Trancón y Widemann, B: From bialgebraic semantics to universal simulators of cellular automata, Preliminary Proceedings 21st International Workshop on Algebraic Development Techniques (WADT 2012) Technical Report 08/12, 104-106 (2012)
The structural operational semantics (SOS) approach of Plotkin [4] is one of the most popular variants of operational semantics, and has been applied practically to a wide variety of programming calculi and languages. It has gained considerable theoretical interest after the categorization by Turi and Plotkin [6]. There, a certain well-behaved SOS rule format is shown to correspond to a distributive law of a syntactical functor  over a behavioral functor B. This view entails numerous nice mathematical properties: Both a syntactical and a denotational model arise automatically as the initial -algebra and the nal B-coalgebra, respectively. A unique bialgebra homomorphism connects the two, giving denotational and operational semantics simultaneously: Denotational semantics because a homomorphism from the initial -algebra can be seen as a syntax-directed interpretation in a semantic domain; operational semantics because a homomorphism into the nal B-coalgebra can be seen as a fully abstract speci cation of machine transitions. For well-behaved behaviour B, there is only one form of bisimulation, and that is a -congruence, making the semantics fully abstract by construction.
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