Information and Computation - Semantics of Data Types
Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
A framework for defining logics
Journal of the ACM (JACM)
Computation and reasoning: a type theory for computer science
Computation and reasoning: a type theory for computer science
An Implementation of LF with Coercive Subtyping & Universes
Journal of Automated Reasoning
Collection Principles in Dependent Type Theory
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
A type-theoretic framework for formal reasoning with different logical foundations
ASIAN'06 Proceedings of the 11th Asian computing science conference on Advances in computer science: secure software and related issues
Weyl's predicative classical mathematics as a logic-enriched type theory
ACM Transactions on Computational Logic (TOCL)
A type-theoretic framework for formal reasoning with different logical foundations
ASIAN'06 Proceedings of the 11th Asian computing science conference on Advances in computer science: secure software and related issues
In the search of a naive type theory
TYPES'07 Proceedings of the 2007 international conference on Types for proofs and programs
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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.