Psi-calculi: a framework for mobile processes with nominal data and logic

Abstract

Abstract. The framework of psi-calculi extends the pi-calculus with nominal datatypes for data structures and for logical assertions and conditions. These can be transmitted between processes and their names can be statically scoped as in the standard pi-calculus. Psi-calculi can capture the same phenomena as other proposed extensions of the pi-calculus such as the applied pi-calculus, the spi-calculus, the fusion calculus, the concurrent constraint pi-calculus, and calculi with polyadic communication channels or pattern matching. Psi-calculi can be even more general, for example by allowing structured channels, higherorder formalisms such as the lambda calculus for data structures, and predicate logic for assertions.We provide ample comparisons to related calculi and discuss a few significant applications. Our labelled operational semantics and definition of bisimulation is straightforward, without a structural congruence. We establish minimal requirements on the nominal data and logic in order to prove general algebraic properties of psi-calculi, all of which have been checked in the interactive theorem prover Isabelle. Expressiveness of psi-calculi significantly exceeds that of other formalisms, while the purity of the semantics is on par with the original pi-calculus.

Broadcast psi-calculi with an application to wireless protocols

“…The proofs of the meta-theoretic results in Section 3.1 [24] are formally verified in the interactive theorem prover Isabelle/Nominal. The full formalisation of broadcast psi-calculi amounts to ca 33 000 lines of Isabelle code, of which about 21 000 lines are re-used from our earlier work [5].…”

“…Strong bisimulation is preserved by all operators except input prefix and satisfies the expected algebraic laws such as scope extension, for details see [4,5].…”

“…This section is a brief recapitulation of psi-calculi; for a more extensive treatment including motivations and examples see [4,5].…”

“…↔ does for unicast communication. However, such a predicate would need to be transitive and symmetric for Theorem 11 to hold, for the same reasons as in the original psi calculus (detailed in [5]). In wireless broadcast communication systems, symmetry and transitivity do not necessarily hold and the requirements would not be reasonable.…”

“…In earlier papers we have shown how psi-calculi can capture the same phenomena as other proposed extensions of the pi-calculus such as the applied pi-calculus, the spi-calculus, the fusion calculus, the concurrent constraint pi-calculus, and calculi with polyadic communication channels or pattern matching. Psi-calculi can be even more general, for example by allowing structured channels, higher-order formalisms such as the lambda calculus for data structures, and predicate logic for assertions [5].…”