Introduction to Part V

Summary

We have seen in the General Introduction that the incarnations of mobility can be quite different. To a first approximation, however, we can distinguish two categories: models involving movement of computational entities, such as processes and parametrized processes, and models involving movement of communication links. Correspondingly, there are two main approaches to representing mobility in process calculi: the higher-order (or process-passing) paradigm, and the first- order (or name-passing) paradigm. The higher-order paradigm inherits from the λ-calculus the idea that a computation step involves instantiation of variables by terms.

The first-order paradigm is the mathematically simpler of the two. A fundamental point - without which the significance of the π-calculus would be strongly diminished - is that communication of names is enough to model communications involving processes. The formalization and validation of this claim is a central topic of this Part. The study has two main motivations. The first is expressiveness - two different paradigms are being compared. The second is semantics of higher-order languages: we wish to understand whether the π-calculus can be used as a metalanguage for describing and reasoning about such languages. Especially interesting is the possibility of using the theory of the π-calculus to derive proof techniques for higher-order languages. Obtaining proof techniques directly on these languages may be hard; see the discussion in the notes at the end of the Part. The basis for the study is laid down in this Part; the study is continued in Part VI, where we look at reduction strategies.

We begin Part V by introducing the Higher-Order π-calculus, HOπ, a higher- order extension of the core calculus Base-π of Section 6.2. In HOπ, parametrized processes, that is, abstractions, may be transmitted. An abstraction has a functional type. Applying an abstraction of type T → ⋄ to an argument of type T yields a process. The argument can itself be an abstraction; therefore the order of an abstraction, that is, the level of arrow nesting in its type, can be arbitrarily high.