Weyl's predicative classical mathematics as a logic-enriched type theory
نویسندگان
چکیده
منابع مشابه
Classical Predicative Logic-Enriched Type Theories
A logic-enriched type theory (LTT) is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named LTT0 and LTT ∗ 0, which we claim correspond closely to the classical predicative systems of second order arithmetic ACA0 and ACA. We justify this claim by translating each second-order system into the corresponding LTT, and proving that these...
متن کاملar X iv : 0 80 9 . 20 61 v 1 [ cs . L O ] 1 1 Se p 20 08 Weyl ’ s Predicative Classical Mathematics as a Logic - Enriched Type Theory
We construct a logic-enriched type theory LTTwthat corresponds closely to the predicative system of foundations presented by Hermann Weyl in Das Kontinuum. We formalise many results from that book in LTTw, including Weyl’s definition of the cardinality of a set and several results from real analysis, using the proof assistant Plastic that implements the logical framework LF. This case study sho...
متن کاملar X iv : 0 80 9 . 20 61 v 2 [ cs . L O ] 1 2 Se p 20 08 Weyl ’ s Predicative Classical Mathematics as a Logic - Enriched Type Theory
We construct a logic-enriched type theory LTTwthat corresponds closely to the predicative system of foundations presented by Hermann Weyl in Das Kontinuum. We formalise many results from that book in LTTw, including Weyl’s definition of the cardinality of a set and several results from real analysis, using the proof assistant Plastic that implements the logical framework LF. This case study sho...
متن کاملar X iv : 0 80 9 . 20 61 v 3 [ cs . L O ] 1 5 Ja n 20 09 Weyl ’ s Predicative Classical Mathematics as a Logic - Enriched Type Theory
We construct a logic-enriched type theory LTTw that corresponds closely to the predicative system of foundations presented by Hermann Weyl in Das Kontinuum. We formalise many results from that book in LTTw, including Weyl’s definition of the cardinality of a set and several results from real analysis, using the proof assistant Plastic that implements the logical framework LF. This case study sh...
متن کاملSemi-simplicial Types in Logic-enriched Homotopy Type Theory
The problem of defining Semi-Simplicial Types (SSTs) in Homotopy Type Theory (HoTT) has been recognized as important during the Year of Univalent Foundations at the Institute of Advanced Study [14]. According to the interpretation of HoTT in Quillen model categories [5], SSTs are type-theoretic versions of Reedy fibrant semi-simplicial objects in a model category and simplicial and semi-simplic...
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ژورنال
عنوان ژورنال: ACM Transactions on Computational Logic
سال: 2010
ISSN: 1529-3785,1557-945X
DOI: 10.1145/1656242.1656246