Inverse factorial in Prolog

Question

Can someone helping me to find a way to get the inverse factorial in Prolog...

For example inverse_factorial(6,X) ===> X = 3.

I have been working on it a lot of time.

I currently have the factorial, but i have to make it reversible. Please help me.

Answer 1

Prolog's predicates are relations, so once you have defined factorial, you have implicitly defined the inverse too. However, regular arithmetics is moded in Prolog, that is, the entire expression in (is)/2 or (>)/2 has to be known at runtime, and if it is not, an error occurs. Constraints overcome this shortcoming:

:- use_module(library(clpfd)).

n_factorial(0, 1).
n_factorial(N, F) :-
   N #> 0, N1 #= N - 1, F #= N * F1,
   n_factorial(N1, F1).

This definition now works in both directions.

?- n_factorial(N,6).
N = 3 ;
false.

?- n_factorial(3,F).
F = 6 ;
false.

Since SICStus 4.3.4 and SWI 7.1.25 also the following terminates:

?- n_factorial(N,N).
   N = 1
;  N = 2
;  false.

See the manual for more.