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Induce-statements and induce-expressions: Constructs for inductive programming

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Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 761))

Abstract

A for-loop is somewhat similar to an inductive argument. Just as the truth of a proposition P(n+1) depends on the truth of P(n), the correctness of iteration n+1 of a for-loop depends on iteration n having been completed correctly.

This paper presents the induce-construct, a new programming construct based on the form of inductive arguments. It is more expressive than the for-loop yet less expressive than the while-loop. Like the for-loop, it is always terminating. Unlike the for-loop, it allows the convenient and concise expression of many algorithms. The for-loop traverses a set of consecutive natural numbers, the induce-construct generalizes to other data types.

The induce-construct is presented in two forms, one for imperative languages and one for functional languages. The expressive power of languages in which this is the only recursion construct is greater than primitive recursion, namely it is the multiply recursive functions in the first order case and the set of functions expressible in Gödel's system T in the general case.

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Authors and Affiliations

  1. Department of Computer Science, University of Toronto, Canada

    Theodore S. Norvell

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  1. Theodore S. Norvell
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Rudrapatna K. Shyamasundar

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© 1993 Springer-Verlag Berlin Heidelberg

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Norvell, T.S. (1993). Induce-statements and induce-expressions: Constructs for inductive programming. In: Shyamasundar, R.K. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1993. Lecture Notes in Computer Science, vol 761. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57529-4_62

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  • DOI: https://doi.org/10.1007/3-540-57529-4_62

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57529-0

  • Online ISBN: 978-3-540-48211-6

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