Towards a Higher-Order Mathematical Operational Semantics

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 compositio...

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Bibliographic Details
Published in:Proceedings of ACM on programming languages Vol. 7; no. POPL; pp. 632 - 658
Main Authors: Goncharov, Sergey, Milius, Stefan, Schröder, Lutz, Tsampas, Stelios, Urbat, Henning
Format: Journal Article
Language:English
Published: New York, NY, USA ACM 09.01.2023
Subjects:
Categorical semantics
Operational semantics
Theory of computation
Categorical semantics
Abstract GSOS
Higher-order reasoning
ISSN:2475-1421, 2475-1421
Online Access:Get full text
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Summary: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 λ-calculus w.r.t. a strong variant of Abramsky’s applicative bisimilarity are obtained as instances.
ISSN:2475-1421
2475-1421
DOI:10.1145/3571215