## 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. For example, the normal, definition of the map function,

``` map f []     = []
map f (x:xs) = f x : map f xs

```
is higher-order because its argument, f, is a function. The alternative formulation

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

```
defines a first-order function, map_f, that is a specialisation of map in its first argument. This can be considered a macro because it works purely by textual substitution, requiring no knowledge about f for its validity.

This is an example of partial evaluation - the call, map f l, has been partially evaluated to yeild an intermediate result. This may be useful in optimising compilation or execution, e.g. if the call to f can be subject to in-lining or when executing map_f on a long list.

Last updated: 2018-05-25

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