Implementing Hybrid Semantics: From Functional to Imperative

TL;DR

This paper introduces an imperative version of a hybrid programming language with a simpler, executable semantics, enabling practical hybrid system simulation and tool development while maintaining formal soundness and adequacy.

Contribution

It presents an imperative counterpart to the existing functional hybrid language HybCore, with a simpler, executable semantics closely related to the original, facilitating implementation and simulation.

Findings

Developed an imperative hybrid language with executable semantics.

Established soundness and adequacy of the semantics.

Created a web-based prototype for hybrid program evaluation.

Abstract

Hybrid programs combine digital control with differential equations, and naturally appear in a wide range of application domains, from biology and control theory to real-time software engineering. The entanglement of discrete and continuous behaviour inherent to such programs goes beyond the established computer science foundations, producing challenges related to e.g. infinite iteration and combination of hybrid behaviour with other effects. A systematic treatment of hybridness as a dedicated computational effect has emerged recently. In particular, a generic idealized functional language HybCore with a sound and adequate operational semantics has been proposed. The latter semantics however did not provide hints to implementing HybCore as a runnable language, suitable for hybrid system simulation (e.g. the semantics features rules with uncountably many premises). We introduce an imperative counterpart of HybCore, whose semantics is simpler and runnable, and yet intimately related with the semantics of HybCore at the level of hybrid monads. We then establish a corresponding soundness and adequacy theorem. To attest that the resulting semantics can serve as a firm basis for the implementation of typical tools of programming oriented to the hybrid domain, we present a web-based prototype implementation to evaluate and inspect hybrid programs, in the spirit of GHCi for Haskell and UTop for OCaml. The major asset of our implementation is that it formally follows the operational semantic rules.