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Proof principles for datatypes with iterated recursion

  • Ulrich Hensel
  • Bart Jacobs
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1290)

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Ulrich Hensel
    • 1
  • Bart Jacobs
    • 2
  1. 1.Inst. Theor. Inf., TU DresdenDresdenGermany
  2. 2.Dep. Comp. Sci.Univ. NijmegenGL NijmegenThe Netherlands

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