Information and Computation - Semantics of Data Types
TACS '97 Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software
A Generic Normalisation Proof for Pure Type Systems
TYPES '96 Selected papers from the International Workshop on Types for Proofs and Programs
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Extensional Equality in Intensional Type Theory
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
A Model for Impredicative Type Systems, Universes, Intersection Types and Subtyping
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Journal of Functional Programming
A computational view of implicit coercions in type theory
Mathematical Structures in Computer Science
Towards Constructive Homological Algebra in Type Theory
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
The implicit calculus of constructions as a programming language with dependent types
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Formalizing projective plane geometry in Coq
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
TLDI '12 Proceedings of the 8th ACM SIGPLAN workshop on Types in language design and implementation
On the strength of proof-irrelevant type theories
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
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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It is well-known that the Calculus of Constructions (CC) bears a simple set-theoretical model in which proof-terms are mapped onto a single object--a property which is known as proof-irrelevance. In this paper, we show that when going into the (generally omitted) technical details, this naive model raises several unexpected difficulties related to the interpretation of the impredicative level, especially for the soundness property which is surprisingly difficult to be given a correct proof in this simple framework. We propose a way to tackle these difficulties, thus giving a (more) detailed elementary consistency proof of CC without going back to a translation to F?. We also discuss some possible alternatives and possible extensions of our construction.