I'm trying to implement n_factors/2 predicate that works in all directions.
:- use_module(library(clpz)).
n_factors(N, Fs) :-
integer(N),
N > 1,
primes(Ps),
n_factors0(N, Fs, Ps),
!.
n_factors(N, Fs) :-
var(N),
primes(Ps),
N #> 1,
above(2, N),
n_factors0(N, Fs, Ps).
above(I, I).
above(I, N) :- I1 is I + 1, above(I1, N).
n_factors0(N, [F|Fs], [P|Ps]) :-
N #> 1,
F #=< N,
P #=< N,
( P * P #> N ->
F = N, Fs = []
; ( N #= N1 * P ->
F #= P, n_factors0(N1, Fs, [P|Ps])
; F #> P, n_factors0(N, [F|Fs], Ps)
)
).
When I am issuing the following query I get:
?- C #> 6, C #< 12, n_factors(A, [B,C]).
C = 7, A = 14, B = 2
; C = 7, A = 21, B = 3
; C = 11, A = 22, B = 2
; C = 11, A = 33, B = 3
; C = 7, A = 35, B = 5
; C = 7, A = 49, B = 7
; C = 11, A = 55, B = 5
; C = 11, A = 77, B = 7
; C = 11, A = 121, B = 11
;
before the program moves on to exploring the realm of rather large numbers. So the question I've go is the following: knowing for certain that the mathematical problem is constraint enough to terminate, how do I find the missing constraint in my program? What I am doing right now is staring at the screen before trying to add "invariant" conditions here and there and see if they help.
primes(Ps) is a "frozen" infinite list with all prime numbers. I don't think the implementation thereof is important for this question but just in case
primes(Ps) :-
Ps = [2,3|T],
primes0(5, Ps, Ps, T),
!.
primes0(C, [D|Ds], Ps, T) :-
( D * D > C ->
T = [C|T1], C1 is C + 2, freeze(T1, primes0(C1, Ps, Ps, T1))
; ( C mod D =:= 0 ->
C1 is C + 2, primes0(C1, Ps, Ps, T)
; primes0(C, Ds, Ps, T)
)
).
