%	some examples of higher order stuff
%
%	It would be nice to have a better syntax for "fapply"
%	eg, :/2 (currently op declarations for : is a problem)
%	Also, : is currently used for "else".  Maybe @, # or $ ?

:- function fapply/2.

	% shorthand for function application
:- op(20, yfx, @).	% change precedence?
F @ X == fapply(F, X).

	% apply function twice to arg
% twice(F, X) = F : (F : X).
twice(F, X) = fapply(F, fapply(F, X)).

	% until first arg applied to X is true
	% apply second arg to X
	% as in Miranda
until(P, F, X) = ( call(P, X) ? X : until(P, F, fapply(F, X))).

	% round up to next power of 2
round2(N) = until(=<(N), *(2), 1).

	% foldr as in Miranda
foldr(F, B, []) = B.
foldr(F, B, H.T) = F @ H @ foldr(F, B, T).

	% foldl as in Miranda
foldl(F, B, []) = B.
foldl(F, B, H.T) = foldl(F, F @ B @ H, T).

	% sum of elements in a list
	% sum/1 is defined in test.ne
sum1(X) = foldl(+, 0, X).

	% product of elements in a list
product(X) = foldl(*, 1, X).

	% flatten list of lists into a list
	% concat/2 is defined in test.ne
flatten(X) = foldr(concat, [], X).

	% function composition
:- op(40, xfy, o).
o(F, G, X) = F @ (G @ X).

cons(A, As) = A.As.

map_f(F, As) = foldr(cons o F, [], As).