. Vec is a higher-order functional language of nested arrays, which includes a general folding operation. Static computation of the shape of its programs is used to support a compositional cost calculus based on a cost monad. This, in turn, is based on a cost algebra, whose operations may be customized to handle different cost regimes, especially for parallel programming. We present examples based on sequential costing and on the PRAM model of parallel computation. The latter has been implemented in Haskell, and applied to some linear algebra examples. 1 Introduction Second-order combinators such as map, fold and zip provide programmers with a concise, abstract language for writing skeletons for implicitly parallel programs, as in [Ski94], but there is a hitch. These combinators are defined for list programs (see [BW88]), but efficient implementations (which is the point of parallelism, after all) are based on arrays. This disparity becomes acute when working with nested arrays, which...

Portable, efficient, parallel programming requires cost models to compare different possible implementations. In turn, these require knowledge of the shapes of the data structures being used, as well as knowledge of the hardware parameters. This paper shows how shape analysis techniques developed in the FISh programming language could be exploited to produce a data parallel language with an accurate, portable cost model. 1 Introduction The problem of constructing portable efficient parallel programs is still unsolved. It originates in the observation that an algorithm that executes efficiently in one setting may be extremely inefficient in another. Hence, the challenge is to automatically adapt the algorithm to match the circumstances. To do this during compilation requires a cost model that is able to identify which of two alternative algorithms is faster. To date, most work has focussed on measuring the impact of changes to hardware as observed through a small suite of hardwar...