  The Refinement Calculus of Reactive Systems (RCRS) is a compositional formal
framework for modeling and reasoning about reactive systems. RCRS provides a
language which allows to describe atomic components as symbolic transition
systems or QLTL formulas, and composite components formed using three primitive
composition operators: serial, parallel, and feedback. The semantics of the
language is given in terms of monotonic property transformers, an extension to
reactive systems of monotonic predicate transformers, which have been used to
give compositional semantics to sequential programs. RCRS allows to specify
both safety and liveness properties. It also allows to model input-output
systems which are both non-deterministic and non-input-receptive (i.e., which
may reject some inputs at some points in time), and can thus be seen as a
behavioral type system. RCRS provides a set of techniques for symbolic
computer-aided reasoning, including compositional static analysis and
verification. RCRS comes with a publicly available implementation which
includes a complete formalization of the RCRS theory in the Isabelle proof
assistant.
