Improve the notation

F_mu_ref_conc/examples/stack/refinement.v

@@ -209,7 +209,7 @@ Section Stack_refinement.
     unfold FG_read_iter, CG_snap_iter. unlock.
     simpl_subst/=.
     iApply bin_log_related_arrow; eauto.
-    iAlways. iIntros ([f1 f2]) "#Hff".
+    iAlways. iIntros ([f1 f2]) "#Hff /=".
     rel_rec_r.
     rel_rec_l.
     Transparent FG_iter CG_iter. unlock FG_iter CG_iter.
@@ -298,8 +298,7 @@ Section Stack_refinement.
         by iApply "IH".
       + clear.
         iClear "IH Histk HLK_tail HLK HLK' Hτ".
-        iApply related_ret.
-        iApply "Hff".
+        iApply (related_ret with "[Hff]"). done.
   Qed.
 End Stack_refinement.
 

F_mu_ref_conc/logrel_binary.v

@@ -398,11 +398,13 @@ Section bin_log_def.
 End bin_log_def.
 
 Notation "'{' E1 ',' E2 ';' Δ ';' Γ '}' ⊨ e '≤log≤' e' : τ" :=
-  (bin_log_related E1 E2 Δ Γ e%E e'%E τ) (at level 74, E1,E2, e, e', τ at next level).
+  (bin_log_related E1 E2 Δ Γ e%E e'%E τ) (at level 74, E1,E2, e, e', τ at next level,
+   format "'{' E1 ',' E2 ';' Δ ';' Γ '}'  ⊨  e  '≤log≤'  e'  :  τ").
 Notation "'{' E1 ',' E2 ';' Γ '}' ⊨ e '≤log≤' e' : τ" :=
   (∀ Δ, bin_log_related E1 E2 Δ Γ e%E e'%E τ)%I (at level 74, E1,E2, e, e', τ at next level).
 Notation "Γ ⊨ e '≤log≤' e' : τ" :=
-  (∀ Δ, bin_log_related ⊤ ⊤ Δ Γ e%E e'%E τ)%I (at level 74, e, e', τ at next level).
+  (∀ Δ, bin_log_related ⊤ ⊤ Δ Γ e%E e'%E τ)%I (at level 74, e, e', τ at next level,
+  format "Γ  ⊨  e  '≤log≤'  e'  :  τ").
 
 Section monadic.
   Context `{logrelG Σ}.

F_mu_ref_conc/notation.v

@@ -19,12 +19,7 @@ Coercion BNamed : string >-> binder.
 Notation "<>" := BAnon : binder_scope.
 
 Notation Lam x e := (Rec BAnon x e).
-Notation Let x e1 e2 := (App (Lam x e2) e1).
-Notation Seq e1 e2 := (Let BAnon e1 e2).
 Notation LamV x e := (RecV BAnon x e).
-Notation LetCtx x e2 := (AppRCtx (LamV x e2)).
-Notation SeqCtx e2 := (LetCtx BAnon e2).
-Notation Skip := (Seq tt tt).
 
 (* No scope for the values, does not conflict and scope is often not inferred
 properly. *)
@@ -78,10 +73,6 @@ Notation "λ: x , e" := (locked (LamV x%bind e%E))
   (at level 102, x at level 1, e at level 200) : val_scope.
 Notation "λ: x y .. z , e" := (locked (LamV x%bind (Lam y%bind .. (Lam z%bind e%E) .. )))
   (at level 102, x, y, z at level 1, e at level 200) : val_scope.
-Notation "e1 ;; e2" := (Lam BAnon e2%E e1%E)
-  (at level 100, e2 at level 200, format "e1  ;;  e2") : expr_scope.
-Notation "e1 ;; e2" := (LamV BAnon e2%E e1%E)
-  (at level 100, e2 at level 200, format "e1  ;;  e2") : val_scope.
 
 Notation "'if:' e1 'then' e2 'else' e3" := (If e1%E e2%E e3%E)
   (at level 200, e1, e2, e3 at level 200) : expr_scope.
@@ -93,7 +84,9 @@ Notation "'Λ:' e" := (TLam e%E)
 Notation "'Λ:' e" := (TLamV e%E)
   (at level 102, e at level 200) : val_scope.
 
-Notation "'let:' x := e1 'in' e2" := (Let x%bind e1%E e2%E)
+Notation "'let:' x := e1 'in' e2" := (Lam x%bind e2%E e1%E)
   (at level 102, x at level 1, e1, e2 at level 200,
    format "'[' '[hv' 'let:'  x  :=  '[' e1 ']'  'in'  ']' '/' e2 ']'") : expr_scope.
 
+Notation "e1 ;; e2" := (Lam BAnon e2%E e1%E)
+  (at level 100, e2 at level 200, format "e1  ;;  e2") : expr_scope.

F_mu_ref_conc/relational_properties.v

@@ -254,7 +254,7 @@ Section properties.
    (Hclosed1 : Closed ∅ e1) 
    (Hclosed2 : Closed ∅ e2) : 
    ▷ ({E,E;Δ;Γ} ⊨ fill K e1 ≤log≤ t : τ)
-   ⊢ {E,E;Δ;Γ} ⊨ fill K (If (#♭ true) e1 e2) ≤log≤ t : τ.
+   ⊢ {E,E;Δ;Γ} ⊨ fill K (If true e1 e2) ≤log≤ t : τ.
   Proof.
     iIntros "Hlog".
     iApply (bin_log_pure_l with "Hlog"); auto; intros.