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 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 λ-calculus, as well as in a simple non-deterministic variant.

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

Domaines: Logique en informatique [cs.LO]

Tom Hirschowitz, Ambroise Lafont. A categorical framework for congruence of applicative bisimilarity in higher-order languages. 2021. ⟨hal-02966439v3⟩