What is Constraint Programming?
Constraint Programming represents one of the closest approaches computer science
has yet made to the Holy Grail of programming: the user states the problem, the
computer solves it.
(E. Freuder)
Slides Introducing Constraint Programming
Other Slides Introducing Constraint Programming
The use of constraints had its scientific and commercial breakthrough in the
1990s. Programming with constraints makes it possible to model and specify
problems with uncertain, incomplete information and to solve combinatorial
problems, as they are abundant in industry and commerce, such as scheduling,
planning, transportation, resource allocation, layout, design, and
analysis. Constraint-based programming languages enjoy elegant theoretical
properties, conceptual simplicity, and practical success.
The idea of constraint-based programming is to solve problems by simply stating
constraints (conditions, properties) which must be satisfied by a solution of
the problem. Constraints can be considered as pieces of partial
information. Constraints describe properties of unknown objects and
relationships between them. Constraints are formalized as distinguished,
predefined predicates in first-order predicate logic. The unknown objects are
modeled as variables.
For example, consider a bicycle number lock. We forgot the first digit, but
remember some constraints about it: The digit was an odd number, greater than 1,
and not a prime number. Combining the pieces of partial information expressed by
these constraints (digit, greater than 1, odd, not prime) we are able to derive
that the digit we are looking for is "9".
As it runs, a constraint program successively generates constraints. As a
special program, the constraint solver stores, combines, and simplifies the
constraints until a solution is found. The partial solutions can be used to
influence the run of the program.
Book and Course Description
Introduction section
of the book
The formally well-founded presentation introduces the common classes of constraint programming
languages and constraint systems in a uniform way. It also includes application examples
from real life. We first introduce the basic ideas behind the family of (concurrent) constraint logic programming languages
in a calculus-based framework. Constraint solving algorithms are specified and
implemented in the constraint handling rules language (CHR) in a uniform
high-level executable notation.
The most common constraint domains, their solvers and applications such as
Boolean constraints for circuit design, terms and trees for unification, linear
polynomial equations for financial and engineering applications and finite
domains for scheduling, are presented.
The family of (concurrent) constraint logic programming languages
Preliminaries of Syntax and Semantics
Constraint logic programming (incl. Prolog)
Concurrent committed-choice constraint logic programming
Constraint handling rules (CHR)
Constraint systems and their solvers
Rational Trees
Feature Terms, Description Logic (not in book)
Boolean Constraints
Finite Domains
Linear polynomial equations
Non-Linear polynomial equations
Applications
Commercial applications, market and companies
Case study Munich rent advisor on the internet
Case study Planning wireless telecommunication
Case study Timetabling and Roomplanning
Constraint Programming Cheat Sheet
Course Slides
Courses by the authors were held at the University of Pisa in
1999 and 2002, at the University of Venice in 2004 and yearly at
the University of Munich from 1998-2001, and at the University of Ulm since
2002, at the German University of Cairo since 2004.
Constraint Programming and Reasoning (short version, 366 Slides, 1
on 1, 2013, pdf)
Constraint Programming and Reasoning (401 Slides, 1
on 1, 2009, pdf)
Additional slides, 2013, (pdf):
Global Constraints
Additional slides, 2002, (ps.gz):
Theorem Proving - Resolution Variants
University Timetabling Application
Optimal
Sender Placement Application
Practical Lab Course
The course can be combined with a practical lab course using a constraint logic programming language such as:
SWI Prolog
(SWI Prolog Reference Manual),
Sicstus Prolog,
Yap Prolog.
These Prolog implmentations come with the Constraint Handling Rules (CHR) language library:
Constraint Handling Rules (CHR) Web Pages
Test-Drive CHR. Run CHR online now!
Exercises, 2013 (link to pdf)
Exercises, 2012 (link to pdf)
Exercises, 2009
Exercise 1
-
Exercise 2
-
Exercise 3
-
Exercise 4 (boole.pl)
-
Exercise 5
-
Exercise 6 (dl-ex6.pl)
-
Exercise 7 (fd-ex7.pl).
Exercises, 2006
Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
- Exercise 9
- Exercise 10
- Exercise 11
- Exercise 12
- Exercise 13.
Constraint Programming Links
Thom Frühwirth et. al.,
Constraint logic programming: An informal introduction (ps.gz),
Chapter in Logic Programming in Action (G. Comyn et al., Eds.), Springer LNCS 636, 1992.
Constraint
Papers
Constraint Programming
Links
Constraint Programming Languages
Constraint Handling Rules (CHR)
Popular Prolog implementations with constraints and CHR:
SWI Prolog,
Sicstus Prolog,
Yap Prolog.
More constraint programming languages:
Ilog Optimization Suite,
Mozart (former OZ),
Cosytec CHIP,
IF Prolog.
Thom Frühwirth,
updated April 8, 2013
