Coalgebras for Binary Methods: Properties of Bisimulations and Invariants

Hendrik Tews

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 35, Issue: 1, page 83-111
  • ISSN: 0988-3754

Abstract

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Coalgebras for endofunctors 𝒞 → 𝒞 can be used to model classes of object-oriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors 𝒞 o p × 𝒞 → 𝒞 . This extension allows the incorporation of binary methods into coalgebraic class specifications. The paper also discusses how to define bisimulation and invariants for coalgebras of extended polynomial functors and proves many standard results.

How to cite

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Tews, Hendrik. "Coalgebras for Binary Methods: Properties of Bisimulations and Invariants." RAIRO - Theoretical Informatics and Applications 35.1 (2010): 83-111. <http://eudml.org/doc/222043>.

@article{Tews2010,
abstract = { Coalgebras for endofunctors $\{\mathcal C\}\rightarrow\{\mathcal C\}$ can be used to model classes of object-oriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors$\{\mathcal C\}^\{op\} \times \{\mathcal C\}\rightarrow\{\mathcal C\}$. This extension allows the incorporation of binary methods into coalgebraic class specifications. The paper also discusses how to define bisimulation and invariants for coalgebras of extended polynomial functors and proves many standard results. },
author = {Tews, Hendrik},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Binary method; coalgebra; bisimulation; invariant; object-orientation.; coalgebras for endofunctors; object-oriented languages},
language = {eng},
month = {3},
number = {1},
pages = {83-111},
publisher = {EDP Sciences},
title = {Coalgebras for Binary Methods: Properties of Bisimulations and Invariants},
url = {http://eudml.org/doc/222043},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Tews, Hendrik
TI - Coalgebras for Binary Methods: Properties of Bisimulations and Invariants
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 1
SP - 83
EP - 111
AB - Coalgebras for endofunctors ${\mathcal C}\rightarrow{\mathcal C}$ can be used to model classes of object-oriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors${\mathcal C}^{op} \times {\mathcal C}\rightarrow{\mathcal C}$. This extension allows the incorporation of binary methods into coalgebraic class specifications. The paper also discusses how to define bisimulation and invariants for coalgebras of extended polynomial functors and proves many standard results.
LA - eng
KW - Binary method; coalgebra; bisimulation; invariant; object-orientation.; coalgebras for endofunctors; object-oriented languages
UR - http://eudml.org/doc/222043
ER -

References

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