 
Summary: Weyl's Predicative Classical Mathematics as a
LogicEnriched Type Theory #
Robin Adams and Zhaohui Luo
Dept of Computer Science, Royal Holloway, Univ of London
{robin,zhaohui}@cs.rhul.ac.uk
Abstract. In Das Kontinuum, Weyl showed how a large body of clas
sical mathematics could be developed on a purely predicative founda
tion. We present a logicenriched 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 re
sults 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 nonconstructive foundation for
mathematics.
Key words: logicenriched type theory, predicativism, formalisation
1 Introduction
Type theories have proven themselves remarkably successful in the formalisation
of mathematical proofs. There are several features of type theory that are of
particular benefit in such formalisations, including the fact that each object
carries a type which gives information about that object, and the fact that the
