feat(hott,library): add additional spacing hints

hott/hit/trunc.hlean

@@ -114,7 +114,7 @@ namespace trunc
 
   notation `exists` binders `,` r:(scoped P, Exists P) := r
   notation `∃` binders `,` r:(scoped P, Exists P) := r
-  notation A `\/` B := or A B
+  notation A ` \/ ` B := or A B
   notation A ∨ B    := or A B
 
   definition merely.intro   [reducible] [constructor] (a : A) : ∥ A ∥             := tr a

hott/init/function.hlean

@@ -58,11 +58,11 @@ precedence `on`:1
 precedence `$`:1
 
 
-infixr  ∘                  := compose
-infixr  ∘'                 := dcompose
-infixl  on                 := on_fun
-infixr  $                  := app
-notation f `-[` op `]-` g  := combine f op g
+infixr  ∘                    := compose
+infixr  ∘'                   := dcompose
+infixl  on                   := on_fun
+infixr  $                    := app
+notation f ` -[` op `]- ` g  := combine f op g
 
 end function
 

hott/init/path.hlean

@@ -458,14 +458,14 @@ namespace eq
 
   -- In Coq the variables P, Q and b are explicit, but in Lean we can probably have them implicit
   -- using the following notation
-  notation p `▸D`:65 x:64 := transportD _ p _ x
+  notation p ` ▸D `:65 x:64 := transportD _ p _ x
 
   -- Transporting along higher-dimensional paths
   definition transport2 [unfold 7] (P : A → Type) {x y : A} {p q : x = y} (r : p = q) (z : P x) :
     p ▸ z = q ▸ z :=
   ap (λp', p' ▸ z) r
 
-  notation p `▸2`:65 x:64 := transport2 _ p _ x
+  notation p ` ▸2 `:65 x:64 := transport2 _ p _ x
 
   -- An alternative definition.
   definition tr2_eq_ap10 (Q : A → Type) {x y : A} {p q : x = y} (r : p = q)
@@ -486,7 +486,7 @@ namespace eq
     {x1 x2 : A} (p : x1 = x2) (y : B x1) (z : C x1) (w : D x1 y z) : D x2 (p ▸ y) (p ▸ z) :=
   eq.rec_on p w
 
-  notation p `▸D2`:65 x:64 := transportD2 _ _ _ p _ _ x
+  notation p ` ▸D2 `:65 x:64 := transportD2 _ _ _ p _ _ x
 
   definition ap_tr_con_tr2 (P : A → Type) {x y : A} {p q : x = y} {z w : P x} (r : p = q)
       (s : z = w) :

hott/init/pathover.hlean

@@ -20,7 +20,7 @@ namespace eq
   inductive pathover.{l} (B : A → Type.{l}) (b : B a) : Π{a₂ : A}, a = a₂ → B a₂ → Type.{l} :=
   idpatho : pathover B b (refl a) b
 
-  notation b `=[`:50 p:0 `]`:0 b₂:50 := pathover _ b p b₂
+  notation b ` =[`:50 p:0 `] `:0 b₂:50 := pathover _ b p b₂
 
   definition idpo [reducible] [constructor] : b =[refl a] b :=
   pathover.idpatho b

hott/init/reserved_notation.hlean

@@ -33,62 +33,62 @@ num.succ (num.succ (num.succ (num.succ (num.succ (num.succ (num.succ (num.succ (
 /- Logical operations and relations -/
 
 reserve prefix `¬`:40
-reserve prefix `~`:40
-reserve infixr `∧`:35
-reserve infixr `/\`:35
-reserve infixr `\/`:30
-reserve infixr `∨`:30
-reserve infix `<->`:20
-reserve infix `↔`:20
-reserve infix `=`:50
-reserve infix `≠`:50
-reserve infix `≈`:50
-reserve infix `~`:50
-reserve infix `≡`:50
+reserve prefix ` ~ `:40
+reserve infixr ` ∧ `:35
+reserve infixr ` /\ `:35
+reserve infixr ` \/ `:30
+reserve infixr ` ∨ `:30
+reserve infix ` <-> `:20
+reserve infix ` ↔ `:20
+reserve infix ` = `:50
+reserve infix ` ≠ `:50
+reserve infix ` ≈ `:50
+reserve infix ` ~ `:50
+reserve infix ` ≡ `:50
 
-reserve infixr `∘`:60                   -- input with \comp
+reserve infixr ` ∘ `:60                   -- input with \comp
 reserve postfix `⁻¹`:std.prec.max_plus  -- input with \sy or \-1 or \inv
 
-reserve infixl `⬝`:75
-reserve infixr `▸`:75
+reserve infixl ` ⬝ `:75
+reserve infixr ` ▸ `:75
 
 /- types and type constructors -/
 
-reserve infixr `⊎`:25
-reserve infixr `×`:30
+reserve infixr ` ⊎ `:25
+reserve infixr ` × `:30
 
 /- arithmetic operations -/
 
-reserve infixl `+`:65
-reserve infixl `-`:65
-reserve infixl `*`:70
-reserve infixl `div`:70
-reserve infixl `mod`:70
-reserve infixl `/`:70
-reserve prefix `-`:100
-reserve infix `^`:80
+reserve infixl ` + `:65
+reserve infixl ` - `:65
+reserve infixl ` * `:70
+reserve infixl ` div `:70
+reserve infixl ` mod `:70
+reserve infixl ` / `:70
+reserve prefix ` - `:100
+reserve infix ` ^ `:80
 
-reserve infix `<=`:50
-reserve infix `≤`:50
-reserve infix `<`:50
-reserve infix `>=`:50
-reserve infix `≥`:50
-reserve infix `>`:50
+reserve infix ` <= `:50
+reserve infix ` ≤ `:50
+reserve infix ` < `:50
+reserve infix ` >= `:50
+reserve infix ` ≥ `:50
+reserve infix ` > `:50
 
 /- boolean operations -/
 
-reserve infixl `&&`:70
-reserve infixl `||`:65
+reserve infixl ` && `:70
+reserve infixl ` || `:65
 
 /- set operations -/
 
-reserve infix `∈`:50
-reserve infix `∉`:50
-reserve infixl `∩`:70
-reserve infixl `∪`:65
+reserve infix ` ∈ `:50
+reserve infix ` ∉ `:50
+reserve infixl ` ∩ `:70
+reserve infixl ` ∪ `:65
 
 /- other symbols -/
 
-reserve infix `∣`:50
-reserve infixl `++`:65
-reserve infixr `::`:65
+reserve infix ` ∣ `:50
+reserve infixl ` ++ `:65
+reserve infixr ` :: `:65

hott/init/types.hlean

@@ -32,10 +32,10 @@ end unit
 -- Sigma type
 -- ----------
 
-notation `Σ` binders `,` r:(scoped P, sigma P) := r
+notation `Σ` binders `, ` r:(scoped P, sigma P) := r
 
 namespace sigma
-  notation `⟨`:max t:(foldr `,` (e r, mk e r)) `⟩`:0 := t --input ⟨ ⟩ as \< \>
+  notation `⟨`:max t:(foldr `, ` (e r, mk e r)) `⟩`:0 := t --input ⟨ ⟩ as \< \>
 
   namespace ops
   postfix `.1`:(max+1) := pr1
@@ -52,8 +52,8 @@ namespace sum
   infixr ⊎ := sum
   infixr + := sum
   namespace low_precedence_plus
-    reserve infixr `+`:25  -- conflicts with notation for addition
-    infixr `+` := sum
+    reserve infixr ` + `:25  -- conflicts with notation for addition
+    infixr ` + ` := sum
   end low_precedence_plus
 
   variables {a b c d : Type}
@@ -81,7 +81,7 @@ abbreviation pair [constructor] := @prod.mk
 namespace prod
 
   -- notation for n-ary tuples
-  notation `(` h `,` t:(foldl `,` (e r, prod.mk r e) h) `)` := t
+  notation `(` h `, ` t:(foldl `,` (e r, prod.mk r e) h) `)` := t
   infixr × := prod
 
   namespace ops
@@ -94,8 +94,8 @@ namespace prod
 
   namespace low_precedence_times
 
-    reserve infixr `*`:30  -- conflicts with notation for multiplication
-    infixr `*` := prod
+    reserve infixr ` * `:30  -- conflicts with notation for multiplication
+    infixr ` * ` := prod
 
   end low_precedence_times
 

hott/types/W.hlean

@@ -13,7 +13,7 @@ inductive Wtype.{l k} {A : Type.{l}} (B : A → Type.{k}) : Type.{max l k} :=
 sup : Π (a : A), (B a → Wtype.{l k} B) → Wtype.{l k} B
 
 namespace Wtype
-  notation `W` binders `,` r:(scoped B, Wtype B) := r
+  notation `W` binders `, ` r:(scoped B, Wtype B) := r
 
   universe variables u v
   variables {A A' : Type.{u}} {B B' : A → Type.{v}} {C : Π(a : A), B a → Type}
@@ -28,7 +28,7 @@ namespace Wtype
   namespace ops
   postfix `.1`:(max+1) := Wtype.pr1
   postfix `.2`:(max+1) := Wtype.pr2
-  notation `⟨` a `,` f `⟩`:0 := Wtype.sup a f --input ⟨ ⟩ as \< \>
+  notation `⟨` a `, ` f `⟩`:0 := Wtype.sup a f --input ⟨ ⟩ as \< \>
   end ops
   open ops
 

library/data/set/basic.lean

@@ -53,12 +53,12 @@ assume h, absurd rfl (and.elim_right h)
 /- bounded quantification -/
 
 abbreviation bounded_forall (a : set X) (P : X → Prop) := ∀⦃x⦄, x ∈ a → P x
-notation `forallb` binders `∈` a `,` r:(scoped:1 P, P) := bounded_forall a r
-notation `∀₀` binders `∈` a `,` r:(scoped:1 P, P) := bounded_forall a r
+notation `forallb` binders `∈` a `, ` r:(scoped:1 P, P) := bounded_forall a r
+notation `∀₀` binders `∈` a `, ` r:(scoped:1 P, P) := bounded_forall a r
 
 abbreviation bounded_exists (a : set X) (P : X → Prop) := ∃⦃x⦄, x ∈ a ∧ P x
-notation `existsb` binders `∈` a `,` r:(scoped:1 P, P) := bounded_exists a r
-notation `∃₀` binders `∈` a `,` r:(scoped:1 P, P) := bounded_exists a r
+notation `existsb` binders `∈` a `, ` r:(scoped:1 P, P) := bounded_exists a r
+notation `∃₀` binders `∈` a `, ` r:(scoped:1 P, P) := bounded_exists a r
 
 theorem bounded_exists.intro {P : X → Prop} {s : set X} {x : X} (xs : x ∈ s) (Px : P x) :
   ∃₀ x ∈ s, P x :=

library/init/function.lean

@@ -56,15 +56,11 @@ rfl
 theorem uncurry_curry (f : A × B → C) : uncurry (curry f) = f :=
 funext (λ p, match p with (a, b) := rfl end)
 
-precedence `∘'`:60
-precedence `on`:1
-precedence `$`:1
-
-infixr  ∘                  := compose
-infixr  ∘'                 := dcompose
-infixl  on                 := on_fun
-infixr  $                  := app
-notation f `-[` op `]-` g  := combine f op g
+infixr  ` ∘ `            := compose
+infixr  ` ∘' `:60        := dcompose
+infixl  ` on `:1         := on_fun
+infixr  ` $ `:1          := app
+notation f ` -[` op `]- ` g  := combine f op g
 
 lemma left_id (f : A → B) : id ∘ f = f := rfl
 

library/init/setoid.lean

@@ -11,7 +11,7 @@ structure setoid [class] (A : Type) :=
 (r : A → A → Prop) (iseqv : equivalence r)
 
 namespace setoid
-  infix `≈` := setoid.r
+  infix ` ≈ ` := setoid.r
 
   variable {A : Type}
   variable [s : setoid A]

library/logic/quantifiers.lean

@@ -75,7 +75,7 @@ end
 definition exists_unique {A : Type} (p : A → Prop) :=
 ∃x, p x ∧ ∀y, p y → y = x
 
-notation `∃!` binders `,` r:(scoped P, exists_unique P) := r
+notation `∃!` binders `, ` r:(scoped P, exists_unique P) := r
 
 theorem exists_unique.intro {A : Type} {p : A → Prop} (w : A) (H1 : p w) (H2 : ∀y, p y → y = w) :
   ∃!x, p x :=