Data flow fusion with series expressions in Haskell

Existing approaches to array fusion can deal with straight-line producer consumer pipelines, but cannot fuse branching data flows where a generated array is consumed by several different consumers. Branching data flows are common and natural to write, but a lack of fusion leads to the creation of an intermediate array at every branch point. We present a new array fusion system that handles branches, based on Waters's series expression framework, but extended to work in a functional setting. Our system also solves a related problem in stream fusion, namely the introduction of duplicate loop counters. We demonstrate speedup over existing fusion systems for several key examples.