Interactive Theorem Proving and Program Development


Book Description

A practical introduction to the development of proofs and certified programs using Coq. An invaluable tool for researchers, students, and engineers interested in formal methods and the development of zero-fault software.




Certified Programming with Dependent Types


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.




Interactive Theorem Proving


Book Description

The LNCS series reports state-of-the-art results in computer science research, development, and education, at a high level and in both printed and electronic form. Enjoying tight cooperation with the R&D community, with numerous individuals, as well as with prestigious organizations and societies, LNCS has grown into the most comprehensive computer science research forum available. The scope of LNCS, including its subseries LNAI and LNBI, spans the whole range of computer science and information technology including interdisciplinary topics in a variety of application fields. In parallel to the printed book, each new volume is published electronically in LNCS Online.




Interactive Theorem Proving


Book Description

This book constitutes the proceedings of the 5th International Conference on Interactive Theorem Proving, ITP 2014, Held as Part of the Vienna Summer of Logic, VSL 2014, in Vienna, Austria, in July 2014. The 35 papers presented in this volume were carefully reviewed and selected from 59 submissions. The topics range from theoretical foundations to implementation aspects and applications in program verification, security and formalization of mathematics.




Type-Driven Development with Idris


Book Description

Summary Type-Driven Development with Idris, written by the creator of Idris, teaches you how to improve the performance and accuracy of your programs by taking advantage of a state-of-the-art type system. This book teaches you with Idris, a language designed to support type-driven development. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the Technology Stop fighting type errors! Type-driven development is an approach to coding that embraces types as the foundation of your code - essentially as built-in documentation your compiler can use to check data relationships and other assumptions. With this approach, you can define specifications early in development and write code that's easy to maintain, test, and extend. Idris is a Haskell-like language with first-class, dependent types that's perfect for learning type-driven programming techniques you can apply in any codebase. About the Book Type-Driven Development with Idris teaches you how to improve the performance and accuracy of your code by taking advantage of a state-of-the-art type system. In this book, you'll learn type-driven development of real-world software, as well as how to handle side effects, interaction, state, and concurrency. By the end, you'll be able to develop robust and verified software in Idris and apply type-driven development methods to other languages. What's Inside Understanding dependent types Types as first-class language constructs Types as a guide to program construction Expressing relationships between data About the Reader Written for programmers with knowledge of functional programming concepts. About the Author Edwin Brady leads the design and implementation of the Idris language. Table of Contents PART 1 - INTRODUCTION Overview Getting started with IdrisPART 2 - CORE IDRIS Interactive development with types User-defined data types Interactive programs: input and output processing Programming with first-class types Interfaces: using constrained generic types Equality: expressing relationships between data Predicates: expressing assumptions and contracts in types Views: extending pattern matching PART 3 - IDRIS AND THE REAL WORLD Streams and processes: working with infinite data Writing programs with state State machines: verifying protocols in types Dependent state machines: handling feedback and errors Type-safe concurrent programming




Interactive Theorem Proving


Book Description

This book constitutes the refereed proceedings of the 8th International Conference on Interactive Theorem Proving, ITP 2017, held in Brasilia, Brazil, in September 2017. The 28 full papers, 2 rough diamond papers, and 3 invited talk papers presented were carefully reviewed and selected from 65 submissions. The topics range from theoretical foundations to implementation aspects and applications in program verification, security and formalization of mathematical theories.




Computer-Aided Reasoning


Book Description

Computer-Aided Reasoning: ACL2 Case Studies illustrates how the computer-aided reasoning system ACL2 can be used in productive and innovative ways to design, build, and maintain hardware and software systems. Included here are technical papers written by twenty-one contributors that report on self-contained case studies, some of which are sanitized industrial projects. The papers deal with a wide variety of ideas, including floating-point arithmetic, microprocessor simulation, model checking, symbolic trajectory evaluation, compilation, proof checking, real analysis, and several others. Computer-Aided Reasoning: ACL2 Case Studies is meant for two audiences: those looking for innovative ways to design, build, and maintain hardware and software systems faster and more reliably, and those wishing to learn how to do this. The former audience includes project managers and students in survey-oriented courses. The latter audience includes students and professionals pursuing rigorous approaches to hardware and software engineering or formal methods. Computer-Aided Reasoning: ACL2 Case Studies can be used in graduate and upper-division undergraduate courses on Software Engineering, Formal Methods, Hardware Design, Theory of Computation, Artificial Intelligence, and Automated Reasoning. The book is divided into two parts. Part I begins with a discussion of the effort involved in using ACL2. It also contains a brief introduction to the ACL2 logic and its mechanization, which is intended to give the reader sufficient background to read the case studies. A more thorough, textbook introduction to ACL2 may be found in the companion book, Computer-Aided Reasoning: An Approach. The heart of the book is Part II, where the case studies are presented. The case studies contain exercises whose solutions are on the Web. In addition, the complete ACL2 scripts necessary to formalize the models and prove all the properties discussed are on the Web. For example, when we say that one of the case studies formalizes a floating-point multiplier and proves it correct, we mean that not only can you read an English description of the model and how it was proved correct, but you can obtain the entire formal content of the project and replay the proofs, if you wish, with your copy of ACL2. ACL2 may be obtained from its home page. The results reported in each case study, as ACL2 input scripts, as well as exercise solutions for both books, are available from this page.




Interactive Theorem Proving


Book Description

This book constitutes the refereed proceedings of the 4th International Conference on Interactive Theorem Proving, ITP 2013, held in Rennes, France, in July 2013. The 26 regular full papers presented together with 7 rough diamond papers, 3 invited talks, and 2 invited tutorials were carefully reviewed and selected from 66 submissions. The papers are organized in topical sections such as program verfication, security, formalization of mathematics and theorem prover development.




Fundamental Proof Methods in Computer Science


Book Description

A textbook that teaches students to read and write proofs using Athena. Proof is the primary vehicle for knowledge generation in mathematics. In computer science, proof has found an additional use: verifying that a particular system (or component, or algorithm) has certain desirable properties. This book teaches students how to read and write proofs using Athena, a freely downloadable computer language. Athena proofs are machine-checkable and written in an intuitive natural-deduction style. The book contains more than 300 exercises, most with full solutions. By putting proofs into practice, it demonstrates the fundamental role of logic and proof in computer science as no other existing text does. Guided by examples and exercises, students are quickly immersed in the most useful high-level proof methods, including equational reasoning, several forms of induction, case analysis, proof by contradiction, and abstraction/specialization. The book includes auxiliary material on SAT and SMT solving, automated theorem proving, and logic programming. The book can be used by upper undergraduate or graduate computer science students with a basic level of programming and mathematical experience. Professional programmers, practitioners of formal methods, and researchers in logic-related branches of computer science will find it a valuable reference.




Interactive Theorem Proving


Book Description

This book constitutes the refereed proceedings of the 9th International Conference on Interactive Theorem Proving, ITP 2018, held in Oxford, UK, in July 2018. The 32 full papers and 5 short papers presented were carefully reviewed and selected from 65 submissions. The papers feature research in the area of logical frameworks and interactive proof assistants. The topics include theoretical foundations and implementation aspects of the technology, as well as applications to verifying hardware and software systems to ensure their safety and security, and applications to the formal verication of mathematical results. Chapters 2, 10, 26, 29, 30 and 37 are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.