Problem Statement

While implementing a recursive function, it often happens that we must resort to a separate   helper function   to handle the actual recursion. This is usually the case when directly calling the current function would waste too many resources (stack space, execution time), causing unwanted side-effects,   and/or the function doesn't have the right arguments and/or return values. So we end up inventing some silly name like   foo2   or   foo_helper.   I have always found it painful to come up with a proper name, and see some disadvantages: Some languages allow you to embed recursion directly in-place.   This might work via a label, a local gosub instruction, or some special keyword. Anonymous recursion can also be accomplished using the   Y combinator.

If possible, demonstrate this by writing the recursive version of the fibonacci function   (see Fibonacci sequence)   which checks for a negative argument before doing the actual recursion.

Let's start with the solution:

:- use_module(lambda).

fib(N, _F) :-
	N < 0, !,
	write('fib is undefined for negative numbers.'), nl.

fib(N, F) :-
    % code of Fibonacci
    PF     = \Nb^R^Rr1^(Nb < 2 ->
			  R = Nb
                        ;
			  N1 is Nb - 1,
			  N2 is Nb - 2,
			  call(Rr1,N1,R1,Rr1),
			  call(Rr1,N2,R2,Rr1),
			  R is R1 + R2
			),

    % The Y combinator.

    Pred = PF +\Nb2^F2^call(PF,Nb2,F2,PF),

    call(Pred,N,F).