In search of a map: using program slicing to discover potential parallelism in recursive functions

Recursion schemes, such as the well-known map, can be used as loci of potential parallelism, where schemes are replaced with an equivalent parallel implementation. This paper formalises a novel technique, using program slicing, that automatically and statically identifies computations in recursive functions that can be lifted out of the function and then potentially performed in parallel. We define a new program slicing algorithm, build a prototype implementation, and demonstrate its use on 12 Haskell examples, including benchmarks from the NoFib suite and functions from the standard Haskell Prelude. In all cases, we obtain the expected results in terms of finding potential parallelism. Moreover, we have tested our prototype against synthetic benchmarks, and found that our prototype has quadratic time complexity. For the NoFib benchmark examples we demonstrate that relative parallel speedups can be obtained (up to 32.93× the sequential performance on 56 hyperthreaded cores).