So I'm having a hard time trying with Peano and I need some help. I want to know if a Peano number is even and if yes then add:
0 + s(s(0)) = s(s(0))
0 + s(0) = No because one of the numbers odd
The code I have so far:
s(0).
s(X):-
X.
add(0,Y,Y).
add(s(X), Y, s(Z)):-
add(X,Y,Z).
Do not think about Peano numbers as numbers but as symbols.
Realize that the even Paeno numbers are 0 and a repeat of the pattern s(s(X)) where X can be 0 or the pattern s(s(X))
Also I look at 0 and s(0) etc. as data, and you are using s as a predicate name. I am not saying it will not work this way, but that is not how I think about this.
The name of the predicate is paeno_even and it takes one argument.
The base case is
paeno_even(0).
next for recursive case
paeno_even(P)
and the processing on P just removes s(s(X)) so do that in the head as
paeno_even(s(s(X)))
and then just do the recursive call
paeno_even(s(s(X))) :-
paeno_even(X).
A few test to demonstrate:
?- paeno_even(0).
true.
?- paeno_even(s(0)).
false.
?- paeno_even(s(s(0))).
true.
?- paeno_even(s(s(s(0)))).
false.
The entire code as one snippet:
paeno_even(0).
paeno_even(s(s(X))) :-
paeno_even(X).