Polymorphism: Difference between revisions

Revision as of 18:00, 30 April 2012

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.

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

Examples

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

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

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

1 :: (Num t) => t

References

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

Type polymorphism at Wikipedia

@@ Line 10: / Line 10: @@
 == Examples ==
 <haskell>
-foldr :: forall a b. (a -> b -> b) -> b -> [a] -> b
+foldr :: (a -> b -> b) -> b -> [a] -> b
 </haskell>
-<hask>foldr</hask> is a parametric polymorphic [[function]]. When actually used, it may take on any of a variety of types, for example:
+<hask>foldr</hask> is a parametrically polymorphic [[function]]. When actually used, it may take on any of a variety of types, for example:
 <haskell>
-::(Char ->Int->Int)->Int->String->Int
+:: (Char -> Int -> Int) -> Int -> String -> Int -- a = Char, b = Int
-::(String->String->String)->String->[String]->String
+:: (String -> String -> String) -> String -> [String] -> String -- a = b = String
 </haskell>
-An "integer literal" is a parametric polymorphic data type:
+Numeric literals are overloaded (i.e. subject to ad-hoc polymorphism):
 <haskell>
-:: forall t. (Num t) => t
+:: (Num t) => t
 </haskell>