Category theory for operational semantics

  • Authors:
  • Marina Lenisa;John Power;Hiroshi Watanabe

  • Affiliations:
  • Dipartimento di Matematica e Informatica, Università di Udine, I-33100 Udine, Italy;Laboratory for the Foundations of Computer Science, University of Edinburgh, King's Buildings, Edinburgh EH9 3JZ, Scotland, UK;Laboratory for Verification and Semantics, AIST, Amagasaki 661-0974, Japan

  • Venue:
  • Theoretical Computer Science - Selected papers of CMCS'03
  • Year:
  • 2004

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Abstract

We use the concept of a distributive law of a monad over a copointed endofunctor to define and develop a reformulation and mild generalisation of Turi and Plotkin's notion of an abstract operational rule. We make our abstract definition and give a precise analysis of the relationship between it and Turi and Plotkin's definition. Following Tuff and Plotkin, our definition, suitably restricted, agrees with the notion of a set of GSOS-rules, allowing one to construct both an operational model and a canonical, internally fully abstract denotational model. Going beyond Turi and Plotkin, we construct what might be seen as large-step operational semantics from small-step operational semantics and we show how our definition allows one to combine distributive laws, in particular accounting for the combination of operational semantics with congruences.