fix(frontends/lean/pp): remove unnecessary parenthesis when pretty printing (A -> (Pi (b : B), C b))

src/frontends/lean/pp.cpp

@@ -846,7 +846,8 @@ static bool is_default_arrow(expr const & e) {
 auto pretty_fn::pp_pi(expr const & e) -> result {
     if (is_default_arrow(e)) {
         result lhs = pp_child(binding_domain(e), get_arrow_prec());
-        result rhs = pp_child(lift_free_vars(binding_body(e), 1), get_arrow_prec()-1);
+        expr   b   = lift_free_vars(binding_body(e), 1);
+        result rhs = is_pi(b) ? pp(b) : pp_child(b, get_arrow_prec()-1);
         format r   = group(lhs.fmt() + space() + (m_unicode ? *g_arrow_n_fmt : *g_arrow_fmt) + line() + rhs.fmt());
         return result(get_arrow_prec(), get_arrow_prec()-1, r);
     } else {

tests/lean/584c.lean.expected.out

@@ -2,4 +2,4 @@ tst₁ : Π A, A → A
 tst₂ : Π {A}, A → A
 symm₂ : ∀ {A} a b, a = b → b = a
 tst₃ : Π A, A → A
-foo : ∀ {A} {a b}, a = b → (∀ c, c = b → c = a)
+foo : ∀ {A} {a b}, a = b → ∀ c, c = b → c = a

tests/lean/652.lean.expected.out

@@ -1,6 +1,6 @@
 R : Π {b c}, Prop
 R2 : bool → bool → Prop
 R3 : bool → bool → Prop
-R4 : bool → (Π {c}, Prop)
+R4 : bool → Π {c}, Prop
 R5 : Π {b c}, Prop
 R6 : Π {b}, bool → Prop

tests/lean/acc.lean.expected.out

@@ -1,2 +1,2 @@
 acc.rec :
-  Π {A} {R} {C}, (Π x, (∀ y, R y x → acc A R y) → (Π y, R y x → C y) → C x) → (Π {a}, acc A R a → C a)
+  Π {A} {R} {C}, (Π x, (∀ y, R y x → acc A R y) → (Π y, R y x → C y) → C x) → Π {a}, acc A R a → C a

tests/lean/bug1.lean.expected.out

@@ -1,13 +1,13 @@
 bug1.lean:9:7: error: type mismatch at definition 'and_intro1', has type
-  ∀ p q, p → q → (∀ c, (p → q → c) → c)
+  ∀ p q, p → q → ∀ c, (p → q → c) → c
 but is expected to have type
   ∀ p q, p → q → a
 bug1.lean:13:7: error: type mismatch at definition 'and_intro2', has type
-  ∀ p q, p → q → (∀ c, (p → q → c) → c)
+  ∀ p q, p → q → ∀ c, (p → q → c) → c
 but is expected to have type
   ∀ p q, p → q → p ∧ p
 bug1.lean:17:7: error: type mismatch at definition 'and_intro3', has type
-  ∀ p q, p → q → (∀ c, (p → q → c) → c)
+  ∀ p q, p → q → ∀ c, (p → q → c) → c
 but is expected to have type
   ∀ p q, p → q → q ∧ p
 and_intro4 : ∀ p q, p → q → p ∧ q

tests/lean/check.lean.expected.out

@@ -1,4 +1,4 @@
 and.intro : ?M_1 → ?M_2 → ?M_1 ∧ ?M_2
 or.elim : ?M_1 ∨ ?M_2 → (?M_1 → ?M_3) → (?M_2 → ?M_3) → ?M_3
 eq : ?M_1 → ?M_1 → Prop
-eq.rec : ?M_3 ?M_2 → (Π {a}, ?M_2 = a → ?M_3 a)
+eq.rec : ?M_3 ?M_2 → Π {a}, ?M_2 = a → ?M_3 a

tests/lean/elab6.lean.expected.out

@@ -1,10 +1,10 @@
 H : @transitive.{1} nat R
-@F.{l_1} ?M_1 : Π ⦃a : ?M_1⦄ {b : ?M_1}, ?M_1 → (Π ⦃e : ?M_1⦄, ?M_1 → ?M_1 → ?M_1)
+@F.{l_1} ?M_1 : Π ⦃a : ?M_1⦄ {b : ?M_1}, ?M_1 → Π ⦃e : ?M_1⦄, ?M_1 → ?M_1 → ?M_1
 @F.{1} bool ?M_1 ?M_2 bool.tt : Π ⦃e : bool⦄, bool → bool → bool
 @F.{1} bool ?M_1 ?M_2 bool.tt ?M_3 bool.tt : bool → bool
 @F.{1} bool ?M_1 ?M_2 bool.tt ?M_3 bool.tt bool.tt : bool
 H : @transitive.{1} nat R
-@F.{l_1} ?M_1 : Π ⦃a : ?M_1⦄ {b : ?M_1}, ?M_1 → (Π ⦃e : ?M_1⦄, ?M_1 → ?M_1 → ?M_1)
+@F.{l_1} ?M_1 : Π ⦃a : ?M_1⦄ {b : ?M_1}, ?M_1 → Π ⦃e : ?M_1⦄, ?M_1 → ?M_1 → ?M_1
 @F.{1} bool ?M_1 ?M_2 bool.tt : Π ⦃e : bool⦄, bool → bool → bool
 @F.{1} bool ?M_1 ?M_2 bool.tt ?M_3 bool.tt : bool → bool
 @F.{1} bool ?M_1 ?M_2 bool.tt ?M_3 bool.tt bool.tt : bool

tests/lean/elab9.lean.expected.out

@@ -2,6 +2,6 @@
 [_inst_3 : has_add A] (H : @eq A a (@add A _inst_3 (@zero A _inst_2) (@zero A _inst_2))), @add A _inst_3 a a :
   Π (A : Type) [_inst_1 : has_add A] [_inst_2 : has_zero A] (a : A),
     @eq A (@add A _inst_1 a (@zero A _inst_2)) a →
-    (Π [_inst_3 : has_add A], @eq A a (@add A _inst_3 (@zero A _inst_2) (@zero A _inst_2)) → A)
+    Π [_inst_3 : has_add A], @eq A a (@add A _inst_3 (@zero A _inst_2) (@zero A _inst_2)) → A
 λ (a b : nat) (H : @gt nat nat.nat_has_lt a b) [_inst_4 : has_lt nat], @lt nat _inst_4 a b :
-  Π (a b : nat), @gt nat nat.nat_has_lt a b → (Π [_inst_4 : has_lt nat], Prop)
+  Π (a b : nat), @gt nat nat.nat_has_lt a b → Π [_inst_4 : has_lt nat], Prop

tests/lean/let1.lean.expected.out

@@ -2,8 +2,8 @@ let bool := Prop,
     and := λ p q, Π c, (p → q → c) → c,
     and_intro := λ p q H1 H2 c H, H H1 H2
 in and_intro :
-  ∀ p q, p → q → (∀ c, (p → q → c) → c)
+  ∀ p q, p → q → ∀ c, (p → q → c) → c
 let1.lean:19:19: error: invalid type ascription, expression has type
-  ∀ p q, p → q → (∀ c, (p → q → c) → c)
+  ∀ p q, p → q → ∀ c, (p → q → c) → c
 but is expected to have type
   ∀ p q, p → q → (λ p q, ∀ c, (p → q → c) → c) q p

tests/lean/omit.lean.expected.out

@@ -1,4 +1,4 @@
 omit.lean:5:7: error: invalid omit command, 'A' has not been included
 omit.lean:7:10: error: invalid include command, 'A' has already been included
-foo : Π A, A → A → (Π B, B → B)
+foo : Π A, A → A → Π B, B → B
 tst : Π A, A → A → Type → Type

tests/lean/private_structure.lean.expected.out

@@ -3,7 +3,7 @@ point.rec_on ==> private.1706149582.point.rec_on
 bla : Type₁
 point : Type₁
 point.mk : ℕ → ℕ → point
-point.rec : (Π x y, ?M_1 (point.mk x y)) → (Π n, ?M_1 n)
+point.rec : (Π x y, ?M_1 (point.mk x y)) → Π n, ?M_1 n
 point.rec_on : Π n, (Π x y, ?M_1 (point.mk x y)) → ?M_1 n
 point.cases_on : Π n, (Π x y, ?M_1 (point.mk x y)) → ?M_1 n
 point.induction_on : ∀ n, (∀ x y, ?M_1 (point.mk x y)) → ?M_1 n

tests/lean/run/def_brec3.lean

@@ -18,3 +18,4 @@ rfl
 
 example (n : nat) (b1 b2 : bool) (v1 v2 : bv n) : map2 f (cons n b1 v1) (cons n b2 v2) = cons n (f b1 b2) (map2 f v1 v2) :=
 rfl
+print map2

tests/lean/sec_param_pp2.lean.expected.out

@@ -1,4 +1,4 @@
 id2 : (A → B → A) → A
 id2 : (A → B → A) → A
 id2 : ?M_1 → (A → ?M_1 → A) → A
-id2 : ?M_1 → (Π {B}, B → (?M_1 → B → ?M_1) → ?M_1)
+id2 : ?M_1 → Π {B}, B → (?M_1 → B → ?M_1) → ?M_1

tests/lean/var2.lean.expected.out

@@ -1 +1 @@
-foo : Π B, B → (Π A, A → A = B → Prop)
+foo : Π B, B → Π A, A → A = B → Prop