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Proof principles for datatypes with iterated recursion

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Category Theory and Computer Science (CTCS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1290))

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Abstract

Data types like trees which are finitely branching and of (possibly) infinite depth are described by iterating initial algebras and terminal coalgebras. We study proof principles for such data types in the context of categorical logic, following and extending the approach of [14, 15]. The technical contribution of this paper involves a description of initial algebras and terminal coalgebras in total categories of fibrations for lifted “datafunctors”. These lifted functors are used to formulate our proof principles. We test these principles by proving some elementary results for four kinds of trees (with finite or infinite breadth or depth) using the proof tool Pvs.

This paper was written during a visit of Ulrich Hensel to the Computing Science Institute of the University of Nijmegen.

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Author information

Authors and Affiliations

  1. Inst. Theor. Inf., TU Dresden, D-01062, Dresden, Germany

    Ulrich Hensel

  2. Dep. Comp. Sci., Univ. Nijmegen, P.O. Box 9010, 6500, GL Nijmegen, The Netherlands

    Bart Jacobs

Authors
  1. Ulrich Hensel
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  2. Bart Jacobs
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Editor information

Eugenio Moggi Giuseppe Rosolini

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© 1997 Springer-Verlag Berlin Heidelberg

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Hensel, U., Jacobs, B. (1997). Proof principles for datatypes with iterated recursion. In: Moggi, E., Rosolini, G. (eds) Category Theory and Computer Science. CTCS 1997. Lecture Notes in Computer Science, vol 1290. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0026991

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  • DOI: https://doi.org/10.1007/BFb0026991

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  • Print ISBN: 978-3-540-63455-3

  • Online ISBN: 978-3-540-69552-3

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