F.D. Kamareddine,T. Laan,Rob Nederpelt's A Modern Perspective on Type Theory: From Its Origins Until 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 rules and the final inspiration of features. Self-application of services was once on the center of Russell's paradox. This led Russell to introduce style thought which will steer clear of the ambiguity. on the grounds that, the 20th century has visible an grand variety of theories desirous about forms and features and lots of functions. growth in laptop technology additionally intended a growing number of emphasis at the use of common sense, forms and services to review 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 by means of delivering a number of extensions of sort conception which were proven to carry many merits. This publication gathers a lot in their influential paintings and is extremely steered for somebody drawn to style concept. the most emphasis is on:

- varieties: from Russell to Ramsey, to Church, to the fashionable natural style platforms and a few in their extensions.

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

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

- The function of sorts in computation: extensions of sort theories which may larger version evidence checkers and programming languages are given.

The first a part of the ebook is ancient, but while, locations ancient structures (like Russell's RTT) within the smooth surroundings. the second one half offers with sleek variety conception because it built because the Nineteen Forties, and with the function of propositions as varieties (or proofs as terms), yet whilst, locations one other historic procedure (the facts checker Automath) within the glossy atmosphere. The 3rd half makes use of this bridging within the first components among ancient and sleek structures to suggest new structures that convey extra merits jointly. This booklet has a lot to supply to mathematicians, logicians and to machine scientists mostly. it's going to have significant impact 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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