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Weyl's Predicative Classical Mathematics as a LogicEnriched Type Theory #
 

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

  

Source: Adams, Robin - Department of Computer Science, Royal Holloway, University of London

 

Collections: Computer Technologies and Information Sciences