Compiling Laziness Using Projection Types

Strictness analysis is accepted as an important tool for the eecient implementation of lazy functional languages. However, the analyses are usually rst-order and the optimisations that follow may be ad hoc. Using projections to represent static properties of programs is appealing because they naturally describe component-wise demand on data structures and can handle latent demands such as head-strictness. However their extension to higher-order functions is problematic. This paper introduces projection types, a notation for expressing static information about higher-order functions that combines the dual aspects of demand on arguments and behaviour of functional arguments. A strictness analysis using projection types is presented and later extended to an optimisation scheme that translates expressions into a language with explicit closure construction and evaluation operations. An important advantage of this approach is that the optimisations are veriied correctness-preserving transformations. This paper extends and complements the results of Ross Paterson, \Compiling Laziness with Projections" presented at the 3rd Static Analysis Symposium, 1996.