More monads

Besides Maybe and State, a number of other applicative functor examples we saw in the previous chapter also have a monad structure. We revisit them here.

The Identity monad

Our first example is the Identity functor, which models pure computations. Its monad instance provides a sequential notation for function application:

Control.Monad.Identity
instance Monad Identity where
  Identity x >>= f = f x

When emphasizing the monad structure, this type is usually called the Identity monad rather than the Identity functor.

Instead of writing a nested function application f (g (h x)), we can write this in successive steps as Identity (f x) >>= (Identity . g) >>= (Identity . h). This isn’t particularly convenient, but it looks a bit more familiar to imperative programmers when we use the do notation (and ignore the Identity wrappers):

do y <- Identity (f x)
   z <- Identity (g y)
   Identity ...