Type Driven Development With Idris

Author: Edwin Brady
Publisher: Manning Publications
ISBN: 1617293024
Size: 10.42 MB
Format: PDF, ePub, Docs
View: 64

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.

Certified Programming With Dependent Types

Author: Adam Chlipala
Publisher: MIT Press
ISBN: 9780262317887
Size: 14.29 MB
Format: PDF, ePub, 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.

Verified Functional Programming In Agda

Author: Aaron Stump
Publisher: Morgan & Claypool
ISBN: 9781970001266
Size: 16.10 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.

Haskell Design Patterns

Author: Ryan Lemmer
Publisher: Packt Publishing Ltd
ISBN: 9781783988730
Size: 14.97 MB
Format: PDF
View: 56

Take your Haskell and functional programming skills to the next level by exploring new idioms and design patterns About This Book Explore Haskell on a higher level through idioms and patterns Get an in-depth look into the three strongholds of Haskell: higher-order functions, the Type system, and Lazy evaluation Expand your understanding of Haskell and functional programming, one line of executable code at a time Who This Book Is For If you're a Haskell programmer with a firm grasp of the basics and ready to move more deeply into modern idiomatic Haskell programming, then this book is for you. What You Will Learn Understand the relationship between the “Gang of Four” OOP Design Patterns and Haskell Try out three ways of Streaming I/O: imperative, Lazy, and Iteratee based Explore the pervasive pattern of Composition: from function composition through to high-level composition with Lenses Synthesize Functor, Applicative, Arrow and Monad in a single conceptual framework Follow the grand arc of Fold and Map on lists all the way to their culmination in Lenses and Generic Programming Get a taste of Type-level programming in Haskell and how this relates to dependently-typed programming Retrace the evolution, one key language extension at a time, of the Haskell Type and Kind systems Place the elements of modern Haskell in a historical framework In Detail Design patterns and idioms can widen our perspective by showing us where to look, what to look at, and ultimately how to see what we are looking at. At their best, patterns are a shorthand method of communicating better ways to code (writing less, more maintainable, and more efficient code). This book starts with Haskell 98 and through the lens of patterns and idioms investigates the key advances and programming styles that together make "modern Haskell". Your journey begins with the three pillars of Haskell. Then you'll experience the problem with Lazy I/O, together with a solution. You'll also trace the hierarchy formed by Functor, Applicative, Arrow, and Monad. Next you'll explore how Fold and Map are generalized by Foldable and Traversable, which in turn is unified in a broader context by functional Lenses. You'll delve more deeply into the Type system, which will prepare you for an overview of Generic programming. In conclusion you go to the edge of Haskell by investigating the Kind system and how this relates to Dependently-typed programming. Style and approach Using short pieces of executable code, this guide gradually explores the broad pattern landscape of modern Haskell. Ideas are presented in their historical context and arrived at through intuitive derivations, always with a focus on the problems they solve.

The Formal Semantics Of Programming Languages

Author: Glynn Winskel
Publisher: MIT Press
ISBN: 0262731037
Size: 19.67 MB
Format: PDF
View: 22

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.