  We give a rigorous framework for the interaction of physical computing
devices with abstract computation. Device and program are mediated by the
non-logical 'representation relation'; we give the conditions under which
representation and device theory give rise to commuting diagrams between
logical and physical domains, and the conditions for computation to occur. We
give the interface of this new framework with currently existing formal
methods, showing in particular its close relationship to refinement theory, and
the implications for questions of meaning and reference in theoretical computer
science. The case of hybrid computing is considered in detail, addressing in
particular the example of an internet-mediated 'social machine', and the
abstraction/representation framework used to provide a formal distinction
between heterotic and hybrid computing. This forms the basis for future use of
the framework in formal treatments of nonstandard physical computers.
