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Abstract: We present a semantical proof of existence of normal forms for system F including j-equality. A reduction-free normalisation function can be obtained from this. The proof uses the method of glueing (a variant of) the term model along the global sections functor, carried out in the internal language of a category of presheaves. As a by-product we obtain an semantical explanation of higherorder abstract syntax. The paper extends a previous one (Altenkirch, Hofmann, and Streicher 1996) in which a... (Update)
Context of citations to this paper: More
...s Set one needs to consider presheaves relative to some constructive set theory which supports such universes in the first place. See [1] for details. Being a topos every presheaf category also supports a notion of predicates, propositions, and higher order logic: a predicate on...
.... been presented, overwhelmingly for simple types only, as an inverse to the evaluation functional [5] reduction free normalisation [1, 2], type directed partial evaluation [8] as the computational content of Tait s typed method for proving Strong Normalisation [3] as a...
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BibTeX entry: (Update)
T. Altenkirch, M. Hofmann, and T. Streicher. Reduction-free normalisation for system F . Unpublished. Available from www.dcs.ed.ac.uk/home/mxh/papers, May 1996. http://citeseer.ist.psu.edu/article/altenkirch96reductionfree.html More
@inproceedings{ altenkirch96reductionfree,
author = "Thorsten Altenkirch and Martin Hofmann and Thomas Streicher",
title = "Reduction-Free Normalization for a Polymorphic System",
booktitle = "Proceedings of the 11th Annual Symposium on Logic in Computer Science",
publisher = "IEEE Computer Society Press",
address = "New Brunswick, New Jersey",
editor = "E. Clarke",
pages = "98--106",
year = "1996",
url = "citeseer.ist.psu.edu/article/altenkirch96reductionfree.html" }
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Documents on the same site (http://www.tcs.informatik.uni-muenchen.de/~alti/abstracts.html):
A user's guide to ALF - Altenkirch, Gaspes, Nordström, von.. (1994) (Correct)
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