Editing Constraint programming (section)

{{Short description|Programming paradigm wherein relations between variables are stated in the form of constraints}}
{{Original research|date=June 2011}}

'''Constraint programming (CP)'''<ref name=":0">{{Cite book|url=https://books.google.com/books?id=Kjap9ZWcKOoC&q=handbook+of+constraint+programming&pg=PP1|title=Handbook of Constraint Programming|last1=Rossi|first1=Francesca|author1link = Francesca Rossi|last2=Beek|first2=Peter van|last3=Walsh|first3=Toby|author3link = Toby Walsh|date=2006-08-18|publisher=Elsevier|isbn=9780080463803|language=en}}</ref> is a paradigm for solving [[combinatorial]] problems that draws on a wide range of techniques from [[artificial intelligence]], [[computer science]], and [[operations research]]. In constraint programming, users declaratively state the [[Constraint (mathematics)|constraints]] on the feasible solutions for a set of decision variables. Constraints differ from the common [[Language primitive|primitives]] of [[imperative programming]] languages in that they do not specify a step or sequence of steps to execute, but rather the properties of a solution to be found. In addition to constraints, users also need to specify a method to solve these constraints. This typically draws upon standard methods like chronological [[backtracking]] and [[constraint propagation]], but may use customized code like a problem-specific branching [[Heuristic (computer science)|heuristic]].

Constraint programming takes its root from and can be expressed in the form of [[constraint logic programming]], which embeds constraints into a [[logic program]]. This variant of logic programming is due to Jaffar and Lassez,<ref>Jaffar, Joxan, and J-L. Lassez. "[https://dl.acm.org/citation.cfm?id=41635 Constraint logic programming]." Proceedings of the 14th [[ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages]]. ACM, 1987.</ref> who extended in 1987 a specific class of constraints that were introduced in [[Prolog II]]. The first implementations of constraint logic programming were [[Prolog III]], [[CLP(R)]], and [[CHIP (programming language)|CHIP]].

Instead of logic programming, constraints can be mixed with [[functional programming]], [[term rewriting]], and [[imperative language]]s.
Programming languages with built-in support for constraints include [[Oz programming language|Oz]] (functional programming) and [[Kaleidoscope programming language|Kaleidoscope]] (imperative programming). Mostly, constraints are implemented in imperative languages via ''constraint solving toolkits'', which are separate libraries for an existing imperative language.