%=================================================
% Arithmetic
%=================================================

%--------------------------------
%Counting Down with Recursion
%--------------------------------
count(0,[]) :- !.          %The cut will eliminate the fail call to second clause.
count(X,[X | Rest]) :-
         X > 0,
         Y is X - 1,
         count(Y,Rest).


%--------------------------------
%Summing Up with Recursion
%
% - Produce the Sum of the numbers 
%   in the input list.
%--------------------------------
sum([],0).
sum([H | Rest] ,Sum) :-
         sum(Rest,RSum),
         Sum is H + RSum.


%--------------------------------
%Computing Factorial with Recursion
%--------------------------------
fact(0,1).
fact(N,Nfact) :-
     N > 0,
     M is N - 1,
     fact(M,Mfact),
     Nfact is N * Mfact.