Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Thierry Coquand and Gérard Huet. The Calculus of Constructions. Inf. Comp., 76:95–120, 1988.
Thierry Coquand. An analysis of Girard’s paradox. In Proceedings of the First Symposium on Logic in Computer Science, Cambridge, MA, June 1986. IEEE Comp. Soc. Press.
Judicaël Courant. A Module Calculus for Pure Type Systems. In Typed Lambda Calculi and Applications’ 97, Lecture Notes in Computer Science, pages 112–128. Springer-Verlag, 1997.
Judicaël Courant. MC2: A Module Calculus for Pure Type Systems. Research Report 1292, LRI, September 2001.
James G. Hook and Douglas J. Howe. Impredicative Strong Existential Equivalent to Type:Type. Technical Report TR86-760, Cornell University, 1986.
R. Harper and R. Pollack. Type checking, universe polymorphism, and typical ambiguity in the calculus of constructions. Theoretical Computer Science, 89(1), 1991.
Paul B. Jackson. The Nuprl Proof Development System, Version 4.I Reference Manual and User’s Guide. Cornell University, Ithaca, NY, 1994.
Paul B. Jackson. Enhancing the Nuprl Proof Development System and Applying it to Computational Abstract Algebra. PhD thesis, Cornell University, 1995.
Zhaohui Luo. ECC: an Extended Calculus of Constructions. In Proceedings of the Fourth Annual Symposium on Logic in Computer Science, Pacific Grove, California, 1989. IEEE Comp. Soc. Press.
Zhaohui Luo. An Extended Calculus of Constructions. PhD thesis, University of Edinburgh, 1990.
Robin Milner, Mads Tofte, Robert Harper, and David MacQueen. The Definition of Standard ML (Revised). MIT Press, 1997.
M. Takahashi. Parallel reductions in λ-calculus. Technical report, Department of Information Science, Tokyo Institute of Technology, 1993. Internal report.
L.S. van Benthem Jutting, J. McKinna, and R. Pollack. Checking algorithms for pure type systems. In Types for Proofs and Programs: International Workshop TYPES’93, volume 806 of Lecture Notes in Computer Science, May 1993.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Courant, J. (2002). Explicit Universes for the Calculus of Constructions. In: Carreño, V.A., Muñoz, C.A., Tahar, S. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2002. Lecture Notes in Computer Science, vol 2410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45685-6_9
Download citation
DOI: https://doi.org/10.1007/3-540-45685-6_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44039-0
Online ISBN: 978-3-540-45685-8
eBook Packages: Springer Book Archive