Correct way of writing recursive functions in CLP(R) with Prolog

Question

I am very confused in how CLP works in Prolog. Not only do I find it hard to see the benefits (I do see it in specific cases but find it hard to generalise those) but more importantly, I can hardly make up how to correctly write a recursive predicate. Which of the following would be the correct form in a CLP(R) way?

factorial(0, 1).
factorial(N, F):- {
  N > 0,
  PrevN = N - 1,
  factorial(PrevN, NewF),
  F = N * NewF}.

or

factorial(0, 1).
factorial(N, F):- {
  N > 0,
  PrevN = N - 1,
  F = N * NewF},
  factorial(PrevN, NewF).

In other words, I am not sure when I should write code outside the constraints. To me, the first case would seem more logical, because PrevN and NewF belong to the constraints. But if that's true, I am curious to see in which cases it is useful to use predicates outside the constraints in a recursive function.

Answer 1

There are several overlapping questions and issues in your post, probably too many to coherently address to your complete satisfaction in a single post.

Therefore, I would like to state a few general principles first, and then—based on that—make a few specific comments about the code you posted.

First, I would like to address what I think is most important in your case:

LP ⊆ CLP

This means simply that CLP can be regarded as a superset of logic programming (LP). Whether it is to be considered a proper superset or if, in fact, it makes even more sense to regard them as denoting the same concept is somewhat debatable. In my personal view, logic programming without constraints is much harder to understand and much less usable than with constraints. Given that also even the very first Prolog systems had a constraint like dif/2 and also that essential built-in predicates like (=)/2 perfectly fit the notion of "constraint", the boundaries, if they exist at all, seem at least somewhat artificial to me, suggesting that:

LP ≈ CLP

Be that as it may, the key concept when working with CLP (of any kind) is that the constraints are available as predicates, and used in Prolog programs like all other predicates.

Therefore, whether you have the goal factorial(N, F) or { N > 0 } is, at least in principle, the same concept: Both mean that something holds.

Note the syntax: The CLP(ℛ) constraints have the form { C }, which is {}(C) in prefix notation.

Note that the goal factorial(N, F) is not a CLP(ℛ) constraint! Neither is the following:

?- { factorial(N, F) }.
ERROR: Unhandled exception: type_error({factorial(_3958,_3960)},...)

Thus, { factorial(N, F) } is not a CLP(ℛ) constraint either!

Your first example therefore cannot work for this reason alone already. (In addition, you have a syntax error in the clause head: factorial (, so it also does not compile at all.)

When you learn working with a constraint solver, check out the predicates it provides. For example, CLP(ℛ) provides {}/1 and a few other predicates, and has a dedicated syntax for stating relations that hold about floating point numbers (in this case).

Other constraint solver provide their own predicates for describing the entities of their respective domains. For example, CLP(FD) provides (#=)/2 and a few other predicates to reason about integers. dif/2 lets you reason about any Prolog term. And so on.

From the programmer's perspective, this is exactly the same as using any other predicate of your Prolog system, whether it is built-in or stems from a library. In principle, it's all the same:

A goal like list_length(Ls, L) can be read as: "The length of the list Ls is L."

A goal like { X = A + B } can be read as: The number X is equal to the sum of A and B. For example, if you are using CLP(Q), it is clear that we are talking about rational numbers in this case.

In your second example, the body of the clause is a conjunction of the form (A, B), where A is a CLP(ℛ) constraint, and B is a goal of the form factorial(PrevN, NewF).

The point is: The CLP(ℛ) constraint is also a goal! Check it out:

?- write_canonical({a,b,c}).
{','(a,','(b,c))}
true.

So, you are simply using {}/1 from library(clpr), which is one of the predicates it exports.

You are right that PrevN and NewF belong to the constraints. However, factorial(PrevN, NewF) is not part of the mini-language that CLP(ℛ) implements for reasoning over floating point numbers. Therefore, you cannot pull this goal into the CLP(ℛ)-specific part.

From a programmer's perspective, a major attraction of CLP is that it blends in completely seamlessly into "normal" logic programming, to the point that it can in fact hardly be distinguished at all from it: The constraints are simply predicates, and written down like all other goals.

Whether you label a library predicate a "constraint" or not hardly makes any difference: All predicates can be regarded as constraints, since they can only constrain answers, never relax them.

Note that both examples you post are recursive! That's perfectly OK. In fact, recursive predicates will likely be the majority of situations in which you use constraints in the future.

However, for the concrete case of factorial, your Prolog system's CLP(FD) constraints are likely a better fit, since they are completely dedicated to reasoning about integers.