Theory

Parametric polymorphism lets one data description work for any element type.

data List a = Nil | Cons a (List a)

List is a type constructor; a is a type parameter.

Benefits

Code reuse – functions like map, length work for every a.
Type safety – operations preserve element type.

Example

data Tree a
  = Empty
  | Node a (Tree a) (Tree a)
 
singleton :: a -> Tree a
singleton x = Node x Empty Empty

Generation and pattern-matching mirror concrete types:

count :: Tree a -> Int
count Empty        = 0
count (Node _ l r) = 1 + count l + count r