define `id` function using point-free notation

Question

In Haskell language function id defined to be unit of composition:

id :: a -> a
id x = x

Is there a way to define haskell' id function using point-free notation? I mean not to directly referencing it like:

same :: a -> a
same = id

Answer 1

The pointfree version of id is... well, id. id is often taken as a fundamental operator in pointfree constructions, a sort of a primitive upon which more combinators are constructed.

If you really want, you can reconstruct id from other more complex operators, e.g. exploiting the Monad ((->) a) instance:

id = join const

or the Applicative ((->) a) instance

id = const <*> const

(in combinatory logic, this is I = S K K since <*> is S and const is K)

Nothing can be simpler than id itself, though.