Programming in Martin-Löf's Type Theory PDF Download
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Author: Bengt Nordström
Publisher: Oxford University Press, USA
ISBN:
Category : Computers
Languages : en
Pages : 240
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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: Bengt Nordström
Publisher: Oxford University Press, USA
ISBN:
Category : Computers
Languages : en
Pages : 240
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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: Per Martin-Löf
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 116
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Book Description
Author: Johan Georg Granström
Publisher: Springer Science & Business Media
ISBN: 9400717369
Category : Philosophy
Languages : en
Pages : 198
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Book Description
Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.
Author: Rob Nederpelt
Publisher: Cambridge University Press
ISBN: 1316061086
Category : Computers
Languages : en
Pages : 465
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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: Ana Bove
Publisher:
ISBN: 9789171978615
Category :
Languages : en
Pages : 117
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Book Description
Author:
Publisher: Univalent Foundations
ISBN:
Category :
Languages : en
Pages : 484
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Book Description
Author: Giovanni Sambin
Publisher: Clarendon Press
ISBN: 0191606936
Category : Mathematics
Languages : en
Pages : 292
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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: Bengt Nordström
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 25
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Book Description
Author: Simon Thompson
Publisher: Addison Wesley Publishing Company
ISBN:
Category : Computers
Languages : en
Pages : 396
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Book Description
This book explores the role of Martin-Lof s constructive type theory in computer programming. The main focus of the book is how the theory can be successfully applied in practice. Introductory sections provide the necessary background in logic, lambda calculus and constructive mathematics, and exercises and chapter summaries are included to reinforce understanding.
Author: Takayasu Itō
Publisher: Springer Science & Business Media
ISBN: 9783540544159
Category : Computers
Languages : en
Pages : 788
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Book Description
TACS'91 is the first International Conference on Theoretical Aspects of Computer Science held at Tohoku University, Japan, in September 1991. This volume contains 37 papers and an abstract for the talks presented at the conference. TACS'91 focused on theoretical foundations of programming, and theoretical aspects of the design, analysis and implementation of programming languages and systems. The following range of topics is covered: logic, proof, specification and semantics of programs and languages; theories and models of concurrent, parallel and distributed computation; constructive logic, category theory, and type theory in computer science; theory-based systems for specifying, synthesizing, transforming, testing, and verifying software.
