Lambda calculi and linear speedups

Authors:
David Sands;Jörgen Gustavsson;Andrew Moran
Affiliations:
Department of Computing Science, Chalmers University of Technology and Göteborg University, Sweden;Department of Computing Science, Chalmers University of Technology and Göteborg University, Sweden;Galois Connections, Oregon
Venue:
The essence of computation
Year:
2002

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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 (λx.M) V → M [V/x] 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.