A family of syntactic models for the calculus of construction with universes (CC ω) is
described, all of them preserving conversion of the calculus definitionally, and thus giving …

Reynolds' abstraction theorem (Reynolds, JC (1983) Types, abstraction and parametric
polymorphism, Inf. Process. 83 (1), 513–523) shows how a ty** judgement in System F …

We extend Martin-Löf's Logical Framework with special constructions and ty** rules
providing internalized parametricity. Compared to previous similar proposals, this version …

We define the exceptional translation, a syntactic translation of the Calculus of Inductive
Constructions (CIC) into itself, that covers full dependent elimination. The new resulting type …

Programming with dependent types is a blessing and a curse. It is a blessing to be able to
bake invariants into the definition of datatypes: we can finally write correct-by-construction …

Dependent type-theory aims to become the standard way to formalize mathematics at the
same time as displacing traditional platforms for high-assurance programming. However …

We define a monadic translation of type theory, called the weaning translation, that allows
for a large range of effects in dependent type theory-such as exceptions, non-termination …

Reynold's abstraction theorem is now a well-established result for a large class of type
systems. We propose here a definition of relational parametricity and a proof of the …

Reynolds' abstraction theorem has recently been extended to lambda-calculi with
dependent types. In this paper, we show how this theorem can be internalized. More …

Modern constructive type theory is based on pure dependently typed lambda calculus,
augmented with user-defined datatypes. This paper presents an alternative called the …