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arXiv · 1003.5197

Lazy Evaluation and Delimited Control

Ronald Garcia·Andrew Lumsdaine·Amr Sabry
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Abstract

The call-by-need lambda calculus provides an equational framework for reasoning syntactically about lazy evaluation. This paper examines its operational characteristics. By a series of reasoning steps, we systematically unpack the standard-order reduction relation of the calculus and discover a novel abstract machine definition which, like the calculus, goes "under lambdas." We prove that machine evaluation is equivalent to standard-order evaluation. Unlike traditional abstract machines, delimited control plays a significant role in the machine's behavior. In particular, the machine replaces the manipulation of a heap using store-based effects with disciplined management of the evaluation stack using control-based effects. In short, state is replaced with control. To further articulate this observation, we present a simulation of call-by-need in a call-by-value language using delimited control operations.

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Ronald Garcia, Andrew Lumsdaine, Amr Sabry. 2010-03-26. Lazy Evaluation and Delimited Control. https://doi.org/10.2168/lmcs-6(3:1)2010

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