>> The version without ! looks identical to the version with ! except only the ! is removed - is this a joke? That's just showing getting rid of the cut in two

>> The version without ! looks identical to the version with ! except only the ! is removed - is this a joke? That's just showing getting rid of the cut in two stages. The line that makes it possible to remove it is this one: N #> 0, Markus Triskas' argument is that if you use the #> etc versions of declarative arithmetic operators, instead of the > ones, you can then call the factorial predicate with both arguments as variables, i.e. without inputs, just outputs, to enumerate the entire factorial relation. Like this: ?- n_factorial(N, F). N = 0, F = 1 ; N = 1, F = 1 ; N = 2, F = 2 ; N = 3, F = 6 ; ... . If you use > instead of #> the line N > 0 will raise an exception if N is a variable, which will be the case if you call it as above. This stops you from enumerating the relation, which declarative arithmetic allows. Of course there are other ways to write a factorial predicate (or any predicate) so that it always enumerates a relation but they are more verbose. Then again, you do need a special library to use declarative arithmetic anyway, so.