Distributive Laws for Monotone Specifications

Jurriaan Rot
(Radboud University)

Turi and Plotkin introduced an elegant approach to structural operational semantics based on universal coalgebra, parametric in the type of syntax and the type of behaviour. Their framework includes abstract GSOS, a categorical generalisation of the classical GSOS rule format, as well as its categorical dual, coGSOS. Both formats are well behaved, in the sense that each specification has a unique model on which behavioural equivalence is a congruence. Unfortunately, the combination of the two formats does not feature these desirable properties. We show that monotone specifications - that disallow negative premises - do induce a canonical distributive law of a monad over a comonad, and therefore a unique, compositional interpretation.

In Kirstin Peters and Simone Tini: Proceedings Combined 24th International Workshop on Expressiveness in Concurrency and 14th Workshop on Structural Operational Semantics (EXPRESS/SOS 2017), Berlin, Germany, 4th September 2017, Electronic Proceedings in Theoretical Computer Science 255, pp. 83–97.
Published: 31st August 2017.

ArXived at: http://dx.doi.org/10.4204/EPTCS.255.6 bibtex PDF
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