# Initial algebra and final coalgebra semantics for concurrency

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## Abstract

The aim of this paper is to relate *initial algebra semantics* and *final coalgebra semantics*. It is shown how these two approaches to the semantics of programming languages are each others dual, and some conditions are given under which they coincide. More precisely, it is shown how to derive initial semantics from final semantics, using the initiality and finality to ensure their equality. Moreover, many facts about *congruences* (on algebras) and (generalized) *bisimulations* (on coalgebras) are shown to be dual as well.

## Keywords

Algebra coalgebra initiality finality Σ-algebra labelled transition system congruence bisimulation induction coinduction## Preview

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© Springer-Verlag Berlin Heidelberg 1994