An Adequate While-Language for Hybrid Computation

Abstract: Hybrid computation combines discrete and continuous dynamics in the form of an entangled mixture inherently present both in various natural phenomena, and in applications ranging from control theory to microbiology. The emergent behaviours bear signs of both computational and physical processes, and thus present difficulties not only for analysis, but also for describing them adequately in a structural, well-founded way. Here, we introduce a language for hybrid computation, inspired by the fine-grain call-by-value paradigm, and equip it with a denotational and computationally adequate denotational semantics. Our denotational semantics crucially relies on a hybrid monad supporting an (Elgot) iteration operator, we developed elsewhere. As an intermediate step we introduce a more lightweight duration semantics furnished with analogous results and drawing on a new duration monad that we introduce as a lightweight counterpart to the hybrid monad.