feat(library): add has_equiv type class

doc/changes.md

@@ -38,6 +38,8 @@ master branch (aka work in progress branch)
 - Add support for structure instance notation `{...}` in patterns. Use `..` to ignore
   unmatched fields.
 
+- Type class has_equiv for `≈` notation.
+
 *Changes*
 
 - `string` is now a list of unicode scalar values. Moreover, in the VM,

library/init/core.lean

@@ -315,6 +315,7 @@ class has_andthen  (α : Type u) (β : Type v) (σ : inout Type w) := (andthen :
 class has_union    (α : Type u) := (union : α → α → α)
 class has_inter    (α : Type u) := (inter : α → α → α)
 class has_sdiff    (α : Type u) := (sdiff : α → α → α)
+class has_equiv    (α : Sort u) := (equiv : α → α → Prop)
 class has_subset   (α : Type u) := (subset : α → α → Prop)
 class has_ssubset  (α : Type u) := (ssubset : α → α → Prop)
 /- Type classes has_emptyc and has_insert are
@@ -351,6 +352,7 @@ infix ∩        := has_inter.inter
 infix ⊆        := has_subset.subset
 infix ⊂        := has_ssubset.ssubset
 infix \        := has_sdiff.sdiff
+infix ≈        := has_equiv.equiv
 
 export has_append (append)
 

library/init/data/setoid.lean

@@ -10,14 +10,15 @@ universes u
 class setoid (α : Sort u) :=
 (r : α → α → Prop) (iseqv : equivalence r)
 
-namespace setoid
-infix ` ≈ ` := setoid.r
+instance setoid_has_equiv {α : Sort u} [setoid α] : has_equiv α :=
+⟨setoid.r⟩
 
+namespace setoid
 variable {α : Sort u}
 variable [s : setoid α]
 include s
 
-@[refl] lemma refl (a : α) : a ≈ a :=
+@[refl] lemma refl [setoid α] (a : α) : a ≈ a :=
 match setoid.iseqv α with
 | ⟨h_refl, h_symm, h_trans⟩ := h_refl a
 end

tests/lean/struct_class.lean.expected.out

@@ -5,6 +5,7 @@ has_append : Type u → Type u
 has_div : Type u → Type u
 has_dvd : Type u → Type u
 has_emptyc : Type u → Type u
+has_equiv : Sort u → Sort (max 1 u)
 has_insert : (inout Type u) → Type v → Type (max u v)
 has_inter : Type u → Type u
 has_inv : Type u → Type u
@@ -31,6 +32,7 @@ has_append : Type u → Type u
 has_div : Type u → Type u
 has_dvd : Type u → Type u
 has_emptyc : Type u → Type u
+has_equiv : Sort u → Sort (max 1 u)
 has_insert : (inout Type u) → Type v → Type (max u v)
 has_inter : Type u → Type u
 has_inv : Type u → Type u