Some Chemical Abstract Machines

This paper explains by a series of examples the use of the notion of a Chemical Abstract Machine. This is a framework for parallel computations which builds upon the chemical metaphor of Banâtre and Le Métayer. We first illustrate the CHAM style by describing the operational semantics of process calculi constructs. Then we apply our approach to the λ-calculus, designing a CHAM for the weak β-reduction with sharing, and specializing it into a CHAM for the call-by-need reduction strategy. Our last example is the π-calculus. We discuss the notions of “asynchronous” and “fully asynchronous” reductions, and some π-calculus encodings of the λ-calculus.