Programming with Broadcasts

[Pra91, Pra92] develop CBS, a CCS-like calculus [Mil89] where processes communicate by broadcasting values along a single channel. These values are hidden or restricted by translation to noise. This paper types CBS and restricts it to processes with a unique response to each input. Nondeterminism arises only if two processes in parallel both wish to transmit. These restrictions do not reduce the programming power of CBS. But strong and weak bisimulation can now be de ned exactly as in CCS, yet capture observationally meaningful relations. Weak bisimulation is a congruence. This paper also shows how to program in CBS in a (lazy) ML framework. A simple CBS simulator is given, and a parallel implementation discussed. The simulator represents data evaluation, recursion and conditionals directly in Lazy ML. It implements an extended CBS with evaluation as well as communication transitions. [Pra91, Pra92] develop a CCS-like [Mil89] calculus of broadcasting systems, CBS. This paper continues the development, restricting the calculus without losing programming power, and yet simplifying the semantics substantially. The new CBS is presented in Sections 1 to 4. [Pra91, Pra92] should be consulted for more motivation, discussion of design, and comparison with CCS. No knowledge of these papers is necessary, however. Familiarity with CCS will be helpful. This paper also describes a way to program in CBS in a (lazy) functional programming framework [BW88], using a CBS simulator implemented in Lazy ML [AJ93] (LML for short). The resulting language is powerful, natural and welltyped. This part of the paper (Sections 5 to 7) is informal. It is not yet clear how to link proofs about the LML programs with proofs about CBS. Nonetheless, the programming concepts seem simple, and are now quite old; they are therefore reported here. The type system and many of the examples predate [Pra92]. The simpli ed CBS of this paper was inspired by programming experience. CBS compares well with attempts to combine CCS with ML, including PFL [Hol83], Facile [GMP89], and LCS [Ber93]. CML [Rep91, BMT92] adds concurrency primitives to ML, but its relationship to process calculi is unclear. All these