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Towards a Higher-Order Mathematical Operational Semantics

Published:11 January 2023Publication History
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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 λ-calculus w.r.t. a strong variant of Abramsky’s applicative bisimilarity are obtained as instances.

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      • Published in

        cover image Proceedings of the ACM on Programming Languages
        Proceedings of the ACM on Programming Languages  Volume 7, Issue POPL
        January 2023
        2196 pages
        EISSN:2475-1421
        DOI:10.1145/3554308
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        Association for Computing Machinery

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        Publication History

        • Published: 11 January 2023
        Published in pacmpl Volume 7, Issue POPL

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