Basic Simple Type Theory PDF Download
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Author | : J. Roger Hindley |
Publisher | : Cambridge University Press |
Total Pages | : 200 |
Release | : 1997 |
Genre | : Computers |
ISBN | : 0521465184 |
Download Basic Simple Type Theory Book in PDF, ePub and Kindle
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.
Author | : J. Roger Hindley |
Publisher | : Cambridge University Press |
Total Pages | : 0 |
Release | : 2008-01-21 |
Genre | : Computers |
ISBN | : 9780521054225 |
Download Basic Simple Type Theory Book in PDF, ePub and Kindle
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.
Author | : B. Jacobs |
Publisher | : Gulf Professional Publishing |
Total Pages | : 784 |
Release | : 2001-05-10 |
Genre | : Computers |
ISBN | : 9780444508539 |
Download Categorical Logic and Type Theory Book in PDF, ePub and Kindle
This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.
Author | : Rob Nederpelt |
Publisher | : Cambridge University Press |
Total Pages | : 465 |
Release | : 2014-11-06 |
Genre | : Computers |
ISBN | : 1316061086 |
Download Type Theory and Formal Proof Book in PDF, ePub and Kindle
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.
Author | : |
Publisher | : Univalent Foundations |
Total Pages | : 484 |
Release | : |
Genre | : |
ISBN | : |
Download Homotopy Type Theory: Univalent Foundations of Mathematics Book in PDF, ePub and Kindle
Author | : Tom Leinster |
Publisher | : Cambridge University Press |
Total Pages | : 193 |
Release | : 2014-07-24 |
Genre | : Mathematics |
ISBN | : 1107044243 |
Download Basic Category Theory Book in PDF, ePub and Kindle
A short introduction ideal for students learning category theory for the first time.
Author | : Alfred North Whitehead |
Publisher | : |
Total Pages | : 696 |
Release | : 1910 |
Genre | : Logic, Symbolic and mathematical |
ISBN | : |
Download Principia Mathematica Book in PDF, ePub and Kindle
Author | : Christoph Benzmüller |
Publisher | : |
Total Pages | : 467 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9781904987703 |
Download Reasoning in Simple Type Theory Book in PDF, ePub and Kindle
Reasoning in Simple Type Theory is a collection of papers that includes reprints of eight seminal papers in this area as well as thirteen new contributed articles. For the reprints we have chosen a paper by Alonzo Church (introducing his simple theory of types), a paper by Leon Henkin (proving completeness of Church's type theory relative to Henkin's semantics) and some of the most important papers by Peter Andrews. The new articles were contributed by Peter Andrews and his students and collaborators as well as a number of researchers his work has influenced. The volume intends to show the historical development of this important area of formal reasoning up to its current state of art and appears in honor of Peter Andrews on his 70th birthday.
Author | : A. S. Troelstra |
Publisher | : Cambridge University Press |
Total Pages | : 436 |
Release | : 2000-07-27 |
Genre | : Computers |
ISBN | : 9780521779111 |
Download Basic Proof Theory Book in PDF, ePub and Kindle
This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.
Author | : Roy L. Crole |
Publisher | : Cambridge University Press |
Total Pages | : 362 |
Release | : 1993 |
Genre | : Computers |
ISBN | : 9780521457019 |
Download Categories for Types Book in PDF, ePub and Kindle
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.