An Algebra of Dataaow Networks

y Abstract. This paper describes an algebraic framework for the study of dataaow networks, which form a paradigm for concurrent computation in which a collection of concurrently and asynchronously executing processes communicate by sending messages between ports connected via FIFO message channels. A syntactic dataaow calculus is deened, having two kinds of terms which represent networks and computations, respectively. By imposing suitable equivalences on networks and computations , we obtain the free dataaow algebra, in which the dataaow networks with m input ports and n output ports are regarded as the objects of a category S n m , and the computations of such networks are represented by the arrows. Functors deened on S n m label each computation by the input buuer consumed and the output buuer produced during that computation, so that each S n m is a span in Cat. It is shown that the free dataaow algebra construction underlies a monad in the category of collections S = fS n m : m; n 0g of spans in Cat. The algebras of this monad, called dataaow algebras, have a monoid structure representing parallel composition, and are also equipped with an action of a certain collection of continuous functions, thereby representing the formation of feedback loops. The two structures are related by a distributive law of feedback over parallel composition. We also observe the following connection with the theory of brations: if S is a dataaow algebra, then each S n m is a split biibration in Cat.