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Using Structural Recursion for Corecursion

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Types for Proofs and Programs (TYPES 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5497))

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Abstract

We propose a (limited) solution to the problem of constructing stream values defined by recursive equations that do not respect the guardedness condition. The guardedness condition is imposed on definitions of corecursive functions in Coq, AGDA, and other higher-order proof assistants. In this paper, we concentrate in particular on those non-guarded equations where recursive calls appear under functions. We use a correspondence between streams and functions over natural numbers to show that some classes of non-guarded definitions can be modelled through the encoding as structural recursive functions. In practice, this work extends the class of stream values that can be defined in a constructive type theory-based theorem prover with inductive and coinductive types, structural recursion and guarded corecursion.

Work is partially supported by the INRIA CORDI post-doctoral program, the ANR project “A3Pat” ANR-05-BLAN-0146 and by EPSRC postdoctoral grant EP/F044046/1.

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Author information

Authors and Affiliations

  1. INRIA Sophia Antipolis, France

    Yves Bertot

  2. School of Computer Science, University of St Andrews, UK

    Ekaterina Komendantskaya

Authors
  1. Yves Bertot
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  2. Ekaterina Komendantskaya
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università di Torino, Corso Svizzera 185, 10149, Torino, Italy

    Stefano Berardi  & Ugo de’Liguoro  & 

  2. Dipartimento di Informatica, Università di Torino, Corso Svizzera, 185, I-10149, Torino, Italy

    Ferruccio Damiani

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Bertot, Y., Komendantskaya, E. (2009). Using Structural Recursion for Corecursion. In: Berardi, S., Damiani, F., de’Liguoro, U. (eds) Types for Proofs and Programs. TYPES 2008. Lecture Notes in Computer Science, vol 5497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02444-3_14

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  • DOI: https://doi.org/10.1007/978-3-642-02444-3_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02443-6

  • Online ISBN: 978-3-642-02444-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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