A relational model of non-deterministic dataflow

THOMAS T. HILDEBRANDT, PRAKASH PANANGADEN, GLYNN WINSKEL
2004 Mathematical Structures in Computer Science  
We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits with the view of categories of models for concurrency and the general treatment of bisimulation they provide. In particular it fits with the recent categorical formulation of feedback using traced
more » ... dal categories. The payoffs are: (1) explicit relations to existing models and semantics, especially the usual axioms of monotone IO automata are read off from the definition of profunctors, (2) a new definition of bisimulation for dataflow, the proof of the congruence of which benefits from the preservation properties associated with open maps and (3) a treatment of higherorder dataflow as a biproduct, essentially by following the geometry of interaction programme. 1. the general functoriality and naturality properties of presheaves automatically imply the usually postulated axioms for asynchronous, monotone automata [27, 32] 2. we get a notion of bisimulation, which is crucial when one includes both synchronous and asynchronous primitives together, 3. it is closely connected to the extant models [15] expressed in terms of trace sets, but also provides a relational viewpoint which allows one to think of composing network components as a (kind of) relational composition, 4. gives a semantics of higher-order networks almost for "free" by using the passage from traced monoidal categories to compact-closed categories [2, 18] (the "geometry of interaction" construction).
doi:10.1017/s0960129504004293 fatcat:wtfyjpeubnckjgnqytosrfk5uy