improve function type notation

theories/typing/examples/get_x.v

@@ -12,7 +12,7 @@ Section get_x.
 
   Lemma get_x_type :
     typed_instruction_ty [] [] [] get_x
-        fn(∀ α, [☀α]; &uniq{α} Π[int; int] → &shr{α} int).
+        (fn(∀ α, [☀α]; &uniq{α} Π[int; int]) → &shr{α} int).
   (* FIXME: The above is pretty-printed with some explicit scope annotations,
      and without using 'typed_instruction_ty'.  I think that's related to
      the list notation that we added to %TC. *)

theories/typing/examples/init_prod.v

@@ -13,7 +13,7 @@ Section init_prod.
 
   Lemma init_prod_type :
     typed_instruction_ty [] [] [] init_prod
-        fn([]; int, int → Π[int;int]).
+        (fn([]; int, int) → Π[int;int]).
   Proof.
     apply type_fn; try apply _. move=> /= [] ret p. inv_vec p=>x y. simpl_subst.
     eapply type_deref; [solve_typing..|apply read_own_move|done|]=>x'. simpl_subst.

theories/typing/examples/lazy_lft.v

@@ -18,7 +18,7 @@ Section lazy_lft.
 
   Lemma lazy_lft_type :
     typed_instruction_ty [] [] [] lazy_lft
-        fn([]; → unit).
+        (fn([]) → unit).
   Proof.
     apply type_fn; try apply _. move=> /= [] ret p. inv_vec p. simpl_subst.
     eapply (type_newlft []); [solve_typing|]=>α.

theories/typing/examples/option_as_mut.v

@@ -16,7 +16,7 @@ Section option_as_mut.
 
   Lemma option_as_mut_type τ :
     typed_instruction_ty [] [] [] option_as_mut
-        fn(∀ α, [☀α]; &uniq{α} Σ[unit; τ] → Σ[unit; &uniq{α}τ]).
+        (fn(∀ α, [☀α]; &uniq{α} Σ[unit; τ]) → Σ[unit; &uniq{α}τ]).
   Proof.
     apply type_fn; try apply _. move=> /= α ret p. inv_vec p=>o. simpl_subst.
     eapply (type_cont [_] [] (λ r, [o ◁ _; r!!!0 ◁ _])%TC) ; [solve_typing..| |].

theories/typing/examples/rebor.v

@@ -17,7 +17,7 @@ Section rebor.
 
   Lemma rebor_type :
     typed_instruction_ty [] [] [] rebor
-        fn([]; Π[int; int], Π[int; int] → int).
+        (fn([]; Π[int; int], Π[int; int]) → int).
   Proof.
     apply type_fn; try apply _. move=> /= [] ret p. inv_vec p=>t1 t2. simpl_subst.
     eapply (type_newlft []). apply _. move=> α.

theories/typing/examples/unbox.v

@@ -12,7 +12,7 @@ Section unbox.
 
   Lemma ubox_type :
     typed_instruction_ty [] [] [] unbox
-        fn(∀ α, [☀α]; &uniq{α}box (Π[int; int]) → &uniq{α} int).
+        (fn(∀ α, [☀α]; &uniq{α}box (Π[int; int])) → &uniq{α} int).
   Proof.
     apply type_fn; try apply _. move=> /= α ret b. inv_vec b=>b. simpl_subst.
     eapply type_deref; [solve_typing..|by apply read_own_move|done|].

theories/typing/examples/unwrap_or.v

@@ -13,7 +13,7 @@ Section unwrap_or.
 
   Lemma unwrap_or_type τ :
     typed_instruction_ty [] [] [] (unwrap_or τ)
-        fn([]; Σ[unit; τ], τ → τ).
+        (fn([]; Σ[unit; τ], τ) → τ).
   Proof.
     apply type_fn; try apply _. move=> /= [] ret p. inv_vec p=>o def. simpl_subst.
     eapply type_case_own; [solve_typing..|]. constructor; last constructor; last constructor.

theories/typing/function.v

@@ -67,20 +67,22 @@ End fn.
 
 (* TODO: Once we depend on 8.6pl1, extend this to recursive binders so that
    patterns like '(a, b) can be used. *)
-Notation "'fn(∀' x ',' E ';' T1 ',' .. ',' TN '→' R ')'" :=
+Notation "'fn(∀' x ',' E ';' T1 ',' .. ',' TN ')' '→' R" :=
   (fn (λ x, E%EL) (λ x, (Vector.cons T1 .. (Vector.cons TN Vector.nil) ..)%T) (λ x, R%T))
-  (at level 0, E, T1, TN, R at level 50) : lrust_type_scope.
-Notation "'fn(∀' x ',' E ';' '→' R ')'" :=
+  (at level 99, R at level 200,
+   format "'fn(∀' x ','  E ';'  T1 ','  .. ','  TN ')'  '→'  R") : lrust_type_scope.
+Notation "'fn(∀' x ',' E ')' '→' R" :=
   (fn (λ x, E%EL) (λ x, Vector.nil) (λ x, R%T))
-  (at level 0, E, R at level 50) : lrust_type_scope.
-Notation "'fn(' E ';' T1 ',' .. ',' TN '→' R ')'" :=
+  (at level 99, R at level 200,
+   format "'fn(∀' x ','  E ')'  '→'  R") : lrust_type_scope.
+Notation "'fn(' E ';' T1 ',' .. ',' TN ')' '→' R" :=
   (fn (λ _:(), E%EL) (λ _, (Vector.cons T1 .. (Vector.cons TN Vector.nil) ..)%T) (λ _, R%T))
-  (at level 0, E, T1, TN, R at level 50,
-   format "'fn(' E ';'  T1 ','  .. ','  TN  '→'  R ')'") : lrust_type_scope.
-Notation "'fn(' E ';' '→' R ')'" :=
+  (at level 99, R at level 200,
+   format "'fn(' E ';'  T1 ','  .. ','  TN ')'  '→'  R") : lrust_type_scope.
+Notation "'fn(' E ')' '→' R" :=
   (fn (λ _:(), E%EL) (λ _, Vector.nil) (λ _, R%T))
-  (at level 0, E, R at level 50,
-   format "'fn(' E ';' '→'  R ')'") : lrust_type_scope.
+  (at level 99, R at level 200,
+   format "'fn(' E ')'  '→'  R") : lrust_type_scope.
 
 Section typing.
   Context `{typeG Σ}.

theories/typing/soundness.v

@@ -24,7 +24,7 @@ Section type_soundness.
   Definition exit_cont : val := λ: [<>], #().
 
   Definition main_type `{typeG Σ} :=
-    fn (λ _, []) (λ _, [# ]) (λ _:(), box unit).
+    (fn([]) → unit)%T.
 
   Theorem type_soundness `{typePreG Σ} (main : val) σ t :
     (∀ `{typeG Σ}, typed_instruction_ty [] [] [] main main_type) →

theories/typing/unsafe/cell.v

@@ -81,7 +81,7 @@ Section typing.
 
   Lemma cell_new_type ty :
     typed_instruction_ty [] [] [] cell_new
-        fn([]; ty → cell ty).
+        (fn([]; ty) → cell ty).
   Proof.
     apply type_fn; [apply _..|]. move=>/= _ ret arg. inv_vec arg=>x. simpl_subst.
     eapply (type_jump [_]); first solve_typing.
@@ -93,7 +93,7 @@ Section typing.
 
   Lemma cell_into_inner_type ty :
     typed_instruction_ty [] [] [] cell_into_inner
-        fn([]; cell ty → ty).
+        (fn([]; cell ty) → ty).
   Proof.
     apply type_fn; [apply _..|]. move=>/= _ ret arg. inv_vec arg=>x. simpl_subst.
     eapply (type_jump [_]); first solve_typing.
@@ -105,7 +105,7 @@ Section typing.
 
   Lemma cell_get_mut_type ty :
     typed_instruction_ty [] [] [] cell_get_mut
-      fn(∀ α, [☀α]; &uniq{α} (cell ty) → &uniq{α} ty).
+      (fn(∀ α, [☀α]; &uniq{α} (cell ty)) → &uniq{α} ty).
   Proof.
     apply type_fn; [apply _..|]. move=>/= α ret arg. inv_vec arg=>x. simpl_subst.
     eapply (type_jump [_]). solve_typing. rewrite /tctx_incl /=.
@@ -122,7 +122,7 @@ Section typing.
 
   Lemma cell_get_type `(!Copy ty) :
     typed_instruction_ty [] [] [] (cell_get ty)
-        fn(∀ α, [☀α]; &shr{α} (cell ty) → ty).
+        (fn(∀ α, [☀α]; &shr{α} (cell ty)) → ty).
   Proof.
     apply type_fn; [apply _..|]. move=>/= α ret arg. inv_vec arg=>x. simpl_subst.
     eapply type_deref; [solve_typing..|apply read_own_move|done|]=>x'. simpl_subst.
@@ -142,7 +142,7 @@ Section typing.
 
   Lemma cell_set_type ty :
     typed_instruction_ty [] [] [] (cell_set ty)
-        fn(∀ α, [☀α]; &shr{α} cell ty, ty → unit).
+        (fn(∀ α, [☀α]; &shr{α} cell ty, ty) → unit).
   Proof.
     apply type_fn; try apply _. move=> /= α ret arg. inv_vec arg=>c x. simpl_subst.
     eapply type_deref; [solve_typing..|by apply read_own_move|done|].

theories/typing/unsafe/refcell/refmut_code.v

@@ -122,7 +122,7 @@ Section refmut_functions.
 
   Lemma refmut_drop_type ty :
     typed_instruction_ty [] [] [] refmut_drop
-      fn(∀ α, [☀α]; refmut α ty → unit).
+      (fn(∀ α, [☀α]; refmut α ty) → unit).
   Proof.
     apply type_fn; [apply _..|]. move=>/= α ret arg. inv_vec arg=>x. simpl_subst.
     iIntros "!# * #LFT Hna Hα HL Hk Hx".