Contextual Equivalence for Higher-Order π-Calculus Revisited

The higher-order @p-calculus is an extension of the @p-calculus to allow communication of abstractions of processes rather than names alone. It has been studied intensively by Sangiorgi in his thesis where a characterisation of a contextual equivalence for higher-order @p-calculus is provided using labelled transition systems and normal bisimulations. Unfortunately the proof technique used there requires a restriction of the language to only allow finite types. We revisit this calculus and offer an alternative presentation of the labelled transition system and a novel proof technique which allows us to provide a fully abstract characterisation of contextual equivalence using labelled transitions and bisimulations for higher-order @p-calculus with recursive types also.