Call-by-need is clairvoyant call-by-value

Abstract

Call-by-need evaluation, also known as lazy evaluation, provides two key benefits: compositional programming and infinite data. The standard semantics for laziness is Launchbury's natural semantics [1993], which uses a heap to memoise the results of delayed evaluations. However, the stateful nature of this heap greatly complicates reasoning about the operational behaviour of lazy programs. In this article, we propose an alternative semantics for laziness, clairvoyant evaluation, that replaces the state effect with nondeterminism, and prove this semantics equivalent in a strong sense to the standard semantics. We show how this new semantics greatly simplifies operational reasoning, admitting much simpler proofs of a number of results from the literature, and how it leads to the first denotational cost semantics for lazy evaluation.