Parametric polymorphism: Difference between revisions

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right->replace_all (new_value);

}</lang>

=={{header|Clean}}==

<lang clean>::Tree a = Empty | Node a (Tree a) (Tree a)

mapTree :: (a -> b) (Tree a) -> (Tree b)

mapTree f Empty = Empty

mapTree f (Node x l r) = Node (f x) (mapTree f l) (mapTree f r)</lang>

A digression:

Note that for the most usefulness in practical programming, a map operation like this should not be defined with a separate name but rather as <code>fmap</code> in an ''instance'' of the <code>Functor</code> ''type class'':

<lang clean>instance Functor Tree where

fmap f Empty = Empty

fmap f (Node x l r) = Node (f x) (fmap f l) (fmap f r)</lang>

<code>fmap</code> can then be used exactly where <code>mapTree</code> can, but doing this also allows the use of <code>Tree</code>s with other components which are parametric over ''any type which is a Functor''. For example, this function will add 1 to any collection of any kind of number:

<lang clean>add1Everywhere :: (f a) -> (f a) | Functor f & Num a

add1Everywhere nums = fmap (\x = x + 1) nums</lang>

If we have a tree of integers, i.e. <var>f</var> is <code>Tree</code> and <var>a</var> is <code>Integer</code>, then the type of <code>add1Everywhere</code> is <code>Tree Integer -> Tree Integer</code>.

</small></blockquote>

=={{header|D}}==

D template can parametric by constant.

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fmap f (Node x l r) = Node (f x) (fmap f l) (fmap f r)</lang>

<code>fmap</code> can then be used exactly where <code>mapTree</code> can, but doing this also allows the use of <code>Tree</code>s with other components which are parametric over ''any type which is a Functor''. For example, this function will add 1 to any collection of any kind of number:

<lang haskell>add1Everywhere :: (Functor f, Num a) => f a -> f a