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1 GlynWebster 1 Higher-order functions are functions that take other functions as parameters, create functions or return functions.
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3 The use of higher-order functions with PolymorphicTypes results in a style of programming that rivals ObjectOrientation for expressiveness. Some may assert it beats it.
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5 [ML], [Haskell], [LISP], [Python] all allow full use of high-order functions. [C] allows you to pass functions as arguments, but their usefulness is rather limited.
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7 !!!An Example
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9 (This follows on from the the example in PolymorphicTypes.)
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11 Glyn want make new trees from old ones by changing the leaves. So he writes a function to do this for him. One of its parameters will be a function that takes the value of a leaf and returns the changed value.
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13 # __let rec__ map change tree =
14 __match__ t __with__
15 | Leaf value -> Leaf (change value)
16 | Node (left, right) -> Node (map change left, map change right) ;;
17 ''val map : ('a -> 'b) -> 'a tree -> 'b tree = <fun>''
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19 Once again Ocaml has worked out the types for itself. (__a -> b -> c__ is ML for "function that takes parameters of the types __a__ and __b__ and returns a value of type __c__.) It's also noted that if the __change__ function doesn't return the same type as its given then the __map__ function will return a tree of a different type. Good. That's what Glyn wanted. (If it wasn't he could add some type annotations to say so.)
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21 Here's a function that can be used as a __change__ parameter:
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23 # string_of_int ;;
24 ''- : int -> string = <fun>''
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26 You can guess what that does. __map__'s type is __('a -> 'b) -> 'a tree -> 'b tree__, so if I give it __string_of_int__ as its first parameter then __'a__ will be __string__ and __'b__ will be __int__, so __map__ should return a __string tree__...
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28 # __let__ numtree = Node (Node (Leaf 1, Leaf 2), Leaf 3) ;;
29 ''val numtree : int tree = Node (Node (Leaf 1, Leaf 2), Leaf 3)''
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31 # map string_of_int numtree ;;
32 ''- : string tree = Node (Node (Leaf "1", Leaf "2"), Leaf "3")''
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34 And it does!
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36 If he writes a few more functions like this he will have a reusable library of binary tree operations. ML makes writing reusable code and easy and ''reliable'' process.
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38 There's a lot more things you can do with higher-order functions, some of them very painful. What I've shown you there's at least ''one'' good thing you can do with them.