Invariants, Bisimulations and the Correctness of Coalgebraic Refinements (1997)
| Venue: | Techn. Rep. CSI-R9704, Comput. Sci. Inst., Univ. of Nijmegen |
| Citations: | 9 - 4 self |
BibTeX
@INPROCEEDINGS{Jacobs97invariants,bisimulations,
author = {Bart Jacobs},
title = {Invariants, Bisimulations and the Correctness of Coalgebraic Refinements},
booktitle = {Techn. Rep. CSI-R9704, Comput. Sci. Inst., Univ. of Nijmegen},
year = {1997},
pages = {276--291}
}
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Abstract
. Coalgebraic specifications are used to formally describe the behaviour of classes in object-oriented languages. In this paper, a general notion of refinement between two such coalgebraic specifications is defined, capturing the idea that one "concrete" class specification realises the behaviour of the other, "abstract" class specification. Two (complete) proof-techniques are given to establish such refinements: one involving an invariant (a predicate that is closed under transitions) on the concrete class, and one involving a bisimulation (a relation that is closed under transitions) between the concrete and the abstract class. The latter can only be used if the abstract class is what we call totally specified. Parts of the underlying theory of invariants and bisimulations in a coalgebraic setting are included, involving least and greatest invariants and connections between invariants and bisimulations. Also, the proof-principles are illustrated in examples (which are fully formalise...
