Monad is:exact package:base set:included-with-ghc

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:

• Left identity return a >>= k = k a
• Right identity m >>= return = m
• Associativity m >>= (\x -> k x >>= h) = (m >>= k) >>= h

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

• pure = return

• m1 <*> m2 = m1 >>= (\x1 -> m2
  >>= (\x2 -> return (x1 x2)))

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.

The Functor, Monad and MonadPlus classes, with some useful operations on monads.