  This paper presents an abstraction of Hoare logic to traced symmetric
monoidal categories, a very general framework for the theory of systems. Our
abstraction is based on a traced monoidal functor from an arbitrary traced
monoidal category into the category of pre-orders and monotone relations. We
give several examples of how our theory generalises usual Hoare logics (partial
correctness of while programs, partial correctness of pointer programs), and
provide some case studies on how it can be used to develop new Hoare logics
(run-time analysis of while programs and stream circuits).
