COSTING NESTED ARRAY CODES

Abstract

We discuss a language-based cost model for array programs built 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. Flat arrays lend themselves to a particularly efficient implementation on standard hardware, but the overall efficiency of the approach depends on the flattening transformation preserving the asymptotic complexity of the nested array codes. Blelloch has characterised a class of first-order array programs, called contained programs, for which flattening preserves the asymptotic depth complexity. However, his result is restricted to programs processing only arrays and tuples. In the present paper, we extend Blelloch's result to array programs processing data structures containing arrays as well as arbitrary recursive product-sum types. Moreover, we replace the notion of containment by the more general concept of fold programs.