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:
Furthermore, the
Monad and
Applicative operations should
relate as follows:
The above laws imply:
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.