higher-order function

(HOF) A function that can take one or more functions as argument and/or return a function as its value. E.g. map in (map f l) which returns the list of results of applying function f to each of the elements of list l. See also curried function.

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higher-order macro

A means of expressing certain higher-order functions in a first order language. Proposed by Phil Wadler. Higher-order macros cannot be recursive at the top level but they may contain recursive definitions. E.g.

	map f l = m l
		  m []	   = []
		  m (x:xs) = f x : m xs

Expanding a call to this macro is equivalent to specialising a call to map in its first argument.

See partial evaluation.

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