Free monads are useful for many tree-like structures and domain specific
languages.
If f is a Functor then the free Monad on f is the type of trees whose nodes
are labeled with the constructors of f. The word "free" is used in the
sense of "unrestricted" rather than "zero-cost": Free f makes no
constraining assumptions beyond those given by f and the definition of
Monad. As used here it is a standard term from the mathematical theory of
adjoint functors.
Cofree comonads are dual to free monads. They provide convenient ways to
talk about branching streams and rose-trees, and can be used to annotate
syntax trees. The cofree comonad can be seen as a stream parameterized by a
Functor that controls its branching factor.
