
     all: try match goal with |- to_val _ = _ => auto using to_of_val end.

F_mu_ref_par/examples/stack/CG_stack.v

@@ -7,17 +7,17 @@ Definition CG_StackType τ :=
 
 (* Coarse-grained push *)
 Definition CG_push (st : expr) : expr :=
-  Lam (Store
+  Rec (Store
          (st.[ren (+2)]) (Fold (InjR (Pair (Var 1) (Load st.[ren (+ 2)]))))).
 
 Definition CG_locked_push (st l : expr) := with_lock (CG_push st) l.
 Definition CG_locked_pushV (st l : expr) : val := with_lockV (CG_push st) l.
 
 Definition CG_pop (st : expr) : expr :=
-  Lam (Case (Unfold (Load st.[ren (+ 2)]))
+  Rec (Case (Unfold (Load st.[ren (+ 2)]))
             (InjL Unit)
             (
-              App (Lam (InjR (Fst (Var 2))))
+              App (Rec (InjR (Fst (Var 2))))
                   (Store st.[ren (+ 3)] (Snd (Var 0)))
             )
       ).
@@ -25,35 +25,35 @@ Definition CG_pop (st : expr) : expr :=
 Definition CG_locked_pop (st l : expr) := with_lock (CG_pop st) l.
 Definition CG_locked_popV (st l : expr) : val := with_lockV (CG_pop st) l.
 
-Definition CG_snap (st l : expr) :=  with_lock (Lam (Load st.[ren (+2)])) l.
-Definition CG_snapV (st l : expr) : val := with_lockV (Lam (Load st.[ren (+2)])) l.
+Definition CG_snap (st l : expr) :=  with_lock (Rec (Load st.[ren (+2)])) l.
+Definition CG_snapV (st l : expr) : val := with_lockV (Rec (Load st.[ren (+2)])) l.
 
 Definition CG_iter (f : expr) : expr :=
-  Lam (Case (Unfold (Var 1))
+  Rec (Case (Unfold (Var 1))
             Unit
             (
-              App (Lam (App (Var 3) (Snd (Var 2))))
+              App (Rec (App (Var 3) (Snd (Var 2))))
                   (App f.[ren (+3)] (Fst (Var 0)))
             )
       ).
 
 Definition CG_iterV (f : expr) : val :=
-  LamV (Case (Unfold (Var 1))
+  RecV (Case (Unfold (Var 1))
             Unit
             (
-              App (Lam (App (Var 3) (Snd (Var 2))))
+              App (Rec (App (Var 3) (Snd (Var 2))))
                   (App f.[ren (+3)] (Fst (Var 0)))
             )
       ).
 
 Definition CG_snap_iter (st l : expr) : expr :=
-  Lam (App (CG_iter (Var 1)) (App (CG_snap st.[ren (+2)] l.[ren (+2)]) Unit)).
+  Rec (App (CG_iter (Var 1)) (App (CG_snap st.[ren (+2)] l.[ren (+2)]) Unit)).
 Definition CG_stack_body (st l : expr) : expr :=
   Pair (Pair (CG_locked_push st l) (CG_locked_pop st l))
        (CG_snap_iter st l).
 
 Definition CG_stack : expr :=
-  TLam (App (Lam (App (Lam (CG_stack_body (Var 1) (Var 3)))
+  TLam (App (Rec (App (Rec (CG_stack_body (Var 1) (Var 3)))
                 (Alloc (Fold (InjL Unit))))) newlock).
 
 Section CG_Stack.
@@ -82,7 +82,7 @@ Section CG_Stack.
     ={E}=> j ⤇ fill K Unit ★ st ↦ₛ FoldV (InjRV (PairV w v)).
   Proof.
     intros HNE. iIntros "[#Hspec [Hx Hj]]". unfold CG_push.
-    iPvs (step_lam _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iPvs (step_rec _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
     asimpl.
     iPvs (step_load _ _ j (K ++ [StoreRCtx (LocV _); FoldCtx;
                                    InjRCtx; PairRCtx _])
@@ -179,7 +179,7 @@ Section CG_Stack.
       ={E}=> j ⤇ fill K (InjR (# w)) ★ st ↦ₛ v.
   Proof.
     intros HNE. iIntros "[#Hspec [Hx Hj]]". unfold CG_pop.
-    iPvs (step_lam _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iPvs (step_rec _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
     asimpl.
     iPvs (step_load _ _ j (K ++ [CaseCtx _ _; UnfoldCtx])
                     _ _ _ with "[Hj Hx]") as "[Hj Hx]"; eauto.
@@ -193,16 +193,16 @@ Section CG_Stack.
     rewrite ?fill_app. simpl.
     iPvs (step_case_inr _ _ j K _ _ _ _ _ with "[Hj]") as "Hj"; eauto.
     asimpl.
-    iPvs (step_snd _ _ j (K ++ [AppRCtx (LamV _); StoreRCtx (LocV _)]) _ _ _ _
+    iPvs (step_snd _ _ j (K ++ [AppRCtx (RecV _); StoreRCtx (LocV _)]) _ _ _ _
                    _ _ with "[Hj]") as "Hj"; eauto.
     rewrite ?fill_app. simpl.
     iFrame "Hspec Hj"; trivial.
-    iPvs (step_store _ _ j (K ++ [AppRCtx (LamV _)]) _ _ _ _ _ _
+    iPvs (step_store _ _ j (K ++ [AppRCtx (RecV _)]) _ _ _ _ _ _
           with "[Hj Hx]") as "[Hj Hx]"; eauto.
     rewrite ?fill_app. simpl.
     iFrame "Hspec Hj"; trivial.
     rewrite ?fill_app. simpl.
-    iPvs (step_lam _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iPvs (step_rec _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
     asimpl.
     iPvs (step_fst _ _ j (K ++ [InjRCtx]) _ _ _ _ _ _
           with "[Hj]") as "Hj"; eauto.
@@ -222,7 +222,7 @@ Section CG_Stack.
       ={E}=> j ⤇ fill K (InjL Unit) ★ st ↦ₛ FoldV (InjLV UnitV).
   Proof.
     iIntros {HNE} "[#Hspec [Hx Hj]]". unfold CG_pop.
-    iPvs (step_lam _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iPvs (step_rec _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
     asimpl.
     iPvs (step_load _ _ j (K ++ [CaseCtx _ _; UnfoldCtx])
                     _ _ _ with "[Hj Hx]") as "[Hj Hx]"; eauto.
@@ -348,7 +348,7 @@ Section CG_Stack.
     iPvs (steps_with_lock _ _ j K _ _ _ _ v UnitV _ _
           with "[Hj Hx Hl]") as "Hj"; last done; [|by iFrame "Hspec Hx Hl Hj"].
     iIntros {K'} "[#Hspec [Hx Hj]]".
-    iPvs (step_lam _ _ j K' _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iPvs (step_rec _ _ j K' _ _ _ _ with "[Hj]") as "Hj"; eauto.
     asimpl.
     iPvs (step_load _ _ j K' _ _ _ _
           with "[Hj Hx]") as "[Hj Hx]"; eauto.
@@ -364,10 +364,10 @@ Section CG_Stack.
   (* Coarse-grained iter *)
   Lemma CG_iter_folding (f : expr) :
     CG_iter f =
-    Lam (Case (Unfold (Var 1))
+    Rec (Case (Unfold (Var 1))
               Unit
               (
-                App (Lam (App (Var 3) (Snd (Var 2))))
+                App (Rec (App (Var 3) (Snd (Var 2))))
                     (App f.[ren (+3)] (Fst (Var 0)))
               )
         ).
@@ -410,13 +410,13 @@ Section CG_Stack.
       ={E}=>
     j ⤇ fill K
           (App
-             (Lam
+             (Rec
                 (App ((CG_iter (# f)).[ren (+2)])
                      (Snd (Pair ((# w).[ren (+2)]) (# v).[ren (+2)]))))
              (App (# f) (# w))).
   Proof.
     iIntros {HNE} "[#Hspec Hj]". unfold CG_iter.
-    iPvs (step_lam _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iPvs (step_rec _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
     rewrite -CG_iter_folding. Opaque CG_iter. asimpl.
     iPvs (step_Fold _ _ j (K ++ [CaseCtx _ _])
                     _ _ _ with "[Hj]") as "Hj"; eauto.
@@ -425,7 +425,7 @@ Section CG_Stack.
     rewrite ?fill_app. asimpl.
     iPvs (step_case_inr _ _ j K _ _ _ _ _ with "[Hj]") as "Hj"; eauto.
     asimpl.
-    iPvs (step_fst _ _ j (K ++ [AppRCtx (LamV _); AppRCtx f]) _ _ _ _
+    iPvs (step_fst _ _ j (K ++ [AppRCtx (RecV _); AppRCtx f]) _ _ _ _
                    _ _ with "[Hj]") as "Hj"; eauto.
     rewrite ?fill_app /=.
     iFrame "Hspec Hj"; trivial.
@@ -443,7 +443,7 @@ Section CG_Stack.
       ={E}=> j ⤇ fill K Unit.
   Proof.
     iIntros {HNE} "[#Hspec Hj]". unfold CG_iter.
-    iPvs (step_lam _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
+    iPvs (step_rec _ _ j K _ _ _ _ with "[Hj]") as "Hj"; eauto.
     rewrite -CG_iter_folding. Opaque CG_iter. asimpl.
     iPvs (step_Fold _ _ j (K ++ [CaseCtx _ _])
                     _ _ _ with "[Hj]") as "Hj"; eauto.
@@ -509,7 +509,7 @@ Section CG_Stack.
   Qed.
 
   Lemma CG_stack_type Γ :
-    typed Γ (CG_stack)
+    typed Γ CG_stack
           (TForall
              (TProd
                 (TProd

F_mu_ref_par/examples/stack/FG_stack.v

@@ -4,7 +4,7 @@ Definition FG_StackType τ :=
   TRec (Tref (TSum TUnit (TProd τ.[ren (+1)] (TVar 0)))).
 
 Definition FG_push (st : expr) : expr :=
-  Lam (App (Lam
+  Rec (App (Rec
               (* try push *)
               (If (CAS (st.[ren (+4)]) (Var 1)
                        (Fold (Alloc (InjR (Pair (Var 3) (Var 1)))))
@@ -16,7 +16,7 @@ Definition FG_push (st : expr) : expr :=
            (Load st.[ren (+2)]) (* read the stack pointer *)
       ).
 Definition FG_pushV (st : expr) : val :=
-  LamV (App (Lam
+  RecV (App (Rec
               (* try push *)
               (If (CAS (st.[ren (+4)]) (Var 1)
                        (Fold (Alloc (InjR (Pair (Var 3) (Var 1)))))
@@ -29,9 +29,9 @@ Definition FG_pushV (st : expr) : val :=
        ).
 
 Definition FG_pop (st : expr) : expr :=
-  Lam (App (Lam
+  Rec (App (Rec
               (App
-                 (Lam
+                 (Rec
                     (
                       Case (Var 1)
                            (InjL Unit)
@@ -55,11 +55,11 @@ Definition FG_pop (st : expr) : expr :=
            (Unfold (Load st.[ren (+ 2)]))
       ).
 Definition FG_popV (st : expr) : val :=
-  LamV
+  RecV
     (App
-       (Lam
+       (Rec
           ( App
-              (Lam
+              (Rec
                  (
                    Case (Var 1)
                         (InjL Unit)
@@ -84,36 +84,36 @@ Definition FG_popV (st : expr) : val :=
     ).
 
 Definition FG_iter (f : expr) : expr :=
-  Lam
+  Rec
     (Case (Load (Unfold (Var 1)))
           Unit
-          (App (Lam (App (Var 3) (Snd (Var 2)))) (* recursive_call *)
+          (App (Rec (App (Var 3) (Snd (Var 2)))) (* recursive_call *)
                (App f.[ren (+3)] (Fst (Var 0)))
           )
     ).
 Definition FG_iterV (f : expr) : val :=
-  LamV
+  RecV
     (Case (Load (Unfold (Var 1)))
           Unit
-          (App (Lam (App (Var 3) (Snd (Var 2)))) (* recursive_call *)
+          (App (Rec (App (Var 3) (Snd (Var 2)))) (* recursive_call *)
                (App f.[ren (+3)] (Fst (Var 0)))
           )
     ).
 Definition FG_read_iter (st : expr) : expr :=
-  Lam (App (FG_iter (Var 1)) (Load st.[ren (+2)])).
+  Rec (App (FG_iter (Var 1)) (Load st.[ren (+2)])).