Handbook of logic in computer science (vol. 2)
Introduction to Mathematical Logic and Type Theory: To Truth through Proof
Introduction to Mathematical Logic and Type Theory: To Truth through Proof
A Simplification of Girard's Paradox
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Extensions of Pure Type Systems
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Lectures on the Curry-Howard Isomorphism, Volume 149 (Studies in Logic and the Foundations of Mathematics)
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
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
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This paper consists of two parts. In the first part we argue that an appropriate "naive type theory" should replace naive set theory (as understood in Halmos' book) in everyday mathematical practice, especially in teaching mathematics to Computer Science students. In the second part we make the first step towards developing such a theory: we discuss a certain pure type system with powerset types. While the system only covers very initial aspects of the intended theory, we believe it can be used as an initial formalism to be further developed. The consistency of this basic system is established by proving strong normalization.