2013 | OriginalPaper | Chapter
Comodels and Effects in Mathematical Operational Semantics
Authors : Faris Abou-Saleh, Dirk Pattinson
Published in: Foundations of Software Science and Computation Structures
Publisher: Springer Berlin Heidelberg
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In the mid-nineties, Turi and Plotkin gave an elegant categorical treatment of denotational and operational semantics for process algebra-like languages, proving compositionality and adequacy by defining operational semantics as a distributive law of syntax over behaviour. However, its applications to stateful or effectful languages, incorporating (co)models of a countable Lawvere theory, have been elusive so far. We make some progress towards a coalgebraic treatment of such languages, proposing a congruence format related to the evaluation-in-context paradigm. We formalise the denotational semantics in suitable Kleisli categories, and prove adequacy and compositionality of the semantic theory under this congruence format.