Equational Logic As A Programming Language

Author : Michael J. O'Donnell
Publisher : MIT Press (MA)
Page : 334 pages
File Size : 40,5 Mb
Release : 1985
Category : Computers
ISBN : UOM:39015009841308

Get Book

Equational Logic as a Programming Language by Michael J. O'Donnell Pdf

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
Page : 193 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461217787

Get Book

Solving Higher-Order Equations by Christian Prehofer Pdf

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 : Unknown
Page : 268 pages
File Size : 52,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 366216213X

Get Book

Foundations of Equational Logic Programming by Steffen Holldobler Pdf

Author : Steffen Hölldobler
Publisher : Lecture Notes in Artificial Intelligence
Page : 264 pages
File Size : 40,9 Mb
Release : 1989
Category : Computers
ISBN : UCAL:B4340292

Get Book

Foundations of Equational Logic Programming by Steffen Hölldobler Pdf

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 : Doug DeGroot,Gary Lindstrom
Publisher : Prentice Hall
Page : 584 pages
File Size : 44,6 Mb
Release : 1986
Category : Computers
ISBN : UOM:39015010490137

Get Book

Logic Programming, Functions, Relations, and Equations by Doug DeGroot,Gary Lindstrom Pdf

Setting the stage; Unification and functional programming; Symmetric combinations; Programming with equality; Augmented unification; Semantic foundations.

Author : Stephen L. Bloom,Zoltan Esik
Publisher : Springer Science & Business Media
Page : 636 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642780349

Get Book

Iteration Theories by Stephen L. Bloom,Zoltan Esik Pdf

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 : Krzysztof R. Apt
Publisher : Unknown
Page : 358 pages
File Size : 47,7 Mb
Release : 1997
Category : Computers
ISBN : UOM:39015038545011

Get Book

From Logic Programming to Prolog by Krzysztof R. Apt Pdf

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 : Răzvan Diaconescu
Publisher : Unknown
Page : 120 pages
File Size : 48,9 Mb
Release : 1994
Category : Categories (Mathematics)
ISBN : 0902928910

Get Book

Category-based Semantics for Equational and Constraint Logic Programming by Răzvan Diaconescu Pdf

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 : Jaan Penjam
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 46,5 Mb
Release : 1994-08-24
Category : Computers
ISBN : 3540584021

Get Book

Programming Language Implementation and Logic Programming by Jaan Penjam Pdf

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.

Author : Hélène Kirchner,Giorgio Levi
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 51,6 Mb
Release : 1992-08-19
Category : Computers
ISBN : 354055873X

Get Book

Algebraic and Logic Programming by Hélène Kirchner,Giorgio Levi Pdf

This volume contains the proceedings of the Third International Conference on Algebraic and Logic Programming, held in Pisa, Italy, September 2-4, 1992. Like the two previous conferences in Germany in 1988 and France in 1990, the third conference aims at strengthening the connections betweenalgebraic techniques and logic programming. On the one hand, logic programming has been very successful during the last decades and more and more systems compete in enhancing its expressive power. On the other hand, concepts like functions, equality theory, and modularity are particularly well handled in an algebraic framework. Common foundations of both approaches have recently been developed, and this conference is a forum for people from both areas to exchange ideas, results, and experiences. The book covers the following topics: semantics ofalgebraic and logic programming; integration of functional and logic programming; term rewriting, narrowing, and resolution; constraintlogic programming and theorem proving; concurrent features in algebraic and logic programming languages; and implementation issues.

Author : Dov M. Gabbay,C. J. Hogger,J. A. Robinson
Publisher : Clarendon Press
Page : 818 pages
File Size : 53,6 Mb
Release : 1998-01-08
Category : Computers
ISBN : 9780191546280

Get Book

Handbook of Logic in Artificial Intelligence and Logic Programming: Volume 5: Logic Programming by Dov M. Gabbay,C. J. Hogger,J. A. Robinson Pdf

The Handbook of Logic in Artificial Intelligence and Logic Programming is a multi-volume work covering all major areas of the application of logic to artificial intelligence and logic programming. The authors are chosen on an international basis and are leaders in the fields covered. Volume 5 is the last in this well-regarded series. Logic is now widely recognized as one of the foundational disciplines of computing. It has found applications in virtually all aspects of the subject, from software and hardware engineering to programming languages and artificial intelligence. In response to the growing need for an in-depth survey of these applications the Handbook of Logic in Artificial Intelligence and its companion, the Handbook of Logic in Computer Science have been created. The Handbooks are a combination of authoritative exposition, comprehensive survey, and fundamental research exploring the underlying themes in the various areas. Some mathematical background is assumed, and much of the material will be of interest to logicians and mathematicians. Volume 5 focuses particularly on logic programming. The chapters, which in many cases are of monograph length and scope, emphasize possible unifying themes.

Author : Jan Małuszyński,Martin Wirsing
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 46,8 Mb
Release : 1991-08-14
Category : Computers
ISBN : 3540544445

Get Book

Programming Language Implementation and Logic Programming by Jan Małuszyński,Martin Wirsing Pdf

This volume contains the papers which have been accepted for presentation atthe Third International Symposium on Programming Language Implementation andLogic Programming (PLILP '91) held in Passau, Germany, August 26-28, 1991. The aim of the symposium was to explore new declarative concepts, methods and techniques relevant for the implementation of all kinds of programming languages, whether algorithmic or declarative ones. The intention was to gather researchers from the fields of algorithmic programming languages as well as logic, functional and object-oriented programming. This volume contains the two invited talks given at the symposium by H. Ait-Kaci and D.B. MacQueen, 32 selected papers, and abstracts of several system demonstrations. The proceedings of PLILP '88 and PLILP '90 are available as Lecture Notes in Computer Science Volumes 348 and 456.

Author : Ralph W. Wilkerson
Publisher : Intellect Books
Page : 288 pages
File Size : 49,5 Mb
Release : 1992
Category : Computers
ISBN : UOM:39015029253070

Get Book

Advances in Logic Programming and Automated Reasoning by Ralph W. Wilkerson Pdf

This series reviews research contributions in logic programming and automated reasoning and is desinged to stimulate and sustain new, productive lines of investigation into symbolic and algebraic computing techniques as they relate to logic programming and automate reasoning. Topics covered include equational reasoning, parallel programming in logic, term rewriting systems, control of logic programs, completion procedures, unification and matching algorithms, design and implementation of deduction systems, logical methods of knowledge representation, logic-based inference techniques, and programs synthesis and verification.

Author : Jan Grabowski,Pierre Lescanne,Wolfgang Wechler
Publisher : Springer
Page : 277 pages
File Size : 45,5 Mb
Release : 2005-07-06
Category : Computers
ISBN : 9783540460633

Get Book

Algebraic and Logic Programming by Jan Grabowski,Pierre Lescanne,Wolfgang Wechler Pdf

This volume contains the proceedings of the First International Workshop on Algebraic and Logic Programming held in Gaussig (German Democratic Republic) from November 14 to 18, 1988. The workshop was devoted to Algebraic Programming, in the sense of programming by algebraic specifications and rewrite rule systems, and Logic Programming, in the sense of Horn clause specifications and resolution systems. This includes combined algebraic/logic programming systems, mutual relations and mutual implementation of programming paradigms, completeness and efficiency considerations in both fields, as well as related topics.

Author : Timo Lepistö,Arto Salomaa
Publisher : Springer Science & Business Media
Page : 762 pages
File Size : 53,9 Mb
Release : 1988
Category : Computers
ISBN : 3540194886

Get Book

Automata, Languages and Programming by Timo Lepistö,Arto Salomaa Pdf

This volume contains the proceedings of ICALP 88, held at Tampere University of Technology, Finland, July 11-15, 1988. ICALP 88 is the 15th International Colloquium on Automata, Languages and Programming in a series of meetings sponsored by the European Association for Theoretical Computer Science (EATCS). It is a broadly based conference covering all aspects of theoretical computer science including topics such as computability, automata, formal languages, analysis of algorithms, computational complexity, data types and data structures, theory of data bases and knowledge bases, semantics of programming languages, program specification, transformation and verification, foundations of logic programming, theory of logical design and layout, parallel and distributed computation, theory of concurrency, symbolic and algebraic computation, term rewriting systems, cryptography, and theory of robotics.