Colimit-Based Composition of High-Level Computing Devices

Abstract

Models of High-level Computation (MHCs) provide effective means to describe complex real-world computing systems because they offer formal foundations for the specification of interacting computing devices, as opposed to describing individual ones, which has been the focus of classical models such as Turing machines or the lambda calculus itself. Despite numerous proposals over the past half century, there is still no canonical MHC akin to Turing machines for (compositionally) reasoning about computation in the large. One of the major drawbacks of state- and data-oriented MHCs is that they extensively neglect control flow, a well-known semantic property that defines computation order. Only control-oriented MHCs treat control explicitly at the expense of ignoring data flow or assuming that data follows control. Mixing data and control within the same framework leads to inefficient methods for formal analysis and verification. To address this, the computon model has recently emerged as a category-theoretic MHC that separates data and control and makes control explicit by supporting composition operators characterised as finite colimit constructions. Such constructions allow the formation of sequential, parallel, branching and iterative computing devices. Unfortunately, the computon model is still a generic reference rather than a concrete realisation. In this paper, we provide a variation of it to enable functional computing devices, introduce a new branching operator, discuss how to define synchronous parallelising out of sequencing and asynchronous parallelising, describe concrete operational semantics for computon execution and provide the first implementation of the model. The implementation yields an open-source programming environment that realises the underlying categorical semantics with partial type-level guarantees. This tool is publicly available for building complex computing devices with a high degree of structural correctness by construction.