Put the locations into the type of literals

theories/F_mu_ref_conc/lang.v

@@ -16,14 +16,15 @@ Module lang.
   Instance binop_dec_eq (op op' : binop) : Decision (op = op').
   Proof. solve_decision. Defined.
 
-  Inductive Literal := Unit | Nat (n : nat) | Bool (b : bool).
+  Inductive literal := Unit | Nat (n : nat) | Bool (b : bool) | Loc (l : loc).
+
   Inductive expr :=
   | Var (x : string)
   (* λ-rec *)
   | Rec (f x : binder) (e : expr)
   | App (e1 e2 : expr)
   (* Constants *)
-  | Lit (l : Literal)
+  | Lit (l : literal)
   | BinOp (op : binop) (e1 e2 : expr)
   (* If then else *)
   | If (e0 e1 e2 : expr)
@@ -47,7 +48,6 @@ Module lang.
   (* Concurrency *)
   | Fork (e : expr)
   (* Reference Types *)
-  | Loc (l : loc) (* Should not be present in the surface syntax *)
   | Alloc (e : expr)
   | Load (e : expr)
   | Store (e1 : expr) (e2 : expr)
@@ -58,8 +58,9 @@ Module lang.
   (* Notation for bool and nat *)
   Notation "#♭ b" := (Lit (Bool b)) (at level 20).
   Notation "#n n" := (Lit (Nat n)) (at level 20).
+  Notation "#l l" := (Lit (Loc l)) (at level 20).
   
-  Instance literal_dec_eq (l l' : Literal) : Decision (l = l').
+  Instance literal_dec_eq (l l' : literal) : Decision (l = l').
   Proof. solve_decision. Defined.
 
   Instance expr_dec_eq (e e' : expr) : Decision (e = e').
@@ -70,7 +71,7 @@ Module lang.
     match e with
     | Var x => bool_decide (x ∈ X)
     | Rec f x e => is_closed (x :b: f :b: X) e
-    | Lit _ | Loc _  => true
+    | Lit _ => true
     | Fst e | Snd e | InjL e | InjR e | Fork e | Alloc e | Load e | Fold e | Unfold e | TLam e | TApp e | Pack e => 
       is_closed X e
     | App e1 e2 | BinOp _ e1 e2 | Pair e1 e2 | Store e1 e2 =>
@@ -98,13 +99,12 @@ Module lang.
   Inductive val :=
   | RecV (f x : binder) (e : expr) `{!Closed (x :b: f :b: ∅) e}
   | TLamV (e : expr) `{!Closed ∅ e} (* only closed lambdas are values *)
-  | LitV (l : Literal)
+  | LitV (l : literal)
   | PairV (v1 v2 : val)
   | InjLV (v : val)
   | InjRV (v : val)
   | FoldV (v : val)
-  | PackV (v : val)
-  | LocV (l : loc).
+  | PackV (v : val).
   Bind Scope val_scope with val.
 
   (* Notation for bool and nat *)
@@ -134,7 +134,6 @@ Module lang.
     | InjRV v => InjR (of_val v)
     | FoldV v => Fold (of_val v)
     | PackV v => Pack (of_val v)
-    | LocV l => Loc l
     end.
 
   Fixpoint to_val (e : expr) : option val :=
@@ -153,7 +152,6 @@ Module lang.
     | InjR e => InjRV <$> to_val e
     | Fold e => v ← to_val e; Some (FoldV v)
     | Pack e => v ← to_val e; Some (PackV v)
-    | Loc l => Some (LocV l)
     | _ => None
     end.
 
@@ -241,7 +239,6 @@ Module lang.
     | TLam e => TLam (subst x es e)
     | TApp e => TApp (subst x es e)
     | Lit l => Lit l
-    | Loc l => Loc l
     | BinOp op e1 e2 => BinOp op (subst x es e1) (subst x es e2)
     | If e0 e1 e2 => If (subst x es e0) (subst x es e1) (subst x es e2)
     | Pair e1 e2 => Pair (subst x es e1) (subst x es e2)
@@ -325,22 +322,22 @@ Module lang.
   (* Reference Types *)
   | AllocS e v σ l :
      to_val e = Some v → σ !! l = None →
-     head_step (Alloc e) σ (Loc l) (<[l:=v]>σ) []
+     head_step (Alloc e) σ (Lit (Loc l)) (<[l:=v]>σ) []
   | LoadS l v σ :
      σ !! l = Some v →
-     head_step (Load (Loc l)) σ (of_val v) σ []
+     head_step (Load (Lit (Loc l))) σ (of_val v) σ []
   | StoreS l e v σ :
      to_val e = Some v → is_Some (σ !! l) →
-     head_step (Store (Loc l) e) σ (Lit Unit) (<[l:=v]>σ) []
+     head_step (Store (Lit (Loc l)) e) σ (Lit Unit) (<[l:=v]>σ) []
   (* Compare and swap *)
   | CasFailS l e1 v1 e2 v2 vl σ :
      to_val e1 = Some v1 → to_val e2 = Some v2 →
      σ !! l = Some vl → vl ≠ v1 →
-     head_step (CAS (Loc l) e1 e2) σ (#♭ false) σ []
+     head_step (CAS (Lit (Loc l)) e1 e2) σ (#♭ false) σ []
   | CasSucS l e1 v1 e2 v2 σ :
      to_val e1 = Some v1 → to_val e2 = Some v2 →
      σ !! l = Some v1 →
-     head_step (CAS (Loc l) e1 e2) σ (#♭ true) (<[l:=v2]>σ) [].
+     head_step (CAS (Lit (Loc l)) e1 e2) σ (#♭ true) (<[l:=v2]>σ) [].
 
   Definition is_atomic (e : expr) : Prop :=
     match e with
@@ -383,7 +380,7 @@ Module lang.
 
   Lemma alloc_fresh e v σ :
     let l := fresh (dom _ σ) in
-    to_val e = Some v → head_step (Alloc e) σ (Loc l) (<[l:=v]>σ) [].
+    to_val e = Some v → head_step (Alloc e) σ (Lit (Loc l)) (<[l:=v]>σ) [].
   Proof. by intros; apply AllocS, (not_elem_of_dom (D:=gset _)), is_fresh. Qed.
 End lang.
 

theories/F_mu_ref_conc/notation.v

@@ -9,11 +9,16 @@ Coercion App : expr >-> Funclass.
 Coercion Var : string >-> expr.
 Coercion of_val : val >-> expr.
 
-Coercion Nat : nat >-> Literal.
-Coercion Bool : bool >-> Literal.
+Coercion Nat : nat >-> literal.
+Coercion Bool : bool >-> literal.
+Coercion Loc : loc >-> literal.
 Notation "'tt'" := lang.Unit.
-Coercion litunit (z : ()) : Literal := Unit.
-Coercion Lit : Literal >-> expr.
+Notation "()" := lang.Unit : val_scope.
+
+(* No scope for the values, does not conflict and scope is often not inferred
+properly. *)
+Notation "# l" := (LitV l%V) (at level 8, format "# l").
+Notation "# l" := (Lit l%V) (at level 8, format "# l") : expr_scope.
 
 Coercion BNamed : string >-> binder.
 Notation "<>" := BAnon : binder_scope.
@@ -21,11 +26,6 @@ Notation "<>" := BAnon : binder_scope.
 Notation Lam x e := (Rec BAnon x e).
 Notation LamV x e := (RecV BAnon x e).
 
-(* No scope for the values, does not conflict and scope is often not inferred
-properly. *)
-Notation "# l" := (LocV l%Z%V) (at level 8, format "# l").
-Notation "# l" := (Loc l%Z%V) (at level 8, format "# l") : expr_scope.
-
 (** Syntax inspired by Coq/Ocaml. Constructions with higher precedence come
     first. *)
 Notation "( e1 , e2 , .. , en )" := (Pair .. (Pair e1 e2) .. en) : expr_scope.

theories/F_mu_ref_conc/pureexec.v

@@ -89,7 +89,7 @@ split; intros ?.
 Qed.
 
 Instance pure_if_true e1 e2 :
-  PureExec True (If true e1 e2) e1.
+  PureExec True (If #true e1 e2) e1.
 Proof.
 split; intros ?.
 - intros. do 3 eexists. econstructor; eauto using to_of_val.
@@ -97,7 +97,7 @@ split; intros ?.
 Qed.
 
 Instance pure_if_false e1 e2 :
-  PureExec True (If false e1 e2) e2.
+  PureExec True (If #false e1 e2) e2.
 Proof.
 split; intros ?.
 - intros. do 3 eexists. econstructor; eauto using to_of_val.

theories/F_mu_ref_conc/reflection.v

@@ -10,7 +10,7 @@ Inductive expr :=
   | Rec (f x : binder) (e : expr)
   | App (e1 e2 : expr)
   (* Base Types *)
-  | Lit (l : Literal)
+  | Lit (l : literal)
   | BinOp (op : binop) (e1 e2 : expr)
   (* If then else *)
   | If (e0 e1 e2 : expr)
@@ -34,7 +34,6 @@ Inductive expr :=
   (* Concurrency *)
   | Fork (e : expr)
   (* Reference Types *)
-  | Loc (l : loc)
   | Alloc (e : expr)
   | Load (e : expr)
   | Store (e1 : expr) (e2 : expr)
@@ -49,7 +48,6 @@ Fixpoint to_expr (e : expr) : lang.expr :=
   | Rec f x e => lang.Rec f x (to_expr e)
   | App e1 e2 => lang.App (to_expr e1) (to_expr e2)
   | Lit l => lang.Lit l
-  | Loc l => lang.Loc l
   | BinOp op e1 e2 => lang.BinOp op (to_expr e1) (to_expr e2)
   | If e0 e1 e2 => lang.If (to_expr e0) (to_expr e1) (to_expr e2)
   | Pair e1 e2 => lang.Pair (to_expr e1) (to_expr e2)
@@ -78,7 +76,6 @@ Ltac of_expr e :=
   | lang.App ?e1 ?e2 =>
      let e1 := of_expr e1 in let e2 := of_expr e2 in constr:(App e1 e2)
   | lang.Lit ?l => constr:(Lit l)
-  | lang.Loc ?l => constr:(Loc l)
   | lang.BinOp ?op ?e1 ?e2 =>
      let e1 := of_expr e1 in let e2 := of_expr e2 in constr:(BinOp op e1 e2)
   | lang.If ?e0 ?e1 ?e2 =>
@@ -125,7 +122,6 @@ Fixpoint is_closed (X : stringset) (e : expr) : bool :=
   | ClosedExpr e _ => true
   | Var x => bool_decide (x ∈ X)
   | Lit l => true
-  | Loc l => true
   | Rec f x e => is_closed (x :b: f :b: X) e
   | App e1 e2 | BinOp _ e1 e2 | Pair e1 e2 | Store e1 e2 | Unpack e1 e2 =>
     is_closed X e1 && is_closed X e2
@@ -147,7 +143,6 @@ Fixpoint subst (x : string) (es : expr) (e : expr)  : expr :=
   | TLam e => TLam (subst x es e)
   | TApp e => TApp (subst x es e)
   | Lit l => Lit l
-  | Loc l => Loc l
   | BinOp op e1 e2 => BinOp op (subst x es e1) (subst x es e2)
   | If e0 e1 e2 => If (subst x es e0) (subst x es e1) (subst x es e2)
   | Pair e1 e2 => Pair (subst x es e1) (subst x es e2)
@@ -193,7 +188,6 @@ Fixpoint to_val (e : expr) : option val :=
      if decide (is_closed ∅ e) is left H
      then Some (@TLamV (to_expr e) (is_closed_correct _ _ H)) else None
   | Lit l => Some (LitV l)
-  | Loc l => Some (LocV l)
   | Pair e1 e2 => v1 ← to_val e1; v2 ← to_val e2; Some (PairV v1 v2)
   | InjL e => InjLV <$> to_val e
   | InjR e => InjRV <$> to_val e

theories/F_mu_ref_conc/rules.v

@@ -40,7 +40,7 @@ Section lang_rules.
   (** Base axioms for core primitives of the language: Stateful reductions. *)
   Lemma wp_alloc E e v :
     to_val e = Some v →
-    {{{ True }}} Alloc e @ E {{{ l, RET (LocV l); l ↦ᵢ v }}}.
+    {{{ True }}} Alloc e @ E {{{ l, RET (LitV (Loc l))%E; l ↦ᵢ v }}}.
   Proof.
     iIntros (<-%of_to_val Φ) "HΦ". iApply wp_lift_atomic_head_step_no_fork; auto.
     iIntros (σ1) "Hσ !>"; iSplit; first by auto.
@@ -50,7 +50,7 @@ Section lang_rules.
   Qed.
 
   Lemma wp_load E l q v :
-  {{{ ▷ l ↦ᵢ{q} v }}} Load (Loc l) @ E {{{ RET v; l ↦ᵢ{q} v }}}.
+  {{{ ▷ l ↦ᵢ{q} v }}} (! # l)%E @ E {{{ RET v; l ↦ᵢ{q} v }}}.
   Proof.
     iIntros (Φ) ">Hl HΦ". iApply wp_lift_atomic_head_step_no_fork; auto.
     iIntros (σ1) "Hσ !>". iDestruct (@gen_heap_valid with "Hσ Hl") as %?.
@@ -61,7 +61,7 @@ Section lang_rules.
   
   Lemma wp_store E l v' e v :
     to_val e = Some v →
-    {{{ ▷ l ↦ᵢ v' }}} Store (Loc l) e @ E
+    {{{ ▷ l ↦ᵢ v' }}} # l <- e @ E
     {{{ RET (LitV tt); l ↦ᵢ v }}}.
   Proof.
     iIntros (<-%of_to_val Φ) ">Hl HΦ".
@@ -74,7 +74,7 @@ Section lang_rules.
 
   Lemma wp_cas_fail E l q v' e1 v1 e2 v2 :
     to_val e1 = Some v1 → to_val e2 = Some v2 → v' ≠ v1 →
-    {{{ ▷ l ↦ᵢ{q} v' }}} CAS (Loc l) e1 e2 @ E
+    {{{ ▷ l ↦ᵢ{q} v' }}} CAS (# l) e1 e2 @ E
     {{{ RET (LitV false); l ↦ᵢ{q} v' }}}.
   Proof.
     iIntros (<-%of_to_val <-%of_to_val ? Φ) ">Hl HΦ".
@@ -87,7 +87,7 @@ Section lang_rules.
 
   Lemma wp_cas_suc E l e1 v1 e2 v2 :
     to_val e1 = Some v1 → to_val e2 = Some v2 →
-    {{{ ▷ l ↦ᵢ v1 }}} CAS (Loc l) e1 e2 @ E
+    {{{ ▷ l ↦ᵢ v1 }}} CAS (# l) e1 e2 @ E
     {{{ RET (LitV true); l ↦ᵢ v2 }}}.
   Proof.
     iIntros (<-%of_to_val <-%of_to_val Φ) ">Hl HΦ".
@@ -177,21 +177,21 @@ Section lang_rules.
   Lemma wp_fork E e Φ :
     ▷ (|={E}=> Φ (LitV tt)) ∗ ▷ WP e {{ _, True }} ⊢ WP Fork e @ E {{ Φ }}.
   Proof.
-  rewrite -(wp_lift_pure_det_head_step (Fork e) tt [e]) //=; eauto.
+  rewrite -(wp_lift_pure_det_head_step (Fork e) #tt [e]) //=; eauto.
   - rewrite -(wp_value_fupd _ _ (Lit tt)); auto.
     by rewrite -step_fupd_intro // right_id later_sep. 
   - intros; inv_head_step; eauto.
   Qed.
 
   Lemma wp_if_true E e1 e2 Φ :
-    ▷ WP e1 @ E {{ Φ }} ⊢ WP If true e1 e2 @ E {{ Φ }}.
+    ▷ WP e1 @ E {{ Φ }} ⊢ WP If #true e1 e2 @ E {{ Φ }}.
   Proof.
     rewrite -(wp_lift_pure_det_head_step_no_fork (If _ _ _) e1); eauto.
     intros; inv_head_step; eauto.
   Qed.
 
   Lemma wp_if_false E e1 e2 Φ :
-    ▷ WP e2 @ E {{ Φ }} ⊢ WP If false e1 e2 @ E {{ Φ }}.
+    ▷ WP e2 @ E {{ Φ }} ⊢ WP If #false e1 e2 @ E {{ Φ }}.
   Proof.
     rewrite -(wp_lift_pure_det_head_step_no_fork (If _ _ _) e2); eauto.
     intros; inv_head_step; eauto.

theories/F_mu_ref_conc/subst.v

@@ -18,7 +18,6 @@ Fixpoint subst_p (es : stringmap val) (e : expr) : expr :=
   | TLam e => TLam (subst_p es e)
   | TApp e => TApp (subst_p es e)
   | Lit l => Lit l
-  | Loc l => Loc l
   | BinOp op e1 e2 => BinOp op (subst_p es e1) (subst_p es e2)
   | If e0 e1 e2 => If (subst_p es e0) (subst_p es e1) (subst_p es e2)
   | Pair e1 e2 => Pair (subst_p es e1) (subst_p es e2)

theories/F_mu_ref_conc/tactics.v

@@ -21,7 +21,6 @@ Ltac reshape_val e tac :=
   | InjR ?e => let v := go e in constr:(InjRV v)
   | Fold ?e => let v := go e in constr:(FoldV v)
   | Pack ?e => let v := go e in constr:(PackV v)
-  | Loc ?l => constr:(LocV l)
   end in let v := go e in tac v.
 
 Ltac reshape_expr e tac :=

theories/F_mu_ref_conc/typing.v

@@ -44,9 +44,9 @@ Reserved Notation "Γ ⊢ₜ e : τ" (at level 74, e, τ at next level).
 
 Inductive typed (Γ : stringmap type) : expr → type → Prop :=
   | Var_typed x τ : Γ !! x = Some τ → Γ ⊢ₜ Var x : τ
-  | Unit_typed : Γ ⊢ₜ tt : TUnit
-  | Nat_typed n : Γ ⊢ₜ #n n : TNat
-  | Bool_typed b : Γ ⊢ₜ #♭ b : TBool
+  | Unit_typed : Γ ⊢ₜ #tt : TUnit
+  | Nat_typed (n : nat) : Γ ⊢ₜ #n n : TNat
+  | Bool_typed (b : bool) : Γ ⊢ₜ #♭ b : TBool
   | BinOp_typed_nat op e1 e2 τ :      
      Γ ⊢ₜ e1 : TNat → Γ ⊢ₜ e2 : TNat → 
      binop_nat_res_type op = Some τ →

theories/examples/bit.v

@@ -9,14 +9,14 @@ Definition bitτ : type :=
 Hint Unfold bitτ : typeable.
 
 Definition bit_bool : val :=
-  PackV ((λ: "b", "b"), (λ: "b", "b" ⊕ true), #♭v true).
+  PackV ((λ: "b", "b"), (λ: "b", "b" ⊕ #true), #true).
 
 Definition flip_nat : val := λ: "n",
-  if: "n" = 0
-  then 1
-  else 0.
+  if: "n" = #0
+  then #1
+  else #0.
 Definition bit_nat : val :=
-  PackV ((λ: "b", "b" = 0), flip_nat, #nv 0).
+  PackV ((λ: "b", "b" = #0), flip_nat, #0).
 
 (** * Typeability *)
 (** ** Boolean bit *)
@@ -106,7 +106,7 @@ Definition heapify : val := λ: "b", Unpack "b" $ λ: "b'",
   let: "x" := ref "init" in
   let: "flip_ref" := λ: <>, "x" <- "flip" (!"x") in
   let: "view_ref" := λ: <>, "view" (!"x") in
-  Pack ("view_ref", "flip_ref", ()).
+  Pack ("view_ref", "flip_ref", #()).
 
 Lemma heapify_type Γ :
   typed Γ heapify (TArrow bitτ bitτ).
@@ -200,7 +200,7 @@ Section heapify_refinement.
       tp_store j.
       iMod ("Hcl" with "[-Hj]").
       { iNext. iExists (_,_). by iFrame. }
-      iModIntro. iExists (LitV ()); iFrame "Hj". eauto.
+      iModIntro. iExists (#()); iFrame "Hj". eauto.
     - rel_vals; simpl; eauto.
   Qed.
 

theories/examples/counter.v

@@ -4,24 +4,24 @@ From iris_logrel.examples Require Import lock.
 
 Definition CG_increment : val := λ: "x" "l" <>,
   acquire "l";;
-  "x" <- 1 + !"x";;
+  "x" <- #1 + !"x";;
   release "l".
 
 Definition counter_read : val := λ: "x" <>, !"x".
 
 Definition CG_counter : val := λ: <>,
-  let: "l" := newlock () in
-  let: "x" := ref 0 in
+  let: "l" := newlock #() in
+  let: "x" := ref #0 in
   (CG_increment "x" "l", counter_read "x").
 
 Definition FG_increment : val := λ: "v", rec: "inc" <> :=
   let: "c" := !"v" in
-  if: CAS "v" "c" (1 + "c")
-  then ()
-  else "inc" ().
+  if: CAS "v" "c" (#1 + "c")
+  then #()
+  else "inc" #().
 
 Definition FG_counter : val := λ: <>,
-  let: "x" := ref 0 in
+  let: "x" := ref #0 in
   (FG_increment "x", counter_read "x").
 
 Section CG_Counter.
@@ -36,12 +36,12 @@ Section CG_Counter.
 
   Hint Resolve CG_increment_type : typeable.
 
-  Lemma bin_log_related_CG_increment_r Γ K E1 E2 t τ x (n : nat) l :
+  Lemma bin_log_related_CG_increment_r Γ K E1 E2 t τ (x l : loc) (n : nat) :
     nclose specN ⊆ E1 →
     (x ↦ₛ (#nv n) -∗ l ↦ₛ (#♭v false) -∗
     (x ↦ₛ (#nv S n) -∗ l ↦ₛ (#♭v false) -∗
-      ({E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (Lit ()) : τ)) -∗
-    {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K ((CG_increment $/ LocV x $/ LocV l) ())%E : τ)%I.
+      ({E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (Lit tt) : τ)) -∗
+    {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K ((CG_increment $/ (LitV (Loc x)) $/ LitV (Loc l)) #())%E : τ)%I.
   Proof.
     iIntros (?) "Hx Hl Hlog".
     unfold CG_increment. unlock. simpl_subst/=.
@@ -78,8 +78,8 @@ Section CG_Counter.
 
   Lemma bin_log_FG_increment_l Γ K E x n t τ :
     x ↦ᵢ (#nv n) -∗
-    (x ↦ᵢ (#nv (S n)) -∗ {E,E;Δ;Γ} ⊨ fill K (Lit ()) ≤log≤ t : τ) -∗
-    {E,E;Δ;Γ} ⊨ fill K (FG_increment #x ()) ≤log≤ t : τ.
+    (x ↦ᵢ (#nv (S n)) -∗ {E,E;Δ;Γ} ⊨ fill K (Lit tt) ≤log≤ t : τ) -∗
+    {E,E;Δ;Γ} ⊨ fill K (FG_increment #x #()) ≤log≤ t : τ.
   Proof.
     iIntros "Hx Hlog".
     iApply bin_log_related_wp_l.
@@ -90,7 +90,7 @@ Section CG_Counter.
     iApply wp_value; eauto. simpl. by rewrite decide_left.
     iApply wp_rec; eauto.
     iNext. simpl.
-    wp_bind (Load (Loc x)).
+    wp_bind (Load (# x)).
     iApply (wp_load with "[Hx]"); auto. iNext.
     iIntros "Hx".
     iApply wp_rec; eauto.
@@ -121,7 +121,7 @@ Section CG_Counter.
     x ↦ₛ (#nv n)
     -∗ (x ↦ₛ (#nv n)
          -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (#n n)%E : τ)%I
-    -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K ((counter_read $/ LocV x) ())%E : τ.
+    -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K ((counter_read $/ LitV (Loc x)) #())%E : τ.
   Proof.
     iIntros "Hx Hlog".
     unfold counter_read. unlock. simpl.
@@ -137,8 +137,8 @@ Section CG_Counter.
     □ (|={E1,E2}=> ∃ n, x ↦ᵢ (#nv n) ∗ R(n) ∗
        ((∃ n, x ↦ᵢ (#nv n) ∗ R(n)) ={E2,E1}=∗ True) ∧
         (∀ m, x ↦ᵢ (#nv (S m)) ∗ R(m) -∗ 
-            {E2,E1;Δ;Γ} ⊨ fill K (Lit ()) ≤log≤ t : τ))
-    -∗ ({E1,E1;Δ;Γ} ⊨ fill K ((FG_increment $/ LocV x) ())%E ≤log≤ t : τ).
+            {E2,E1;Δ;Γ} ⊨ fill K (Lit tt) ≤log≤ t : τ))
+    -∗ ({E1,E1;Δ;Γ} ⊨ fill K ((FG_increment $/ LitV (Loc x)) #())%E ≤log≤ t : τ).
   Proof.
     iIntros "#H".
     unfold FG_increment. unlock. simpl.
@@ -180,7 +180,7 @@ Section CG_Counter.
        ((∃ n, x ↦ᵢ (#nv n) ∗ R(n)) ={E2,E1}=∗ True) ∧
         (∀ m, x ↦ᵢ (#nv m) ∗ R(m) -∗
             {E2,E1;Δ;Γ} ⊨ fill K (#n m) ≤log≤ t : τ))
-    -∗ {E1,E1;Δ;Γ} ⊨ fill K ((counter_read $/ LocV x) ())%E ≤log≤ t : τ.
+    -∗ {E1,E1;Δ;Γ} ⊨ fill K ((counter_read $/ LitV (Loc x)) #())%E ≤log≤ t : τ.
   Proof.
     iIntros "#H".
     unfold counter_read. unlock. simpl.
@@ -196,7 +196,7 @@ Section CG_Counter.
   (* TODO: try to use with_lock rules *)
   Lemma FG_CG_increment_refinement l cnt cnt' Γ :
     inv counterN (counter_inv l cnt cnt') -∗
-    {⊤,⊤;Δ;Γ} ⊨ FG_increment $/ LocV cnt ≤log≤ CG_increment $/ LocV cnt' $/ LocV l : TArrow TUnit TUnit.
+    {⊤,⊤;Δ;Γ} ⊨ FG_increment $/ LitV (Loc cnt) ≤log≤ CG_increment $/ LitV (Loc cnt') $/ LitV (Loc l) : TArrow TUnit TUnit.
   Proof.
     iIntros "#Hinv".
     iApply bin_log_related_arrow_val.
@@ -227,7 +227,7 @@ Section CG_Counter.
 
   Lemma counter_read_refinement l cnt cnt' Γ :
     inv counterN (counter_inv l cnt cnt') -∗
-    {⊤,⊤;Δ;Γ} ⊨ counter_read $/ LocV cnt ≤log≤ counter_read $/ LocV cnt' : TArrow TUnit TNat.
+    {⊤,⊤;Δ;Γ} ⊨ counter_read $/ LitV (Loc cnt) ≤log≤ counter_read $/ LitV (Loc cnt') : TArrow TUnit TNat.
   Proof.
     iIntros "#Hinv".
     iApply bin_log_related_arrow_val.
@@ -280,8 +280,8 @@ Section CG_Counter.
       unfold CG_increment. unlock.
       rel_rec_r.
       rel_rec_r.
-      replace (λ: <>, acquire #l ;; #cnt' <- 1 + (! #cnt');; release #l)%E
-        with (CG_increment $/ LocV cnt' $/ LocV l)%E; last first.
+      replace (λ: <>, acquire # l ;; #cnt' <- #1 + (! #cnt');; release # l)%E
+        with (CG_increment $/ LitV (Loc cnt') $/ LitV (Loc l))%E; last first.
       { unfold CG_increment. unlock; simpl_subst/=. reflexivity. }
       iApply (FG_CG_increment_refinement with "Hinv").
     - rel_rec_l.

theories/examples/lateearlychoice.v

@@ -2,14 +2,14 @@ From iris.proofmode Require Import tactics.
 From iris_logrel Require Export logrel.
 
 Definition rand : val := λ: <>,
-  let: "y" := ref false
-  in Fork ("y" <- true);;
+  let: "y" := ref #false
+  in Fork ("y" <- #true);;
      !"y".
 
 Definition lateChoice : val := λ: "x",
-  "x" <- 0;; rand ().
+  "x" <- #0;; rand #().
 Definition earlyChoice : val := λ: "x",
-  let: "r" := rand () in "x" <- 0;; "r".
+  let: "r" := rand #() in "x" <- #0;; "r".
 
 Section Refinement.
   Context `{logrelG Σ}.
@@ -20,7 +20,7 @@ Section Refinement.
     (∃ f, y ↦ᵢ (#♭v f) ∗ y' ↦ₛ (#♭v f))%I.
 
   Lemma wp_rand :
-    (WP rand () {{ v, ⌜v = #♭v true⌝ ∨ ⌜v = #♭v false⌝}})%I.
+    (WP rand #() {{ v, ⌜v = #♭v true⌝ ∨ ⌜v = #♭v false⌝}})%I.
   Proof.
     iStartProof.
     unfold rand. unlock.
@@ -40,7 +40,7 @@ Section Refinement.
   Lemma rand_l Δ Γ E1 K ρ t τ :
     ↑choiceN ⊆ E1 →
     spec_ctx ρ -∗ (∀ b, {E1,E1;Δ;Γ} ⊨ fill K (#♭ b) ≤log≤ t : τ)
-    -∗ {E1,E1;Δ;Γ} ⊨ fill K (rand ())%E ≤log≤ t : τ.
+    -∗ {E1,E1;Δ;Γ} ⊨ fill K (rand #())%E ≤log≤ t : τ.
   Proof.
     iIntros (?) "#Hs Hlog".
     unfold rand. unlock. simpl.
@@ -73,7 +73,7 @@ Section Refinement.
     ↑choiceN ⊆ E1 →
     spec_ctx ρ -∗
     {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (#♭ b) : τ -∗
-    {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (rand ())%E : τ.
+    {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (rand #())%E : τ.
   Proof.
     iIntros (??) "#Hs Hlog".
     unfold rand. unlock.

theories/examples/lock.v

 From iris.proofmode Require Import tactics.
 From iris_logrel Require Export logrel.
 
-Definition newlock : val := λ: <>, ref false.
+Definition newlock : val := λ: <>, ref #false.
 Definition acquire : val := rec: "acquire" "x" :=
-  if: CAS "x" false true
-  then ()
+  if: CAS "x" #false #true
+  then #()
   else "acquire" "x".
 
-Definition release : val := λ: "x", "x" <- false.
+Definition release : val := λ: "x", "x" <- #false.
 Definition with_lock : val := λ: "e" "l" "x",
   acquire "l";;
   let: "v" := "e" "x" in
@@ -45,8 +45,8 @@ Section proof.
 
   Lemma steps_newlock ρ j K
     (Hcl : nclose specN ⊆ E1) :
-    spec_ctx ρ -∗ j ⤇ fill K (newlock ())%E
-    ={E1}=∗ ∃ l, j ⤇ fill K (Loc l) ∗ l ↦ₛ (#♭v false).
+    spec_ctx ρ -∗ j ⤇ fill K (newlock #())%E
+    ={E1}=∗ ∃ l : loc, j ⤇ fill K (of_val (# l)) ∗ l ↦ₛ (#♭v false).
   Proof.
     iIntros "#Hspec Hj".
     unfold newlock. unlock.
@@ -57,8 +57,8 @@ Section proof.
 
   Lemma bin_log_related_newlock_r Γ K t τ 
     (Hcl : nclose specN ⊆ E1) :
-    (∀ l : loc, l ↦ₛ (#♭v false) -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (Loc l) : τ)%I
-    -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (newlock ())%E: τ.
+    (∀ l : loc, l ↦ₛ (#♭v false) -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (Lit (Loc l)) : τ)%I
+    -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (newlock #())%E: τ.
   Proof.
     iIntros "Hlog".
     unfold newlock. unlock.
@@ -72,13 +72,13 @@ Section proof.
   Transparent acquire. 
   Lemma steps_acquire ρ j K l
     (Hcl : nclose specN ⊆ E1) :
-    spec_ctx ρ -∗ l ↦ₛ (#♭v false) -∗ j ⤇ fill K (App acquire (Loc l))
+    spec_ctx ρ -∗ l ↦ₛ (#♭v false) -∗ j ⤇ fill K (App acquire (Lit (Loc l)))
     ={E1}=∗ j ⤇ fill K (Lit Unit) ∗ l ↦ₛ (#♭v true).
   Proof.
     iIntros "#Hspec Hl Hj". 
     unfold acquire. unlock.
     tp_rec j.
-    tp_cas_suc j. 
+    tp_cas_suc j. simpl.
     tp_if_true j.
     by iFrame.
   Qed.
@@ -87,7 +87,7 @@ Section proof.
     (Hcl : nclose specN ⊆ E1) :
     l ↦ₛ (#♭v false) -∗
     (l ↦ₛ (#♭v true) -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (Lit Unit) : τ)%I
-    -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (App acquire (Loc l)) : τ.
+    -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (App acquire (# l)) : τ.
   Proof.
     iIntros "Hl Hlog".
     unfold acquire. unlock.
@@ -102,7 +102,7 @@ Section proof.
   Transparent release.
   Lemma steps_release ρ j K l b
     (Hcl : nclose specN ⊆ E1) :
-    spec_ctx ρ -∗ l ↦ₛ (#♭v b) -∗ j ⤇ fill K (App release (Loc l))
+    spec_ctx ρ -∗ l ↦ₛ (#♭v b) -∗ j ⤇ fill K (App release (# l))
     ={E1}=∗ j ⤇ fill K (Lit Unit) ∗ l ↦ₛ (#♭v false).
   Proof.
     iIntros "#Hspec Hl Hj". unfold release. unlock.
@@ -115,7 +115,7 @@ Section proof.
     (Hcl : nclose specN ⊆ E1) :
     l ↦ₛ (#♭v b) -∗
     (l ↦ₛ (#♭v false) -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (Lit Unit) : τ)%I
-    -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (App release (Loc l)) : τ.
+    -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (App release (# l)) : τ.
   Proof.
     iIntros "Hl Hlog".
     unfold release. unlock.
@@ -132,7 +132,7 @@ Section proof.
             ={E1}=∗ j ⤇ fill K' (of_val v) ∗ Q) →
     (nclose specN ⊆ E1) →
     spec_ctx ρ -∗ P -∗ l ↦ₛ (#♭v false)
-    -∗ j ⤇ fill K (App (with_lock e (Loc l)) (of_val w))
+    -∗ j ⤇ fill K (App (with_lock e (# l)) (of_val w))
     ={E1}=∗ j ⤇ fill K (of_val v) ∗ Q ∗ l ↦ₛ (#♭v false).
   Proof.
     iIntros (Hev Hpf ?) "#Hspec HP Hl Hj".
@@ -140,7 +140,7 @@ Section proof.
     tp_rec j.
     tp_rec j.
     tp_rec j.
-    tp_bind j (App acquire (Loc l)).
+    tp_bind j (App acquire (# l)).
     tp_apply j steps_acquire with "Hl" as "Hl".
     tp_rec j.
     tp_bind j (App e _).
@@ -163,16 +163,16 @@ Section proof.
         {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (App e ew) : τ) -∗
     l ↦ₛ (#♭v false) -∗
     (Q -∗ l ↦ₛ (#♭v false) -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K ev : τ)%I
-    -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (with_lock e (Loc l) ew) : τ.
+    -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (with_lock e (# l) ew) : τ.
   Proof.
     iIntros (????) "HA Hl Hlog".
     rel_bind_r (with_lock e).
     unfold with_lock. unlock. (*TODO: unlock here needed *)
     iApply (bin_log_related_rec_r); eauto. simpl_subst.
-    rel_bind_r (App _ (#l)%E).
+    rel_bind_r (App _ (# l)).
     iApply (bin_log_related_rec_r); eauto. simpl_subst.
     iApply (bin_log_related_rec_r); eauto. simpl_subst.
-    rel_bind_r (App acquire (Loc l)).
+    rel_bind_r (App acquire (# l)).
     iApply (bin_log_related_acquire_r Γ (_ :: K) l with "Hl"); auto.
     iIntros "Hl". simpl.
     iApply (bin_log_related_rec_r); eauto. simpl_subst/=.

theories/examples/par.v

@@ -2,15 +2,15 @@ From iris.proofmode Require Import tactics.
 From iris_logrel Require Export logrel.