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Author: Ernest G. Manes
Publisher: Springer Science & Business Media
ISBN: 1461249627
Category : Computers
Languages : en
Pages : 358
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Book Description
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.
Author: Ernest G. Manes
Publisher: Springer Science & Business Media
ISBN: 1461249627
Category : Computers
Languages : en
Pages : 358
Get Book Here
Book Description
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.
Author: M. Nivat
Publisher: CUP Archive
ISBN: 9780521267939
Category : Computers
Languages : en
Pages : 664
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Book Description
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.
Author: Augusto Sampaio
Publisher: World Scientific
ISBN: 9789810223915
Category : Computers
Languages : en
Pages : 216
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Book Description
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.
Author: Glynn Winskel
Publisher: MIT Press
ISBN: 9780262731034
Category : Computers
Languages : en
Pages : 388
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Book Description
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.
Author: Donald Sannella
Publisher: Springer Science & Business Media
ISBN: 3642173365
Category : Computers
Languages : en
Pages : 594
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Book Description
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.
Author: Stephen Brookes
Publisher: Springer Science & Business Media
ISBN: 9783540580270
Category : Computers
Languages : en
Pages : 664
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Book Description
This volume is the proceedings of the Ninth International Conference on the Mathematical Foundations of Programming Semantics, held in New Orleans in April 1993. The focus of the conference series is the semantics of programming languages and the mathematics which supports the study of the semantics. The semantics is basically denotation. The mathematics may be classified as category theory, lattice theory, or logic. Recent conferences and workshops have increasingly emphasized applications of the semantics and mathematics. The study of the semantics develops with the mathematics and the mathematics is inspired by the applications in semantics. The volume presents current research in denotational semantics and applications of category theory, logic, and lattice theory to semantics.
Author: Bozzano G Luisa
Publisher: Elsevier
ISBN: 0080933920
Category : Mathematics
Languages : en
Pages : 1288
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Book Description
The second part of this Handbook presents a choice of material on the theory of automata and rewriting systems, the foundations of modern programming languages, logics for program specification and verification, and some chapters on the theoretic modelling of advanced information processing.
Author: J.T. Schwartz
Publisher: Springer Science & Business Media
ISBN: 1461395755
Category : Computers
Languages : en
Pages : 508
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Book Description
The programming language SETL is a relatively new member of the so-called "very-high-level" class of languages, some of whose other well-known mem bers are LISP, APL, SNOBOL, and PROLOG. These languages all aim to reduce the cost of programming, recognized today as a main obstacle to future progress in the computer field, by allowing direct manipulation of large composite objects, considerably more complex than the integers, strings, etc., available in such well-known mainstream languages as PASCAL, PL/I, ALGOL, and Ada. For this purpose, LISP introduces structured lists as data objects, APL introduces vectors and matrices, and SETL introduces the objects characteristic for it, namely general finite sets and maps. The direct availability of these abstract, composite objects, and of powerful mathematical operations upon them, improves programmer speed and pro ductivity significantly, and also enhances program clarity and readability. The classroom consequence is that students, freed of some of the burden of petty programming detail, can advance their knowledge of significant algorithms and of broader strategic issues in program development more rapidly than with more conventional programming languages.
Author: Franck van Breughel
Publisher: Springer Science & Business Media
ISBN: 146124160X
Category : Computers
Languages : en
Pages : 232
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Book Description
During the last three decades several different styles of semantics for program ming languages have been developed. This book compares two of them: the operational and the denotational approach. On the basis of several exam ples we show how to define operational and denotational semantic models for programming languages. Furthermore, we introduce a general technique for comparing various semantic models for a given language. We focus on different degrees of nondeterminism in programming lan guages. Nondeterminism arises naturally in concurrent languages. It is also an important concept in specification languages. In the examples discussed, the degree of non determinism ranges from a choice between two alternatives to a choice between a collection of alternatives indexed by a closed interval of the real numbers. The former arises in a language with nondeterministic choices. A real time language with dense choices gives rise to the latter. We also consider the nondeterministic random assignment and parallel composition, both couched in a simple language. Besides non determinism our four example languages contain some form of recursion, a key ingredient of programming languages.
Author: Suad Alagic
Publisher: Springer Science & Business Media
ISBN: 1461235189
Category : Computers
Languages : en
Pages : 330
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Book Description
The major topic of this book is the integration of data and programming languages and the associated methodologies. To my knowledge, this is the first book on modern programming languages and programming meth odology devoted entirely to database application environments. At the same time, it is written with the goal of reconciling the relational and object-oriented approaches to database management. One of the reasons that influenced my decision to write this book is my dissatisfaction with the fact that the existing books on programming methodology and the associated concepts, techniques, and programming language notation are largely based on mathematical problems and math ematically oriented algorithms. As such, they give the impression that modern program structures, associated techniques, and methodologies, not to speak of the formal ones, are applicable only to problems of that sort. Although important, such problems are of limited applicability and scale. This does not apply to books in which modem concepts, techniques, methodologies, and programming language notation are applied to systems programming. But, even so, this does not demonstrate that in entirely application-oriented problems-those in which modern computer tech nology is most widely used-modern programming methodology is just as important. This book is meant to be a step toward providing a more convincing support of such a claim and, thus, is based entirely on common, what one might call business-oriented, problems in which database technology has been successfully used.
