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Normalisation of the Theory T of Cartesian Closed Categories andConservativityof Extensions T[x]of T

Published online by Cambridge University Press:  15 August 2002

Anne Preller  and
P. Duroux
Anne Preller
Affiliation:
LIRMM, 161 rue ADA, 34392 Montpellier, France; preller@lirmm.fr.
P. Duroux
Affiliation:
LIRMM, 161 rue ADA, 34392 Montpellier, France; duroux@lirmm.fr.
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Abstract

Using an inductive definition of normal terms of thetheory of Cartesian ClosedCategories with a given graph of distinguished morphisms, we give a reduction freeproof of the decidability of this theory. This inductive definition enables us toshow via functional completeness that extensions of such a theory by new constants (“indeterminates”) are conservative.

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Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 33 , Issue 3 , May 1999 , pp. 227 - 257
Copyright
© EDP Sciences, 1999

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References

T. Altenkirch, M. Hofmann and T. Streicher, Categorical reconstruction of a reduction free normalisation proof, preliminary version, P. Dybjer and R. Pollacks, Eds., Proceedings CTCS '95, Springer, Lecture Notes in Computer Science 953 (1995) 182-199.
U. Berger and H. Schwichtenberg, An inverse to the evaluation functional for typed λ-calculus, in Proc. of the 6th Annual IEEE Symposium of Logic in Computer Science (1991) 203-211.
D. Cubric', Embedding of a free Cartesian Closed Category in the Category of Sets. J. Pure and Applied Algebra (to appear).
Cubric', D., Dybjer, P. and Scott, P., Normalization and the Yoneda Embedding, MSCS 8 (1998) 153-192.
R. Di Cosmo, Isomorphisms of Types, Birkhaeuser (1995).
K. Dosen and Z. Petric', The maximality of Cartesian Categories, Rapport Institut de Recherche de Toulouse, CNRS, 97-42-R (1997).
J. Lambek and P.J. Scott, Introduction to Higher Order Categorical Logic, Cambridge University Press (1989).
Obtu, A. \l owicz, Algebra of constructions I. The word problem for partial algebras. Inform. and Comput. 73 (1987) 129-173.