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Derivation of algorithms by introduction of generation functions

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Abstract

A specification is a mathematical description of the intent we want a program to behave, while an algorithm is a formal description of a program that satisfies the specification. When we want to write an algorithm by defining data domains and functions over these domains, it is common to use recursion equations for function definitions. However, recursion equations lack imaginability such as existential quantifiers in predicate calculus. In this paper we show how executable algorithms are derived from specifications written in ordinary set-theoretic formulas, and illustrate it by deriving several kinds of sorting algorithms as well as a graph algorithm.

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Author information

Authors and Affiliations

  1. Information Engineering Course, Graduate School, Division of Engineering, The University of Tokyo, Tokyo, Japan

    Liangwei Xu

  2. Educational Computer Centre, The University of Tokyo, Tokyo, Japan

    Hideya Iwasaki

  3. Department of Mathematical Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan

    Masato Takeichi

Authors
  1. Liangwei Xu
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  2. Hideya Iwasaki
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  3. Masato Takeichi
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Additional information

Liangwei Xu: He is currently a graduate student of Doctor Course of Division of Engineering, The University of Tokyo. He received the B. E. degree from Shanghai Jiao Tong University (P. R. China) in 1982 and the M. E. degree from The University of Tokyo in 1992. His research interests are computational model, program transformation and derivation methodology.

Hideya Iwasaki, Dr. Eng.: He is an Associate Professor of Educational Computer Center, The University of Tokyo. He received the M. E. degree in 1985, the Dr. Eng. degree in 1988 from The University of Tokyo. He has been working on list processing languages, functional languages, and parallel processing.

Masato Takeichi, Dr. Eng.: He is a Professor of Department of Mathematical Engineering, Faculty of Engineering, The University of Tokyo. His research interests are functional programming, language implementation and constructive algorithmics.

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Xu, L., Iwasaki, H. & Takeichi, M. Derivation of algorithms by introduction of generation functions. New Gener Comput 13, 75–98 (1994). https://doi.org/10.1007/BF03038309

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  • DOI: https://doi.org/10.1007/BF03038309

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