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Ad-hoc polymorphism

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#REDIRECT [[Polymorphism#Ad-hoc polymorphism]]
A value is [[polymorphism|polymorphic]] if, depending on its context, it can assume more than one type. If the value is specified separately for each type it can have, this is called '''ad-hoc polymorphism''', also known as '''overloading'''. Ad-hoc polymorphic values may be used at a limited number of pre-specified types.
 
 
For instance, in C++, the addition operator may be used on any numeric type, like <tt>int</tt> or <tt>float</tt>, and may be applied to new types provided you write a definition for it using those types as arguments. The range of possible types of <tt>+</tt> in C++ is limited to those built-in and those for which the programmer has provided a definition. Similarly, in C, the operator <tt>+</tt> may operate on <tt>int</tt> or <tt>float</tt> or pointers. However, the programmer cannot supply their own definitions, and only the built-in types can be used.
 
 
In Haskell, type classes are used as a mechanism for "principled overloading", i.e. ad-hoc polymorphism. For instance, the following function:
 
<haskell>
 
show :: (Show a) => a -> String
 
</haskell>
 
may adopt any of the following types:
 
<haskell>
 
Int -> String
 
Float -> String
 
(Maybe Int, String, Either Char Float) -> String
 
</haskell>
 
The types which <hask>show</hask> can adopt are precisely those which have an instance of the standard <hask>Show</hask> class defined. Each instance gives a definition of the <hask>show</hask> function to be used when the types match. Unlike in C++ function overloading, Haskell also allows overloaded ''values'', like <hask>maxBound</hask>, that adopt a different value based on their type (e.g. <hask>maxBound :: Bool</hask> is equal to <hask>True</hask>, while <hask>maxBound :: Int</hask> may be <hask>2147483647</hask>).
 
 
Contrast ad-hoc polymorphism with [[parametric polymorphism]]: e.g. the function <hask>length :: [a] -> Int</hask> may be applied to lists of ''any'' type, but has only one definition which it uses regardless of which type it adopts.
 

Latest revision as of 21:59, 4 September 2012

  1. REDIRECT Polymorphism#Ad-hoc polymorphism