By Thom Frühwirth, Slim Abdennadher (auth.)

The booklet is a brief, concise and whole presentation of constraint programming and reasoning. using constraints had its clinical and advertisement leap forward within the Nineties. Programming with constraints makes it attainable to version and clear up issues of doubtful, incomplete info and combinatorial difficulties, as they're ample in and trade, comparable to scheduling, making plans, transportation, source allocation, format, layout and research. The theoretically well-founded presentation contains program examples from genuine lifestyles. It introduces the typical sessions of constraint programming languages and constraint platforms in a uniform approach. Constraint fixing algorithms are precise and applied within the constraint dealing with principles language (CHR).

This e-book is supreme as a textbook for graduate scholars and as a source for researchers and practitioners. the net aid comprises educating fabric, software program, newest information and on-line use and examples of the CHR language.

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Sequence S is already known (even though we just know that it starts with 1). We implement three processes mults, which multiply the numbers of S with 2, 3, and 5, respectively, as soon as the numbers are known. Two merge processes combine the three resulting sequences into an ordered one without duplicates. However, this sequence is the desired sequence S. hamming(S) +--mults(S,2,S2) A mults(S,3,S3) A mults(S,5,S5) A merge(S2,S3,S23) A merge(S5,S23,S) mults(XoS,N,XSN) +--- XSN~X*NoSN A mults(S,N,SN) merge (Xolnl, Yoln2, XYOut) +--- X~Y I XYOut~XoOut A merge (Inl, In2, Out) merge (Xolnl , Yoln2,XYOut) +--- XY I XYOut~YoOut A merge(Xolnl,In2,Out) A process mults (S, N, SN) delays (suspends) until the first argument S is a sequence with a known first element.

Constraints will be handled by the additional transition rule Solve. The Unfold transition behaves as follows: If the equation between head of the clause and selected atom is consistent together with the current constraint store, then the atom is replaced by the body of the clause and the equality is added to the constraint store. Otherwise the derivation fails by applying the transition rule Failure. The transition Unfold of the LP calculus computes the most general unifier between the head B of clause and the atom A in the context of substitution () and adds the unifier to ().

5. An answer (constraint) of a goal G is the logical reading of a final state of a derivation starting with . We are now ready to consider a simple example that will guide us through the various classes of constraint programming languages. 1. Consider the following constraint logic program which implements the predicate min/3. min (X, Y, Z) means that Z is the minimum of X and Y: min (X, Y, Z) +--- X:;Y /\ X~Z min(X, Y ,Z) +--- Y:;X /\ Y~Z (cl) (c2) where :; and ~ are constraints with the usual meaning as total order and syntactic equality.

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