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+% 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).
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