The worker/wrapper transformation is a general technique for improving the performance of recursive programs by changing their types. The previous formalisation (Gill & Hutton, 2009) was based upon a simple fixed point semantics of recursion. In this article we develop a more structured approach, based upon initial algebra semantics. In particular, we show how the worker/wrapper transformation can be applied to programs defined using the structured pattern of recursion captured by fold operators, and illustrate our new technique with a number of examples.

this paper

Modern multi-paradigm declarative languages integrate features from functional, logic, and concurrent programming. In this work, we consider the adaptation of the logic programming transformation based on the introduction of difference-lists to an integrated setting. Unfortunately, the use of difference-lists is impractical due to the absence of non-strict equality in lazy (call-by-name) languages. Despite all, we have developed a novel, stepwise transformation which achieves a similar effect over functional logic programs. We also show a simple and practical approach to incorporate the optimization into a real compiler. Finally, we have conducted a number of experiments which show the practicality of our proposal.

We introduce a new transformation method to eliminate intermediate data structures occurring in functional programs due to repeated list concatenations and other data manipulations (additionally exemplified with list reversal and mapping of functions over lists). The general idea is to uniformly abstract from data constructors and manipulating operations by means of rank-2 polymorphic combinators that exploit algebraic properties of these operations to provide an optimized implementation. The correctness of transformations is proved by using the free theorems derivable from parametric polymorphic types.

We describe a transformation which takes a higher-order program, and produces an equivalent first-order program. Unlike Reynoldsstyle defunctionalisation, it does not introduce any new data types, and the results are more amenable to subsequent analysis operations. We can use our method to improve the results of existing analysis operations, including strictness analysis, pattern-match safety and termination checking. Our transformation is implemented, and works on a Core language to which Haskell programs can be reduced. Our method cannot always succeed in removing all functional values, but in practice is remarkably successful. D.3 [Software]: Program-

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

Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS

Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS

We implement statically-typed multi-holed contexts in OCaml using an underlying algebraic datatype augmented with phantom types. Existing approaches require dynamic checks or more complex type systems. In order to support concatenation we use two type parameters to represent the number of holes in a context as the difference between two Peano numbers. In order to support plugging a context with contexts of different arity we introduce a datatype of lists of contexts of length n with a total of m holes. Further, we extend our representation to allow holes to be marked with additional type information. As an example, we use these marks to implement statically-typed multi-holed XHTML contexts. We take advantage of Garrigue’s relaxed value restriction.

The worker/wrapper transformation is a general technique for improving the performance of recursive programs by changing their types. The previous formalisation (Gill & Hutton, 2009) was based upon a simple fixed point semantics of recursion. In this article we develop a more structured approach, based upon initial algebra semantics. In particular, we show how the worker/wrapper transformation can be applied to programs defined using the structured pattern of recursion captured by fold operators, and illustrate our new technique with a number of examples.