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

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 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.

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

References in corpus (1)

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

Cited by in corpus (3)

• Weyl's Predicative Classical Mathematics as a Logic-Enriched Type Theory
• Extending Homotopy Type Theory with Strict Equality
• Classical Predicative Logic-Enriched Type Theories