Constraints in Computational Logics: Theory and Applications by Jean-Pierre Jouannaud, Ralf Treinen (auth.), Gerhard Goos,

By Jean-Pierre Jouannaud, Ralf Treinen (auth.), Gerhard Goos, Juris Hartmanis, Jan van Leeuwen, Hubert Comon, Claude Marché, Ralf Treinen (eds.)

Constraints offer a declarative means of representing countless units of information. they're compatible for combining various logical or programming paradigms as has been recognized for constraint good judgment programming because the Nineteen Eighties and extra lately for practical programming. using constraints in computerized deduction is more moderen and has proved to be very winning, relocating the keep watch over from the meta-level to the restrictions, that are now top quality objects.
This monograph-like ebook offers six completely reviewed and revised lectures given via top researchers on the summer season college prepared through the ESPRIT CCL operating staff in Gif-sur-Yvette, France, in September 1999. The publication deals coherently written chapters on constraints and constraint fixing, constraint fixing on phrases, combining constraint fixing, constraints and theorem proving, useful and constraint good judgment programming, and development commercial applications.

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Additional resources for Constraints in Computational Logics: Theory and Applications International Summer School, CCL ’99 Gif-sur-Yvette, France, September 5–8, 1999 Revised Lectures

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Given a feature tree τ , we write Dτ for its tree domain and Lτ for its labeling function. 4. The root of τ is the node ε. The root label of τ is Lτ (ε), and f ∈ F is a root feature of τ if f ∈ Dτ . Given a tree τ and a root feature f of τ , we write as τ [f ] the subtree of τ at path f ; formally Dτ [f ] = {π | f π ∈ Dτ } and Lτ [f ] = {(π , A) | (f π , A) ∈ Lτ }. An atomic CFT constraint is one of the following forms: A(x), x[f ]y, x{f1 , . . , fn }, x = y where A ∈ L and f, f1 , . . , fn ∈ F.

Gert Smolka and Ralf Treinen. Records for logic programming. Journal of Logic Programming, 18(3):229–258, April 1994. Ralf Treinen. Feature constraints with first-class features. In Andrzej M. Borzyszkowski and Stefan Sokolowski, editors, Proc. 18th Mathematical Foundations of Computer Science, volume 711 of Lecture Notes in Computer Science, pages 734–743, Gda´ nsk, Poland, 30 August–3 September 1993. Springer-Verlag. 1 Introduction In this chapter, we focus on constraint solving on terms, also called Herbrand constraints in the introductory chapter, and we follow the main concepts introduced in that chapter.

Proof. We show this using a lexicographic combination of measuring function ψ1 , ψ2 , . . , each mapping a constraint to some natural number. To show termination of the system it is sufficient to show that if c reduces to d then there is some i such that ψ1 to ψi−1 are unchanged and ψi strictly decreases. More precisely, we define three measuring functions: • ψ1 (φ) is the number of subtree constraints of φ, • ψ2 (φ) is the number of atomic constraints of φ, • ψ3 (φ) is the number of variables of φ that are not eliminated in φ.

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