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.

Logic functions and equations are (some of) the most important concepts of Computer Science with many applications such as Binary Arithmetics, Coding, Complexity, Logic Design, Programming, Computer Architecture and Artificial Intelligence. They are very often studied in a minimum way prior to or together with their respective applications. Based on our long-time teaching experience, a comprehensive presentation of these concepts is given, especially emphasising a thorough understanding as well as numerical and computer-based solution methods. Any applications and examples from all the respective areas are given that can be dealt with in a unified way. They offer a broad understanding of the recent developments in Computer Science and are directly applicable in professional life. Logic Functions and Equations is highly recommended for a one- or two-semester course in many Computer Science or computer Science-oriented programmes. It allows students an easy high-level access to these methods and enables sophisticated applications in many different areas. It elegantly bridges the gap between Mathematics and the required theoretical foundations of Computer Science.

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.

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.

What sets this book apart from others on logic programming is the breadth of its coverage. The authors have achieved a fine balance between a clear and authoritative treatment of the theory and a practical, problem-solving approach to its applications. This edition introduces major new developments in a continually evolving field and includes such topics as concurrency and equational and constraint logic programming.

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.

Maude is a language and system based on rewriting logic. In this comprehensive account, you’ll discover how Maude and its formal tool environment can be used in three mutually reinforcing ways: as a declarative programming language, as an executable formal specification language, and as a formal verification system. Examples used throughout the book illustrate key concepts, features, and the many practical uses of Maude.