We describe a facility for improving optimization of Haskell programs using rewrite rules. Library authors can use rules to express domain-specific optimizations that the compiler cannot discover for itself. The compiler can also generate rules internally to propagate information obtained from automated analyses. The rewrite mechanism is fully implemented in the released Glasgow Haskell Compiler. Our system is very simple, but can be effective in optimizing real programs. We describe two practical applications involving short-cut deforestation, for lists and for rose trees, and document substantial performance improvements on a range of programs. 1 Introduction Optimising compilers perform program transformations that improve the efficiency of the program. However, a compiler can only use relatively shallow reasoning to guarantee the correctness of its optimisations. In contrast, the programmer has much deeper information about the program and its intended behaviour. For example, a programmer may know that

Program transformation is used in a wide range of applications including compiler construction, optimization, program synthesis, refactoring, software renovation, and reverse engineering. Complex program transformations are achieved through a number of consecutive modifications of a program. Transformation rules define basic modifications. A transformation strategy is an algorithm for choosing a path in the rewrite relation induced by a set of rules. This paper surveys the support for the definition of strategies in program transformation systems. After a discussion of kinds of program transformation and choices in program representation, the basic elements of a strategy system are discussed and the choices in the design of a strategy language are considered. Several styles of strategy systems as provided in existing languages are then analyzed.

Graphics cards for personal computers have recently undergone a radical transformation from fixed-function graphics pipelines to multi-processor, programmable architectures. Multi-processor architectures are clearly advantageous for graphics for the simple reason that graphics computations are naturally concurrent, mapping well to stateless stream processing. They therefore parallelize easily and need no random access to memory with its problematic latencies. This paper presents Vertigo, a purely functional, Haskell-embedded language for 3D graphics and an optimizing compiler that generates graphics processor code. The language integrates procedural surface modeling, shading, and texture generation, and the compiler exploits the unusual processor architecture. The shading sublanguage is based on a simple and precise semantic model, in contrast to previous shading languages. Geometry and textures are also defined via a very simple denotational semantics. The formal semantics yields not only programs that are easy to understand and reason about, but also very efficient implementation, thanks to a compiler based on partial evaluation and symbolic optimization, much in the style of Pan [2]. Haskell’s overloading facility is extremely useful throughout Vertigo. For instance, math operators are used not just for floating point numbers, but also expressions (for differentiation and compilation), tuples, and functions. Typically, these overloadings cascade, as in the case of surfaces, which may be combined via math operators, though they are really functions over tuples of expressions on floating point numbers. Shaders may be composed with the same notational convenience. Functional dependencies are exploited for vector spaces, cross products, and derivatives.

An algebra consists of a set of objects and a set of operators that act on those objects. We treat shader programs as first-class objects and define two operators: connection and combination. Connection is functional composition: the outputs of one shader are fed into the inputs of another. Combination concatenates the input channels, output channels, and computations of two shaders. Similar operators can be used to manipulate streams and apply computational kernels expressed as shaders to streams. Connecting a shader program to a stream applies that program to all elements of the stream; combining streams concatenates the record definitions of those streams.

As heterogeneous parallel systems become dominant, application developers are being forced to turn to an incompatible mix of low level programming models (e.g. OpenMP, MPI, CUDA, OpenCL). However, these models do little to shield developers from the difficult problems of parallelization, data decomposition and machine-specific details. Most programmers are having a difficult time using these programming models effectively. To provide a programming model that addresses the productivity and performance requirements for the average programmer, we explore a domainspecific approach to heterogeneous parallel programming. We propose language virtualization as a new principle that enables the construction of highly efficient parallel domain specific languages that are embedded in a common host language. We define criteria for language virtualization and present techniques to achieve them. We present two concrete case studies of domain-specific languages that are implemented using our virtualization approach.

Achieving peak performance from library subroutines usually requires extensive, machine-dependent tuning by hand. Automatic tuning systems have emerged in response, and they typically operate by (1) generating a large number of possible implementations of a subroutine, and (2) selecting the fastest implementation by an exhaustive, empirical search. This paper presents quantitative data that motivates the development of such a search-based system, and discusses two problems which arise in the context of search. First, we develop a heuristic for stopping an exhaustive compile-time search early if a near-optimal implementation is found. Second, we show how to construct run-time decision rules, based on run-time inputs, for selecting from among a subset of the best implementations.

detected or enforced by their host language. We show how to use macros to easily implement partial evaluation of embedded interpreters in order to capture invariants encoded in embedded programs and render them explicit in the terms of their host language. We demonstrate the effectiveness of this technique in improving the results of a value flow analysis.

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.

We introduce a handful of modules for manipulating Template Haskell datastructures, building up to modules that allow simplication and recursion unrolling of Haskell code. To illustrate their use, and to demonstrate the performance improvements that motivate this work, we also discuss an example application Fraskell [5], showing how we can get more than an order of magnitude performance increase with minimal changes to the source.

Experiences are presented from a new case study of embedding domain-specific languages in the lazy functional language Haskell. The domain languages come from the Odin software build system. Thus, in contrast to most previous embedding projects, a design and implementation of the domain languages existed when the project began. Consequently, the design could not be varied to suit the target language and it was possible to evaluate the success or otherwise of the embedding process in more detail than if the languages were designed from scratch. Experiences were mostly positive. The embedded implementation is significantly smaller than its Odin equivalent. Many benefits are obtained from having the full power of an expressive programming language available to the domain programmer. The project also demonstrates in a practical software engineering setting the utility of modern functional programming techniques such as lazy evaluation and monads for structuring programs. On the down side, the efficiency of the embedded version compares unfavourably to the original system.