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What is an efficient implementation of the λ-calculus?

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Functional Programming Languages and Computer Architecture (FPCA 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 523))

Abstract

We propose to measure the efficiency of any implementation of the λ-calculus as a function of a new parameter v, that is itself a function of any λ-expression.

Complexity is expressed here as a function of v just as runtime is expressed as a function of the input size n in ordinary analysis of algorithms. This enables implementations to be compared for worst case efficiency.

We argue that any implementation must have complexity Ω(v), i.e. a linear lower bound. Furthermore, we show that implementations based upon Turner Combinators or Hughes Super-combinators have complexities 2Ω(v), i.e. an exponential lower bound.

It is open whether any implementation of polynomial complexity, v O(1), exists, although some implementations have been implicitly claimed to have this complexity.

This research was partially carried out, while visiting Dartmouth College, New Hampshire

This research was partially carried out, while supported by the Danish Natural Science Research Council (grant No. 11-7991) and while supported by the ESPRIT II Basic Research Actions Program of the EC under contract No. 3075 (project ALCOM).

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Authors and Affiliations

  1. Department of Computer Science, Aarhus University, Denmark

    Gudmund S. Frandsen

  2. Department of Computer Science, University of Minnesota, USA

    Carl Sturtivant

Authors
  1. Gudmund S. Frandsen
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  2. Carl Sturtivant
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John Hughes

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© 1991 Springer-Verlag Berlin Heidelberg

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Frandsen, G.S., Sturtivant, C. (1991). What is an efficient implementation of the λ-calculus?. In: Hughes, J. (eds) Functional Programming Languages and Computer Architecture. FPCA 1991. Lecture Notes in Computer Science, vol 523. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3540543961_14

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  • DOI: https://doi.org/10.1007/3540543961_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54396-1

  • Online ISBN: 978-3-540-47599-6

  • eBook Packages: Springer Book Archive

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