Convert peano number s(N) to integer in Prolog

Question

I came across this natural number evaluation of logical numbers in a tutorial and it\'s been giving me some headache:

natural_number(0).
natural_number(s(N))         


        

Answer 1

No problemo with meta-predicate nest_right/4 in tandem with Prolog lambdas!

:- use_module(library(lambda)).
:- use_module(library(clpfd)).

:- meta_predicate nest_right(2,?,?,?).
nest_right(P_2,N,X0,X) :-
   zcompare(Op,N,0),
   ord_nest_right_(Op,P_2,N,X0,X).

:- meta_predicate ord_nest_right_(?,2,?,?,?).
ord_nest_right_(=,_,_,X,X).
ord_nest_right_(>,P_2,N,X0,X2) :-
   N0 #= N-1,
   call(P_2,X1,X2),
   nest_right(P_2,N0,X0,X1).

Sample queries:

?- nest_right(\X^s(X)^true,3,0,N).
N = s(s(s(0))).                 % succeeds deterministically

?- nest_right(\X^s(X)^true,N,0,s(s(0))).
N = 2 ;                         % succeeds, but leaves behind choicepoint
false.                          % terminates universally