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

Abstract

In Das Kontinuum, Weyl showed how a large body of classical mathematics could be developed on a purely predicative foundation. We present a logic-enriched type theory that corresponds to Weyl's foundational system. A large part of the mathematics in Weyl's book - including Weyl's definition of the cardinality of a set and several results from real analysis - has been formalised, using the proof assistant Plastic that implements a logical framework. This case study shows how type theory can be used to represent a non-constructive foundation for mathematics.