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Abstract: We introduce a family of explicit substitution type theories as internal languages for autonomous (or symmetric monoidal closed) and -autonomous categories, in the same sense that the simplytyped -calculus with surjective pairing is the internal language for cartesian closed categories. The typing rules are given in the style of Gentzen's Sequent Calculus, and our type theory may be regarded as a term assignment system for the sequent calculus of the multiplicative ( ; ( ; ?; 1)-fragment... (Update)
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...binders. This is not the place to justify the design and analyse the syntax of the term language (we direct readers who are interested to [7, 8]) Our aim here is simply to use the term language as a compact (indeed L A T E X able) notation to express LAL derivations (of which...
...semantics for RLL is provided by autonomous (or monoidal closed) categories. Moreover RLL is also the internal language [MRA93,KO99,MMdPR01] for autonomous categories. 2.1 Reduction rules for RLL To perform computations in RLL we need to agree on which reduction rules to...
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BibTeX entry: (Update)
T. W. Koh and C.-H. L. Ong. Explicit substitution internal languages for autonomous and -autonomous categories. To appear in the ENTCS Proceedings of Category Theory and Computer Science 1999, 34pp., ftp-able from Ong's homepage, 1999. http://citeseer.ist.psu.edu/koh99explicit.html More
@misc{ koh99explicit,
author = "T. Koh and C. Ong",
title = "Explicit substitution internal languages for autonomous and -autonomous
categories",
text = "T. W. Koh and C.-H. L. Ong. Explicit substitution internal languages for
autonomous and -autonomous categories. To appear in the ENTCS Proceedings
of Category Theory and Computer Science 1999, 34pp., ftp-able from Ong's
homepage, 1999.",
year = "1999",
url = "citeseer.ist.psu.edu/koh99explicit.html" }
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