  The rather unintuitive nature of quantum theory has led numerous people to
develop sets of (physically motivated) principles that can be used to derive
quantum mechanics from the ground up, in order to better understand where the
structure of quantum systems comes from. From a computer scientist's
perspective we would like to study quantum theory in a way that allows
interesting transformations and compositions of systems and that also includes
infinite-dimensional datatypes. Here we present such a compositional
reconstruction of quantum theory that includes infinite-dimensional systems.
This reconstruction is noteworthy for three reasons: it is only one of a few
that includes no restrictions on the dimension of a system; it allows for both
classical, quantum, and mixed systems; and it makes no a priori reference to
the structure of the real (or complex) numbers. This last point is possible
because we frame our results in the language of category theory, specifically
the categorical framework of effectus theory.
