Lazy evaluation and delimited control

  • Authors:

  • Ronald Garcia;Andrew Lumsdaine;Amr Sabry

  • Affiliations:

  • Rice University, Houston, TX, USA;Indiana University, Bloomington, IN, USA;Indiana University, Bloomington, IN, USA

  • Venue:
  • Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
  • Year:
  • 2009

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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.