% Compute the nth number in the fibonacci sequence
fib(0, 0).
fib(1, 1).
fib(X, Res):-
    X1 is X - 1,
    X2 is X - 2,
    fib(X1, Tmp1),
    fib(X2, Tmp2),
    Res is Tmp1 + Tmp2.

% Compute the nth element of the integer factorial
fac(0, 1).
fac(X, Res):-
    X1 is X - 1,
    fac(X1, Tmp),
    Res is Tmp * X.

% Sums all integer numbers between and inclusive X and inclusive Y and writes the result to Res.
%
% example: sum(0, 9, X).
% output: X = 45
% explanation: 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 9
sum(X, X, X).
sum(X, Y, Res):-
    X < Y,
    X1 is X + 1,
    sum(X1, Y, Tmp),
    Res is Tmp + X.
sum(X, Y, Res):- % if X is bigger than Y, swap the operands and call sum again
    X > Y,
    sum(Y, X, Res).