On the Expressive Power of Joint Input

The join-calculus was introduced as anèxtended subset' of the asynchronous-calculus by amalgamating the three operators for input, restriction, and replication into a single operator, called deenition, but with the additional capability to describe the atomic joint reception of values from two diierent channels. In this paper, we just extend the asynchronous-calculus with joint input. By studying its expressive power, using slight variations of previously investigated choice encodings, we also conclude on the expressiveness of the join-calculus. 1 Join-calculus Fournet and Gonthier FG96] introduced the join-calculus as anèxtended sub-set' of the asynchronous-calculus, making the latter|ooering an attractive basis for concurrent programming PT98]|more amenable to distributed implementations. Syntactically, the amalgamation of the three operators input, restriction, and replication from the-calculus into the deenition operator def uhvi = P in Q def = (u) (! u(v):P j Q) (1) and its extension to admit joint inputs leads to the pleasantly simple grammar: where D represents the joint deenition with u; w called the deened names and v; x called the received names, which are all accessible from within P. The construct def D in Q represents the amalgamated operator that limits the further scope of the deened names of D to Q (see also Equation 1).