Equational Logic As A Programming Language

Author : Michael J. O'Donnell
Publisher : MIT Press (MA)
ISBN 13 :
Total Pages : 334 pages
Book Rating : 4.08/5 ( download)

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Download or read book Equational Logic as a Programming Language written by Michael J. O'Donnell and published by MIT Press (MA). This book was released on 1985 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes an ongoing equational programming project that started in 1975. Within the project an equational programming language interpreter has been designed and implemented. The first part of the text (Chapters 1-10) provides a user's manual for the current implementation. The remaining sections cover the following topics: programming techniques and applications, theoretical foundations, implementation issues. Giving a brief account of the project's history (Chapter 11), the author devotes a large part of the text to techniques of equational programming at different levels of abstraction. Chapter 12 discusses low-level techniques including the distinction of constructors and defined functions, the formulation of conditional expressions and error and exception handling. High-level techniques are treated in Chapter 15 by discussing concurrency, nondeterminism, the relationship to dataflow programs and the transformation of recursive programs called dynamic programming. In Chapter 16 the author shows how to efficiently implement common data structures by equational programs. Modularity is discussed in Chapter 14. Several applications are also presented in the book. The author demonstrates the versatility of equational programming style by implementing syntactic manipulation algorithms (Chapter 13). Theoretical foundations are introduced in Chapter 17 (term rewriting systems, herein called term reduction systems). In Chapter 19 the author raises the question of a universal equational machine language and discusses the suitability of different variants of the combinator calculus for this purpose. Implementation issues are covered in Chapters 18 and 20 focused around algorithms for efficient pattern matching, sequencing and reduction. Aspects of design and coordination of the syntactic processors are presented as well.

Author : Christian Prehofer
Publisher : Springer Science & Business Media
ISBN 13 : 1461217784
Total Pages : 193 pages
Book Rating : 4.87/5 ( download)

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Download or read book Solving Higher-Order Equations written by Christian Prehofer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops techniques for equational reasoning in higher-order logic. Due to its expressiveness, higher-order logic is used for specification and verification of hardware, software, and mathematics. In these applica tions, higher-order logic provides the necessary level of abstraction for con cise and natural formulations. The main assets of higher-order logic are quan tification over functions or predicates and its abstraction mechanism. These allow one to represent quantification in formulas and other variable-binding constructs. In this book, we focus on equational logic as a fundamental and natural concept in computer science and mathematics. We present calculi for equa tional reasoning modulo higher-order equations presented as rewrite rules. This is followed by a systematic development from general equational rea soning towards effective calculi for declarative programming in higher-order logic and A-calculus. This aims at integrating and generalizing declarative programming models such as functional and logic programming. In these two prominent declarative computation models we can view a program as a logical theory and a computation as a deduction.

Author : Steffen Holldobler
Publisher :
ISBN 13 : 9783662162132
Total Pages : 268 pages
Book Rating : 4.3X/5 ( download)

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Download or read book Foundations of Equational Logic Programming written by Steffen Holldobler and published by . This book was released on 2014-01-15 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Steffen Hölldobler
Publisher : Lecture Notes in Artificial Intelligence
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4.92/5 ( download)

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Download or read book Foundations of Equational Logic Programming written by Steffen Hölldobler and published by Lecture Notes in Artificial Intelligence. This book was released on 1989 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Equations play a vital role in many fields of mathematics, computer science, and artificial intelligence. Therefore, many proposals have been made to integrate equational, functional, and logic programming. This book presents the foundations of equational logic programming. After generalizing logic programming by augmenting programs with a conditional equational theory, the author defines a unifying framework for logic programming, equation solving, universal unification, and term rewriting. Within this framework many known results are developed. In particular, a presentation of the least model and the fixpoint semantics of equational logic programs is followed by a rigorous proof of the soundness and the strong completeness of various proof techniques: SLDE-resolution, where a universal unification procedure replaces the traditional unification algorithm; linear paramodulation and special forms of it such as rewriting and narrowing; complete sets of transformations for conditional equational theories; and lazy resolution combined with any complete set of inference rules for conditional equational theories.

Author : Stephen L. Bloom
Publisher : Springer Science & Business Media
ISBN 13 : 3642780342
Total Pages : 636 pages
Book Rating : 4.49/5 ( download)

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Download or read book Iteration Theories written by Stephen L. Bloom and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains the results of our joint research over the last ten years on the logic of the fixed point operation. The intended au dience consists of graduate students and research scientists interested in mathematical treatments of semantics. We assume the reader has a good mathematical background, although we provide some prelimi nary facts in Chapter 1. Written both for graduate students and research scientists in theoret ical computer science and mathematics, the book provides a detailed investigation of the properties of the fixed point or iteration operation. Iteration plays a fundamental role in the theory of computation: for example, in the theory of automata, in formal language theory, in the study of formal power series, in the semantics of flowchart algorithms and programming languages, and in circular data type definitions. It is shown that in all structures that have been used as semantical models, the equational properties of the fixed point operation are cap tured by the axioms describing iteration theories. These structures include ordered algebras, partial functions, relations, finitary and in finitary regular languages, trees, synchronization trees, 2-categories, and others.

Author : Doug DeGroot
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 584 pages
Book Rating : 4.37/5 ( download)

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Download or read book Logic Programming, Functions, Relations, and Equations written by Doug DeGroot and published by Prentice Hall. This book was released on 1986 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Setting the stage; Unification and functional programming; Symmetric combinations; Programming with equality; Augmented unification; Semantic foundations.

Author : Răzvan Diaconescu
Publisher :
ISBN 13 : 9780902928916
Total Pages : 120 pages
Book Rating : 4.10/5 ( download)

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Download or read book Category-based Semantics for Equational and Constraint Logic Programming written by Răzvan Diaconescu and published by . This book was released on 1994 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "This thesis proposes a general framework for equational logic programming, called category-based equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equational deduction to an arbitrary category satisfying certain natural conditions; completeness is proved under a hypothesis of quantifier projectivity, using a semantic treatment that regards quantifiers as models rather than variables, and regards valuations as model morphisms rather than functions. This is used as a basis for a model theoretic category-based approach to a paramodulation- based operational semantics for equational logic programming languages. Category-based equational logic in conjunction with the theory of institutions is used to give mathematical foundations for modularisation in equational logic programming. We study the soundness and completeness problem for module imports in the context of a category-based semantics for solutions to equational logic programming queries. Constraint logic programming is integrated into the equational logic programming paradigm by showing that constraint logics are a particular case of category-based equational logic. This follows the methodology of free expansions of models for built-ins along signature inclusions as sketched by Goguen and Meseguer in their papers on Eqlog. The mathematical foundations of constraint logic programming are based on a Herbrand Theorem for constraint logics; this is obtained as an instance of a more general category-based version of Herbrand's Theorem. The results in this thesis apply to equational and constraint logic programming languages that are based on a variety of equational logical systems including many and order sorted equational logics, Horn clause logic, equational logic modulo a theory, constraint logics, and more, as well as any possible combination between them. More importantly, this thesis gives the possibility for developing the equational logic (programming) paradigm over non-conventional structures and thus significantly extending it beyond its tradition."

Author : Krzysztof R. Apt
Publisher :
ISBN 13 :
Total Pages : 358 pages
Book Rating : 4.11/5 ( download)

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Download or read book From Logic Programming to Prolog written by Krzysztof R. Apt and published by . This book was released on 1997 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a systematic introduction to the theory of logic programming and shows how this theory can be applied to reason about pure Prolog programs. The text includes an introduction to programming in Prolog and deals with such programming issues as determination, occur-check freedom and absence of errors. It covers both the natural interpretations of logic programming, as declarative specification and as procedure for computer execution.

Author : Christian Posthoff
Publisher : Springer
ISBN 13 : 3030024202
Total Pages : 511 pages
Book Rating : 4.08/5 ( download)

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Download or read book Logic Functions and Equations written by Christian Posthoff and published by Springer. This book was released on 2018-12-31 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: The expanded and updated 2nd edition of this classic text offers the reader a comprehensive introduction to the concepts of logic functions and equations and their applications across computer science. The approach emphasizes a thorough understanding of the fundamental principles as well as numerical and computer-based solution methods. Updated throughout, some major additions for the 2nd edition include: - an expanded introductory section on logic equations; - a new chapter on sets, lattices, and classes of logic functions; - a new chapter about SAT-problems; - a new chapter about methods to solve extremely complex problems; and - an expanded section with new decomposition methods utilizing the Boolean Differential Calculus extended to lattices of logic functions. The book provides insight into applications across binary arithmetic, coding, complexity, logic design, programming, computer architecture, and artificial intelligence. Based on the extensive teaching experience of the authors, Logic Functions and Equations is highly recommended for a one- or two-semester course in computer science and related programs. It provides straightforward high-level access to these methods and enables sophisticated applications, elegantly bridging the gap between mathematics and the theoretical foundations of computer science.

Author : Jaan Penjam
Publisher : Springer Science & Business Media
ISBN 13 : 9783540584025
Total Pages : 488 pages
Book Rating : 4.21/5 ( download)

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Download or read book Programming Language Implementation and Logic Programming written by Jaan Penjam and published by Springer Science & Business Media. This book was released on 1994-08-24 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the proceedings of the 6th International Symposium on Programming Language Implementation and Logic Programming (PLILP '94), held in Madrid, Spain in September 1994. The volume contains 27 full research papers selected from 67 submissions as well as abstracts of full versions of 3 invited talks by renowned researchers and abstracts of 11 system demonstrations and poster presentations. Among the topics covered are parallelism and concurrency; implementation techniques; partial evaluation, synthesis, and language issues; constraint programming; meta-programming and program transformation; functional-logic programming; and program analysis and abstract interpretation.