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Monotone recursive definition of predicates and its realizability interpretation

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Theoretical Aspects of Computer Software (TACS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 526))

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Abstract

The main aim of the paper is to construct a logic by which we can formalize properties of programs. Inductive definition or recursive definition plays a very important role for this purpose. Inductive definition has been studied for untyped theories, predicative typed theories and impredicative typed theories. Monotone recursive definition in an untyped theory is studied in this paper. The main point is realizability interpretation of monotone recursive definition.

Untyped predicative theory TID 0 and TID 1 are presented, which have monotone recursive definition of predicates. TID 1 has full monotone recursive definition and TID 0 has only restricted monotone recursive definition. q-realizability interpretation of TID 0 and TID 1 is defined. It is proved that the realizability interpretation of TID 0 is sound and that the realizability interpretation of TID 1 is not sound, though TID 1 and its interpretation seem very natural.

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Author information

Authors and Affiliations

  1. Research Institute of Electrical Communication, Tohoku University, 980, Sendai, Japan

    Makoto Tatsuta

Authors
  1. Makoto Tatsuta
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Takayasu Ito Albert R. Meyer

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© 1991 Springer-Verlag Berlin Heidelberg

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Tatsuta, M. (1991). Monotone recursive definition of predicates and its realizability interpretation. In: Ito, T., Meyer, A.R. (eds) Theoretical Aspects of Computer Software. TACS 1991. Lecture Notes in Computer Science, vol 526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54415-1_40

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  • DOI: https://doi.org/10.1007/3-540-54415-1_40

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54415-9

  • Online ISBN: 978-3-540-47617-7

  • eBook Packages: Springer Book Archive

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