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. 1

Streams, or infinite lists, have many applications in functional programming, and are naturally defined using recursive equations. But how do we ensure that such equations make sense, i.e. that they actually produce well-defined streams? In this article we present a new approach to this problem, based upon the topological notion of contractive functions on streams. In particular, we give a sound and complete representation theorem for contractive functions on streams, illustrate the use of this theorem as a practical means to produce well-defined streams, and show how the efficiency of the resulting definitions can be improved using another representation of contractive functions.

Streams, or infinite lists, have many applications in functional programming, and are naturally defined using recursive equations. But how do we ensure that such equations make sense, i.e. that they actually produce well-defined streams? In this article we present a new approach to this problem, based upon the topological notion of contractive functions on streams. In particular, we give a sound and complete representation theorem for contractive functions on streams, illustrate the use of this theorem as a practical means to produce well-defined streams, and show how the efficiency of the resulting definitions can be improved using another representation of contractive functions.