Prolog recursively count numbers in a list

Question

I need a program to count all the numbers in a list, no matter how DEEPLY NESTED they are. I was able to count numbers in the case where they were not inside another list, but recursing through deeply nested elements is not working out. I have this so far:

count([],0).
count([H|Tail], N) :-
    count(Tail, N1),
    (  number(H)
    ->N is N1 + 1
    ;   is_list(H)
    -> count(H,N)  
    ;   N = N1
    ).

So, if I were to call count([a,1,[2,b],3],N), the output should be N=3; however, I only get N=2. Could someone please help me add to my second case test? All available solutions here do not work for deeply nested numerical elements.

Thank you!

Answer 1

Your code is incorrect for the is_list(H) branch: in that case you ignore the value of N1, which is not correct, you want N to be the sum of N1 with the count on H.

Complete code:

:- use_module(library(clpfd)).

count([], 0).
count([H|T], N) :-
    count(T, N1),
    (   number(H) ->
        N #= N1 + 1
    ;   is_list(H) ->
        N #= N1 + N2,
        count(H, N2)
    ;   N1 = N
    ).