The worker/wrapper transformation

Abstract

The worker/wrapper transformation is a technique for changing the type of a computation, usually with the aim of improving its performance. It has been used by compiler writers for many years, but the technique is little known in the wider functional programming community, and has never been described precisely. In this article we explain, formalise and explore the generality of the worker/wrapper transformation. We also provide a systematic recipe for its use as an equational reasoning technique for improving the performance of programs, and illustrate the power of this recipe using a range of examples.

ChalkBoard: Mapping Functions to Polygons

“…-ChalkBoard is intended as a system for constructing complex images, consisting of perhaps tens of thousands of individual components. The functional representation precludes this being efficiently rendered, though techniques like the worker/wrapper transformation [5] could be used to translate an explicit function into something like our abstract representation.…”

Work it, wrap it, fix it, fold it

“…The original formalisation (Gill & Hutton 2009) was based upon a least-fixed-point semantics of recursive programs. Within this setting the worker/wrapper transformation 114 N. Sculthorpe and G. Hutton was explained and formalised, proved correct, and a range of programming applications presented.…”

“…The paper is aimed at readers who are familiar with the basics of a least-fixed-point semantics (Schmidt 1986), initial-algebra semantics (Bird & de Moor 1997), and the worker/ wrapper transformation (Gill & Hutton 2009;Hutton et al 2010), but all necessary concepts and results are reviewed. A mechanical verification of the proofs in Agda is available as online supplementary material at dx.doi.org/10.1017/S0956796814000045, along with an extended version of this paper that includes a series of worked examples and all proofs.…”

“…For example, the technique has played a key role in the Glasgow Haskell Compiler since its inception more than 20 years ago, to replace the use of boxed data structures by more efficient unboxed data structures (Peyton Jones & Launchbury 1991). However, it is only recently -in two articles that lay the foundations for the present work (Gill & Hutton 2009;Hutton et al 2010) -that the worker/wrapper transformation has been formalised, and considered as a general approach to program optimisation.The original formalisation (Gill & Hutton 2009) was based upon a least-fixed-point semantics of recursive programs. Within this setting the worker/wrapper transformation 114 N. Sculthorpe and G. Hutton was explained and formalised, proved correct, and a range of programming applications presented.…”

“…The purpose of this new paper is to show how this can be achieved, and to explore the benefits that result. More precisely, the paper makes the following contributions:• We show how the least-fixed-point and initial-algebra approaches to the worker/ wrapper transformation can be generalised in a uniform manner by combining their different sets of correctness conditions (Sections 3 and 5).• We identify necessary conditions for the correctness of the worker/wrapper technique, in addition to the existing sufficient conditions, thereby ensuring that the theory is as widely applicable as possible 1 (Sections 3 and 5).• We use our new theory to develop a specialised worker/wrapper theory for folds in CPO that eliminates all unnecessary strictness conditions (Section 6).The paper is aimed at readers who are familiar with the basics of a least-fixed-point semantics (Schmidt 1986), initial-algebra semantics (Bird & de Moor 1997), and the worker/ wrapper transformation (Gill & Hutton 2009;Hutton et al 2010), but all necessary concepts and results are reviewed. A mechanical verification of the proofs in Agda is available as online supplementary material at dx.doi.org/10.1017/S0956796814000045, along with an extended version of this paper that includes a series of worked examples and all proofs.…”