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arXiv · 2405.16708

Higher-order bialgebraic semantics

Sergey Goncharov·Stefan Milius·Lutz Schröder·Stelios Tsampas·Henning Urbat
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Abstract

Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which provides off-the-shelf compositionality results for first-order languages, so far does not apply to higher-order languages. In the present work, we develop a theory of abstract GSOS specifications for higher-order languages, in effect transferring the core principles of Turi and Plotkin's framework to a higher-order setting. In our theory, the operational semantics of higher-order languages is represented by certain dinatural transformations that we term (pointed) higher-order GSOS laws. We give a general compositionality result that applies to all systems specified in this way and discuss how compositionality of combinatory logics and the lambda-calculus w.r.t. a strong variant of Abramsky's applicative bisimilarity are obtained as instances.

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Sergey Goncharov, Stefan Milius, Lutz Schröder, Stelios Tsampas, Henning Urbat. 2024-05-26. Higher-order bialgebraic semantics. https://doi.org/10.46298/jfp.17738

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