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Integrating Observational and Computational Features in the Specification of State-Based, Dynamical Systems

Published online by Cambridge University Press:  15 April 2002

Corina Cîrstea
Corina Cîrstea*
Affiliation:
Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, U.K.; e-mail: corina.cirstea@comlab.ox.ac.uk
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Abstract

We present an abstract equational framework for the specification of systems having bothobservational and computational features. Our approach is based on a clear separation between the twocategories of features, and uses algebra, respectively coalgebra to formalise them. This yields acoalgebraically-defined notion of observational indistinguishability, as well as an algebraically-definednotion of reachability under computations. The relationship between the computations yielding new systemstates and the observations that can be made about these states is specified using liftings of thecoalgebraic 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 theassociated notions of satisfaction abstracting away observationally indistinguishable, respectivelyunreachable states, and with the resulting prooftechniques employing coinduction, respectively induction.

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