ECC, and extended calculus of constructions
Proceedings of the Fourth Annual Symposium on Logic in computer science
Closure under alpha-conversion
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
An algorithm for type-checking dependent types
Science of Computer Programming - Special issue on mathematics of program construction
A compiled implementation of strong reduction
Proceedings of the seventh ACM SIGPLAN international conference on Functional programming
A short and flexible proof of Strong Normalization for the Calculus of Constructions
TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
A Simple Model Construction for the Calculus of Constructions
TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
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
Formal certification of a compiler back-end or: programming a compiler with a proof assistant
Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Pure type systems with judgemental equality
Journal of Functional Programming
Normalization by Evaluation for Martin-Lof Type Theory with Typed Equality Judgements
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Verifying a Semantic βη-Conversion Test for Martin-Löf Type Theory
MPC '08 Proceedings of the 9th international conference on Mathematics of Program Construction
A Modular Type-Checking Algorithm for Type Theory with Singleton Types and Proof Irrelevance
TLCA '09 Proceedings of the 9th 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
A formalisation of a dependently typed language as an inductive-recursive family
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
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We consider the Calculus of Constructions with typed beta-eta equality and an algorithm which computes long normal forms. The normalization algorithm evaluates terms into a semantic domain, and reifies the values back to terms in normal form. To show termination, we interpret types as partial equivalence relations between values and type constructors as operators on PERs. This models also yields consistency of the beta-eta-Calculus of Constructions. The model construction can be carried out directly in impredicative type theory, enabling a formalization in Coq.