A.9.1 Introduction

This library provides CLP(FD): Constraint Logic Programming over Finite Domains. This is an instance of the general CLP(X) scheme (section 8), extending logic programming with reasoning over specialised domains. CLP(FD) lets us reason about integers in a way that honors the relational nature of Prolog.

Read The Power of Prolog to understand how this library is meant to be used in practice.

There are two major use cases of CLP(FD) constraints:

1. declarative integer arithmetic (section A.9.3)
2. solving combinatorial problems such as planning, scheduling and allocation tasks.

The predicates of this library can be classified as:

• arithmetic constraints like #=/2, #>/2 and #\=/2 (section A.9.17.1)
• the membership constraints in/2 and ins/2 (section A.9.17.2)
• the enumeration predicates indomain/1, label/1 and labeling/2 (section A.9.17.3)
• combinatorial constraints like all_distinct/1 and global_cardinality/2 (section A.9.17.4)
• reification predicates such as #<==>/2 (section A.9.17.5)
• reflection predicates such as fd_dom/2 (section A.9.17.6)

In most cases, arithmetic constraints (section A.9.2) are the only predicates you will ever need from this library. When reasoning over integers, simply replace low-level arithmetic predicates like (is)/2 and (>)/2 by the corresponding CLP(FD) constraints like #=/2 and #>/2 to honor and preserve declarative properties of your programs. For satisfactory performance, arithmetic constraints are implicitly rewritten at compilation time so that low-level fallback predicates are automatically used whenever possible.

Almost all Prolog programs also reason about integers. Therefore, it is highly advisable that you make CLP(FD) constraints available in all your programs. One way to do this is to put the following directive in your <config>/init.pl initialisation file:

:- use_module(library(clpfd)).

All example programs that appear in the CLP(FD) documentation assume that you have done this.

Important concepts and principles of this library are illustrated by means of usage examples that are available in a public git repository: github.com/triska/clpfd

If you are used to the complicated operational considerations that low-level arithmetic primitives necessitate, then moving to CLP(FD) constraints may, due to their power and convenience, at first feel to you excessive and almost like cheating. It isn't. Constraints are an integral part of all popular Prolog systems, and they are designed to help you eliminate and avoid the use of low-level and less general primitives by providing declarative alternatives that are meant to be used instead.

When teaching Prolog, CLP(FD) constraints should be introduced before explaining low-level arithmetic predicates and their procedural idiosyncrasies. This is because constraints are easy to explain, understand and use due to their purely relational nature. In contrast, the modedness and directionality of low-level arithmetic primitives are impure limitations that are better deferred to more advanced lectures.

We recommend the following reference (PDF: metalevel.at/swiclpfd.pdf) for citing this library in scientific publications:

@inproceedings{Triska12,
  author    = {Markus Triska},
  title     = {The Finite Domain Constraint Solver of {SWI-Prolog}},
  booktitle = {FLOPS},
  series    = {LNCS},
  volume    = {7294},
  year      = {2012},
  pages     = {307-316}
}

More information about CLP(FD) constraints and their implementation is contained in: metalevel.at/drt.pdf

The best way to discuss applying, improving and extending CLP(FD) constraints is to use the dedicated clpfd tag on stackoverflow.com. Several of the world's foremost CLP(FD) experts regularly participate in these discussions and will help you for free on this platform.