% Peano representation of natural numbers:
% a natural number is 0 (Funktor: o) or the successor s(n) of a natural number n

isPeano(o).
isPeano(s(N)) :- isPeano(N).

% Operations on Peano numbers: successor and predecessor
succ(N, s(N)).
pred(s(N), N).

% add operation on Peano numbers:
add(o   ,Y,Y).
add(s(X),Y,s(Z)) :- add(X,Y,Z).

% subtraction, i.e., compute the difference Z between X and Y (with X>=Y)
sub(X,Y,Z) :- add(Y,Z,X).

% multiply operation on Peano numbers:
mult(o   ,_,o).
mult(s(X),Y,Z) :- mult(X,Y,XY), add(XY,Y,Z).

% less-or-equal:
leq(o,_).
leq(s(X),s(Y)) :- leq(X,Y).