Polymorphism

A value is polymorphic if, depending on the context where it's used, it can take on more than one type.

There are different kinds of polymorphism.

1. Parametric polymorphism; mostly found in functional languages
2. Ad-hoc polymorphism or overloading
3. Inclusion polymorphism; mostly found in object oriented languages

Examples

foldr :: (a -> b -> b) -> b -> [a] -> b

The type of foldr involves unrestricted type variables, so it is a parametrically polymorphic function. When actually used, it may take on any of a variety of types, for example:

:: (Char -> Int -> Int) -> Int -> String -> Int -- a = Char, b = Int (note String = [Char])
:: (String -> String -> String) -> String -> [String] -> String -- a = b = String

Numeric literals are overloaded (i.e. subject to ad-hoc polymorphism):

1 :: (Num t) => t

The difference is that the type variable here is constrained – it must be an instance of Num.

References

• On Understanding Types, Data Abstraction, and Polymorphism (1985), by Luca Cardelli, Peter Wegner in ACM Computing Surveys.

• Type polymorphism at Wikipedia