This work presents a purely classical first-order logical approach to the field of study in theoretical computer science sometimes referred to as the theory of programs, or programming theory. This field essentially attempts to provide a precise mathematical basis for the common activities involved in reasoning about computer programs and programming languages, and it also attempts to find practical applications in the areas of program specification, verification and programming language design. Many different approaches with different mathematical frameworks have been proposed as a basis for programming theory. They differ in the mathe matical machinery they use to define and investigate programs and program properties and they also differ in the concepts they deal with to understand the programming paradigm. Different approaches use different tools and viewpoints to characterize the data environment of programs. Most of the approaches are related to mathe matical logic and they provide their own logic. These logics, however, are very eclectic since they use special entities to reflect a special world of programs, and also, they are usually incomparable with each other. This Babel's mess irritated us and we decided to peel off the eclectic com ponents and try to answer all the questions by using classical first-order logic.

This book proposes a purely classical first-order logical approach to the theory of programming. The authors, leading members of the famous 'Hungarian school', use this approach to give a unified and systematic presentation of the theory. This approach provides formal methods and tools for reasoning about computer programs and programming languages by allowing the syntactic and semantic characterization of programs, the description of program properties, and ways to check whether a given program satisfies certain properties. The basic methods are logical extension, inductive definition and their combination, all of which admit an appropriate first-order representation of data and time. The framework proposed by the authors allows the investigation and development of different programming theories and logics from a unified point of view. Dynamic and temporal logics, for example, are investigated and compared with respect to their expressive and proof-theoretic powers. The book should appeal to both theoretical researchers and students. For researchers in computer science the book provides a coherent presentation of a new approach which permits the solution of various problems in programming theory in a unified manner by the use of first-order logical tools. The book may serve as a basis for graduate courses in programming theory and logic as it covers all important questions arising between the theory of computation and formal descriptive languages and presents an appropriate derivation system.

This book explores the role of Martin-Lof s constructive type theory in computer programming. The main focus of the book is how the theory can be successfully applied in practice. Introductory sections provide the necessary background in logic, lambda calculus and constructive mathematics, and exercises and chapter summaries are included to reinforce understanding.

This volume contains the papers selected for presentation at the Sixth International Symposium on Methodol- ogies for Intelligent Systems held in Charlotte, North Carolina, in October 1991. The symposium was hosted by UNC-Charlotte and sponsored by IBM-Charlotte, ORNL/CESAR and UNC-Charlotte. The papers discuss topics in the following major areas: - Approximate reasoning, - Expert systems, - Intelligent databases, - Knowledge representation, - Learning and adaptive systems, - Logic for artificial intelligence. The goal of the symposium was to provide a platform for a useful exchange and cross-fertilization of ideas between theoreticians and practitioners in these areas.

This Festschrift volume, dedicated to He Jifeng on the occasion of his 70th birthday in September 2013, includes 24 refereed papers by leading researchers, current and former colleagues, who congratulated at a celebratory symposium held in Shanghai, China, in the course of the 10th International Colloquium on Theoretical Aspects of Computing, ICTAC 2013. The papers cover a broad spectrum of subjects, from foundational and theoretical topics to programs and systems issues and to applications, comprising formal methods, software and systems modeling, semantics, laws of programming, specification and verification, as well as logics. He Jifeng is known for his seminal work in the theories of programming and formal methods for software engineering. He is particularly associated with Unifying Theories of Programming (UTP) , the theory of data refinement and the laws of programming, and the rCOS formal method for object and component system construction. His book on UTP with Tony Hoare has been widely read and followed by a large number of researchers, and it has been used in many postgraduate courses. He was a senior researcher at Oxford during 1984-1998, and then a senior research fellow at the United Nations University International Institute for Software Technology (UNU-IIST) in Macau during 1998-2005. He has been a professor and currently the Dean of the Institute of Software Engineering at East China Normal University, Shanghai, China. In 2005, He Jifeng was elected as an academician to the Chinese Academy of Sciences. He also received an honorary doctorate from the University of York. He won a number of prestigious science and technology awards, including a 2nd prize of Natural Science Award from the State Council of China, a 1st prize of Natural Science Award from the Ministry of Education of China, a 1st prize of Technology Innovation from the Ministry of Electronic Industry, and a number awards from Shanghai government.

In recent years, several formalisms for program construction have appeared. One such formalism is the type theory developed by Per Martin-Löf. Well suited as a theory for program construction, it makes possible the expression of both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. This book contains a thorough introduction to type theory, with information on polymorphic sets, subsets, monomorphic sets, and a full set of helpful examples.

The subject of (static) optimization, also called mathematical programming, is one of the most important and widespread branches of modern mathematics, serving as a cornerstone of such scientific subjects as economic analysis, operations research, management sciences, engineering, chemistry, physics, statistics, computer science, biology, and social sciences. This book presents a unified, progressive treatment of the basic mathematical tools of mathematical programming theory. The authors expose said tools, along with results concerning the most common mathematical programming problems formulated in a finite-dimensional setting, forming the basis for further study of the basic questions on the various algorithmic methods and the most important particular applications of mathematical programming problems. This book assumes no previous experience in optimization theory, and the treatment of the various topics is largely self-contained. Prerequisites are the basic tools of differential calculus for functions of several variables, the basic notions of topology and of linear algebra, and the basic mathematical notions and theoretical background used in analyzing optimization problems. The book is aimed at both undergraduate and postgraduate students interested in mathematical programming problems but also those professionals who use optimization methods and wish to learn the more theoretical aspects of these questions.