A Modern Perspective on Type Theory: From Its Origins Until by F.D. Kamareddine,T. Laan,Rob Nederpelt PDF

By F.D. Kamareddine,T. Laan,Rob Nederpelt

ISBN-10: 1402023340

ISBN-13: 9781402023347

ISBN-10: 904816639X

ISBN-13: 9789048166398

`Towards the tip of the 19th century, Frege gave us the abstraction ideas and the final inspiration of capabilities. Self-application of features used to be on the middle of Russell's paradox. This led Russell to introduce sort idea for you to keep away from the anomaly. when you consider that, the 20 th century has visible an awesome variety of theories interested in forms and capabilities and plenty of functions. development in laptop technological know-how additionally intended a growing number of emphasis at the use of common sense, kinds and services to check the syntax, semantics, layout and implementation of programming languages and theorem provers, and the correctness of proofs and courses. The authors of this booklet have themselves been prime the best way via offering quite a few extensions of kind concept which were proven to carry many merits. This ebook gathers a lot in their influential paintings and is very prompt for someone attracted to sort concept. the most emphasis is on:

- varieties: from Russell to Ramsey, to Church, to the trendy natural sort structures and a few in their extensions.

- features: from Frege, to Russell to Church, to Automath and using capabilities in arithmetic, programming languages and theorem provers.

- The function of sorts in common sense: Kripke's idea of fact, the evolution and function of the propositions as forms proposal and its use in logical frameworks.

- The function of varieties in computation: extensions of sort theories which could greater version facts checkers and programming languages are given.

The first a part of the booklet is old, but while, areas historic platforms (like Russell's RTT) within the glossy atmosphere. the second one half bargains with sleek style idea because it constructed because the Forties, and with the position of propositions as kinds (or proofs as terms), yet whilst, locations one other historic method (the evidence checker Automath) within the glossy environment. The 3rd half makes use of this bridging within the first elements among old and sleek platforms to suggest new platforms that deliver extra merits jointly. This publication has a lot to supply to mathematicians, logicians and to computing device scientists ordinarily. it is going to have huge impression for a few years to come.' - Henk Barendregt

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A Modern Perspective on Type Theory: From Its Origins Until Today: 29 (Applied Logic Series) by F.D. Kamareddine,T. Laan,Rob Nederpelt


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