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.
Work supported by ECC Science MASK grant and MURST 40% grants.
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© 1994 Springer-Verlag Berlin Heidelberg
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Forti, M., Honsell, F., Lenisa, M. (1994). Processes and hyperuniverses. In: Prívara, I., Rovan, B., Ruzička, P. (eds) Mathematical Foundations of Computer Science 1994. MFCS 1994. Lecture Notes in Computer Science, vol 841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58338-6_82
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DOI: https://doi.org/10.1007/3-540-58338-6_82
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