Higher-Order Mathematical Operational Semantics (Early Ideas)

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

doi:10.4230/LIPIcs.CALCO.2023.24

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Document Identifiers

DOI: 10.4230/LIPIcs.CALCO.2023.24
URN: urn:nbn:de:0030-drops-188213

Author Details

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

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.CALCO.2023.24

Abstract

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

Keywords

Abstract GSOS
lambda-calculus
applicative bisimilarity
bialgebra

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References

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