Abstract
The equational theories at the core of most functional programming are variations on the standard lambda calculus. The best known of these is the call-by-value lambda calculus whose core is the value-beta computation rule (λχ.M) V → M[V/χ] where V is restricted to be a value rather than an arbitrary term. This paper investigates the transformational power of this core theory of functional programming. The main result is that the equational theory of the call-by-value lambda calculus cannot speed up (or slow down) programs by more than a constant factor. The corresponding result also holds for call-by-need but we show that it does not hold for call-byname: there are programs for which a single beta reduction can change the program’s asymptotic complexity.
Author’s current address: Galois Connections, Oregon. moran@galcon.com
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Sands, D., Gustavsson, J., Moran, A. (2002). Lambda Calculi and Linear Speedups. In: Mogensen, T.Æ., Schmidt, D.A., Sudborough, I.H. (eds) The Essence of Computation. Lecture Notes in Computer Science, vol 2566. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36377-7_4
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DOI: https://doi.org/10.1007/3-540-36377-7_4
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