Implicit Coercions in Type Systems (1995)
| Venue: | In Selected Papers from the International Workshop TYPES '95 |
| Citations: | 13 - 1 self |
BibTeX
@INPROCEEDINGS{Barthe95implicitcoercions,
author = {Gilles Barthe},
title = {Implicit Coercions in Type Systems},
booktitle = {In Selected Papers from the International Workshop TYPES '95},
year = {1995},
pages = {1--15},
publisher = {Springer-Verlag}
}
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Abstract
. We propose a notion of pure type system with implicit coercions. In our framework, judgements are extended with a context of coercions \Delta and the application rule is modified so as to allow coercions to be left implicit. The setting supports multiple inheritance and can be applied to all type theories with \Pi-types. One originality of our work is to propose a computational interpretation for implicit coercions. In this paper, we demonstrate how this interpretation allows a strict control on the logical properties of pure type systems with implicit coecions. 1 Introduction The increasing importance of mathematical software has been accompanied by a drift of mainstream mathematics towards mathematical logic and the foundations of mathematics. Before mathematical software, formal systems were generally seen both by logicians and mathematicians as safe heavens into which mathematics could theoretically be embedded. With powerful mathematical software, there is now a genuine interes...
