Related papers: Cellular Monads from Positive GSOS Specifications
The bialgebraic abstract GSOS framework by Turi and Plotkin provides an elegant categorical approach to modelling the operational and denotational semantics of programming and process languages. In abstract GSOS, bisimilarity is always a…
This paper is a contribution to the search for efficient and high-level mathematical tools to specify and reason about (abstract) programming languages or calculi. Generalising the reduction monads of Ahrens et al., we introduce transition…
General frameworks have been recently proposed as unifying theories for processes combining non-determinism with quantitative aspects (such as probabilistic or stochastically timed executions), aiming to provide general results and tools.…
In this article we give a construction of a polynomial 2-monad from an operad and describe the algebras of the 2-monads which then arise. This construction is different from the standard construction of a monad from an operad in that the…
Recently, some general frameworks have been proposed as unifying theories for processes combining non-determinism with quantitative aspects (such as probabilistic or stochastically timed executions), aiming to provide general results and…
Some formats of well-behaved operational specifications, correspond to natural transformations of certain types (for example, GSOS and coGSOS laws). These transformations have a common generalization: distributive laws of monads over…
We show that every action operad gives rise to a notion of monoidal category via the categorical version of the Borel construction, embedding action operads into the category of 2-monads on $\mathbf{Cat}$. We characterize those 2-monads in…
Several notions of bisimulation relations for probabilistic non-deterministic transition systems have been considered in the literature. We consider a novel testing-based behavioral equivalence called upper-expectation bisimilarity and…
Inspired by the classical theory of modules over a monoid, we give a first account of the natural notion of module over a monad. The associated notion of morphism of left modules ("Linear" natural transformations) captures an important…
In this paper, we introduce an extension of the GSOS rule format with predicates such as termination, convergence and divergence. For this format we generalize the technique proposed by Aceto, Bloom and Vaandrager for the automatic…
Monads in category theory are algebraic structures that can be used to model computational effects in programming languages. We show how the notion of "centre", and more generally "centrality", i.e. the property for an effect to commute…
Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which…
It came to the attention of myself and the coauthors of (S., Rozowski, Silva, Rot, 2022) that a number of process calculi can be obtained by algebraically presenting the branching structure of the transition systems they specify. Labelled…
Process calculi and graph transformation systems provide models of reactive systems with labelled transition semantics. While the semantics for process calculi is compositional, this is not the case for graph transformation systems, in…
This paper introduces the counterpart of strong bisimilarity for labelled transition systems extended with time-out transitions. It supports this concept through a modal characterisation, congruence results for a standard process algebra…
Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explicit description of the information required to define any…
We introduce dicodensity monads: a generalisation of pointwise codensity monads generated by functors to monads generated by mixed-variant bifunctors. Our construction is based on the notion of strong dinaturality (also known as Barr…
Stream GSOS is a specification format for operations and calculi on infinite sequences. The notion of bisimilarity provides a canonical proof technique for equivalence of closed terms in such specifications. In this paper, we focus on open…
We develop the theory of strong and commutative monads in the 2-dimensional setting of bicategories. This provides a framework for the analysis of effects in many recent models which form bicategories and not categories, such as those based…
We prove that the relation of bisimilarity between countable labelled transition systems is $\Sigma_1^1$-complete (hence not Borel), by reducing the set of non-wellorders over the natural numbers continuously to it. This has an impact on…