[zmonx]

Please see my profile page: It contains links that I find relevant for learning modern Prolog features.

Every predicate you impose on the set of solutions can be regarded as a constraint, because it can at most restrict the set of solutions, never increase it.

So, in fact, every Prolog goal you invoke is a constraint. When reasoning over Herbrand terms, the only constraints are equality and disequality of terms, which are implemented by the predicates (=)/2 and dif/2, respectively.

In addition to these basic constraints over terms, modern Prolog systems also provide constraints over more specialized domains, such as constraints on integers, rational numbers and Boolean values. For combinatorial tasks such as map coloring, constraints over integers are especially useful.

For example, here is a constraint on integers, using GNU Prolog:

    | ?- 3 #= 1+Y.
    
    Y = 2

In this case, the system has correctly deduced that Y can only be 2 subject to the constraint that 3 is equal to the result of the arithmetic integer expression 1+Y, where Y is constrained to integral values.

Constraints implement relations between their arguments and can be used in all directions. This is the reason why Prolog predicates are typically more general than functions in other languages. However, to truly benefit from this, you must consistently use these comparatively new language features instead of lower-level ones. I say comparatively because these language features have been available for several decades by now in professional Prolog systems such as SICStus.

[jononor]

How does using constraints in Prolog relate to using a (finite domain) constraint solver?

[zmonx]

The beauty of this is that a constraint solver (over finite domains, Boolean values, sets etc.) blends in completely seamlessly into the way Prolog works.

From the perspective of Prolog and its users, a constraint solver is simply available just like any other predicate! All the internal reasoning a constraint solver performs is completely abstracted away. The only interface is typically a few Prolog predicates that let you access the features of the solver by stating what must hold about the involved variables.

So, to use a constraint solver in Prolog, you simply use the predicates it provides, just as you would use any other Prolog predicate. In the example above, I am using the constraint (#=)/2, which is a predicate that is true iff its arguments evaluate to the same integer.

From the perspective of implementors, Prolog is a great implementation language for constraint solvers due to its built-in search and backtracking mechanisms. It also allows you to use the standardized Prolog syntax that many users are already familiar with, instead of having to devise yet another modeling language on top of your solver.

Thus, I would describe the relation as a natural symbiosis: It is natural to use constraint solvers in Prolog, and natural to implement them in Prolog.