) James Riely 1 and Jan Prins 2 1 DePaul University 2 University of North Carolina at Chapel Hill Abstract. Flattening is a program transformation that eliminates nested parallel constructs, introducing flat parallel (vector) operations in their place. We define a sufficient syntactic condition for the correctness of flattening, providing a static approximation of Blelloch's "containment". This is acheived using a typing system that tracks the control flow of programs. Using a weak improvement preorder, we then show that the flattening transformations are intensionally correct for all well-typed programs. 1 Introduction The study of program transformations has largely been concerned with functional correctness, i.e. whether program transformations preserve program meaning. However, if we include an execution cost-model as part of the programming language semantics, then we can ask whether program transformations additionally preserve or "improve" program performance. One progra...

We discuss a language-based cost model for array programs build on the notions of work complexity and parallel depth. The programs operate over data structures comprising nested arrays and recursive product-sum types. In a purely functional setting, such programs can be implemented by way of the flattening transformation that converts codes over nested arrays into vectorised code over flat arrays.

FISh is an array-based programming language that combines imperative and functional programming styles. Static shape analysis uses partial evaluation to convert arbitrary programs into simple, efficient imperative programs.