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We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved. Many types of graphical structures used in computer science are shown to be examples of adhesive categories. Double-pushout graph rewriting generalises well to rewriting on arbitrary adhesive categories.
The theory of reactive systems, introduced by Leifer and Milner and previously extended by the authors, allows the derivation of well-behaved labelled transition systems (LTS) for semantic models with an underlying reduction semantics. The derivation procedure requires the presence of certain colimits (or, more usually and generally, bicolimits) which need… (More)
We introduce G-relative-pushouts (GRPO) which are a 2-categorical generalisation of relative-pushouts (RPO). They are suitable for deriving labelled transition systems (LTS) for process calculi where terms are viewed modulo structural congruence. We develop their basic properties and show that bisimulation on the LTS derived via GRPOs is a congruence,… (More)
We present a new labelled transition system (lts) for the ambient calculus on which ordinary bisimilarity coincides with contextual equivalence. The key feature of this lts is that it is the fruit of ongoing work on developing a systematic procedure for deriving ltss in the structural style from the underlying reduction semantics and observability. Notably,… (More)
G-relative pushouts (GRPOs) have recently been proposed by the authors as a new foundation for Leifer and Milner’s approach to deriving labelled bisimulation congruences from reduction systems. This paper develops the theory of GRPOs further, arguing that they provide a simple and powerful basis towards a comprehensive solution. As an example, we construct… (More)
We re-examine the standard structural operational semantics of the π-calculus with the view that both process structure and contextual observational power should play roles in describing the behavioural theory. To that end we provide a decomposition of the operational semantics of π which allows for a systematic definition of labelled transitions. These are… (More)
Groupoidal relative pushouts (GRPOs) have recently been proposed by the authors as a new foundation for Leifer and Milner’s approach to deriving labelled bisimulation congruences from reduction systems. In this paper, we develop the theory of GRPOs further, proving that well-known equivalences, other than bisimulation, are congruences. To demonstrate the… (More)
The use of 2,4,6-trinitrobenzenesulfonic acid (TNBS) as a reagent for determining the concentrations of amines has been widely accepted (1-3) since its introduction in 1960 by Satake et al. (4). The original procedure has since been modified by Mokrasch (5) to permit the determination of amines, amino acids, and proteins in mixtures. In both procedures the… (More)
We consider open terms and parametric rules in the context of the systematic derivation of labelled transitions from reduction systems.