Weyl's predicative classical mathematics as a logic-enriched type theory
Journal article, 2010
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.
predicativism
formalization of mathematics
logic-enriched type theory
Author
Robin Adams
Royal Holloway University of London
Zhaohui Luo
Royal Holloway University of London
ACM Transactions on Computational Logic
1529-3785 (ISSN) 1557945x (eISSN)
Vol. 11 2 11Subject Categories
Algebra and Logic
Computer Science
Areas of Advance
Information and Communication Technology
Roots
Basic sciences
DOI
10.1145/1656242.1656246