Compositional Separation of Control Flow and Data Flow

Every constructive model of computation (CMC) has an underlying composition mechanism for combining simple computation devices into more complex ones. Composition can be done by (explicitly or implicitly) defining control flow, data flow or any combination thereof. Control flow specifies the order in which individual computation devices are activated, whereas data flow defines how data is exchanged among them. Unfortunately, traditional CMCs either mix data and control or only consider one dimension explicitly, which makes it difficult to reason about data flow and control flow separately. Reasoning about these dimensions orthogonally is a crucial desideratum for optimisation, maintainability and verification purposes. In this paper, we introduce a novel model that explicitly treats data flow and control flow as separate dimensions, while providing modularity. As the model is rooted in category theory, it provides category-theoretic operations for compositionally constructing sequential or parallel composites. Compositionality entails that a composite exhibits the same properties as its respective constituents, including separation of concerns and modularity.