Identity function returns the same _value_.

If it's only the same _type_, but the value is not the same, then it's an endomorphism. The function definitions look the same `a -> a`.

string reversal, integer negation or toUpperCase are classical examples of endomorphisms.

Identity is a specific case of endomorphism.

string reversal, integer negation or toUpperCase are classical examples of functions which will not compile as `a -> a`

The function which will compile as `a -> a` is the identity function.

That's correct, but I'm not sure how it relates to my comment as I said that `a -> a` is just an endomorphism.

identity, uppercase or negate are all endomorphisms, with identity being the only generic one.