:- initializing, add_function(eval, 1).
:- initializing, add_function(evalLazy, 1).
:- initializing, add_function(+, 2).
:- initializing, add_function(-, 2).
:- initializing, add_function(*, 2).
:- initializing, add_function(//, 2).
:- initializing, add_function(univ_f, 1).
:- initializing, add_function(univ_l, 1).
:- initializing, add_function(concat, 2).
:- initializing, add_function(append3, 3).
:- initializing, add_function(sum_tree, 1).
:- initializing, add_function(flatten_tree, 1).
:- initializing, add_function(sum, 1).
:- initializing, add_function(nmax, 2).
:- initializing, add_function(max_l, 1).
:- initializing, add_function(max_l1, 2).
:- initializing, add_function(add_lists, 2).
:- initializing, add_function(isort, 1).
:- initializing, add_function(insert, 2).
:- initializing, add_function(isort1, 1).
:- initializing, add_function(isort1a, 2).
:- initializing, add_function(fact, 1).
:- initializing, add_function(fact1, 1).
:- initializing, add_function(f91, 1).
:- initializing, add_function(qs, 1).
:- initializing, add_function(zip2, 2).
:- initializing, add_function(insertlast, 2).
+(A9, B9, A) :-
	A is A9 + B9.
-(A9, B9, A) :-
	A is A9 - B9.
*(A9, B9, A) :-
	A is A9 * B9.
//(A9, B9, A) :-
	A is A9 // B9.
univ_f(A9, A) :-
	A9 =.. A.
univ_l(A9, A) :-
	A =.. A9.

:- fact1(7, A), writeln(A).
:- concat([], A, B) when ever.
concat([], A9, A9).
:- concat([A|B], C, D) when ever.
concat([A9|B9], C9, [A9|A]) :-
	concat(B9, C9, A).
:- append3(A, B, C, D) when ever.
append3(A9, B9, C9, A) :-
	concat(B9, C9, B),
	concat(A9, B, A).
:- sum_tree(nil, A) when ever.
sum_tree(nil, 0).
:- sum_tree(t(A, B, C), D) when ever.
sum_tree(t(A9, B9, C9), A) :-
	sum_tree(A9, B),
	C is B + B9,
	sum_tree(C9, D),
	A is C + D.
:- flatten_tree(nil, A) when ever.
flatten_tree(nil, []).
:- flatten_tree(t(nil, A, B), C) when ever.
flatten_tree(t(nil, A9, B9), [A9|A]) :-
	flatten_tree(B9, A).
:- flatten_tree(t(t(A, B, C), D, E), F) when ever.
flatten_tree(t(t(A9, B9, C9), D9, E9), A) :-
	flatten_tree(t(A9, B9, t(C9, D9, E9)), A).
:- sum([], A) when ever.
sum([], 0).
:- sum([A|B], C) when ever.
sum([A9|B9], A) :-
	sum(B9, B),
	A is A9 + B.
:- nmax(A, B, C) when ever.
nmax(A9, B9, A) :-
	(if A9 >= B9 then
		A = A9
	else
		A = B9
	).
:- max_l([A|B], C) when ever.
max_l([A9|B9], A) :-
	max_l1(A9, B9, A).
:- max_l1(A, [], B) when ever.
max_l1(A9, [], A9).
:- max_l1(A, [B|C], D) when ever.
max_l1(A9, [B9|C9], A) :-
	nmax(A9, B9, B),
	max_l1(B, C9, A).
:- add_lists([], A, B) when ever.
add_lists([], A9, []).
:- add_lists([A|B], [], C) when ever.
add_lists([A9|B9], [], []).
:- add_lists([A|B], [C|D], E) when ever.
add_lists([A9|B9], [C9|D9], [A|B]) :-
	A is A9 + C9,
	add_lists(B9, D9, B).
:- isort([], A) when ever.
isort([], []).
:- isort([A|B], C) when ever.
isort([A9|B9], A) :-
	isort(B9, B),
	insert(A9, B, A).
:- insert(A, [], B) when ever.
insert(A9, [], [A9]).
:- insert(A, [B|C], D) when ever.
insert(A9, [B9|C9], A) :-
	(if A9 =< B9 then
		A = [A9, B9|C9]
	else
		insert(A9, C9, B),
		A = [B9|B]
	).
:- isort1(A, B) when ever.
isort1(A9, A) :-
	isort1a(A9, [], A).
:- isort1a([], A, B) when ever.
isort1a([], A9, A9).
:- isort1a([A|B], C, D) when ever.
isort1a([A9|B9], C9, A) :-
	insert(A9, C9, B),
	isort1a(B9, B, A).
:- fact(0, A) when ever.
fact(0, 1).
% Error: equations for fact/1 not mutually exclusive
fact(A9, A) :-
	A9 > 0,
	B is A9 - 1,
	fact(B, C),
	A is A9 * C.
:- fact1(A, B) when ever.
fact1(A9, A) :-
	(if A9 > 0 then
		B is A9 - 1,
		fact1(B, C),
		D is A9 * C,
		A = D
	else
		A = 1
	).
:- f91(A, B) when ever.
f91(A9, A) :-
	(if A9 > 100 then
		B is A9 - 10,
		A = B
	else
		C is A9 + 11,
		f91(C, D),
		f91(D, E),
		A = E
	).
:- qs([], A) when ever.
qs([], []).
:- qs([A|B], C) when ever.
qs([A9|B9], A) :-
	part(A9, B9, B, C),
	qs(B, D),
	qs(C, E),
	concat(D, [A9|E], A).
part(A, [], [], []).
part(A, [B|C], [B|D], E) :-
	B =< A,
	part(A, C, D, E).
part(A, [B|C], D, [B|E]) :-
	B > A,
	part(A, C, D, E).
gt_l(A, B) :-
	max_l(A, C),
	max_l(B, D),
	C > D.
:- zip2([], A, B) when ever.
zip2([], A9, []).
:- zip2([A|B], [], C) when ever.
zip2([A9|B9], [], []).
:- zip2([A|B], [C|D], E) when ever.
zip2([A9|B9], [C9|D9], [(A9, C9)|A]) :-
	zip2(B9, D9, A).
:- insertlast(A, [], B) when ever.
insertlast(A9, [], [A9]).
:- insertlast(A, [B|C], D) when ever.
insertlast(A9, [B9|C9], [B9|A]) :-
	insertlast(A9, C9, A).