class Functor f where Source

The Functor class is used for types that can be mapped over. Instances of Functor should satisfy the following laws:

fmap id  ==  id
fmap (f . g)  ==  fmap f . fmap g

The instances of Functor for lists, Maybe and IO satisfy these laws.

class Applicative m => Monad m where Source

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Instances of Monad should satisfy the following laws:

• return a >>= k  =  k a

• m >>= return  =  m

• m >>= (x -> k x >>= h)  =  (m >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

• pure = return

• (<*>) = ap

The above laws imply:

• fmap f xs  =  xs >>= return . f

• (>>) = (*>)

and that pure and (<*>) satisfy the applicative functor laws.

The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.