Recursion on Prolog

I'm trying to write a Prolog recursion that will return the following representation for numbers:

1 --> s(0)

2 --> s(s(0))

3 --> s(s(s(0))) ...

I used the following code:

retnum(s(0),1). %Stop Condition
retnum(S,Z):-
    retnum(s(S),Z1),
    Z is Z1+1.

but when I try to run prediction :

retnum(A,2).

I get result A=0, and if I continue I get error with stuck limit exceeded. I was expecting to get a result A = s(s(0)). I tried also to add additional stop condition : retnum(0,0).

Any idea where is my mistake and if there is better way to do it?

Solution

You are using the recursive call incorrectly. The argument to the recursive instance should be smaller than the original (more generally: converging to a boundary condition). This might give you what you want:

retnum(s(0), 1).
retnum(s(S), Z) :-
    retnum(S, Z1),
    Z is Z1 + 1.

But this is even better.

retnum1(s(0), 1).
retnum1(s(S), Z) :-
    Z > 1, Z1 is Z - 1,
    retnum1(S, Z1).

Try to trace/0 and see why it is so.