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A new approach to abstract data types II computation on ADTs as ordinary computation

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Computer Science Logic (CSL 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 626))

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Abstract

A notion of abstract computational procedure is introduced here which meets the criteria for computation over ADTs, for the general theory of such presented in Part I of this paper. This is provided by a form of generalized recursion theory (g.r.t.) which uses schemata for explicit definition, conditional definition and least fixed point (LFP) recursion in partial functions and functionals of type level ≤2 over any appropriate structure. It is shown that each such procedure is preserved under isomorphism and thus determines an abstract procedure over ADTs. The main new feature of the g.r.t. developed here is that abstract computational procedures reduce to computational procedures in the ordinary sense when confined to data structures in a recursion-theoretic interpretation.

Research supported by NSF grant #CCR-8917606. Invited paper for the conference CSL '91, Berne Oct. 7–11, 1991.

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References

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, 94305, Stanford, CA, USA

    Solomon Feferman

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  1. Solomon Feferman
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Egon Börger Gerhard Jäger Hans Kleine Büning Michael M. Richter

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© 1992 Springer-Verlag Berlin Heidelberg

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Feferman, S. (1992). A new approach to abstract data types II computation on ADTs as ordinary computation. In: Börger, E., Jäger, G., Kleine Büning, H., Richter, M.M. (eds) Computer Science Logic. CSL 1991. Lecture Notes in Computer Science, vol 626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023759

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  • DOI: https://doi.org/10.1007/BFb0023759

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55789-0

  • Online ISBN: 978-3-540-47285-8

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