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

Tom Hirschowitz, Ambroise Lafont

Applicative bisimilarity is a coinductive characterisation of observational equivalence in call-by-name lambda-calculus, introduced by Abramsky in 1990. Howe (1989) gave a direct proof that it is a congruence. 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 and call-by-value $\lambda$-calculus, as well as in a simple non-deterministic variant.

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