The Little Typer
The Little Typer

Author: Daniel P. Friedman

Publisher: MIT Press

Published: 2018-09-18

Total Pages: 418

ISBN-13: 0262536439

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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.

Type Theory and Formal Proof
Type Theory and Formal Proof

Author: Rob Nederpelt

Publisher: Cambridge University Press

Published: 2014-11-06

Total Pages: 465

ISBN-13: 1316061086

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Type theory is a fast-evolving field at the crossroads of logic, computer science and mathematics. This gentle step-by-step introduction is ideal for graduate students and researchers who need to understand the ins and outs of the mathematical machinery, the role of logical rules therein, the essential contribution of definitions and the decisive nature of well-structured proofs. The authors begin with untyped lambda calculus and proceed to several fundamental type systems, including the well-known and powerful Calculus of Constructions. The book also covers the essence of proof checking and proof development, and the use of dependent type theory to formalise mathematics. The only prerequisite is a basic knowledge of undergraduate mathematics. Carefully chosen examples illustrate the theory throughout. Each chapter ends with a summary of the content, some historical context, suggestions for further reading and a selection of exercises to help readers familiarise themselves with the material.

Basic Simple Type Theory
Basic Simple Type Theory

Author: J. Roger Hindley

Publisher: Cambridge University Press

Published: 1997

Total Pages: 200

ISBN-13: 0521465184

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Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. By concentrating on the principles that make the theory work in practice, the author covers all the key ideas without getting involved in the complications of more advanced systems. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm that lies at the heart of every such system. Also featured are two other interesting algorithms that until now have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making it the first book at this level that can be used as an introduction to type theory for computer scientists.

An Introduction to Functional Programming Through Lambda Calculus
An Introduction to Functional Programming Through Lambda Calculus

Author: Greg Michaelson

Publisher: Courier Corporation

Published: 2013-04-10

Total Pages: 338

ISBN-13: 0486280292

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Well-respected text for computer science students provides an accessible introduction to functional programming. Cogent examples illuminate the central ideas, and numerous exercises offer reinforcement. Includes solutions. 1989 edition.

Types and Programming Languages
Types and Programming Languages

Author: Benjamin C. Pierce

Publisher: MIT Press

Published: 2002-01-04

Total Pages: 646

ISBN-13: 0262303825

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A comprehensive introduction to type systems and programming languages. A type system is a syntactic method for automatically checking the absence of certain erroneous behaviors by classifying program phrases according to the kinds of values they compute. The study of type systems—and of programming languages from a type-theoretic perspective—has important applications in software engineering, language design, high-performance compilers, and security. This text provides a comprehensive introduction both to type systems in computer science and to the basic theory of programming languages. The approach is pragmatic and operational; each new concept is motivated by programming examples and the more theoretical sections are driven by the needs of implementations. Each chapter is accompanied by numerous exercises and solutions, as well as a running implementation, available via the Web. Dependencies between chapters are explicitly identified, allowing readers to choose a variety of paths through the material. The core topics include the untyped lambda-calculus, simple type systems, type reconstruction, universal and existential polymorphism, subtyping, bounded quantification, recursive types, kinds, and type operators. Extended case studies develop a variety of approaches to modeling the features of object-oriented languages.

Typing for Beginners
Typing for Beginners

Author: Betty Owen

Publisher: Penguin

Published: 1985-07-23

Total Pages: 82

ISBN-13: 9780399511479

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A basic typing handbook using the self-teaching, learn-at-your-own-speed methods of one of New York’s most successful business schools. This practical guide offers specialized drills, speed and accuracy timings, centering and tabulating, finished business letters, how to make corrections and copies, proofreaders’ symbols, as well as trouble-saving tips.

Discovering Your Personality Type
Discovering Your Personality Type

Author: Don Richard Riso

Publisher: Houghton Mifflin Harcourt

Published: 2003-05-20

Total Pages: 225

ISBN-13: 0547527608

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The bestselling beginner’s guide to identifying and understanding the nine personality profiles and applying them to your daily life. The leading experts in the field, Don Richard Riso and Russ Hudson have set the standard for determining personality type using the enneagram. Their studies of this ancient symbol and their progress in determining type with increasing accuracy are known, taught, and emulated worldwide. Discovering Your Personality Type is the essential introduction to this system, a psychological framework that can be used practically, in many aspects of daily life. This revised and updated edition features the all-new, scientifically validated Riso-Hudson Type Indicator, and has also been refined and simplified to appeal especially to beginners and anyone interested in unlocking the secrets of personality. The most reliable, most accurate, and most accessible way to identify type, the improved enneagram questionnaire helps identify fundamental character traits, revealing invaluable directions for change and growth. The profile that emerges is useful for a wide variety of purposes: professional development, education, relationships, vocational counseling, and more. Discovering Your Personality Type is the book readers need in order to begin to see the possibilities made available by understanding personality types. More Than 1 Million Riso-Hudson Enneagram Books Sold