Constructing Recursive Data Structures

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Adding Peano numbers:

add(z, X, X):- natural(X).
add(s(N), X, s(Y)):- add(N, X, Y).

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Some queries

?- add(s(s(z)), s(z), R).
R = s(s(s(z)))

?- add(s(s(s(z))), T, s(s(s(s(s(z))))).
T = s(z)

?- add(s(s(s(s(z)))), T, s(s(s(z)))).
no

?- add(X, Y, s(s(z))).
X = z, Y = s(s(z)) ;
X = s(z), Y = s(z) ;
X = s(s(z)), Y = z