A Coinduction Principle for Recursive Data Types Based on Bisimulation

The concept of bisimulation from concurrency theory is used to reason about recursively defined data types. From two strong-extensionality theorems stating that the equality (resp. inequality) relation is maximal among all bisimulations, a proof principle for the final coalgebra of an endofunctor on...

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Bibliographic Details
Published inInformation and computation Vol. 127; no. 2; pp. 186 - 198
Main Author Fiore, Marcelo P.
Format Journal Article Conference Proceeding
LanguageEnglish
Published San Diego, CA Elsevier Inc 15.06.1996
Elsevier
Subjects
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Programming languages
Software
Theoretical computing
Data type
Computational methods
Concurrency
Denotational semantics
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Summary:The concept of bisimulation from concurrency theory is used to reason about recursively defined data types. From two strong-extensionality theorems stating that the equality (resp. inequality) relation is maximal among all bisimulations, a proof principle for the final coalgebra of an endofunctor on a category of data types (resp. domains) is obtained. As an application of the theory developed, an internal full abstraction result (in the sense of S. Abramsky and C.-H. L. Ong [Inform. and Comput.105, 159–267 (1993)] for the canonical model of the untyped call-by-valueλ-calculus is proved. Also, the operational notion of bisimulation and the denotational notion of final semantics are related by means of conditions under which both coincide.
ISSN:0890-5401
1090-2651
DOI:10.1006/inco.1996.0058