New-HOPLA: A Higher-order Process Language with Name Generation

This paper introduces new-HOPLA, a concise but powerful language for higher-order nondeterministic processes with name generation. Its origins as a metalan-guage for domain theory are sketched but for the most part the paper concentrateson its operational semantics. The language is typed, the type of a process describingthe shape of the computation paths it can perform. Its transition semantics, bisim-ulation, congruence properties and expressive power are explored. Encodings aregiven of well-known process algebras, including π-calculus, Higher-Order π-calculusand Mobile Ambients. 1 The origins of new-HOPLA This work is part of a general programme (reported in [8]), to develop a domain theorywhich scales up to the intricate languages, models and reasoning techniques used indistributed computation. This ambition led to a concentration on path based models,and initially on presheaf models because they can even encompass causal dependencymodels like event structures; so ‘domains’ is being understood more broadly than usual,to include presheaf categories.The general methodology has been to develop domain theories with a rich enoughlife of their own to suggest powerful metalanguages. The point to emphasise is that inthis way informative domain theories can have a pro-active role; they can yield new met-alanguages, by their nature very expressive, accompanied by novel ways to deconstructexisting notions into more primitive ones, as well as new analysis techniques. A feature ofpresheaf models has been very useful: in key cases there is often a strong correspondencebetween elements of the presheaf denotation and derivations in an operational semantics.In the cases of HOPLA and new-HOPLA the presheaf models have led not only the coreoperations of the language, and a suitable syntax, but also to their operational semantics.This paper reports on new-HOPLA, a compact but expressive language for higher-order nondeterministic processes with name generation. It extends the language HOPLA