Lazy evaluation and delimited control

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 stract machine definition which, like the calculus, goes "under lambdas." We prove that machine evaluation is equivalent to standard-order evaluation. raditional 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. Categories and Subject Descriptors D.3.1 [Software]: Programming Languages--Forma...

• Type: Conference
• Year: 2009
• Where: POPL
• Authors: Ronald Garcia, Andrew Lumsdaine, Amr Sabry
• Keywords: Call-by-need Lambda Calculus, Delimited Control Operations, Lambda Calculus, POPL 2009, Programming Languages