Proofs and types
Type inference: some results, some problems
Fundamenta Informaticae - Special issue: lambda calculus and type theory
Computation and reasoning: a type theory for computer science
Computation and reasoning: a type theory for computer science
A proof-irrelevant model of Martin-Löf's logical framework
Mathematical Structures in Computer Science
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
The not so simple proof-irrelevant model of CC
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Irrelevance in type theory with a heterogeneous equality judgement
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Towards normalization by evaluation for the βη-calculus of constructions
FLOPS'10 Proceedings of the 10th international conference on Functional and Logic Programming
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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 this model is well suited for interpreting intersection types and subtyping too, and we illustrate this by interpreting a variant of ECC with an additional intersection type binder. Furthermore, we propose a general method for interpreting the impredicative level in a non-syntactical way, by allowing the model to be parametrized by an arbitrarily large coherence space in order to interpret inhabitants of impredicative types. As an application, we show that uncountable types such as the type of real numbers or Zermelo-Fränkel sets can safely be axiomatized on the impredicative level of, say, ECC, without harm for consistency.