Exercises in Coalgebraic Specification

  • Authors:
  • Bart Jacobs

  • Affiliations:
  • -

  • Venue:
  • Revised Lectures from the International Summer School and Workshop on Algebraic and Coalgebraic Methods in the Mathematics of Program Construction
  • Year:
  • 2000

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Abstract

An introduction to coalgebraic specification is presented via examples. A coalgebraic specification describes a collection of coalgebras satisfying certain assertions. It is thus an axiomatic description of a particular class of mathematical structures. Such specifications are especially suitable for state-based dynamical systems in general, and for classes in object-oriented programming languages in particular. This chapter will gradually introduce the notions of bisimilarity, invariance, component classes, temporal logic and refinement in a coalgebraic setting. Besides the running example of the coalgebraic specification of (possibly infinite) binary trees, a specification of Peterson's mutual exclusion algorithm is elaborated in detail.