Type Driven Development With Idris

Author: Edwin Brady
Publisher: Manning Publications
ISBN: 9781617293023
Size: 29.40 MB
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Types are often seen as a tool for checking errors, with the programmer writing a complete program first and using the type checker to detect errors. And while tests are used to show presence of errors, they can only find errors that you explicitly test for. In type-driven development, types become your tools for constructing programs and, used appropriately, can show the absence of errors. And you can express precise relationships between data, your assumptions are explicit and checkable, and you can precisely state and verify properties. Type-driven development lets users write extensible code, create simple specifications very early in development, and easily create mock implementation for testing. Type-Driven Development with Idris, written by the creator of Idris, teaches programmers how to improve the performance and accuracy of programs by taking advantage of a state-of-the-art type system. This book teaches readers using Idris, a language designed from the very beginning to support type-driven development. Readers learn how to manipulate types just like any other construct (numbers, strings, lists, etc.). This book teaches how to use type-driven development to build real-world software, as well as how to handle side-effects, state and concurrency, and interoperating with existing systems. By the end of this book, readers will be able to develop robust and verified software in Idris and apply type-driven development methods to programming in other languages. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications.

Lambda Calculus With Types

Author: Henk Barendregt
Publisher: Cambridge University Press
ISBN: 1107276349
Size: 43.17 MB
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This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.

Certified Programming With Dependent Types

Author: Adam Chlipala
Publisher: MIT Press
ISBN: 0262317885
Size: 53.98 MB
Format: PDF, Docs
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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 And Program Development

Author: Yves Bertot
Publisher: Springer Science & Business Media
ISBN: 366207964X
Size: 34.15 MB
Format: PDF, Mobi
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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.

A Beginner S Book Of Tex

Author: Raymond Seroul
Publisher: Springer Science & Business Media
ISBN: 1441986545
Size: 43.81 MB
Format: PDF
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The last two decades have witnessed a revolution in the realm of typography, with the virtual disappearance of hot-lead typesetting in favor of the so-called digital typesetting. The principle behind the new technology is simple: imagine a very fine mesh superimposed on a sheet of paper. Digital typesetting consists in darkening the appropriate pixels (tiny squares) of this mesh, in patterns corresponding to each character and symbol of the text being set. The actual darkening is done by some printing device, say a laser printer or phototypesetter, which must be told exactly where the ink should go. Since the mesh is very fine-the dashes surrounding this sentence are some six pixels thick, and more than 200 pixels long-the printer can only be controlled by a computer program, which takes a "high-level" description of the page in terms of text, fonts, and formatting commands, and digests all of that into "low-level" commands for the printer. TEX is such a program, created by Donald E. Knuth, a computer scientist at Stanford University.

An Introduction To Substructural Logics

Author: Greg Restall
Publisher: Routledge
ISBN: 1135111316
Size: 41.82 MB
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This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. An Introduction to Substrucural Logics is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading.

Type Theory Functional Programming

Author: Simon Thompson
Publisher: Addison Wesley Publishing Company
ISBN: 9780201416671
Size: 55.91 MB
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This book explores the role of Martin-Lof s constructive type theory in computer programming. The main focus of the book is how the theory can be successfully applied in practice. Introductory sections provide the necessary background in logic, lambda calculus and constructive mathematics, and exercises and chapter summaries are included to reinforce understanding.

Verified Functional Programming In Agda

Author: Aaron Stump
Publisher: Morgan & Claypool
ISBN: 1970001267
Size: 56.68 MB
Format: PDF, Docs
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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.

Isabelle Hol

Author: Tobias Nipkow
Publisher: Springer
ISBN: 3540459499
Size: 76.45 MB
Format: PDF, ePub
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This volume is a self-contained introduction to interactive proof in high- order logic (HOL), using the proof assistant Isabelle 2002. Compared with existing Isabelle documentation, it provides a direct route into higher-order logic, which most people prefer these days. It bypasses ?rst-order logic and minimizes discussion of meta-theory. It is written for potential users rather than for our colleagues in the research world. Another departure from previous documentation is that we describe Markus Wenzel’s proof script notation instead of ML tactic scripts. The l- ter make it easier to introduce new tactics on the ?y, but hardly anybody does that. Wenzel’s dedicated syntax is elegant, replacing for example eight simpli?cation tactics with a single method, namely simp, with associated - tions. The book has three parts. – The ?rst part, Elementary Techniques, shows how to model functional programs in higher-order logic. Early examples involve lists and the natural numbers. Most proofs are two steps long, consisting of induction on a chosen variable followed by the auto tactic. But even this elementary part covers such advanced topics as nested and mutual recursion. – The second part, Logic and Sets, presents a collection of lower-level tactics that you can use to apply rules selectively. It also describes I- belle/HOL’s treatment of sets, functions, and relations and explains how to de?ne sets inductively. One of the examples concerns the theory of model checking, and another is drawn from a classic textbook on formal languages.

Ios 9 Programming Fundamentals With Swift

Author: Matt Neuburg
Publisher: "O'Reilly Media, Inc."
ISBN: 149193672X
Size: 40.87 MB
Format: PDF, Kindle
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Move into iOS development by getting a firm grasp of its fundamentals, including the Xcode IDE, the Cocoa Touch framework, and Swift 2.0—the latest version of Apple's acclaimed programming language. With this thoroughly updated guide, you'll learn Swift’s object-oriented concepts, understand how to use Apple's development tools, and discover how Cocoa provides the underlying functionality iOS apps need to have. Explore Swift’s object-oriented concepts: variables and functions, scopes and namespaces, object types and instances Become familiar with built-in Swift types such as numbers, strings, ranges, tuples, Optionals, arrays, dictionaries, and sets Learn how to declare, instantiate, and customize Swift object types—enums, structs, and classes Discover powerful Swift features such as protocols and generics Catch up on Swift 2.0 innovations: option sets, protocol extensions, error handling, guard statements, availability checks, and more Tour the lifecycle of an Xcode project from inception to App Store Create app interfaces with nibs and the nib editor, Interface Builder Understand Cocoa’s event-driven model and its major design patterns and features Find out how Swift communicates with Cocoa’s C and Objective-C APIs Once you master the fundamentals, you'll be ready to tackle the details of iOS app development with author Matt Neuburg's companion guide, Programming iOS 9.