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 xsis 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 xsdefines 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