Context-free languages via coalgebraic trace semantics

  • Authors:

  • Ichiro Hasuo;Bart Jacobs

  • Affiliations:

  • Institute for Computing and Information Sciences, Radboud University Nijmegen, Nijmegen, The Netherlands;Institute for Computing and Information Sciences, Radboud University Nijmegen, Nijmegen, The Netherlands

  • Venue:
  • CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
  • Year:
  • 2005

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Abstract

We show that, for functors with suitable mild restrictions, the initial algebra in the category of sets and functions gives rise to the final coalgebra in the (Kleisli) category of sets and relations. The finality principle thus obtained leads to the finite trace semantics of non-deterministic systems, which extends the trace semantics for coalgebras previously introduced by the second author. We demonstrate the use of our technical result by giving the first coalgebraic account on context-free grammars, where we obtain generated context-free languages via the finite trace semantics. Additionally, the constructions of both finite and possibly infinite parse trees are shown to be monads. Hence our extension of the application domain of coalgebras identifies several new mathematical constructions and structures.