ABSTRACT. If you want to program a parallel computer, a purely functional language like Haskell is a promising starting point. Since the language is pure, it is by-default safe for parallel evaluation, whereas imperative languages are by-default unsafe. But that doesn’t make it easy! Indeed it has proved quite difficult to get robust, scalable performance increases through parallel functional programming, especially as the number of processors increases. A particularly promising and well-studied approach to employing large numbers of processors is data parallelism. Blelloch’s pioneering work on NESL showed that it was possible to combine a rather flexible programming model (nested data parallelism) with a fast, scalable execution model (flat data parallelism). In this paper we describe Data Parallel Haskell, which embodies nested data parallelism in a modern, general-purpose language, implemented in a state-of-the-art compiler, GHC. We focus particularly on the vectorisation transformation, which transforms nested to flat data parallelism. 1

Abstract. Haskell is a functional language, with features such as higher order functions and lazy evaluation, which allow succinct programs. These high-level features present many challenges for optimising compilers. We report practical experiments using novel variants of supercompilation, with special attention to let bindings and the generalisation technique. 1

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User-defined data types, pattern-matching, and recursion are ubiquitous features of Haskell programs. Sometimes a function is called with arguments that are statically known to already be in constructor form, so that the work of pattern-matching is wasted. Even worse, the argument is sometimes freshly-allocated, only to be immediately decomposed by the function. In this paper we describe a simple, modular transformation that specialises recursive functions according to their argument “shapes”. We show that such a transformation has a simple, modular implementation, and that it can be extremely effective in practice, eliminating both pattern-matching and heap allocation. We describe our implementation of this constructor specialisation transformation in the Glasgow Haskell Compiler, and give measurements of its effectiveness.

Arrows are a popular form of abstract computation. Being more general than monads, they are more broadly applicable, and in particular are a good abstraction for signal processing and dataflow computations. Most notably, arrows form the basis for a domain specific language called Yampa, which has been used in a variety of concrete applications, including animation, robotics, sound synthesis, control systems, and graphical user interfaces. computations captured by Yampa. Unfortunately, arrows are not concrete enough to do this with precision. To remedy this situation we introduce the concept of commutative arrows that capture a kind of non-interference property of concurrent computations. We also add an init operator, and identify a crucial law that captures the causal nature of arrow effects. We call the resulting computational model causal commutative arrows. To study this class of computations in more detail, we define an extension to the simply typed lambda calculus called causal commutative arrows (CCA), and study its properties. Our key contribution is the identification of a normal form for CCA called causal commutative normal form (CCNF). By defining a normalization procedure we have developed an optimization strategy that yields dramatic improvements in performance over conventional implementations of arrows. We have implemented this technique in Haskell, and conducted benchmarks that validate the effectiveness of our approach. When combined with stream fusion, the overall methodology can result in speed-ups of greater than two orders of magnitude.

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Free theorems feature prominently in the field of program transformation for pure functional languages such as Haskell. However, somewhat disappointingly, the semantic properties of so based transformations are often established only very superficially. This paper is intended as a case study showing how to use the existing theoretical foundations and formal methods for improving the situation. To that end, we investigate the correctness issue for a new transformation rule in the short cut fusion family. This destroy/build-rule provides a certain reconciliation between the competing foldr/build- and destroy/unfoldr-approaches to eliminating intermediate lists. Our emphasis is on systematically and rigorously developing the rule’s correctness proof, even while paying attention to semantic aspects like potential nontermination and mixed strict/nonstrict evaluation.

We study various shortcut fusion rules for languages like Haskell. Following a careful semantic account of a recently proposed rule for circular program transformation, we propose a new rule that trades circularity for higher-orderedness, and thus attains better semantic properties. This also leads us to revisit the original foldr/build-rule, as well as its dual, and to develop variants that do not suffer from detrimental impacts of Haskell’s mixed strict/nonstrict semantics. Throughout, we offer pragmatic insights about our new rules to investigate also their relative effectiveness, rather than just their semantic correctness.

high-level and platform-independent description of digital signal processing (DSP) algorithms. Feldspar is a pure functional language embedded in Haskell. It offers a high-level dataflow style of programming, as well as a more mathematical style based on vector indices. The key to generating efficient code from such descriptions is a high-level optimization technique called vector fusion. Feldspar is based on a low-level, functional core language which has a relatively small semantic gap to machine-oriented languages like C. The core language serves as the interface to the back-end code generator, which produces C. For very small examples, the generated code performs comparably to hand-written C code when run on a DSP target. While initial results are promising, to achieve good performance on larger examples, issues related to memory access patterns and array copying will have to be addressed. I.

Supercompilation is a technique due to Turchin [1] which allows for the construction of program optimisers that are both simple and extremely powerful. Supercompilation is capable of achieving transformations such as deforestation [2], function specialisation and constructor specialisation [3]. Inspired by Mitchell’s promising results [4], we show how the call-by-need supercompilation algorithm can be recast to be based explicitly on an evaluator, and in the process extend it to deal with recursive let expressions.