Prevent backtracking after first solution to Fibonacci pair

Question

The term fib(N,F) is true when F is the Nth Fibonacci number.

The following Prolog code is generally working for me:

Answer 1

I played a bit with another definition, I wrote in standard arithmetic and translated to CLP(FD) on purpose for this question.

My plain Prolog definition was

fibo(1, 1,0).
fibo(2, 2,1).
fibo(N, F,A) :- N > 2, M is N -1, fibo(M, A,B), F is A+B.

Once translated, since it take too long in reverse mode (or doesn't terminate, don't know), I tried to add more constraints (and moving them around) to see where a 'backward' computation terminates:

fibo(1, 1,0).
fibo(2, 2,1).
fibo(N, F,A) :-
  N #> 2,
  M #= N -1,
  M #>= 0,  % added
  A #>= 0,  % added
  B #< A,   % added - this is key
  F #= A+B,
  fibo(M, A,B). % moved - this is key

After adding B #< A and moving the recursion at last call, now it works.

?- time(fibo(U,377,Y)).
% 77,005 inferences, 0.032 CPU in 0.033 seconds (99% CPU, 2371149 Lips)
U = 13,
Y = 233 ;
% 37,389 inferences, 0.023 CPU in 0.023 seconds (100% CPU, 1651757 Lips)
false.

edit To account for 0 based sequences, add a fact

fibo(0,0,_).

Maybe this explain the role of the last argument: it's an accumulator.