An Algebra-Coalgebra Framework for System Specification
Corina Ĉırstea · Electronic Notes in Theoretical Computer Science · 2000
We present an abstract equational framework for the specification of systems having both observational and computational features. Our approach is based on a clear separation between the two categories of features, and uses algebra, respectively coalgebra to formalise them. This yields a coalgebraically defined notion of observational indistinguishability, as well as an algebraically defined notion of reachability under computations. The relationship between the computations yielding new system states and the observations that can be made about these states is specified using liftings of the coalgebraic structure of state spaces to a coalgebraic structure on computations over these state spaces. Also, correctness properties of system behaviour are formalised using equational sentences, with the associated notions of satisfaction abstracting away observationally indistinguishable, respectively un-reachable states, and with the resulting proof techniques employing coinduction, respectively induction. Suitably instantiating the approach yields a formalism for the specification and verification of objects.