[Jtsummers]

You could try in Prolog. But the other difference is that prolog is. General purpose language (though used in a more specific set of situations). Alloy is not.

Also the search mechanisms are not the same. Prolog uses a backtracking, depth-first search behind the scenes. Alloy does not.

EDIT: I was out earlier and didn't want to make a claim I couldn't verify/backup. Alloy uses a SAT solver behind the scenes to find solutions.