Weyl's predicative classical mathematics as a logic-enriched type theory

Authors:
Robin Adams;Zhaohui Luo
Affiliations:
Royal Holloway, University of London;Royal Holloway, University of London
Venue:
ACM Transactions on Computational Logic (TOCL)
Year:
2010

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Abstract

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 formalize 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 nonconstructive foundation for mathematics.