countable: Countable, Searchable, Finite, Empty classes. class Countable, for countable types class AtLeastOneCountable, for countable types that have at least one value class InfiniteCountable, for infinite countable types class Searchable, for types that can be searched over class Finite, for finite types class Empty, for empty types data Nothing, an empty type Also includes these orphan instances: instance (Searchable a,Eq b) => Eq (a -> b) instance (Finite a) => Foldable ((->) a) instance (Finite a) => Traversable ((->) a) instance (Show a,Finite a,Show b) => Show (a -> b) It turns out Searchable includes some infinite types. Specifically, countable implements this: instance (Countable c,Searchable s) => Searchable (c -> s) using the algorithm described here: http://math.andrej.com/2007/09/28/seemingly-impossible-functional-programs/ I would welcome improvements. http://hackage.haskell.org/package/countable-0.1 cabal install countable darcs get http://code.haskell.org/countable/ See also this thread: http://thread.gmane.org/gmane.comp.lang.haskell.cafe/73275