Although the application of universal algebraic techniques, particularly coalgebras, to the study of processes is not new, this paper attempts to apply these techniques to one particular formalism, Hoare’s communicating sequential processes (CSP). It is only partially successful in this attempt.

The semantics of concurrent deterministic processes are dealt with in the first four sections of this paper, and here the coalgebraic interpretation yields an appealing perspective, equating processes with states in a partial finite automaton. However, the author admits that there are problems in finding an exact analogue of nondeterministic processes. The results on nondeterministic filter automata and nondeterministic operators are presented without formal proofs in most cases.

The work is intended to bridge the gap between two audiences: those with some background in coalgebraic reasoning, and those familiar with CSP. The former group is perhaps slightly better served than the latter; readers with little knowledge of category theory will probably find the presentation lacking in clarity and motivation, and would be better served by first reading the tutorials [1,2] that are cited in the paper’s references. On the other hand, a reader unacquainted with CSP would be well advised to have a copy of Hoare’s book [3] handy, as many of the CSP concepts are indexed by the labels used in that book.