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Issue Theoret. Informatics Appl.
Volume 35, Number 1, January-February 2001
Coalgebraic Methods in Computer Science
Page(s) 83 - 111
DOI 10.1051/ita:2001110

DOI: 10.1051/ita:2001110


Theoret. Informatics Appl. 35, 83-111 (2001)

Coalgebras for Binary Methods: Properties of Bisimulations and Invariants

Hendrik Tews

Institut für Theoretische Informatik, TU Dresden, D-01062 Dresden, Germany;
    e-mail: tews@tcs.inf.tu-dresden.de

(Accepted March 9, 2001.)

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.


AMS Subject: 03E20, 03G30, 68Q55, 68Q65

Key words: Binary method -- coalgebra -- bisimulation -- invariant -- object-orientation.


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