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

Tom Hirschowitz (1) , Ambroise Lafont (2)

1 LAMA - Laboratoire de Mathématiques
2 UNSW - University of New South Wales [Sydney]

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 λ-calculus, and more generally all languages complying with a variant of Howe's format.

Mots clés: Programming languages; categorical semantics; operational semantics; Howe's method

Domaines: Logique en informatique [cs.LO]; Langage de programmation [cs.PL]

Tom Hirschowitz, Ambroise Lafont. A categorical framework for congruence of applicative bisimilarity in higher-order languages. 2022. ⟨hal-02966439v5⟩