By F.D. Kamareddine,T. Laan,Rob Nederpelt
- varieties: from Russell to Ramsey, to Church, to the fashionable natural kind structures and a few in their extensions.
- capabilities: from Frege, to Russell to Church, to Automath and using features in arithmetic, programming languages and theorem provers.
- The position of sorts in good judgment: Kripke's proposal of fact, the evolution and function of the propositions as forms idea and its use in logical frameworks.
- The position of varieties in computation: extensions of variety theories that could greater version evidence checkers and programming languages are given.
The first a part of the e-book is old, but whilst, locations ancient structures (like Russell's RTT) within the sleek atmosphere. the second one half bargains with glossy style conception because it built because the Forties, and with the function of propositions as kinds (or proofs as terms), yet whilst, locations one other old approach (the evidence checker Automath) within the smooth atmosphere. The 3rd half makes use of this bridging within the first components among historic and smooth structures to suggest new structures that convey extra benefits jointly. This e-book has a lot to provide to mathematicians, logicians and to desktop scientists as a rule. it's going to have huge 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