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arXiv · 2302.08200

Weak Similarity in Higher-Order Mathematical Operational Semantics

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

Higher-order abstract GSOS is a recent extension of Turi and Plotkin's framework of Mathematical Operational Semantics to higher-order languages. The fundamental well-behavedness property of all specifications within the framework is that coalgebraic strong (bi)similarity on their operational model is a congruence. In the present work, we establish a corresponding congruence theorem for weak similarity, which is shown to instantiate to well-known concepts such as Abramsky's applicative similarity for the lambda-calculus. On the way, we develop several techniques of independent interest at the level of abstract categories, including relation liftings of mixed-variance bifunctors and higher-order GSOS laws, as well as Howe's method.

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Henning Urbat, Stelios Tsampas, Sergey Goncharov, Stefan Milius, Lutz Schröder. 2023-02-16. Weak Similarity in Higher-Order Mathematical Operational Semantics. https://arxiv.org/abs/2302.08200

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