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 ...
We introduce a new model based on coherence spaces for interpreting large impredicative type systems such as the Extended Calculus of Constructions (ECC). Moreover, we show that t...
The type systems of most typed functional programming languages are based on the Hindley-Milner type system. A practical problem with these type systems is that it is often hard t...
: We study type checking that is complete in the sense that it accepts every program whose subexpressions can all be executed without raising a type error at runtime. In a complete...
In this paper we introduce a new approach to formalizing certain type operations in type theory. Traditionally, many type constructors in type theory are independently axiomatized...