Certified Programming with Dependent Types
Certified Programming with Dependent Types

Author: Adam Chlipala

Publisher: MIT Press

Published: 2013-12-06

Total Pages: 437

ISBN-13: 0262317885

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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.

Certified Programming with Dependent Types
Certified Programming with Dependent Types

Author: Adam Chlipala

Publisher: MIT Press

Published: 2022-06-07

Total Pages: 437

ISBN-13: 0262545748

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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.

Type-Driven Development with Idris
Type-Driven Development with Idris

Author: Edwin Brady

Publisher: Simon and Schuster

Published: 2017-03-13

Total Pages: 744

ISBN-13: 1638352240

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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

Verified Functional Programming in Agda
Verified Functional Programming in Agda

Author: Aaron Stump

Publisher: Morgan & Claypool

Published: 2016-02-01

Total Pages: 328

ISBN-13: 1970001267

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Agda is an advanced programming language based on Type Theory. Agda's type system is expressive enough to support full functional verification of programs, in two styles. In external verification, we write pure functional programs and then write proofs of properties about them. The proofs are separate external artifacts, typically using structural induction. In internal verification, we specify properties of programs through rich types for the programs themselves. This often necessitates including proofs inside code, to show the type checker that the specified properties hold. The power to prove properties of programs in these two styles is a profound addition to the practice of programming, giving programmers the power to guarantee the absence of bugs, and thus improve the quality of software more than previously possible. Verified Functional Programming in Agda is the first book to provide a systematic exposition of external and internal verification in Agda, suitable for undergraduate students of Computer Science. No familiarity with functional programming or computer-checked proofs is presupposed. The book begins with an introduction to functional programming through familiar examples like booleans, natural numbers, and lists, and techniques for external verification. Internal verification is considered through the examples of vectors, binary search trees, and Braun trees. More advanced material on type-level computation, explicit reasoning about termination, and normalization by evaluation is also included. The book also includes a medium-sized case study on Huffman encoding and decoding.

Program Logics for Certified Compilers
Program Logics for Certified Compilers

Author: Andrew W. Appel

Publisher: Cambridge University Press

Published: 2014-04-21

Total Pages: 469

ISBN-13: 110704801X

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This tutorial for graduate students covers practical and theoretical aspects of separation logic with constructions and proofs in Coq.

Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development

Author: Yves Bertot

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 492

ISBN-13: 366207964X

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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 Programs and Proofs
Certified Programs and Proofs

Author: Chris Hawblitzel

Publisher: Springer

Published: 2012-11-08

Total Pages: 314

ISBN-13: 3642353088

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This book constitutes the refereed proceedings of the Second International Conference on Certified Programs and Proofs, CPP 2012, held in Kyoto, Japan, in December 2012. The 18 revised regular papers presented were carefully reviewed and selected from 37 submissions. They deal with those topics in computer science and mathematics in which certification via formal techniques is crucial.

Exploratory Programming for the Arts and Humanities
Exploratory Programming for the Arts and Humanities

Author: Nick Montfort

Publisher: MIT Press

Published: 2016-04-08

Total Pages: 329

ISBN-13: 0262034204

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A book for anyone who wants to learn programming to explore and create, with exercises and projects to help the reader learn by doing. This book introduces programming to readers with a background in the arts and humanities; there are no prerequisites, and no knowledge of computation is assumed. In it, Nick Montfort reveals programming to be not merely a technical exercise within given constraints but a tool for sketching, brainstorming, and inquiring about important topics. He emphasizes programming's exploratory potential—its facility to create new kinds of artworks and to probe data for new ideas. The book is designed to be read alongside the computer, allowing readers to program while making their way through the chapters. It offers practical exercises in writing and modifying code, beginning on a small scale and increasing in substance. In some cases, a specification is given for a program, but the core activities are a series of “free projects,” intentionally underspecified exercises that leave room for readers to determine their own direction and write different sorts of programs. Throughout the book, Montfort also considers how computation and programming are culturally situated—how programming relates to the methods and questions of the arts and humanities. The book uses Python and Processing, both of which are free software, as the primary programming languages.

Certified Programs and Proofs
Certified Programs and Proofs

Author: Georges Gonthier

Publisher: Springer

Published: 2013-12-11

Total Pages: 318

ISBN-13: 3319035452

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This book constitutes the refereed proceedings of the Third International Conference on Certified Programs and Proofs, CPP 2013, colocated with APLAS 2013 held in Melbourne, Australia, in December 2013. The 18 revised regular papers presented together with 1 invited lecture were carefully reviewed and selected from 39 submissions. The papers are organized in topical sections on code verification, elegant proofs, proof libraries, certified transformations and security.