Download or read book Predicate Calculus and Program Semantics written by Edsger W. Dijkstra and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This booklet presents a reasonably self-contained theory of predicate trans former semantics. Predicate transformers were introduced by one of us (EWD) as a means for defining programming language semantics in a way that would directly support the systematic development of programs from their formal specifications. They met their original goal, but as time went on and program derivation became a more and more formal activity, their informal introduction and the fact that many of their properties had never been proved became more and more unsatisfactory. And so did the original exclusion of unbounded nondeterminacy. In 1982 we started to remedy these shortcomings. This little monograph is a result of that work. A possible -and even likely- criticism is that anyone sufficiently versed in lattice theory can easily derive all of our results himself. That criticism would be correct but somewhat beside the point. The first remark is that the average book on lattice theory is several times fatter (and probably less self contained) than this booklet. The second remark is that the predicate transformer semantics provided only one of the reasons for going through the pains of publication.
Download or read book Mathematical Aspects of Logic Programming Semantics written by Pascal Hitzler and published by CRC Press. This book was released on 2016-04-19 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the authors' own state-of-the-art research results, this book presents a rigorous, modern account of the mathematical methods and tools required for the semantic analysis of logic programs. It significantly extends the tools and methods from traditional order theory to include nonconventional methods from mathematical analysis that depend on topology, domain theory, generalized distance functions, and associated fixed-point theory. The authors closely examine the interrelationships between various semantics as well as the integration of logic programming and connectionist systems/neural networks.
Download or read book Computational Semantics with Functional Programming written by Jan van Eijck and published by Cambridge University Press. This book was released on 2010-09-23 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational semantics is the art and science of computing meaning in natural language. The meaning of a sentence is derived from the meanings of the individual words in it, and this process can be made so precise that it can be implemented on a computer. Designed for students of linguistics, computer science, logic and philosophy, this comprehensive text shows how to compute meaning using the functional programming language Haskell. It deals with both denotational meaning (where meaning comes from knowing the conditions of truth in situations), and operational meaning (where meaning is an instruction for performing cognitive action). Including a discussion of recent developments in logic, it will be invaluable to linguistics students wanting to apply logic to their studies, logic students wishing to learn how their subject can be applied to linguistics, and functional programmers interested in natural language processing as a new application area.
Download or read book Mathematical Logic through Python written by Yannai A. Gonczarowski and published by Cambridge University Press. This book was released on 2022-07-31 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a unique pedagogical approach, this text introduces mathematical logic by guiding students in implementing the underlying logical concepts and mathematical proofs via Python programming. This approach, tailored to the unique intuitions and strengths of the ever-growing population of programming-savvy students, brings mathematical logic into the comfort zone of these students and provides clarity that can only be achieved by a deep hands-on understanding and the satisfaction of having created working code. While the approach is unique, the text follows the same set of topics typically covered in a one-semester undergraduate course, including propositional logic and first-order predicate logic, culminating in a proof of Gödel's completeness theorem. A sneak peek to Gödel's incompleteness theorem is also provided. The textbook is accompanied by an extensive collection of programming tasks, code skeletons, and unit tests. Familiarity with proofs and basic proficiency in Python is assumed.
Download or read book The Formal Semantics of Programming Languages written by Glynn Winskel and published by MIT Press. This book was released on 1993-02-05 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Formal Semantics of Programming Languages provides the basic mathematical techniques necessary for those who are beginning a study of the semantics and logics of programming languages. These techniques will allow students to invent, formalize, and justify rules with which to reason about a variety of programming languages. Although the treatment is elementary, several of the topics covered are drawn from recent research, including the vital area of concurency. The book contains many exercises ranging from simple to miniprojects.Starting with basic set theory, structural operational semantics is introduced as a way to define the meaning of programming languages along with associated proof techniques. Denotational and axiomatic semantics are illustrated on a simple language of while-programs, and fall proofs are given of the equivalence of the operational and denotational semantics and soundness and relative completeness of the axiomatic semantics. A proof of Godel's incompleteness theorem, which emphasizes the impossibility of achieving a fully complete axiomatic semantics, is included. It is supported by an appendix providing an introduction to the theory of computability based on while-programs. Following a presentation of domain theory, the semantics and methods of proof for several functional languages are treated. The simplest language is that of recursion equations with both call-by-value and call-by-name evaluation. This work is extended to lan guages with higher and recursive types, including a treatment of the eager and lazy lambda-calculi. Throughout, the relationship between denotational and operational semantics is stressed, and the proofs of the correspondence between the operation and denotational semantics are provided. The treatment of recursive types - one of the more advanced parts of the book - relies on the use of information systems to represent domains. The book concludes with a chapter on parallel programming languages, accompanied by a discussion of methods for specifying and verifying nondeterministic and parallel programs.
Download or read book Predicate Transformer Semantics written by Ernest G. Manes and published by . This book was released on 1992 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a rigorous foundation for defining Boolean categories, in which the relationship between specification and behavior is explored. Boolean categories provide a rich interface between program constructs and techniques familiar from algebra, for instance matrix- or ideal-theoretic methods. The book's distinction is that the approach relies on a single program construct (the first-order theory of categories); others are derived mathematically from four axioms. Development of these axioms (which are obeyed by an abundance of program paradigms) yields Boolean algebras of "predicates" loop-free constructs, and a calculus of partial and total correctness, which is shown to be the standard one of Hoare, Dijkstra, Pratt, and Kozen.
Download or read book Semantic Techniques in Quantum Computation written by Simon Gay and published by Cambridge University Press. This book was released on 2010 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores quantum computation from the perspective of the branch of theoretical computer science known as semantics.
Download or read book Fundamentals of Computation Theory written by Gabriel Ciobanu and published by Springer. This book was released on 2003-07-31 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Symposium on Fundamentals of Computation Theory, FCT '99, held in Iasi, Romania in August/September 1999. The 42 revised full papers presented together with four invited papers were carefully selected from a total of 102 submissions. Among the topics addressed are abstract data types, algorithms and data structures, automata and formal languages, categorical and topological approaches, complexity, computational geometry, concurrency, cryptology, distributed computing, logics in computer science, process algebras, symbolic computation, molecular computing, quantum computing, etc.
Download or read book Programs Recursion and Unbounded Choice written by Wim H. Hesselink and published by Cambridge University Press. This book was released on 1992-05-21 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete account of the predicate transformation calculus semantics of sequential programs.
Download or read book Formal Semantics of Programming Languages written by Randall Rustin and published by Prentice Hall. This book was released on 1972 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Refinement Calculus written by Carroll Morgan and published by Springer. This book was released on 1994 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the Refinement Calculus gives one view of the development of the refinement calculus and its attempt to bring together - among other things - Z specifications and Dijkstra's programming language. It is an excellent source of reference material for all those seeking the background and mathematical underpinnings of the refinement calculus.
Download or read book Algebraic and Coalgebraic Methods in the Mathematics of Program Construction written by Roland Backhouse and published by Springer. This book was released on 2003-07-31 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Program construction is about turning specifications of computer software into implementations. Recent research aimed at improving the process of program construction exploits insights from abstract algebraic tools such as lattice theory, fixpoint calculus, universal algebra, category theory, and allegory theory. This textbook-like tutorial presents, besides an introduction, eight coherently written chapters by leading authorities on ordered sets and complete lattices, algebras and coalgebras, Galois connections and fixed point calculus, calculating functional programs, algebra of program termination, exercises in coalgebraic specification, algebraic methods for optimization problems, and temporal algebra.
Download or read book Program Design Calculi written by Manfred Broy and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of information processing systems requires models, calculi, and theories for the analysis of computations. It is well understood by now that more complex software systems cannot and should not be constructed in one step. A careful, systematic, and disciplined structuring of the development process is most adequate. It should start from basic requirement specifications in which aU the relevant details of the problem to be solved are formalized. The envisaged solution should be developed step by step by adding more and more details and giving evidence-in the best case by formal proof-to show the correctness of the developed steps. The development ends if a description of a solution is obtained that has aU the required properties. The Summer School in Marktoberdorf 1992 showed significant approaches in this area to refinement calculi, to models of computation, and as a special issue to the treatment of reactive timed systems. Like in the many summer schools before, the success of the 1992 Summer School was not only due to the excellent lectures, but even more due to the brilliant students taking part in the discussions at the summer school, the exchange of different views, and the recognition of the similarity of a number of different view points. These were some of the most important contributions of the summer school. fu the following the proceedings of the summer school are collected. They show the maturity of the field in an impressive way.
Download or read book Generic Programming written by Jeremy Gibbons and published by Springer. This book was released on 2013-04-17 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generic programming is about making programs more adaptable by making them more general. Generic programs often embody non-traditional kinds of polymorphism; ordinary programs are obtained from them by suitably instantiating their parameters. In contrast with normal programs, the parameters of a generic program are often quite rich in structure; for example, they may be other programs, types or type constructors, class hierarchies, or even programming paradigms. Generic programming techniques have always been of interest, both to practitioners and to theoreticians, but only recently have generic programming techniques become a specific focus of research in the functional and object-oriented programming language communities. Generic Programming comprises the edited proceedings of the Working Conference on Generic Programming, which was sponsored by the International Federation for Information Processing (IFIP) and held in Dagstuhl, Germany in July 2002. With contributions from leading researchers around the world, this volume captures the state of the art in this important emerging area.
Download or read book Refinement Calculus written by Ralph-Johan Back and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Much current research in computer science is concerned with two questions: is a program correct? And how can we improve a correct program preserving correctness? This latter question is known as the refinement of programs and the purpose of this book is to consider these questions in a formal setting. In fact, correctness turns out to be a special case of refinement and so the focus is on refinement. Although a reasonable background knowledge is assumed from mathematics and CS, the book is a self-contained introduction suitable for graduate students and researchers coming to this subject for the first time. There are numerous exercises provided of varying degrees of challenge.
Download or read book Edsger Wybe Dijkstra written by Krzysztof R. Apt and published by Morgan & Claypool. This book was released on 2022-07-14 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edsger Wybe Dijkstra (1930–2002) was one of the most influential researchers in the history of computer science, making fundamental contributions to both the theory and practice of computing. Early in his career, he proposed the single-source shortest path algorithm, now commonly referred to as Dijkstra’s algorithm. He wrote (with Jaap Zonneveld) the first ALGOL 60 compiler, and designed and implemented with his colleagues the influential THE operating system. Dijkstra invented the field of concurrent algorithms, with concepts such as mutual exclusion, deadlock detection, and synchronization. A prolific writer and forceful proponent of the concept of structured programming, he convincingly argued against the use of the Go To statement. In 1972 he was awarded the ACM Turing Award for “fundamental contributions to programming as a high, intellectual challenge; for eloquent insistence and practical demonstration that programs should be composed correctly, not just debugged into correctness; for illuminating perception of problems at the foundations of program design.” Subsequently he invented the concept of self-stabilization relevant to fault-tolerant computing. He also devised an elegant language for nondeterministic programming and its weakest precondition semantics, featured in his influential 1976 book A Discipline of Programming in which he advocated the development of programs in concert with their correctness proofs. In the later stages of his life, he devoted much attention to the development and presentation of mathematical proofs, providing further support to his long-held view that the programming process should be viewed as a mathematical activity. In this unique new book, 31 computer scientists, including five recipients of the Turing Award, present and discuss Dijkstra’s numerous contributions to computing science and assess their impact. Several authors knew Dijkstra as a friend, teacher, lecturer, or colleague. Their biographical essays and tributes provide a fascinating multi-author picture of Dijkstra, from the early days of his career up to the end of his life.
Download or read book FM 2009 Formal Methods written by Ana Cavalcanti and published by Springer. This book was released on 2009-11-04 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt: th FM 2009, the 16 International Symposium on Formal Methods, marked the 10th an- versary of the First World Congress on Formal Methods that was held in 1999 in Toulouse, France. We wished to celebrate this by advertising and organizing FM 2009 as the Second World Congress in the FM series, aiming to once again bring together the formal methods communities from all over the world. The statistics displayed in the table on the next page include the number of countries represented by the Programme Committee members, as well as of the authors of submitted and accepted papers. Novel this year was a special track on tools and industrial applications. Subm- sions of papers on these topics were especially encouraged, but not given any special treatment. (It was just as hard to get a special track paper accepted as any other paper.) What we did promote, however, was a discussion of how originality, contri- tion, and soundness should be judged for these papers. The following questions were used by our Programme Committee.
