Information and Computation - Semantics of Data Types
ECC, and extended calculus of constructions
Proceedings of the Fourth Annual Symposium on Logic in computer science
TAPSOFT '89 2nd international joint conference on Theory and practice of software development
Checking algorithms for pure type systems
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Enhancing the NUPRL proof development system and applying it to computational abstract algebra
Enhancing the NUPRL proof development system and applying it to computational abstract algebra
The Definition of Standard ML
A Module Calculus for Pure Type Systems
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
Impredicative Strong Existential Equivalent to Type:Type
Impredicative Strong Existential Equivalent to Type:Type
A unified framework and a transparent name-space for the Coq module system
Proceedings of the 1st Workshop on Modules and Libraries for Proof Assistants
Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
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The implicit universe hierarchy implemented in proof assistants such as Coq and Lego, although really needed, is painful, both for the implementer and the user: it interacts badly with modularity features, errors are difficult to report and to understand. Moreover, type-checking is quite complex.We address these issues with a new calculus, the Explicit Polymorphic Extended Calculus of Constructions. EPECC is a conservative extension of Luo's ECC with universe variables and explicit universe constraints declarations. EPECC behaves better with respect to error reporting and modularity than implicit universes, and also enjoys good metatheoretical properties, notably strong normalization and Church-Rosser properties. Type-inference and type-checking in EPECC are decidable. A prototype implementation is available.