  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.
