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Usage analysis with natural reduction types

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Static Analysis (WSA 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 724))

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Abstract

In a functional program the value of an expression may be required several times. If a usage analysis can determine how many times it will be required, certain optimisations are possible, such as converting lazy parameter passing to call-by-name or call-by-value, compile-time garbage collection and in-place update. This paper presents a method for deducing usage information in the λ-calculus, based on a type logic employing reduction types. A system is presented wherein function type constructors are annotated with expressions over the natural numbers to indicate the usage behaviour of λ-terms. This system is shown to be correct by interpreting the type language over a semi-model of the λ-calculus and demonstrating soundness and completeness. Furthermore, we show how the Curry-Howard interpretation naturally relates such types to relevant logic.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Tasmania, 7001, Hobart, Australia

    David A. Wright

  2. Information Sciences and Eng., University of Canberra, 2616, Canberra, Australia

    Clement A. Baker-Finch

Authors
  1. David A. Wright
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  2. Clement A. Baker-Finch
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Editor information

Patrick Cousot Moreno Falaschi Gilberto Filé Antoine Rauzy

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© 1993 Springer-Verlag Berlin Heidelberg

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Wright, D.A., Baker-Finch, C.A. (1993). Usage analysis with natural reduction types. In: Cousot, P., Falaschi, M., Filé, G., Rauzy, A. (eds) Static Analysis. WSA 1993. Lecture Notes in Computer Science, vol 724. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57264-3_46

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  • DOI: https://doi.org/10.1007/3-540-57264-3_46

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57264-0

  • Online ISBN: 978-3-540-48027-3

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