In Idris, is “Eq a” a type, and can I supply a value for it?

Question

In the following, example1 is standard syntax (as documented), with Eq a as a constraint. In example2, I specify Eq a dir

Answer 1

You could use named implementations:

[eq_nat] Eq Nat where { ... }
...
example_of_example2 : Type
example_of_example2 = example2 Nat eq_nat 3 3

A useful application of named implementations are defining multiple implementation of Monoid:

[PlusNatSemi] Semigroup Nat where
  (<+>) x y = x + y

[MultNatSemi] Semigroup Nat where
  (<+>) x y = x * y

[PlusNatMonoid] Monoid Nat using PlusNatSemi where
  neutral = 0

[MultNatMonoid] Monoid Nat using MultNatSemi where
  neutral = 1

---

To comment : To get the default instance

getEq : (a : Type) -> {auto inst : Eq a} -> Eq a
getEq a {inst} = inst

Then you can have your default instance:

getEq (List Nat) -- => implementation of Eq...