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An Algebra-Coalgebra Framework for System Specification

An Algebra-Coalgebra Framework for System Specification
An Algebra-Coalgebra Framework for System Specification
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 unreachable 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.
80-110
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Reichel, H.
8dc80504-8da3-42d9-90b9-4f1f71a7994f
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Reichel, H.
8dc80504-8da3-42d9-90b9-4f1f71a7994f

Cirstea, Corina, (2000) An Algebra-Coalgebra Framework for System Specification Reichel, H. (ed.) At 3rd International Workshop on Coalgebraic Methods in Computer Science. , pp. 80-110.

Record type: Conference or Workshop Item (Paper)

Abstract

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 unreachable 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.

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Published date: 2000
Venue - Dates: 3rd International Workshop on Coalgebraic Methods in Computer Science, 2000-01-01
Organisations: Electronic & Software Systems

Identifiers

Local EPrints ID: 263005
URI: http://eprints.soton.ac.uk/id/eprint/263005
PURE UUID: 7febd6d0-9b1f-4ce6-902f-543c9a67c6f7

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Date deposited: 21 Sep 2006
Last modified: 18 Jul 2017 08:45

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Contributors

Author: Corina Cirstea
Editor: H. Reichel

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