Programs And Their Proofs An Algebraic Approach

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An Algebraic Approach to Compiler Design

Author : Augusto Sampaio
Publisher : World Scientific
ISBN 13 : 9789810223915
Total Pages : 216 pages
Book Rating : 4.2/5 (239 download)

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Book Synopsis An Algebraic Approach to Compiler Design by : Augusto Sampaio

Download or read book An Algebraic Approach to Compiler Design written by Augusto Sampaio and published by World Scientific. This book was released on 1997 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the design of compilers for procedural languages, based on the algebraic laws which these languages satisfy. The particular strategy adopted is to reduce an arbitrary source program to a general normal form, capable of representing an arbitrary target machine. This is achieved by a series of normal form reduction theorems which are proved algebraically from the more basic laws. The normal form and the related reduction theorems can then be instantiated to design compilers for distinct target machines. This constitutes the main novelty of the author's approach to compilation, together with the fact that the entire process is formalised within a single and uniform semantic framework of a procedural language and its algberaic laws. Furthermore, by mechanising the approach using the OBJ3 term rewriting system it is shown that a prototype compiler is developed as a byproduct of its own proof of correctness.

Algebraic Approaches to Program Semantics

Author : Ernest G. Manes
Publisher : Springer Science & Business Media
ISBN 13 : 1461249627
Total Pages : 358 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Algebraic Approaches to Program Semantics by : Ernest G. Manes

Download or read book Algebraic Approaches to Program Semantics written by Ernest G. Manes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 1930s, mathematical logicians studied the notion of "effective comput ability" using such notions as recursive functions, A-calculus, and Turing machines. The 1940s saw the construction of the first electronic computers, and the next 20 years saw the evolution of higher-level programming languages in which programs could be written in a convenient fashion independent (thanks to compilers and interpreters) of the architecture of any specific machine. The development of such languages led in turn to the general analysis of questions of syntax, structuring strings of symbols which could count as legal programs, and semantics, determining the "meaning" of a program, for example, as the function it computes in transforming input data to output results. An important approach to semantics, pioneered by Floyd, Hoare, and Wirth, is called assertion semantics: given a specification of which assertions (preconditions) on input data should guarantee that the results satisfy desired assertions (postconditions) on output data, one seeks a logical proof that the program satisfies its specification. An alternative approach, pioneered by Scott and Strachey, is called denotational semantics: it offers algebraic techniques for characterizing the denotation of (i. e. , the function computed by) a program-the properties of the program can then be checked by direct comparison of the denotation with the specification. This book is an introduction to denotational semantics. More specifically, we introduce the reader to two approaches to denotational semantics: the order semantics of Scott and Strachey and our own partially additive semantics.

Foundations of Algebraic Specification and Formal Software Development

Author : Donald Sannella
Publisher : Springer Science & Business Media
ISBN 13 : 3642173365
Total Pages : 594 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Foundations of Algebraic Specification and Formal Software Development by : Donald Sannella

Download or read book Foundations of Algebraic Specification and Formal Software Development written by Donald Sannella and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides foundations for software specification and formal software development from the perspective of work on algebraic specification, concentrating on developing basic concepts and studying their fundamental properties. These foundations are built on a solid mathematical basis, using elements of universal algebra, category theory and logic, and this mathematical toolbox provides a convenient language for precisely formulating the concepts involved in software specification and development. Once formally defined, these notions become subject to mathematical investigation, and this interplay between mathematics and software engineering yields results that are mathematically interesting, conceptually revealing, and practically useful. The theory presented by the authors has its origins in work on algebraic specifications that started in the early 1970s, and their treatment is comprehensive. This book contains five kinds of material: the requisite mathematical foundations; traditional algebraic specifications; elements of the theory of institutions; formal specification and development; and proof methods. While the book is self-contained, mathematical maturity and familiarity with the problems of software engineering is required; and in the examples that directly relate to programming, the authors assume acquaintance with the concepts of functional programming. The book will be of value to researchers and advanced graduate students in the areas of programming and theoretical computer science.

Algebraic Methods in Semantics

Author : M. Nivat
Publisher : CUP Archive
ISBN 13 : 9780521267939
Total Pages : 664 pages
Book Rating : 4.2/5 (679 download)

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Book Synopsis Algebraic Methods in Semantics by : M. Nivat

Download or read book Algebraic Methods in Semantics written by M. Nivat and published by CUP Archive. This book was released on 1985 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which contains contributions from leading researchers in France, USA and Great Britain, gives detailed accounts of a variety of methods for describing the semantics of programming languages, i.e. for attaching to programs mathematical objects that encompass their meaning. Consideration is given to both denotational semantics, where the meaning of a program is regarded as a function from inputs to outputs, and operational semantics, where the meaning includes the sequence of states or terms generated internally during the computation. The major problems considered include equivalence relations between operational and denotational semantics, rules for obtaining optimal computations (especially for nondeterministic programs), equivalence of programs, meaning-preserving transformations of programs and program proving by assertions. Such problems are discussed for a variety of programming languages and formalisms, and a wealth of mathematical tools is described.

Symbolic Logic and Mechanical Theorem Proving

Author : Chin-Liang Chang
Publisher : Academic Press
ISBN 13 : 0080917283
Total Pages : 349 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Symbolic Logic and Mechanical Theorem Proving by : Chin-Liang Chang

Download or read book Symbolic Logic and Mechanical Theorem Proving written by Chin-Liang Chang and published by Academic Press. This book was released on 2014-06-28 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.

Proof Theory and Algebra in Logic

Author : Hiroakira Ono
Publisher : Springer
ISBN 13 : 9811379971
Total Pages : 164 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Proof Theory and Algebra in Logic by : Hiroakira Ono

Download or read book Proof Theory and Algebra in Logic written by Hiroakira Ono and published by Springer. This book was released on 2019-08-02 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a concise introduction to both proof-theory and algebraic methods, the core of the syntactic and semantic study of logic respectively. The importance of combining these two has been increasingly recognized in recent years. It highlights the contrasts between the deep, concrete results using the former and the general, abstract ones using the latter. Covering modal logics, many-valued logics, superintuitionistic and substructural logics, together with their algebraic semantics, the book also provides an introduction to nonclassical logic for undergraduate or graduate level courses.The book is divided into two parts: Proof Theory in Part I and Algebra in Logic in Part II. Part I presents sequent systems and discusses cut elimination and its applications in detail. It also provides simplified proof of cut elimination, making the topic more accessible. The last chapter of Part I is devoted to clarification of the classes of logics that are discussed in the second part. Part II focuses on algebraic semantics for these logics. At the same time, it is a gentle introduction to the basics of algebraic logic and universal algebra with many examples of their applications in logic. Part II can be read independently of Part I, with only minimum knowledge required, and as such is suitable as a textbook for short introductory courses on algebra in logic.

Programming Concepts and Methods PROCOMET ’98

Author : David Gries
Publisher : Springer
ISBN 13 : 0387353585
Total Pages : 488 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Programming Concepts and Methods PROCOMET ’98 by : David Gries

Download or read book Programming Concepts and Methods PROCOMET ’98 written by David Gries and published by Springer. This book was released on 2013-04-17 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the Proceedings of the IFIP Working Conference PRO COMET'98, held 8-12 June 1998 at Shelter Island, N.Y. The conference is organized by the t'wo IFIP TC 2 Working Groups 2.2 Formal Description of Programming Concepts and 2.3 Programming Methodology. WG2.2 and WG2.3 have been organizing these conferences every four years for over twenty years. The aim of such Working Conferences organized by IFIP Working Groups is to bring together leading scientists in a given area of computer science. Participation is by invitation only. As a result, these conferences distinguish themselves from other meetings by extensive and competent technical discus sions. PROCOMET stands for Programming Concepts and Methods, indicating that the area of discussion for the conference is the formal description of pro gramming concepts and methods, their tool support, and their applications. At PROCOMET working conferences, papers are presented from this whole area, reflecting the interest of the individuals in WG2.2 and WG2.3.

Program Verification

Author : Timothy T.R. Colburn
Publisher : Springer Science & Business Media
ISBN 13 : 9401117934
Total Pages : 454 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Program Verification by : Timothy T.R. Colburn

Download or read book Program Verification written by Timothy T.R. Colburn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the most important problems confronting computer science is that of developing a paradigm appropriate to the discipline. Proponents of formal methods - such as John McCarthy, C.A.R. Hoare, and Edgar Dijkstra - have advanced the position that computing is a mathematical activity and that computer science should model itself after mathematics. Opponents of formal methods - by contrast, suggest that programming is the activity which is fundamental to computer science and that there are important differences that distinguish it from mathematics, which therefore cannot provide a suitable paradigm. Disagreement over the place of formal methods in computer science has recently arisen in the form of renewed interest in the nature and capacity of program verification as a method for establishing the reliability of software systems. A paper that appeared in Communications of the ACM entitled, `Program Verification: The Very Idea', by James H. Fetzer triggered an extended debate that has been discussed in several journals and that has endured for several years, engaging the interest of computer scientists (both theoretical and applied) and of other thinkers from a wide range of backgrounds who want to understand computer science as a domain of inquiry. The editors of this collection have brought together many of the most interesting and important studies that contribute to answering questions about the nature and the limits of computer science. These include early papers advocating the mathematical paradigm by McCarthy, Naur, R. Floyd, and Hoare (in Part I), others that elaborate the paradigm by Hoare, Meyer, Naur, and Scherlis and Scott (in Part II), challenges, limits and alternatives explored by C. Floyd, Smith, Blum, and Naur (in Part III), and recent work focusing on formal verification by DeMillo, Lipton, and Perlis, Fetzer, Cohn, and Colburn (in Part IV). It provides essential resources for further study. This volume will appeal to scientists, philosophers, and laypersons who want to understand the theoretical foundations of computer science and be appropriately positioned to evaluate the scope and limits of the discipline.

Theoretical Approaches to Non-Numerical Problem Solving

Author : R. B. Banerji
Publisher : Springer Science & Business Media
ISBN 13 : 364299976X
Total Pages : 477 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Theoretical Approaches to Non-Numerical Problem Solving by : R. B. Banerji

Download or read book Theoretical Approaches to Non-Numerical Problem Solving written by R. B. Banerji and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in computer technology have pointed out the next important area of computer applications: solution of non-numerical problems. It is hardly necessary to emphasize the importance of these kind of problems. First of all most of the decisions one has to make in real-life situations are non-numerical in the first instance and can be represented as numerical problems only as approximations which are often only partially valid. Second, to use the computer to its full potential it should be employed as a logical machine, capable of deduction, and not just as a numerical calculating machine. Thus the computer would extend man's capability for logical reasoning and not just for his capability to do fast and accurate calculation. It is not a new area; indeed non-numerical problems are central in fields such as artificial intelligence, heuristic programming, pattern recognition, classification and information-processing (and retrival) etc. However, it is fair to assess that progress in the area has not been quite as expected. One of the reasons was a lack of conceptual and theoretical framework in which to investigate different classes of non-numerical problems to improve understanding of various types of problems and methods for their solutions and furthermore to enable the methods which have been proven as effective in one situation to be used in another situation with appropriately similar structure.

FM 2014: Formal Methods

Author : Cliff Jones
Publisher : Springer
ISBN 13 : 331906410X
Total Pages : 766 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis FM 2014: Formal Methods by : Cliff Jones

Download or read book FM 2014: Formal Methods written by Cliff Jones and published by Springer. This book was released on 2014-04-18 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 19th International Symposium on Formal Methods, FM 2014, held in Singapore, May 2014. The 45 papers presented together with 3 invited talks were carefully reviewed and selected from 150 submissions. The focus of the papers is on the following topics: Interdisciplinary Formal Methods, Practical Applications of Formal Methods in Industrial and Research Settings, Experimental Validation of Tools and Methods as well as Construction and Evolution of Formal Methods Tools.

Programming Languages and Their Definition

Author : H. Bekic
Publisher : Springer Science & Business Media
ISBN 13 : 9783540133780
Total Pages : 290 pages
Book Rating : 4.1/5 (337 download)

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Book Synopsis Programming Languages and Their Definition by : H. Bekic

Download or read book Programming Languages and Their Definition written by H. Bekic and published by Springer Science & Business Media. This book was released on 1984-08 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Relational and Algebraic Methods in Computer Science

Author : Peter Höfner
Publisher : Springer
ISBN 13 : 3319062514
Total Pages : 474 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Relational and Algebraic Methods in Computer Science by : Peter Höfner

Download or read book Relational and Algebraic Methods in Computer Science written by Peter Höfner and published by Springer. This book was released on 2014-04-08 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 14th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2014 held in Marienstatt, Germany, in April/May 2014. The 25 revised full papers presented were carefully selected from 37 submissions. The papers are structured in specific fields on concurrent Kleene algebras and related formalisms, reasoning about computations and programs, heterogeneous and categorical approaches, applications of relational and algebraic methods and developments related to modal logics and lattices.

Algebraic and Logic Programming

Author : Jan Grabowski
Publisher : Springer
ISBN 13 : 3540460632
Total Pages : 277 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Algebraic and Logic Programming by : Jan Grabowski

Download or read book Algebraic and Logic Programming written by Jan Grabowski and published by Springer. This book was released on 2005-07-06 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Formalization of Programming Concepts

Author : J. Diaz
Publisher : Springer Science & Business Media
ISBN 13 : 9783540106999
Total Pages : 492 pages
Book Rating : 4.1/5 (69 download)

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Book Synopsis Formalization of Programming Concepts by : J. Diaz

Download or read book Formalization of Programming Concepts written by J. Diaz and published by Springer Science & Business Media. This book was released on 1981-04 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Relational and Algebraic Methods in Computer Science

Author : Uli Fahrenberg
Publisher : Springer Nature
ISBN 13 : 3030435202
Total Pages : 352 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Relational and Algebraic Methods in Computer Science by : Uli Fahrenberg

Download or read book Relational and Algebraic Methods in Computer Science written by Uli Fahrenberg and published by Springer Nature. This book was released on 2020-04-01 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 18th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2020, which was due to be held in Palaiseau, France, in April 2020. The conference was cancelled due to the COVID-19 pandemic. The 20 full papers presented together with 3 invited abstracts were carefully selected from 29 submissions. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond.

The Programming and Proof System ATES

Author : Armand Puccetti
Publisher : Springer Science & Business Media
ISBN 13 : 3642845428
Total Pages : 349 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis The Programming and Proof System ATES by : Armand Puccetti

Download or read book The Programming and Proof System ATES written by Armand Puccetti and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Today, people use a large number of "systems" ranging in complexity from washing machines to international airline reservation systems. Computers are used in nearly all such systems: accuracy and security are becoming increasingly essential. The design of such computer systems should make use of development methods as systematic as those used in other engineering disciplines. A systematic development method must provide a way of writing specifications which are both precise and concise; it must also supply a way of relating design to specification. A concise specification can be achieved by restricting attention to what a system has to do: all considerations of implementation details are postponed. With computer systems, this is done by: 1) building an abstract model of the system -operations being specified by pre-and post-conditions; 2) defining languages by mapping program texts onto some collection of objects modelizing the concepts of the system to be dealt with, whose meaning is understood; 3) defining complex data objects in terms of abstractions known from mathematics. This last topic, the use of abstract data types, pervades all work on specifications and is necessary in order to apply ideas to systems of significant complexity. The use of mathematics based notations is the best way to achieve precision. 1.1 ABSTRACT DATA TYPES, PROOF TECHNIQUES From a practical point of view, a solution to these three problems consists to introduce abstract data types in the programming languages, and to consider formal proof methods.

Programming Language Implementation and Logic Programming

Author : Jaan Penjam
Publisher : Springer Science & Business Media
ISBN 13 : 9783540584025
Total Pages : 488 pages
Book Rating : 4.5/5 (84 download)

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Book Synopsis Programming Language Implementation and Logic Programming by : Jaan Penjam

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.