Peano relation in Prolog using the CLP(FD) that ships with SWI-Prolog.

prolog peano

:- use_module(library(clpfd)).

peano(N,z) :- N #= 0.
peano(N,s(PDec)) :-
        N #> 0,
        N - 1 #= NDec,
        peano(NDec, PDec).

% ?- peano(4, Q).
% Q = s(s(s(s(z)))) ;
% false.

% ?- peano(Q, s(s(s(s(z))))).
% Q = 4.

% ?- peano(0, Q).
% Q = z ;
% false.

% ?- peano(Q, z).
% Q = 0.