Weyl's Predicative Classical Mathematics as a Logic-Enriched Type Theory

Details Weyl's Predicative Classical Mathematics as a Logic-Enriched Type Theory Weyl's Predicative Classical Mathematics as a Logic-Enriched Type Theory

2008-09-11

arxiv.org/abs/0809.2061v3

ACM TOCL 11(2), 2010

Computer Science

Logic in Computer Science

31 pages, 6 figures. Accepted for publication in ACM TOCL. v2: Corrected a broken citation in v1. v3: Final version, revised a

Scientific paper

10.1145/1656242.1656246

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 shows how type theory can be used to represent a non-constructive foundation for mathematics.

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