Fusion, one of the most useful transformation tactics for deriving efficient programs, is the process whereby separate pieces of programs are fused into a single one, leading to an efficient program with no intermediate data structures produced. In this paper, we report our on-going investigation on the design and implementation of an automatic transformation system HYLO which performs fusion transformation in a more systematic and more general way than any other systems. The distinguished point of our system is its calculational feature based on simple application of transformation laws rather than traditional search-based transformation. Keywords Program Transformation, Fusion, Constructive Algorithmics, Bird-Meertens Formalisms 1 INTRODUCTION Program transformation has been advocated as the linchpin of a programming paradigm in which the derivation of efficient programs from naive specification of problems is a formal and mechanically supported process [PP93]. It does not attempt ...

Tupling is a well-known transformation tactic to obtain new efficient recursive functions by grouping some recursive functions into a tuple. It may be applied to eliminate multiple traversals over the common data structure. The major difficulty in tupling transformation is to find what functions are to be tupled and how to transform the tupled function into an efficient one. Previous approaches to tupling transformation are essentially based on fold/unfold transformation. Though general, they suffer from the high cost of keeping track of function calls to avoid infinite unfolding, which prevents them from being used in a compiler. To remedy this situation, we propose a new method to expose recursive structures in recursive definitions and show how this structural information can be explored for calculating out efficient programs by means of tupling. Our new tupling calculation algorithm can eliminate most of multiple data traversals and is easy to be implemented. 1 Introduction Tupli...

This paper presents an automatic deforestation system, stream fusion, based on equational transformations, that fuses a wider range of functions than existing short-cut fusion systems. In particular, stream fusion is able to fuse zips, left folds and functions over nested lists, including list comprehensions. A distinguishing feature of the framework is its simplicity: by transforming list functions to expose their structure, intermediate values are eliminated by general purpose compiler optimisations. We have reimplemented the Haskell standard List library on top of our framework, providing stream fusion for Haskell lists. By allowing a wider range of functions to fuse, we see an increase in the number of occurrences of fusion in typical Haskell programs. We present benchmarks documenting time and space improvements.

Graph algorithms expressed in functional languages often suffer from their inherited imperative, state-based style. In particular, this impedes formal program manipulation. We show how to model persistent graphs in functional languages by graph constructors. This provides a decompositional view of graphs which is very close to that of data types and leads to a "more functional" formulation of graph algorithms. Graph constructors enable the definition of general fold operations for graphs. We present a promotion theorem for one of these folds that allows program fusion and the elimination of intermediate results. Fusion is not restricted to the elimination of tree-like structures, and we prove another theorem that facilitates the elimination of intermediate graphs. We describe an ML-implementation of persistent graphs which efficiently supports the presented fold operators. For example, depth-first-search expressed by a fold over a functional graph has the same complexity as the corresp...

Deforestation optimises a functional program by transforming it into another one that does not create certain intermediate data structures. Short cut deforestation is a deforestation method which is based on a single, local transformation rule. In return, short cut deforestation expects both producer and consumer of the intermediate structure in a certain form. Warm fusion was proposed to automatically transform functions into this form. Unfortunately, it is costly and hard to implement. Starting from the fact that short cut deforestation is based on a parametricity theorem of the second-order typed λ-calculus, we show how the required form of a list producer can be derived through the use of type inference. Typability for the second-order typed λ-calculus is undecidable. However, we present a linear-time algorithm that solves a partial type inference problem and that, together with controlled inlining and polymorphic type instantiation, suffices for deforestation. The resulting new sho...

Stratego is a domain-specic language for the specication of program transformation systems. The design of Stratego is based on the paradigm of rewriting strategies: user-denable programs in a little language of strategy operators determine where and in what order transformation rules are (automatically) applied to a program. The separation of rules and strategies supports modularity of specications. Stratego also provides generic features for specication of program traversals. In this paper we present a case study of Stratego as applied to a non-trivial problem in program transformation. We demonstrate the use of Stratego in eliminating intermediate data structures from (also known as deforesting) functional programs via the warm fusion algorithm of Launchbury and Sheard. This algorithm has been specied in Stratego and embedded in a fully automatic transformation system for kernel Haskell. The entire system consists of about 2600 lines of specication code, which bre...

Many functional programs with accumulating parameters are contained in the class of macro tree transducers. We present a program transformation technique that can be used to solve the efficiency problems due to creation and consumption of intermediate data structures in compositions of such functions, where classical deforestation techniques fail. In order to do so, given two macro tree transducers under appropriate restrictions, we construct a single macro tree transducer that implements the composition of the two original ones. The imposed restrictions are more liberal than those in the literature on macro tree transducer composition, thus generalising previous results.

this paper, we shall formulate accumulations as higher order catamorphisms , and propose several general transformation rules for calculating accumulations (i.e., finding and manipulating accumulations) by calculation-based (rather than a search-based) program transformation methods. Some examples are given for illustration.

This paper presents an attempt to characterize synchronous stream functions within the framework of co-iteration and to use this characterization in building a compiler for (higher order and recursive) synchronous data-flow programs. First length-preserving functions are considered and we show that streams equipped with such functions form a Cartesian-closed category. Then this point of view is extended toward non length-preserving ones and we stress the use of "empty" values in handling this case. Finally, the implementation we did of this material in a synchronous stream package built on top of an ML-like language is briefly described.

Software engineering has to reconcile modularity with e- ciency. One way to grapple with this dilemma is to automatically transform a modular-specied program into an ecient-implementable one.