Fix notations for literals.

theories/F_mu_ref_conc/lang.v

@@ -55,11 +55,6 @@ Module lang.
   | CAS (e0 : expr) (e1 : expr) (e2 : expr).
   Bind Scope expr_scope with expr.
 
-  (* 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').
   Proof. solve_decision. Defined.
 
@@ -108,18 +103,15 @@ Module lang.
   Bind Scope val_scope with val.
 
   (* Notation for bool and nat *)
-  Notation "'#♭v' b" := (LitV (Bool b)) (at level 20).
-  Notation "'#nv' n" := (LitV (Nat n)) (at level 20).
-
   Fixpoint binop_eval (op : binop) (v1 v2 : val) : option val :=
     match op,v1,v2 with
-    | Add,#nv a,#nv b => Some $ #nv(a + b)
-    | Sub,#nv a,#nv b => Some $ #nv(a - b)
-    | Eq,#nv a,#nv b => Some $ if (eq_nat_dec a b) then #♭v true else #♭v false
-    | Eq,#♭v a,#♭v b => Some $ #♭v(eqb a b)
-    | Le,#nv a,#nv b => Some $ if (le_dec a b) then #♭v true else #♭v false
-    | Lt,#nv a,#nv b => Some $ if (lt_dec a b) then #♭v true else #♭v false
-    | Xor,#♭v a,#♭v b => Some $ #♭v(xorb a b)
+    | Add, LitV (Nat a), LitV (Nat b) => Some $ LitV (Nat (a + b))
+    | Sub, LitV (Nat a), LitV (Nat b) => Some $ LitV (Nat (a - b))
+    | Eq, LitV (Nat a), LitV (Nat b) => Some $ if eq_nat_dec a b then LitV (Bool true) else LitV (Bool false)
+    | Eq, LitV (Bool a), LitV (Bool b) => Some $ LitV (Bool (eqb a b))
+    | Le, LitV (Nat a), LitV (Nat b) => Some $ if le_dec a b then LitV (Bool true) else LitV (Bool false)
+    | Lt, LitV (Nat a), LitV (Nat b) => Some $ if lt_dec a b then LitV (Bool true) else LitV (Bool false)
+    | Xor, LitV (Bool a), LitV (Bool b) => Some $ LitV (Bool (xorb a b))
     | _,_,_ => None
     end.
   Instance val_inh : Inhabited val := populate (LitV Unit).
@@ -300,9 +292,9 @@ Module lang.
       head_step (BinOp op e1 e2) σ (of_val v) σ []
   (* If then else *)
   | IfFalse e1 e2 σ :
-      head_step (If (#♭ false) e1 e2) σ e2 σ []
+      head_step (If (Lit (Bool false)) e1 e2) σ e2 σ []
   | IfTrue e1 e2 σ :
-      head_step (If (#♭ true) e1 e2) σ e1 σ []
+      head_step (If (Lit (Bool true)) e1 e2) σ e1 σ []
   (* Recursive Types *)
   | Unfold_Fold e v σ :
       to_val e = Some v →
@@ -333,11 +325,11 @@ Module lang.
   | 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 (Lit (Loc l)) e1 e2) σ (#♭ false) σ []
+     head_step (CAS (Lit (Loc l)) e1 e2) σ (Lit (Bool 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 (Lit (Loc l)) e1 e2) σ (#♭ true) (<[l:=v2]>σ) [].
+     head_step (CAS (Lit (Loc l)) e1 e2) σ (Lit (Bool true)) (<[l:=v2]>σ) [].
 
   Definition is_atomic (e : expr) : Prop :=
     match e with

theories/F_mu_ref_conc/notation.v

@@ -12,7 +12,6 @@ Coercion of_val : val >-> expr.
 Coercion Nat : nat >-> literal.
 Coercion Bool : bool >-> literal.
 Coercion Loc : loc >-> literal.
-Notation "'tt'" := lang.Unit.
 Notation "()" := lang.Unit : val_scope.
 
 (* No scope for the values, does not conflict and scope is often not inferred

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 (LitV (Loc l))%E; l ↦ᵢ v }}}.
+    {{{ True }}} Alloc e @ E {{{ l, RET #l; 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 }}} (! # l)%E @ E {{{ RET v; l ↦ᵢ{q} v }}}.
+  {{{ ▷ l ↦ᵢ{q} v }}} ! #l @ 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 %?.
@@ -58,11 +58,11 @@ Section lang_rules.
     iNext; iIntros (v2 σ2 efs Hstep); inv_head_step.
     iModIntro; iSplit=> //. iFrame. by iApply "HΦ".
   Qed.
-  
+
   Lemma wp_store E l v' e v :
     to_val e = Some v →
-    {{{ ▷ l ↦ᵢ v' }}} # l <- e @ E
-    {{{ RET (LitV tt); l ↦ᵢ v }}}.
+    {{{ ▷ l ↦ᵢ v' }}} #l <- e @ E
+    {{{ RET #(); l ↦ᵢ v }}}.
   Proof.
     iIntros (<-%of_to_val Φ) ">Hl HΦ".
     iApply wp_lift_atomic_head_step_no_fork; auto.
@@ -74,8 +74,8 @@ 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 (# l) e1 e2 @ E
-    {{{ RET (LitV false); l ↦ᵢ{q} v' }}}.
+    {{{ ▷ l ↦ᵢ{q} v' }}} CAS #l e1 e2 @ E
+    {{{ RET #false; l ↦ᵢ{q} v' }}}.
   Proof.
     iIntros (<-%of_to_val <-%of_to_val ? Φ) ">Hl HΦ".
     iApply wp_lift_atomic_head_step_no_fork; auto.
@@ -87,8 +87,8 @@ 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 (# l) e1 e2 @ E
-    {{{ RET (LitV true); l ↦ᵢ v2 }}}.
+    {{{ ▷ l ↦ᵢ v1 }}} CAS #l e1 e2 @ E
+    {{{ RET #true; l ↦ᵢ v2 }}}.
   Proof.
     iIntros (<-%of_to_val <-%of_to_val Φ) ">Hl HΦ".
     iApply wp_lift_atomic_head_step_no_fork; auto.
@@ -172,7 +172,7 @@ Section lang_rules.
 
   Lemma wp_case_inl E e0 v0 e1 e2 Φ :
     to_val e0 = Some v0 →
-    ▷ WP (App e1 e0) @ E {{ Φ }} ⊢ WP Case (InjL e0) e1 e2 @ E {{ Φ }}.
+    ▷ WP App e1 e0 @ E {{ Φ }} ⊢ WP Case (InjL e0) e1 e2 @ E {{ Φ }}.
   Proof.
     intros. rewrite -(wp_lift_pure_det_head_step_no_fork (Case _ _ _) _); eauto.
     intros; inv_head_step; eauto.
@@ -180,17 +180,17 @@ Section lang_rules.
 
   Lemma wp_case_inr E e0 v0 e1 e2 Φ :
     to_val e0 = Some v0 →
-    ▷ WP (App e2 e0) @ E {{ Φ }} ⊢ WP Case (InjR e0) e1 e2 @ E {{ Φ }}.
+    ▷ WP App e2 e0 @ E {{ Φ }} ⊢ WP Case (InjR e0) e1 e2 @ E {{ Φ }}.
   Proof.
     intros. rewrite -(wp_lift_pure_det_head_step_no_fork (Case _ _ _)); eauto.
     intros; inv_head_step; eauto.
   Qed.
 
   Lemma wp_fork E e Φ :
-    ▷ (|={E}=> Φ (LitV tt)) ∗ ▷ WP e {{ _, True }} ⊢ WP Fork e @ E {{ Φ }}.
+    ▷ (|={E}=> Φ #()) ∗ ▷ WP e {{ _, True }} ⊢ WP Fork e @ E {{ Φ }}.
   Proof.
-  rewrite -(wp_lift_pure_det_head_step (Fork e) #tt [e]) //=; eauto.
-  - rewrite -(wp_value_fupd _ _ (Lit tt)); auto.
+  rewrite -(wp_lift_pure_det_head_step (Fork e) #() [e]) //=; eauto.
+  - rewrite -(wp_value_fupd _ _ #()); auto.
     by rewrite -step_fupd_intro // right_id later_sep. 
   - intros; inv_head_step; eauto.
   Qed.

theories/F_mu_ref_conc/typing.v

@@ -44,10 +44,10 @@ 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 : nat) : Γ ⊢ₜ #n n : TNat
-  | Bool_typed (b : bool) : Γ ⊢ₜ #♭ b : TBool
-  | BinOp_typed_nat op e1 e2 τ :      
+  | Unit_typed : Γ ⊢ₜ #() : TUnit
+  | Nat_typed (n : nat) : Γ ⊢ₜ # 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 →
      Γ ⊢ₜ BinOp op e1 e2 : τ
@@ -133,14 +133,14 @@ Tactic Notation "solve_typed" := solve_typed 50.
 
 (** Typeability of binops *)
 Lemma binop_nat_typed_safe (op : binop) (n1 n2 : nat) τ :
-  binop_nat_res_type op = Some τ → is_Some (binop_eval op (#nv n1) (#nv n2)).
+  binop_nat_res_type op = Some τ → is_Some (binop_eval op #n1 #n2).
 Proof.
   destruct op; simpl; eauto.
   inversion 1.
 Qed.
 
 Lemma binop_bool_typed_safe (op : binop) (b1 b2 : bool) τ :
-  binop_bool_res_type op = Some τ → is_Some (binop_eval op (#♭v b1) (#♭v b2)).
+  binop_bool_res_type op = Some τ → is_Some (binop_eval op #b1 #b2).
 Proof.
   destruct op; simpl; eauto; try by inversion 1.
 Qed.

theories/examples/bit.v

 From iris.proofmode Require Import tactics.
-From iris.algebra Require Import agree (* TODO: Why do we need to import this? *).
 From iris_logrel Require Import logrel.
 
 Definition bitτ : type :=
@@ -54,7 +53,7 @@ Section bit_refinement.
   
   (* This is the graph of the `bitf` function *)
   Program Definition bitτi : prodC valC valC -n> iProp Σ := λne vv,
-    (∃ b, ⌜vv.1 = #♭v b⌝ ∗ ⌜vv.2 = #nv (bitf b)⌝)%I.
+    (∃ b : bool, ⌜vv.1 = #b⌝ ∗ ⌜vv.2 = #(bitf b)⌝)%I.
   Next Obligation. solve_proper. Qed.
 
   Instance bitτi_persistent ww : PersistentP (bitτi ww).

theories/examples/counter.v

@@ -27,8 +27,7 @@ Definition FG_counter : val := λ: <>,
 Section CG_Counter.
   Context `{logrelG Σ}.
   Variable (Δ : list (prodC valC valC -n> iProp Σ)).
-  Open Scope expr_scope.
-  
+
   (* Coarse-grained increment *)  
   Lemma CG_increment_type Γ :
     typed Γ CG_increment (TArrow (Tref TNat) (TArrow LockType (TArrow TUnit TUnit))).
@@ -38,10 +37,10 @@ Section CG_Counter.
 
   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 tt) : τ)) -∗
-    {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K ((CG_increment $/ (LitV (Loc x)) $/ LitV (Loc l)) #())%E : τ)%I.
+    (x ↦ₛ # n -∗ l ↦ₛ #false -∗
+    (x ↦ₛ # (S n) -∗ l ↦ₛ #false -∗
+      ({E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K #() : τ)) -∗
+    {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K ((CG_increment $/ (LitV (Loc x)) $/ LitV (Loc l)) #()) : τ)%I.
   Proof.
     iIntros (?) "Hx Hl Hlog".
     unfold CG_increment. unlock. simpl_subst/=.
@@ -76,9 +75,9 @@ Section CG_Counter.
 
   Hint Resolve FG_increment_type : typeable.
 
-  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 tt) ≤log≤ t : τ) -∗
+  Lemma bin_log_FG_increment_l Γ K E x (n : nat) t τ :
+    x ↦ᵢ #n -∗
+    (x ↦ᵢ # (S n) -∗ {E,E;Δ;Γ} ⊨ fill K #() ≤log≤ t : τ) -∗
     {E,E;Δ;Γ} ⊨ fill K (FG_increment #x #()) ≤log≤ t : τ.
   Proof.
     iIntros "Hx Hlog".
@@ -114,14 +113,13 @@ Section CG_Counter.
   Definition counterN : namespace := nroot .@ "counter".
 
   Definition counter_inv l cnt cnt' : iProp Σ :=
-    (∃ n, l ↦ₛ (#♭v false) ∗ cnt ↦ᵢ (#nv n) ∗ cnt' ↦ₛ (#nv n))%I.
+    (∃ n : nat, l ↦ₛ #false ∗ cnt ↦ᵢ #n ∗ cnt' ↦ₛ #n)%I.
 
-  Lemma bin_log_counter_read_r Γ E1 E2 K x n t τ
+  Lemma bin_log_counter_read_r Γ E1 E2 K x (n : nat) t τ
     (Hspec : nclose specN ⊆ E1) :
-    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 $/ LitV (Loc x)) #())%E : τ.
+    x ↦ₛ #n -∗
+    (x ↦ₛ #n -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K #n : 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.
@@ -134,10 +132,10 @@ Section CG_Counter.
      a fine-grained increment with a baked in frame. *)
   (* Unfortunately, the precondition is not baked in the rule so you can only use it when your spatial context is empty *)
   Lemma bin_log_FG_increment_logatomic R Γ E1 E2 K x t τ  :
-    □ (|={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 tt) ≤log≤ t : τ))
+    □ (|={E1,E2}=> ∃ n : nat, x ↦ᵢ #n ∗ R n ∗
+       ((∃ n : nat, x ↦ᵢ #n ∗ R n) ={E2,E1}=∗ True) ∧
+        (∀ m, x ↦ᵢ # (S m) ∗ R m -∗ 
+            {E2,E1;Δ;Γ} ⊨ fill K #() ≤log≤ t : τ))
     -∗ ({E1,E1;Δ;Γ} ⊨ fill K ((FG_increment $/ LitV (Loc x)) #())%E ≤log≤ t : τ).
   Proof.
     iIntros "#H".
@@ -147,7 +145,7 @@ Section CG_Counter.
     iPoseProof "H" as "H2". (* lolwhat *)
     rel_load_l_atomic.
     iMod "H" as (n) "[Hx [HR Hrev]]".  iModIntro.
-    iExists (#nv n). iFrame. iNext. iIntros "Hx".
+    iExists #n. iFrame. iNext. iIntros "Hx".
     iDestruct "Hrev" as "[Hrev _]".
     iApply fupd_logrel.
     iMod ("Hrev" with "[HR Hx]").
@@ -157,13 +155,13 @@ Section CG_Counter.
     rel_cas_l_atomic.
     iMod "H2" as (n') "[Hx [HR HQ]]". iModIntro. simpl.
     destruct (decide (n = n')); subst.
-    - iExists (#nv n'). iFrame.
+    - iExists #n'. iFrame.
       iSplitR; eauto. { iDestruct 1 as %Hfoo. exfalso. done. }
       iIntros "_ !> Hx". simpl.
       iDestruct "HQ" as "[_ HQ]".
       iSpecialize ("HQ" $! n' with "[Hx HR]"). { iFrame. }
       rel_if_true_l. done.
-    - iExists (#nv n'). iFrame. 
+    - iExists #n'. iFrame. 
       iSplitL; eauto; last first.
       { iDestruct 1 as %Hfoo. exfalso. simplify_eq. }
       iIntros "_ !> Hx". simpl.
@@ -176,10 +174,10 @@ Section CG_Counter.
 
   (* A similar atomic specification for the counter_read fn *)
   Lemma bin_log_counter_read_atomic_l R Γ E1 E2 K x t τ :
-    □ (|={E1,E2}=> ∃ n, x ↦ᵢ (#nv n) ∗ R(n) ∗
-       ((∃ 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,E2}=> ∃ n : nat, x ↦ᵢ #n ∗ R n ∗
+       ((∃ n : nat, x ↦ᵢ #n ∗ R n) ={E2,E1}=∗ True) ∧
+        (∀ m : nat, x ↦ᵢ #m ∗ R m -∗
+            {E2,E1;Δ;Γ} ⊨ fill K #m ≤log≤ t : τ))
     -∗ {E1,E1;Δ;Γ} ⊨ fill K ((counter_read $/ LitV (Loc x)) #())%E ≤log≤ t : τ.
   Proof.
     iIntros "#H".
@@ -206,7 +204,7 @@ Section CG_Counter.
     { unfold CG_increment. unlock; simpl_subst/=. solve_closed. }
 
     iAlways. iIntros (v v') "[% %]"; simpl in *; subst.
-    iApply (bin_log_FG_increment_logatomic (fun n => (l ↦ₛ (#♭v false)) ∗ cnt' ↦ₛ #nv n)%I _ _ _ [] cnt with "[Hinv]").
+    iApply (bin_log_FG_increment_logatomic (fun n => (l ↦ₛ #false) ∗ cnt' ↦ₛ #n)%I _ _ _ [] cnt with "[Hinv]").
     iAlways.
     iInv counterN as ">Hcnt" "Hcl". iModIntro.
     iDestruct "Hcnt" as (n) "[Hl [Hcnt Hcnt']]".
@@ -236,7 +234,7 @@ Section CG_Counter.
     { unfold counter_read. unlock. simpl. solve_closed. }
     { unfold counter_read. unlock. simpl. solve_closed. }
     iAlways. iIntros (v v') "[% %]"; simpl in *; subst.
-    iApply (bin_log_counter_read_atomic_l (fun n => (l ↦ₛ (#♭v false)) ∗ cnt' ↦ₛ #nv n)%I _ _ _ [] cnt with "[Hinv]").
+    iApply (bin_log_counter_read_atomic_l (fun n => (l ↦ₛ #false) ∗ cnt' ↦ₛ #n)%I _ _ _ [] cnt with "[Hinv]").
     iAlways. iInv counterN as (n) "[>Hl [>Hcnt >Hcnt']]" "Hclose". 
     iModIntro. 
     iExists n. iFrame "Hcnt Hcnt' Hl". clear n.

theories/examples/lateearlychoice.v

@@ -17,16 +17,15 @@ Section Refinement.
   Definition choiceN : namespace := nroot .@ "choice".
 
   Definition choice_inv y y' : iProp Σ :=
-    (∃ f, y ↦ᵢ (#♭v f) ∗ y' ↦ₛ (#♭v f))%I.
+    (∃ f : bool, y ↦ᵢ #f ∗ y' ↦ₛ #f)%I.
 
   Lemma wp_rand :
-    (WP rand #() {{ v, ⌜v = #♭v true⌝ ∨ ⌜v = #♭v false⌝}})%I.
+    (WP rand #() {{ v, ⌜v = #true⌝ ∨ ⌜v = #false⌝}})%I.
   Proof.
-    iStartProof.
     unfold rand. unlock.
     iApply wp_rec; eauto. iNext. simpl.
     wp_bind (Alloc _). iApply wp_alloc; auto. iNext. iIntros (y) "Hy".
-    iMod (inv_alloc choiceN _ (y ↦ᵢ (#♭v false) ∨ y ↦ᵢ (#♭v true))%I with "[Hy]") as "#Hinv"; eauto.
+    iMod (inv_alloc choiceN _ (y ↦ᵢ #false ∨ y ↦ᵢ #true)%I with "[Hy]") as "#Hinv"; eauto.
     iApply wp_rec; eauto. iNext. simpl.
     wp_bind (Fork _). iApply wp_fork. iNext.
     iSplitL.
@@ -39,15 +38,15 @@ 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.
+    spec_ctx ρ -∗ (∀ b : bool, {E1,E1;Δ;Γ} ⊨ fill K #b ≤log≤ t : τ) -∗
+    {E1,E1;Δ;Γ} ⊨ fill K (rand #()) ≤log≤ t : τ.
   Proof.
     iIntros (?) "#Hs Hlog".
     unfold rand. unlock. simpl.
     rel_rec_l.
     rel_alloc_l as y "Hy". simpl.
     rel_rec_l.
-    iMod (inv_alloc choiceN _ (∃ b, y ↦ᵢ (#♭v b))%I with "[Hy]") as "#Hinv".
+    iMod (inv_alloc choiceN _ (∃ b : bool, y ↦ᵢ #b)%I with "[Hy]") as "#Hinv".
     { iNext. eauto. }
     rel_fork_l. iModIntro.
     iSplitR.
@@ -61,18 +60,18 @@ Section Refinement.
       rel_rec_l.
       rel_load_l_atomic.
       iInv choiceN as (b) "Hy" "Hcl".
-      iExists (#♭v b). iFrame.
+      iExists #b. iFrame.
       iModIntro. iNext. iIntros "Hy".
       iMod ("Hcl" with "[Hy]").
       { iNext. iExists b. iFrame. }
       done. 
   Qed.
 
-  Lemma rand_r b Δ Γ E1 E2 K ρ t τ :
+  Lemma rand_r (b : bool) Δ Γ E1 E2 K ρ t τ :
     ↑specN ⊆ E1 →
     ↑choiceN ⊆ E1 →
     spec_ctx ρ -∗
-    {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (#♭ b) : τ -∗
+    {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K #b : τ -∗
     {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (rand #())%E : τ.
   Proof.
     iIntros (??) "#Hs Hlog".
@@ -90,7 +89,7 @@ Section Refinement.
 
   Lemma lateChoice_l Δ Γ x v ρ t :
     spec_ctx ρ -∗ x ↦ᵢ v -∗
-    (x ↦ᵢ (#nv 0) -∗ ∀ b, {⊤,⊤;Δ;Γ} ⊨ #♭ b ≤log≤ t : TBool) -∗
+    (x ↦ᵢ #0 -∗ ∀ b : bool, {⊤,⊤;Δ;Γ} ⊨ #b ≤log≤ t : TBool) -∗
     {⊤,⊤;Δ;Γ} ⊨ lateChoice #x ≤log≤ t : TBool.
   Proof.
     iIntros "#Hs Hx Hlog".
@@ -103,8 +102,8 @@ Section Refinement.
   Qed.
    
   Lemma prerefinement Δ Γ x x' n ρ :
-    (spec_ctx ρ -∗ x ↦ᵢ (#nv n) -∗ x' ↦ₛ (#nv n) -∗
-      {⊤,⊤;Δ;Γ} ⊨ lateChoice #x ≤log≤ earlyChoice #x' : TBool)%I.
+    spec_ctx ρ -∗ x ↦ᵢ #n -∗ x' ↦ₛ #n -∗
+    {⊤,⊤;Δ;Γ} ⊨ lateChoice #x ≤log≤ earlyChoice #x' : TBool.
   Proof.
     iIntros "#Hspec Hx Hx'".
     iApply (lateChoice_l with "Hspec Hx"). iIntros "Hx".
@@ -120,8 +119,8 @@ Section Refinement.
   Qed.
 
   Lemma prerefinement2 Δ Γ x x' n ρ :
-    (spec_ctx ρ -∗ x ↦ᵢ (#nv n) -∗ x' ↦ₛ (#nv n) -∗
-      {⊤,⊤;Δ;Γ} ⊨ earlyChoice #x ≤log≤ lateChoice #x' : TBool)%I.
+    spec_ctx ρ -∗ x ↦ᵢ #n -∗ x' ↦ₛ #n -∗
+    {⊤,⊤;Δ;Γ} ⊨ earlyChoice #x ≤log≤ lateChoice #x' : TBool.
   Proof.
     iIntros "#Hspec Hx Hx'".
     unfold earlyChoice. unlock.

theories/examples/lock.v

@@ -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 : loc, j ⤇ fill K (of_val (# l)) ∗ l ↦ₛ (#♭v false).
+    spec_ctx ρ -∗ j ⤇ fill K (newlock #())
+    ={E1}=∗ ∃ l : loc, j ⤇ fill K (of_val #l) ∗ l ↦ₛ #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 (Lit (Loc l)) : τ)%I
-    -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (newlock #())%E: τ.
+    (∀ l : loc, l ↦ₛ #false -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K #l : τ) -∗
+    {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (newlock #()): τ.
   Proof.
     iIntros "Hlog".
     unfold newlock. unlock.
@@ -72,8 +72,8 @@ 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 (Lit (Loc l)))
-    ={E1}=∗ j ⤇ fill K (Lit Unit) ∗ l ↦ₛ (#♭v true).
+    spec_ctx ρ -∗ l ↦ₛ #false -∗ j ⤇ fill K (acquire #l)
+    ={E1}=∗ j ⤇ fill K (Lit Unit) ∗ l ↦ₛ #true.
   Proof.
     iIntros "#Hspec Hl Hj". 
     unfold acquire. unlock.
@@ -85,9 +85,9 @@ Section proof.
   
   Lemma bin_log_related_acquire_r Γ K l t τ
     (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 (# l)) : τ.
+    l ↦ₛ #false -∗
+    (l ↦ₛ #true -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (Lit Unit) : τ) -∗
+    {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (acquire #l) : τ.
   Proof.
     iIntros "Hl Hlog".
     unfold acquire. unlock.
@@ -100,22 +100,22 @@ Section proof.
   Global Opaque acquire.
 
   Transparent release.
-  Lemma steps_release ρ j K l b
+  Lemma steps_release ρ j K l (b : bool)
     (Hcl : nclose specN ⊆ E1) :
-    spec_ctx ρ -∗ l ↦ₛ (#♭v b) -∗ j ⤇ fill K (App release (# l))
-    ={E1}=∗ j ⤇ fill K (Lit Unit) ∗ l ↦ₛ (#♭v false).
+    spec_ctx ρ -∗ l ↦ₛ #b -∗ j ⤇ fill K (release #l)
+    ={E1}=∗ j ⤇ fill K (#())%E ∗ l ↦ₛ #false.
   Proof.
     iIntros "#Hspec Hl Hj". unfold release. unlock.
     tp_rec j.
-    tp_store j. tp_normalise j.
+    tp_store j.
     by iFrame.
   Qed.
 
-  Lemma bin_log_related_release_r Γ K l t τ b
+  Lemma bin_log_related_release_r Γ K l t τ (b : bool)
     (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 (# l)) : τ.
+    l ↦ₛ #b -∗
+    (l ↦ₛ #false -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (Lit Unit) : τ) -∗
+    {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K (release #l) : τ.
   Proof.
     iIntros "Hl Hlog".
     unfold release. unlock.
@@ -131,9 +131,9 @@ Section proof.
     (∀ K', spec_ctx ρ -∗ P -∗ j ⤇ fill K' (App e (of_val w))
             ={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 (# l)) (of_val w))
-    ={E1}=∗ j ⤇ fill K (of_val v) ∗ Q ∗ l ↦ₛ (#♭v false).
+    spec_ctx ρ -∗ P -∗ l ↦ₛ #false -∗
+    j ⤇ fill K (with_lock e #l w)
+    ={E1}=∗ j ⤇ fill K (of_val v) ∗ Q ∗ l ↦ₛ #false.
   Proof.
     iIntros (Hev Hpf ?) "#Hspec HP Hl Hj".
     unfold with_lock. unlock.
@@ -161,9 +161,9 @@ Section proof.
     (nclose specN ⊆ E1) →
     (∀ K, (Q -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K ev : τ) -∗
         {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 (# l) ew) : τ.
+    l ↦ₛ #false -∗
+    (Q -∗ l ↦ₛ #false -∗ {E1,E2;Δ;Γ} ⊨ t ≤log≤ fill K ev : 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).

theories/examples/stack/CG_stack.v

@@ -60,7 +60,7 @@ Definition CG_stack_body : val := λ: "st" "l",
 (* Instance: Closed ∅ ((λ: "l", #()) newlock). *)
 (* Proof. solve_closed. Qed *)
 Definition CG_stack : val :=
-  Λ: let: "l" := ref #♭ false in 
+  Λ: let: "l" := ref #false in 
      let: "st" := ref Nile in
      CG_stack_body "st" "l".
 

theories/examples/stack/refinement.v

@@ -11,12 +11,12 @@ Section Stack_refinement.
   Implicit Types Δ : listC D.
   Import lang.
 
-  Definition sinv τi stk stk' l' {SH: stackG Σ} : iProp Σ
-    := (∃ (istk : loc) v