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Author: J. Roger Hindley Publisher: Cambridge University Press ISBN: 0521465184 Category : Computers Languages : en Pages : 200
Book Description
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 ISBN: 0521465184 Category : Computers Languages : en Pages : 200
Book Description
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 ISBN: 9780444508539 Category : Computers Languages : en Pages : 784
Book Description
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 ISBN: 1316061086 Category : Computers Languages : en Pages : 465
Book Description
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: Bengt Nordström Publisher: Oxford University Press, USA ISBN: Category : Computers Languages : en Pages : 240
Book Description
In recent years, several formalisms for program construction have appeared. One such formalism is the type theory developed by Per Martin-Löf. Well suited as a theory for program construction, it makes possible the expression of both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. This book contains a thorough introduction to type theory, with information on polymorphic sets, subsets, monomorphic sets, and a full set of helpful examples.
Author: Giovanni Sambin Publisher: Clarendon Press ISBN: 0191606936 Category : Mathematics Languages : en Pages : 292
Book Description
Per Martin-Löf's work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Löf over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of areas of current activity, but also contains contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-Löf's earliest papers.
Author: Roy L. Crole Publisher: Cambridge University Press ISBN: 9780521457019 Category : Computers Languages : en Pages : 362
Book Description
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.
Author: Christoph Benzmüller Publisher: ISBN: 9781904987703 Category : Mathematics Languages : en Pages : 467
Book Description
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: J. Roger Hindley
Author: J. Roger Hindley
Author: B. Jacobs
Author: Rob Nederpelt
Author: Alfred North Whitehead
Author: Bengt Nordström
Author: Giovanni Sambin
Author: Roy L. Crole
Author: Per Martin-Löf
Author: Christoph Benzmüller
Author: