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Abstract: This paper concerns itself with the categorical semantics of -calculi extended with explicit substitutions. For the simply-typed -calculus, indexed categories seem to provide the right categorical framework but because these structures are inherently non-linear, alternate models are needed for linear -calculi extended with explicit substitutions. We propose to replace indexed categories by presheaves and obtain a semantics which can be specialised to both the linear and the intuitionistic... (Update)
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...Criteria: Although beyond the scope of this paper, there are semantic reasons for believing xDILL to be mathematically convincing. In [14], we described a categorical semantics for both cartesian and linear calculi of explicit substitutions based on pre sheaves. There is a Curry...
...Although beyond the scope of this paper, there are semantic reasons for believing xDILL to be mathematically convincing. In [14], we described a categorical semantics for both cartesian and linear calculi of explicit substitutions based on pre sheaves. There is a Curry...
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BibTeX entry: (Update)
N. Ghani, V. de Paiva, and E. Ritter. Categorical models for explicit substitutions. In W. Thomas, editor, Proc. of FoSSaCS'99, volume 1578 of Lecture Notes in Computer Science. Springer Verlag, 1999. http://citeseer.ist.psu.edu/article/ghani98categorical.html More
@inproceedings{ ghani99categorical,
author = "Neil Ghani and Valeria de Paiva and Eike Ritter",
title = "Categorical Models of Explicit Substitutions",
booktitle = "Foundations of Software Science and Computation Structure",
pages = "197-211",
year = "1999",
url = "citeseer.ist.psu.edu/article/ghani98categorical.html" }
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