A pi-calculus with dynamic typing (original) (raw)

Traditional static typing systems for the pi-calculus are built around capability types that control the read/write access rights on channels and describe the type of their payload. While static typing has proved adequate for reasoning on process behavior in typed contexts, dynamic techniques have often been advocated as more effective for access control in distributed/untyped contexts. Here we develop a new typing discipline for the asynchronous pi-calculus, which we call API@. It combines static and dynamic typing: a static type system associates channels with flat types that only express read/write capabilities and disregard the payload type; a dynamically typed synchronization complements the static type system to guarantee type soundness. We define a typed equational theory, and we give a co-inductive proof technique useful to prove equivalences among processes. We study the relationships between our dynamic approach and the static one of the asynchronous pi calculuS, referred as API, which comes with an entirely standard static typing system. On the one hand, we show that API can be encoded in API@ in a sound manner. On the other hand, we show that API@ can be encoded into API in a fully abstract manner, preserving the respective behavioral equivalences of the two calculi. Besides yielding an interesting expressivity result, the encoding also sheds light on the effectiveness of dynamic typing as a mechanism for access control. Here we take P ∼ = @ Q to mean that P and Q are behaviorally indistinguishable, i.e. they have the same observable behavior when executed in any arbitrary context. The equation (1) is easily disproved by exhibiting a context that interferes with the intended protocol between S and C. A first example is the context C 1 [−] = − | d(x).!x(y).0, that initially behaves as the client, to receive s, but then it steals the jobs intended Work partially supported by M.I.U.R (Italian Ministry of Education, University and Research) under contract n. 2005015785.