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Processes and Hyperuniverses (1994)
| Venue: | Proceedings of the 19th Symposium on Mathematical Foundations of Computer Science 1994, volume 841 of LNCS |
| Citations: | 7 - 0 self |
BibTeX
@INPROCEEDINGS{Forti94processesand,
author = {Marco Forti and Furio Honsell and Marina Lenisa},
title = {Processes and Hyperuniverses},
booktitle = {Proceedings of the 19th Symposium on Mathematical Foundations of Computer Science 1994, volume 841 of LNCS},
year = {1994},
pages = {352--361},
publisher = {Springer-Verlag}
}
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Abstract
. We show how to define domains of processes, which arise in the denotational semantics of concurrent languages, using hypersets, i.e. non-wellfounded sets. In particular we discuss how to solve recursive equations involving set-theoretic operators within hyperuniverses with atoms. Hyperuniverses are transitive sets which carry a uniform topological structure and include as a clopen subset their exponential space (i.e. the set of their closed subsets) with the exponential uniformity. This approach allows to solve many recursive domain equations of processes which cannot be even expressed in standard Zermelo-Fraenkel Set Theory, e.g. when the functors involved have negative occurrences of the argument. Such equations arise in the semantics of concurrrent programs in connection with function spaces and higher order assignment. Finally, we briefly compare our results to those which make use of complete metric spaces, due to de Bakker, America and Rutten. Introduction In the Semantics of ...
Keyphrases
complete metric space exponential uniformity negative occurrence function space non-wellfounded set transitive set recursive equation denotational semantics standard zermelo-fraenkel set theory uniform topological structure closed subset set-theoretic operator exponential space concurrent language concurrrent program order assignment many recursive domain equation
