zlacker

Ah, thanks. There's nothing wrong with that except that it makes code more verbose. An alternative is flattening, where you remove the compound arguments from the heads of predicates by defining them as new predicates.

Let me see if I can apply flattening to the example above:

  % Flattened version:
  foo(a, A1, X) :-
        q(A1)
        ,body(A, X2, X2).

  q(p(X1)):-
    % ... code that binds X1
    .

With flattening only compound terms are replaced, not constants so "a" remains unchanged. It's similar to an ad-hoc type system again, but the cool thing is that it can be done automatically. There's an algorithm for it known to the Inductive Logic Programming (ILP) community. Let me see if I can find that paper... Yep:

Flattening and Saturation: Two Representation Changes for Generalization, Céline Rouveirol, 1994.

https://link.springer.com/content/pdf/10.1023/A:102267821728...

The example is a bit unusual though because it only checks that A1 = p(X1) and doesn't do anything with X1, it even leaves it dangling as a singleton; same with X and X2. That's very unlikely for real-world code where you want to use unification as a mechanism to pass the state of the computation around your program. With flattening you want to have an extra argument in the new predicate that "returns" a value that you want to process further. I think maybe they meant to write it like this:

  foo(a, p(X1), X) :-
        body(a, X1, X).

  foo(A, A1, X) :-
        A = a,
        A1 = p(X1),
        body(a, X1, X).

In which case the flattened version would be like:

  foo(a, A1, X) :-
        q(A1,X1),
        body(a, X1, X).

  q(p(X1),X2):-
    % ... code that binds X2
    .

So, I guess, we see that this is a known gotcha and the logic programming community has different ways to work around it. In the ILP community there's a different motivation (to make a language finite, and therefore decidable, by removing "functions").

>> I'm really enjoying the convington et al read, cool to see that O'Keefe is an author too!

Yeah. I haven't heard much from O'Keefe lately and I miss his advice. He was a regular contributor to the SWI-Prolog mailing list when I was doing my MSc in 2014. I think there was a bit of a problem with the SWI-Prolog community moving to Google and he hasn't returned since, even though the community is now on Discourse.