[zmonx]

I agree with what Sylvain Soliman said about this on Reddit: It's a nice tutorial for the 80's parts of the language:

https://www.reddit.com/r/programming/comments/7hp2xw/introdu...

In modern Prolog systems, you would use more declarative features such as constraints to model combinatorial tasks like map coloring.

Make sure to check out modern Prolog features if you are interested in learning the language seriously!

[kccqzy]

Are there any good materials (articles, books) for this kind of modern Prolog? I’m afraid my only experience with Prolog is those 80s features of Prolog and I’m not sure what you mean by constraints.

[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.

[agumonkey]

are modern prolog just a layer on top of the old semantics or somehow an incompatible paradigm ?

[giardini]

The OP is likely speaking of "Constraint Logic Programming(CLP)".

The set of CLP languages is generally implemented as a superset or add-on package(s) to a Prolog implementation. For example, SICStus Prolog and SWI-Prolog have CLP modules, e.g.:

https://sicstus.sics.se/sicstus/docs/3.7.1/html/sicstus_32.h...

http://www.swi-prolog.org/pldoc/man?section=clp

and "Constraint Handling Rules(CHR):

http://www.swi-prolog.org/pldoc/man?section=chr

To the best of my knowledge the modules are written in Prolog. A look at those links will give you an idea of how CLP is used. There are modules available for CLP(X) where X is one of:

B = boolean,

Z = integers,

Q = rational numbers,

R = real(floating point) numbers,

FD = finite domains (see "CLP(FD) Constraint Logic Programming over Finite Domains" http://www.pathwayslms.com/swipltuts/clpfd/clpfd.html )

etc.

One can understand how constraining the domain of interest (reducing the search space) to say, the integers, might make search more efficient.

[zmonx]

In a sense, yes, these modules are written in Prolog. However, that is not the full story: CLP requires special interface predicates that the underlying Prolog system must provide. You cannot implement CLP "on top" of just any Prolog system with reasonable performance and correctness.

Devising and implementing such suitable interface predicates is quite hard, and only a very small number of Prolog systems have succeeded with this so far.

For example, the SWI interface for CLP is too limited in practice, and its constraint solvers have elementary mistakes also because of the limitations of the interface predicates it provides.

In contrast, SICStus Prolog provides a much more general interface to attributed variables that supports all widely used constraint solvers (finite domains, Boolean variables, rational numbers etc.) with good performance and no known mistakes.

The tutorial you link to has several rather severe shortcomings, and I cannot recommend it for learning CLP(FD). Please see my profile page if you are interested in Prolog resources.

[zmonx]

In fact, the "old semantics" actually included language constructs that are only now becoming available (again) in Prolog systems.

An example of such a construct is dif/2, which is a constraint that was provided in even the very first Prolog system, sometimes called Prolog 0, several decades ago. However, it was not widely available in Prolog systems until much more recently, even though professional Prolog systems such as SICStus have provided it for longer. Also arithmetic constraints were available in early implementations such as Prolog IV. So, in a sense, we are now going "back to the roots" of Prolog by making very old features widely available.

In my personal view, calling modern Prolog an "incompatible paradigm" with the way that Prolog is still being taught is not completely fitting, yet still more right than wrong: The new features are not meant to be used "on top" of old features, but instead! When using modern Prolog features to their fullest extent, you can completely eschew those language constructs that traditionally cause the worst problems for beginners.

Moded arithmetic is a prime example for this, which can be replaced completely by arithmetic constraints in modern Prolog systems. dif/2 is also a good example, which lets you avoid (\+)/1 in many cases by using a more general predicate instead.

Due to their operational semantics that is very hard to explain and understand, rather limited constructs often take significant room in many Prolog courses, and replacing them by more modern alternatives will entail a paradigm shift towards better methods and also make room for even more new material that can be covered instead. This is because on top of being more general, the new language constructs are often also easier to understand for beginners.

[YouAreGreat]

> The new features are not meant to be used "on top" of old features, but instead!

That is very powerful indeed. From incompetently playing around with stuff like that, my impression was that "constraints everywhere" is also extremely slow. That's not surprising, there's a lot of machinery working below the surface to deliver all that power. To recover performance whenever the full generality of the paradigm is not needed, I expect we'd need to work hard, say very smart static analysis, or JIT specialization, or...

But certainly my incompetence made me miss a lot. If you know how "constraints everywhere" can be made "fast everywhere", I'd love to hear about it:-)

[fusiongyro]

A modern Prolog like SWI with CLPFD allows you to apply Prolog's semantics to arithmetic expressions in a way that you never were able to in classic Prolog. Instead of using `is/2`, you use `#=` and some other operators, Prolog can find solutions for expressions that would be very difficult to do in either classic Prolog or any other system.