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arXiv · 2103.16833

A categorical framework for congruence of applicative bisimilarity in higher-order languages

Tom Hirschowitz·Ambroise Lafont
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Abstract

Applicative bisimilarity is a coinductive characterisation of observational equivalence in call-by-name lambda-calculus, introduced by Abramsky (1990). Howe (1996) gave a direct proof that it is a congruence, and generalised the result to all languages complying with a suitable format. We propose a categorical framework for specifying operational semantics, in which we prove that (an abstract analogue of) applicative bisimilarity is automatically a congruence. Example instances include standard applicative bisimilarity in call-by-name, call-by-value, and call-by-name non-deterministic $\lambda$-calculus, and more generally all languages complying with a variant of Howe's format.

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Tom Hirschowitz, Ambroise Lafont. 2021-03-31. A categorical framework for congruence of applicative bisimilarity in higher-order languages. https://doi.org/10.46298/lmcs-18(3:37)2022

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