Formalizing Probability Concepts in a Type Theory

Towards Formalizing Categorical Models of Type Theory in Type Theory

This note is about work in progress on the topic of “internal type theory” where we investigate the internal formalization of the categorical metatheory of constructive type theory in (an extension of) itself. The basic notion is that of a category with families, a categorical notion of model of dependent type theory. We discuss how to formalize the notion of category with families inside type ...

Formalizing Belief Revision in Type Theory

Some Concepts in Probability and Information Theory

Formalizing Type Theory in PVS: a case study

In this case study we investigate the use of PVS for developing type theoretical concepts and verifying the correctness of a typing algorithm. PVS turns out to be very useful for efficient development of a sound basic theory about polymorphic typing. This research contributes to the PoplMark challenge on mechanizing metatheory. The correctness of the typing algorithm is expressed as the so-call...

Formalizing the Halting Problem in a Constructive Type Theory

We present a formalization of the halting problem in Agda, a language based on Martin-Löf’s intuitionistic type theory. The key features are: – We give a constructive proof of the halting problem. The “constructive halting problem” is a natural reformulation of the classic variant. – A new abstract model of computation is introduced, in type theory. – The undecidability of the halting problem i...