[2210.13387] Towards a Higher-Order Mathematical Operational Semantics
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arXiv:2210.13387 (cs)
[Submitted on 24 Oct 2022 (v1), last revised 26 Oct 2022 (this version, v2)]

Title:Towards a Higher-Order Mathematical Operational Semantics

Authors: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 has been successfully applied to obtain 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 the SKI calculus and the $\lambda$-calculus w.r.t. a strong variant of Abramsky's applicative bisimilarity are obtained as instances.
Subjects: Logic in Computer Science (cs.LO); Programming Languages (cs.PL); Category Theory (math.CT)
Cite as: arXiv:2210.13387 [cs.LO]
  (or arXiv:2210.13387v2 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2210.13387

Submission history

From: Stelios Tsampas [view email]
[v1] Mon, 24 Oct 2022 16:38:55 UTC (104 KB)
[v2] Wed, 26 Oct 2022 16:30:59 UTC (103 KB)
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