We present a novel approach to regular, multi-dimensional arrays in Haskell. The main highlights of our approach are that it (1) is purely functional, (2) supports reuse through shape polymorphism, (3) avoids unnecessary intermediate structures rather than relying on subsequent loop fusion, and (4) supports transparent parallelisation.We show how to embed two forms of shape polymorphism into Haskell's type system using type classes and type families. In particular, we discuss the generalisation of regular array transformations to arrays of higher rank, and introduce a type-safe specification of array slices.We discuss the runtime performance of our approach for three standard array algorithms. We achieve absolute performance comparable to handwritten C code. At the same time, our implementation scales well up to 8 processor cores.

Purely functional, embedded array programs are a good match for SIMD hardware, such as GPUs. However, the naive compilation of such programs quickly leads to both code explosion and an excessive use of intermediate data structures. The resulting slowdown is not acceptable on target hardware that is usually chosen to achieve high performance.In this paper, we discuss two optimisation techniques, sharing recovery and array fusion, that tackle code explosion and eliminate superfluous intermediate structures. Both techniques are well known from other contexts, but they present unique challenges for an embedded language compiled for execution on a GPU. We present novel methods for implementing sharing recovery and array fusion, and demonstrate their effectiveness on a set of benchmarks.

We present a novel approach to regular, multi-dimensional arrays in Haskell. The main highlights of our approach are that it (1) is purely functional, (2) supports reuse through shape polymorphism, (3) avoids unnecessary intermediate structures rather than relying on subsequent loop fusion, and (4) supports transparent parallelisation.We show how to embed two forms of shape polymorphism into Haskell's type system using type classes and type families. In particular, we discuss the generalisation of regular array transformations to arrays of higher rank, and introduce a type-safe specification of array slices.We discuss the runtime performance of our approach for three standard array algorithms. We achieve absolute performance comparable to handwritten C code. At the same time, our implementation scales well up to 8 processor cores.

Purely functional, embedded array programs are a good match for SIMD hardware, such as GPUs. However, the naive compilation of such programs quickly leads to both code explosion and an excessive use of intermediate data structures. The resulting slowdown is not acceptable on target hardware that is usually chosen to achieve high performance. In this paper, we discuss two optimisation techniques, sharing recovery and array fusion, that tackle code explosion and eliminate superfluous intermediate structures. Both techniques are well known from other contexts, but they present unique challenges for an embedded language compiled for execution on a GPU. We present novel methods for implementing sharing recovery and array fusion, and demonstrate their effectiveness on a set of benchmarks.

Stencil convolution is a fundamental building block of many scientific and image processing algorithms. We present a declarative approach to writing such convolutions in Haskell that is both efficient at runtime and implicitly parallel. To achieve this we extend our prior work on the Repa array library with two new features: partitioned and cursored arrays. Combined with careful management of the interaction between GHC and its back-end code generator LLVM, we achieve performance comparable to the standard OpenCV library.