Compositional Separation of Control Flow and Data Flow

TL;DR

This paper introduces a category-theoretic model that explicitly separates control flow and data flow, enhancing modularity and reasoning in high-level computation models.

Contribution

It presents a novel high-level computation model that distinctly separates data and control flow, enabling better modularity and compositional reasoning.

Findings

Model supports modular composition of control and data flow

Category-theoretic operations facilitate complex composite structures

Application examples in software engineering and AI demonstrate utility

Abstract

Every Model of High-Level Computation (MHC) has an underlying composition mechanism for combining simple computing 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 computations are activated, whereas data flow defines how data is exchanged among them. Unfortunately, traditional MHCs 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 MHC 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, parallel, branching or iterative composites. Compositionality entails that a composite exhibits the same properties as its respective constituents, including separation of concerns and modularity. We conclude the paper by demonstrating how our proposal can be used to model high-level computations in two different application domains: software engineering and artificial intelligence.