Standard Transformers

Let's look at the standard transformers and look at some simple examples of what we can do with them. Before doing this, it is useful to review the Identity functor. When I introduced it a long time ago, I promised you that we would meet it again in the discussion of monad transformers. The moment has come.

The Identity monad is the simplest monad we can think of. The decoration it provides is exactly nothing:

newtype Identity a = Identity { runIdentity :: a }

It simply wraps a plain old value. return does the wrapping. runIdentity does the unwrapping. And (>>=) is plain old function application.

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

All that Identity does is to allow us to pretend that pure computations without side effects actually use some monad. We'll see in a second why that's useful.