Cellular Monads from Positive GSOS Specifications

Abstract

We give a leisurely introduction to our abstract framework for operational semantics based on cellular monads on transition categories. Furthermore, we relate it for the first time to an existing format, by showing that all Positive GSOS specifications generate cellular monads whose free algebras are all compositional. As a consequence, we recover the known result that bisimilarity is a congruence in the generated labelled transition system.• The treatment of languages with variable binding is significantly more technical than the basic setting [9,8,24].• More importantly, the bialgebraic study of higher-order languages like the λ -calculus or the higherorder π-calculus is only in its infancy [20].This leaves some room for exploring potential alternatives. * Thanks to Jorge Pérez and Jurriaan Rot for the invitation, and to the referees for helpful comments.Lemma 8.2 thus accounts for the factorisation of the original square as on the left in (2): M and R respectively factor as ⋆ M ′

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

“…In previous work [26,25], the first author has proposed an alternative approach to the problem, dropping the coalgebraic notion of bisimulation used by Turi and Plotkin in favour of a notion based on factorisation systems, similar to Joyal et al's [28]. Furthermore, congruence of bisimilarity is notably obtained by assuming that syntax induces a familial monad, in the sense of Diers [15,13,46].…”

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

“…In previous work [Hir19b,Hir19a], the first author has proposed an alternative approach to the problem, dropping the coalgebraic notion of bisimulation used by Turi and Plotkin in favour of a notion based on factorisation systems, similar to Joyal et al's [JNW93]. Furthermore, congruence of bisimilarity is notably obtained by assuming that syntax induces a familial monad [Die78, CJ95,Web07a].…”