Dependent types are a powerful concept that allow us to write proof-carrying code. Idris is a programming language that supports dependent types. We will learn about the mathematical foundations, and then write correct software and mathematically prove properties about it.This book aims to be accessible to novices, and no prior experience beyond high school mathematics is needed. Thus, this book is written in a way to be self-contained.The first part of this book serves as an introduction to the theory behind Idris, while the second part is a practical introduction to Idris with examples.
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
An introduction to dependent types, demonstrating the most beautiful aspects, one step at a time. A program's type describes its behavior. Dependent types are a first-class part of a language, and are much more powerful than other kinds of types; using just one language for types and programs allows program descriptions to be as powerful as the programs they describe. The Little Typer explains dependent types, beginning with a very small language that looks very much like Scheme and extending it to cover both programming with dependent types and using dependent types for mathematical reasoning. Readers should be familiar with the basics of a Lisp-like programming language, as presented in the first four chapters of The Little Schemer. The first five chapters of The Little Typer provide the needed tools to understand dependent types; the remaining chapters use these tools to build a bridge between mathematics and programming. Readers will learn that tools they know from programming—pairs, lists, functions, and recursion—can also capture patterns of reasoning. The Little Typer does not attempt to teach either practical programming skills or a fully rigorous approach to types. Instead, it demonstrates the most beautiful aspects as simply as possible, one step at a time.
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.
This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory, which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specializing in category theory.
Improving existing code--refactoring--is one of the most common tasks you''ll face as a programmer. Five Lines of Code teaches you clear and actionable refactoring rules that you can apply without relying on intuitive judgements such as "code smells." It''s written for working developers, guiding you step by step through applying refactoring patterns to the codebase of a 2D puzzle game. Following the author''s expert perspective--that refactoring and code smells can be learned by following a concrete set of principles--you''ll learn when to refactor your code, what patterns to apply to what problem, and the code characteristics that indicate it''s time for a rework. Thanks to this hands-on guide, you''ll find yourself programming faster while still delivering high-quality code that your teammates will love to work with. about the technology Refactoring is a fact of life. All code is imperfect, and refactoring is a systematic process you can use to improve the quality of your codebase. Whatever your architecture, choice of OO language, or skill as a programmer, the continuous design improvements of refactoring make your code simpler, more readable, and less prone to bugs. You''ll be amazed at the productivity boost of adding refactoring to your code hygiene routine--it''s quicker to hammer out bad code and then improve it than spending hours writing good code in the first place! about the book Five Lines of Code teaches working developers the shortcuts to quality code. You''ll follow author Christian Clausen''s unique approach to teaching refactoring that''s focused on concrete rules, and getting any method down to five lines or less to implement! There''s no jargon or tricky automated-testing skills required, just easy guidelines and patterns illustrated by detailed code samples. Chapter by chapter you''ll put techniques into action by refactoring a complete 2D puzzle game. Before you know it, you''ll be making serious and tangible improvements to your codebase. what''s inside The symptoms of bad code The extracting method, introducing strategy pattern, and many other refactoring patterns Modifying code safely, even when you don''t understand it Writing stable code that enables change-by-addition Proper compiler practices Writing code that needs no comments Real-world practices for great refactoring about the reader For developers who know an object-oriented programming language. about the author Christian Clausen works as a Technical Agile Coach teaching teams how to properly refactor their code. Previously he worked as a software engineer on the Coccinelle semantic patching project, an automated refactoring tool. He has an MSc in computer science, and five years'' experience teaching software quality at a university level.
Summary Functional Programming in JavaScript teaches JavaScript developers functional techniques that will improve extensibility, modularity, reusability, testability, and performance. Through concrete examples and jargon-free explanations, this book teaches you how to apply functional programming to real-life development tasks Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the Technology In complex web applications, the low-level details of your JavaScript code can obscure the workings of the system as a whole. As a coding style, functional programming (FP) promotes loosely coupled relationships among the components of your application, making the big picture easier to design, communicate, and maintain. About the Book Functional Programming in JavaScript teaches you techniques to improve your web applications - their extensibility, modularity, reusability, and testability, as well as their performance. This easy-to-read book uses concrete examples and clear explanations to show you how to use functional programming in real life. If you're new to functional programming, you'll appreciate this guide's many insightful comparisons to imperative or object-oriented programming that help you understand functional design. By the end, you'll think about application design in a fresh new way, and you may even grow to appreciate monads! What's Inside High-value FP techniques for real-world uses Using FP where it makes the most sense Separating the logic of your system from implementation details FP-style error handling, testing, and debugging All code samples use JavaScript ES6 (ES 2015) About the Reader Written for developers with a solid grasp of JavaScript fundamentals and web application design. About the Author Luis Atencio is a software engineer and architect building enterprise applications in Java, PHP, and JavaScript. Table of Contents PART 1 THINK FUNCTIONALLY Becoming functional Higher-order JavaScript PART 2 GET FUNCTIONAL Few data structures, many operations Toward modular, reusable code Design patterns against complexity PART 3 ENHANCING YOUR FUNCTIONAL SKILLS Bulletproofing your code Functional optimizations Managing asynchronous events and data
This book constitutes the refereed proceedings of the 8th International Joint Conference on Automated Reasoning, IJCAR 2016, held in Coimbra, Portugal, in June/July 2016. IJCAR 2014 was a merger of three leading events in automated reasoning, namely CADE (International Conference on Automated Deduction), FroCoS (International Symposium on Frontiers of Combining Systems) and TABLEAUX (International Conference on Automated Reasoning with Analytic Tableaux and Related Methods). The 26 revised full research papers and 9 system descriptions presented together with 4 invited talks were carefully reviewed and selected from 79 submissions. The papers have been organized in topical sections on satisfiability of Boolean formulas, satisfiability modulo theory, rewriting, arithmetic reasoning and mechanizing mathematics, first-order logic and proof theory, first-order theorem proving, higher-order theorem proving, modal and temporal logics, non-classical logics, and verification.
Haskell is an advanced general purpose programming language. This tutorial covers all aspects of Haskell development from foundations to compiler development.MonadsMonad TransformersLanguage ExtensionsType ClassesLazinessPreludeStringsApplicativesError HandlingAdvanced MonadsQuantificationGeneralized Algebraic DatatypesInterpretersTestingType FamiliesPromotionGenericsMathematicsData StructuresForeign Function InterfaceConcurrency and ParallelismGraphicsParsersStream ProcessingCryptographyDate and TimeData Formats and SerialisationNetwork and Web ProgrammingDatabasesGHC CompilerProfilingCompiler DevelopmentTemplate HaskellCategory Theory
