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Author: Samuel Mimram
Publisher:
ISBN:
Category :
Languages : en
Pages : 539
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Book Description
This course provides a first introduction to the Curry-Howard correspondence between programs and proofs, from a theoretical programmer's perspective: we want to understand the theory behind logic and programming languages, but also to write concrete programs (in OCaml) and proofs (in Agda). After an introduction to functional programming languages, we present propositional logic, λ-calculus, the Curry-Howard correspondence, first-order logic, Agda, dependent types and homotopy type theory.
Author: Samuel Mimram
Publisher:
ISBN:
Category :
Languages : en
Pages : 539
Get Book Here
Book Description
This course provides a first introduction to the Curry-Howard correspondence between programs and proofs, from a theoretical programmer's perspective: we want to understand the theory behind logic and programming languages, but also to write concrete programs (in OCaml) and proofs (in Agda). After an introduction to functional programming languages, we present propositional logic, λ-calculus, the Curry-Howard correspondence, first-order logic, Agda, dependent types and homotopy type theory.
Author: K. Rustan M. Leino
Publisher: MIT Press
ISBN: 0262375427
Category : Computers
Languages : en
Pages : 498
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Book Description
This comprehensive and highly readable textbook teaches how to formally reason about computer programs using an incremental approach and the verification-aware programming language Dafny. Program Proofs shows students what it means to write specifications for programs, what it means for programs to satisfy those specifications, and how to write proofs that connect specifications and programs. Writing with clarity and humor, K. Rustan M. Leino first provides an overview of the basic theory behind reasoning about programs. He then gradually builds up to complex concepts and applications, until students are facing real programs using objects, data structures, and non-trivial recursion. To emphasize the practical nature of program proofs, all material and examples use the verification-aware programming language Dafny, but no previous knowledge of Dafny is assumed. Written in a highly readable and student-friendly style Builds up to complex concepts in an incremental manner Comprehensively covers how to write proofs and how to specify and verify both functional programs and imperative programs Uses real program text from a real programming language, not psuedo code Features engaging illustrations and hands-on learning exercises
Author: Adam Chlipala
Publisher: MIT Press
ISBN: 0262317885
Category : Computers
Languages : en
Pages : 437
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Book Description
A handbook to the Coq software for writing and checking mathematical proofs, with a practical engineering focus. The technology of mechanized program verification can play a supporting role in many kinds of research projects in computer science, and related tools for formal proof-checking are seeing increasing adoption in mathematics and engineering. This book provides an introduction to the Coq software for writing and checking mathematical proofs. It takes a practical engineering focus throughout, emphasizing techniques that will help users to build, understand, and maintain large Coq developments and minimize the cost of code change over time. Two topics, rarely discussed elsewhere, are covered in detail: effective dependently typed programming (making productive use of a feature at the heart of the Coq system) and construction of domain-specific proof tactics. Almost every subject covered is also relevant to interactive computer theorem proving in general, not just program verification, demonstrated through examples of verified programs applied in many different sorts of formalizations. The book develops a unique automated proof style and applies it throughout; even experienced Coq users may benefit from reading about basic Coq concepts from this novel perspective. The book also offers a library of tactics, or programs that find proofs, designed for use with examples in the book. Readers will acquire the necessary skills to reimplement these tactics in other settings by the end of the book. All of the code appearing in the book is freely available online.
Author: Daniel J. Velleman
Publisher: Cambridge University Press
ISBN: 0521861241
Category : Mathematics
Languages : en
Pages : 401
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Book Description
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
Author: Bertrand Meyer
Publisher: Springer
ISBN: 3540737707
Category : Computers
Languages : en
Pages : 226
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Book Description
Readers will find here a book that constitutes the thoroughly refereed post-proceedings of the First International Conference on Test and Proofs, held in Zurich, Switzerland in February 2007. The 12 revised full papers presented were carefully reviewed and selected for inclusion in the book. The papers are devoted to the convergence of software proofing and testing and feature current research work that combines ideas from both sides to foster software quality.
Author: Atsushi Ohori
Publisher: Springer Science & Business Media
ISBN: 3540205365
Category : Computers
Languages : en
Pages : 442
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Book Description
This book constitutes the refereed proceedings of the First Asian Symposium on Programming Languages and Systems, APLAS 2003, held in Beijing, China in November 2003. The 24 revised full papers presented together with abstracts of 3 invited talks were carefully reviewed and selected from 75 submissions. The papers are devoted to concurrency and parallelism, language implementation and optimization, mobile computation and security, program analysis and verification, program transformation and calculation, programming paradigms and language design, programming techniques and applications, program semantics, categorical and logical foundations, tools and environments, type theory and type systems.
Author: Armand Puccetti
Publisher: Springer Science & Business Media
ISBN: 3642845428
Category : Computers
Languages : en
Pages : 349
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Book Description
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.
Author: Matthias Felleisen
Publisher: Springer
ISBN: 3642370365
Category : Computers
Languages : en
Pages : 635
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Book Description
This book constitutes the refereed proceedings of the 22nd European Symposium on Programming, ESOP 2013, held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2013, which took place in Rome, Italy, in March 2013. The 31 papers, presented together with a full-length invited talk, were carefully reviewed and selected from 120 full submissions. The contributions have been organized according to ten topical sections on programming techniques; programming tools; separation logic; gradual typing; shared-memory concurrency and verification; process calculi; taming concurrency; model checking and verification; weak-memory concurrency and verification; and types, inference, and analysis.
Author: Peter Müller
Publisher: Springer
ISBN: 3540456511
Category : Computers
Languages : en
Pages : 297
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Book Description
Software systems play an increasingly important role in modern societies. Smart cards for personal identi?cation, e-banking, software-controlled me- cal tools, airbags in cars, and autopilots for aircraft control are only some examples that illustrate how everyday life depends on the good behavior of software. Consequently, techniques and methods for the development of hi- quality, dependable software systems are a central research topic in computer science. A fundamental approach to this area is to use formal speci?cation and veri?cation. Speci?cation languages allow one to describe the crucial p- perties of software systems in an abstract, mathematically precise, and implementation-independent way. By formal veri?cation, one can then prove that an implementation really has the desired, speci?ed properties. Although this formal methods approach has been a research topic for more than 30 years, its practical success is still restricted to domains in which devel- ment costs are of minor importance. Two aspects are crucial to widen the application area of formal methods: – Formal speci?cation techniques have to be smoothly integrated into the software and program development process. – The techniques have to be applicable to reusable software components. This way, the quality gain can be exploited for more than one system, thereby justifying the higher development costs. Starting from these considerations, Peter Muller ̈ has developed new te- niques for the formal speci?cation and veri?cation of object-oriented so- ware. The speci?cation techniques are declarative and implementati- independent. They can be used for object-oriented design and programming.
Author: Phaneendra Nath Vellanky
Publisher: Universal-Publishers
ISBN: 1581129807
Category :
Languages : en
Pages : 591
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Book Description
Computer systems play an important role in our society. Software drives those systems. Massive investments of time and resources are made in developing and implementing these systems. Maintenance is inevitable. It is hard and costly. Considerable resources are required to keep the systems active and dependable. We cannot maintain software unless maintainability characters are built into the products and processes. There is an urgent need to reinforce software development practices based on quality and reliability principles. Though maintenance is a mini development lifecycle, it has its own problems. Maintenance issues need corresponding tools and techniques to address them. Software professionals are key players in maintenance. While development is an art and science, maintenance is a craft. We need to develop maintenance personnel to master this craft. Technology impact is very high in systems world today. We can no longer conduct business in the way we did before. That calls for reengineering systems and software. Even reengineered software needs maintenance, soon after its implementation. We have to take business knowledge, procedures, and data into the newly reengineered world. Software maintenance people can play an important role in this migration process. Software technology is moving into global and distributed networking environments. Client/server systems and object-orientation are on their way. Massively parallel processing systems and networking resources are changing database services into corporate data warehouses. Software engineering environments, rapid application development tools are changing the way we used to develop and maintain software. Software maintenance is moving from code maintenance to design maintenance, even onto specification maintenance. Modifications today are made at specification level, regenating the software components, testing and integrating them with the system. Eventually software maintenance has to manage the evolution and evolutionary characteristics of software systems. Software professionals have to maintain not only the software, but the momentum of change in systems and software. In this study, we observe various issues, tools and techniques, and the emerging trends in software technology with particular reference to maintenance. We are not searching for specific solutions. We are identifying issues and finding ways to manage them, live with them, and control their negative impact.
