Editing Constraint programming (section)

==Perturbation vs refinement models==
Languages for constraint-based programming follow one of two approaches:<ref>{{cite book |last1=Mayoh |first1=Brian |last2=Tyugu |first2=Enn |last3=Penjam |first3=Jaan |date=1993 |title=Constraint Programming |url=https://books.google.com/books?id=B0aqCAAAQBAJ |publisher=[[Springer Science+Business Media]] |page=76 |isbn=9783642859830}}</ref>
* Refinement model: variables in the problem are initially unassigned, and each variable is assumed to be able to contain any value included in its range or domain. As computation progresses, values in the domain of a variable are pruned if they are shown to be incompatible with the possible values of other variables, until a single value is found for each variable.
* Perturbation model: variables in the problem are assigned a single initial value. At different times one or more variables receive perturbations (changes to their old value), and the system propagates the change trying to assign new values to other variables that are consistent with the perturbation.
[[Constraint propagation]] in [[Constraint Satisfaction Problems|constraint satisfaction problems]] is a typical example of a refinement model, and formula evaluation in [[spreadsheet]]s are a typical example of a perturbation model.

The refinement model is more general, as it does not restrict variables to have a single value, it can lead to several solutions to the same problem. However, the perturbation model is more intuitive for programmers using mixed imperative constraint object-oriented languages.<ref>Lopez, G., Freeman-Benson, B., & Borning, A. (1994, January). [ftp://trout.cs.washington.edu/tr/1993/09/UW-CSE-93-09-04.pdf Kaleidoscope: A constraint imperative programming language.]{{dead link|date=May 2025|bot=medic}}{{cbignore|bot=medic}} In ''Constraint Programming'' (pp. 313-329). Springer Berlin Heidelberg.</ref>