Abstract: We introduce a generic framework to systematically investigate the features of a given computational paradigm and its possible extensions. Our motivating examples are probabilistic and hybrid programming, two recent paradigms that combine atypical primitive operations – e.g. systems of differential equations, Bernoulli trials, wait calls – with classical program constructs. By applying our framework to these two cases we list all binary program operations they possess, and show precisely when and if important axioms, such as commutativity and idempotency, hold. We also examine the possibility of incorporating notions of failure and non-determinism: we show that it is possible to combine hybrid computations with non-deterministic ones via a suitable distributive law, and that there is no monad structure on PD (the composition of the powerset functor P with the finitely supported distribution functor D) whatsoever.

Bio: Renato Neves is a postdoctoral researcher at INESC-TEC and University of Minho. He obtained recently a PhD degree on the topic of hybrid systems, programming languages, and coalgebras. Currently, he is interested on reasoning tools, syntax, and semantics for cyber-physical systems, a class of devices that intertwines different aspects of analysis, control theory, and computer science. He has also started working on models of quantum computation.