[Haskell-cafe] Help with identity functor print instance and monad transformers

[wren romano]

On Tue, Jan 20, 2015 at 12:09 AM, Cody Goodman
<codygman.consulting at gmail.com> wrote:
> I understand the error below, but I'm not really sure what an instance of
> liftIO would look like for the Identity functor. I guess I'm not all to
> clear on what an identity functor is.
>
> I'm a little fuzzy on what an identity monad is. I understand that id gives
> the identity of something back pretty well though. Can anyone help?

The identity functor/monad is this:

    newtype Identity a = Identity { runIdentity :: a }

That is, the type constructor `Identity` works like the function `id`,
but on the type level. It doesn't add any sort of special effects, it
just gives us a type constructor that we can use whenever we need
something of kind * -> *, like when working with monad transformer
stacks.

Identity is trivially a monad:

    instance Functor Identity where
        fmap f (Identity x) = Identity (f x)

    instance Applicative Identity where
        pure x = Identity x
        Identity f <*> Identity x = Identity (f x)

    instance Monad Identity where
        return x = Identity x
        Identity x >>= f = f x

If we erase all the newtype un/wrapping, then we can see that all
these functions are just variations on ($) and `id`. That's why we say
it's trivial.

-- 
Live well,
~wren