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Higher-Order Mathematical Operational Semantics (Early Ideas)

Authors Sergey Goncharov , Stefan Milius , Lutz Schröder , Stelios Tsampas , Henning Urbat

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Sergey Goncharov
  • Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
Stefan Milius
  • Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
Lutz Schröder
  • Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
Stelios Tsampas
  • Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
Henning Urbat
  • Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany

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Sergey Goncharov, Stefan Milius, Lutz Schröder, Stelios Tsampas, and Henning Urbat. Higher-Order Mathematical Operational Semantics (Early Ideas). In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 24:1-24:3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


We present a higher-order extension of Turi and Plotkin’s abstract GSOS framework that retains the key feature of the latter: for every language whose operational rules are represented by a higher-order GSOS law, strong bisimilarity on the canonical operational model is a congruence with respect to the operations of the language. We further extend this result to weak (bi-)similarity, for which a categorical account of Howe’s method is developed. It encompasses, for instance, Abramsky’s classical compositionality theorem for applicative similarity in the untyped λ-calculus. In addition, we give first steps of a theory of logical relations at the level of higher-order abstract GSOS.

Subject Classification

ACM Subject Classification
  • Theory of computation → Categorical semantics
  • Abstract GSOS
  • lambda-calculus
  • applicative bisimilarity
  • bialgebra


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