Programs and Their Proofs: an Algebraic Approach

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ISBN 13 :
Total Pages : 50 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Programs and Their Proofs: an Algebraic Approach by : Rodney M. Burstall

Download or read book Programs and Their Proofs: an Algebraic Approach written by Rodney M. Burstall and published by . This book was released on 1968 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results are presented of some applications of universal algebra and automata theory to programming problems. A method of defining some functions as homomorphisms instead of giving recursive or iterative definitions is explained. As a demonstration of the use of this approach, a proof of the correctness of a simple compiler for expressions is given. The method of description is closely related to the methods of proving theorems about the objects described. The report includes a section on basic algebraic concepts as background for the applications, and a section in which functions commonly encountered in programming are expressed as homomorphisms. (Author).

An Algebraic Approach to Compiler Design

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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.

Correctness of Translations of Programming Languages

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ISBN 13 :
Total Pages : 270 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Correctness of Translations of Programming Languages by : Francis Lockwood Morris

Download or read book Correctness of Translations of Programming Languages written by Francis Lockwood Morris and published by . This book was released on 1972 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Programming languages and their sets of meanings can be modelled by general operator algebras; seismic functions and compiling functions by homomorphisms of operator algebras. A restricted class of individual programs, machines, and computations can be modelled in a uniform manner by binary relational algebras. These two applications of algebra to computing are compatible: the semantic function provided by interpreting (running) one binary rational algebra on another is a homomorphism on an operator algebra whose elements are binary relational algebras. Under these mathematical tools, proofs can be provided systematically of the correctness of compilers for fragmentary programming languages, each embodying a single language 'feature'. Exemplary proofs are given for statement sequences, arithmetic expressions, Boolean expressions, assignment statements, and statements. Moreover, proofs of this sort can be combined to provide (synthetic) proofs for, in principle, many different complete programming languages. One example of such a synthesis is given.

Algebraic Methods in Semantics

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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.

Algebra of Programming

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Publisher :
ISBN 13 :
Total Pages : 322 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Algebra of Programming by : Richard Bird

Download or read book Algebra of Programming written by Richard Bird and published by . This book was released on 1997 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describing an algebraic approach to programming, based on a categorical calculus of relations, this book is suitable for the derivation of individual programs and for the study of programming principles in general.

Algebraic and Coalgebraic Methods in the Mathematics of Program Construction

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Publisher : Springer
ISBN 13 : 3540477977
Total Pages : 401 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Algebraic and Coalgebraic Methods in the Mathematics of Program Construction by : Roland Backhouse

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.

Symbolic Logic and Mechanical Theorem Proving

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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.

An algebraic approach to the theory of programs, algorithms, languages and recursiveness

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Publisher :
ISBN 13 :
Total Pages : 56 pages
Book Rating : 4.:/5 (726 download)

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Book Synopsis An algebraic approach to the theory of programs, algorithms, languages and recursiveness by : A. Blikle

Download or read book An algebraic approach to the theory of programs, algorithms, languages and recursiveness written by A. Blikle and published by . This book was released on 1972 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic Approaches to Program Semantics

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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

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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.

Programming Concepts and Methods PROCOMET ’98

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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.

Algebraic Methodology and Software Technology

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Publisher : Springer
ISBN 13 : 354079980X
Total Pages : 442 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Algebraic Methodology and Software Technology by : José Meseguer

Download or read book Algebraic Methodology and Software Technology written by José Meseguer and published by Springer. This book was released on 2008-07-29 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Conference on Algebraic Methodology and Software Technology, AMAST 2008, held in Urbana, IL, USA, in July 2008. The 28 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 58 submissions. Among the topics covered are all current issues in formal methods related to algebraic and logical foundations, software technology, and to programming methodology including concurrent and reactive systems, evolutionary software/adaptive systems, logic and functional programming, object paradigms, constraint programming and concurrency, program verification and transformation, programming calculi, specification languages and tools, formal specification and development case studies, logic, category theory, relation algebra, computational algebra, algebraic foundations for languages and systems, coinduction, theorem proving and logical frameworks for reasoning, logics of programs, as well as algebra and coalgebra.

Types for Proofs and Programs

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Publisher : Springer Science & Business Media
ISBN 13 : 3540314288
Total Pages : 282 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Types for Proofs and Programs by : Jean-Christophe Filliatre

Download or read book Types for Proofs and Programs written by Jean-Christophe Filliatre and published by Springer Science & Business Media. This book was released on 2006-01-25 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 17 revised full papers presented here cover all current issues of formal reasoning and computer programming based on type theory are addressed; in particular languages and computerised tools for reasoning, and applications in several domains such as analysis of programming languages, certified software, formalisation of mathematics and mathematics education.

Relational and Algebraic Methods in Computer Science

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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.

Theoretical Approaches to Non-Numerical Problem Solving

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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.

Types for Proofs and Programs

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Publisher : Springer Science & Business Media
ISBN 13 : 3642024432
Total Pages : 331 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Types for Proofs and Programs by : Ferruccio Damiani

Download or read book Types for Proofs and Programs written by Ferruccio Damiani and published by Springer Science & Business Media. This book was released on 2009-06-19 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of TYPES 2008, the last of a series of meetings of the TYPES working group funded by the European Union between 1993 and 2008; the workshop has been held in Torino, Italy, in March 2008. The 19 revised full papers presented were carefully reviewed and selected from 27 submissions. The topic of the workshop was formal reasoning and computer programming based on type theory: languages and computerized tools for reasoning, and applications in several domains such as analysis of programming languages, certified software, mobile code, formalization of mathematics, mathematics education.

An algebraic approach to mathematical theory of programs

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Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.:/5 (168 download)

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Book Synopsis An algebraic approach to mathematical theory of programs by : Andrzej Blikle

Download or read book An algebraic approach to mathematical theory of programs written by Andrzej Blikle and published by . This book was released on 1973 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: