Circular Coinduction: A Proof Theoretical Foundation

  • Grigore Roşu
  • Dorel Lucanu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5728)


Several algorithmic variants of circular coinduction have been proposed and implemented during the last decade, but a proof theoretical foundation of circular coinduction in its full generality is still missing. This paper gives a three-rule proof system that can be used to formally derive circular coinductive proofs. This three-rule system is proved behaviorally sound and is exemplified by proving several properties of infinite streams. Algorithmic variants of circular coinduction now become heuristics to search for proof derivations using the three rules.


Proof System Proof Tree Entailment Relation Equational Reasoning Proof Task 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Grigore Roşu
    • 1
  • Dorel Lucanu
    • 2
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUSA
  2. 2.Faculty of Computer ScienceAlexandru Ioan Cuza UniversityIaşiRomania

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