Weak Similarity in Higher-Order Mathematical Operational Semantics
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 m...
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Zusammenfassung: | 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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DOI: | 10.48550/arxiv.2302.08200 |