:- initializing, add_function(eval, 1).
:- initializing, add_function(evalLazy, 1).
:- initializing, add_function(fapply, 2).
:- initializing, add_function(@, 2).
:- initializing, add_function(twice, 2).
:- initializing, add_function(until, 3).
:- initializing, add_function(round2, 1).
:- initializing, add_function(foldr, 3).
:- initializing, add_function(foldl, 3).
:- initializing, add_function(sum1, 1).
:- initializing, add_function(product, 1).
:- initializing, add_function(flatten, 1).
:- initializing, add_function(o, 3).
:- initializing, add_function(cons, 2).
:- initializing, add_function(map_f, 2).

:- op(20, yfx, @).
@(A9, B9, A) :-
	fapply(A9, B9, A).
:- twice(A, B, C) when ever.
twice(A9, B9, A) :-
	fapply(A9, B9, B),
	fapply(A9, B, A).
:- until(A, B, C, D) when ever.
until(A9, B9, C9, A) :-
	(if call(A9, C9) then
		A = C9
	else
		fapply(B9, C9, B),
		until(A9, B9, B, C),
		A = C
	).
:- round2(A, B) when ever.
round2(A9, A) :-
	until(=<(A9), *(2), 1, A).
:- foldr(A, B, [], C) when ever.
foldr(A9, B9, [], B9).
:- foldr(A, B, [C|D], E) when ever.
foldr(A9, B9, [C9|D9], A) :-
	fapply(A9, C9, B),
	foldr(A9, B9, D9, C),
	fapply(B, C, A).
:- foldl(A, B, [], C) when ever.
foldl(A9, B9, [], B9).
:- foldl(A, B, [C|D], E) when ever.
foldl(A9, B9, [C9|D9], A) :-
	fapply(A9, B9, B),
	fapply(B, C9, C),
	foldl(A9, C, D9, A).
:- sum1(A, B) when ever.
sum1(A9, A) :-
	foldl(+, 0, A9, A).
:- product(A, B) when ever.
product(A9, A) :-
	foldl(*, 1, A9, A).
:- flatten(A, B) when ever.
flatten(A9, A) :-
	foldr(concat, [], A9, A).

:- op(40, xfy, o).
:- o(A, B, C, D) when ever.
o(A9, B9, C9, A) :-
	fapply(B9, C9, B),
	fapply(A9, B, A).
:- cons(A, B, C) when ever.
cons(A9, B9, [A9|B9]).
:- map_f(A, B, C) when ever.
map_f(A9, B9, A) :-
	foldr(cons o A9, [], B9, A).