Pipes and filters is a popular architecture which connects computational components (filters) through connectors (pipes) so that computations are performed in a stream like fashion. The data are transported through the pipes between filters, gradually transforming inputs to outputs. This kind of stream processing has been made popular through UNIX pipes that serially connect independent components for performing a sequence of tasks. We show in this paper how to foralize this architecture in terms of monads, hereby including relational specifications as special cases. The system is given through a directed acyclic graph the nodes of which carry the computational structure by being labelled with morphisms from the monad, and the edges provide the data for these operations. It is shown how fundamental compositional operations like combining pipes and filters, and refining a system by replacing simple parts through more elaborate ones, are supported through this construction. A notion of bisimular pipes and filters is introduced, it is shown that bisimilarity of components carries over to bisimilarity of entire systems.
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