Abstract
List homomorphisms are functions that are parallelizable using the divide-and-conquer paradigm. We study the problem of finding a homomorphic representation of a given function, based on the Bird-Meertens theory of lists. A previous work proved that to each pair of leftward and rightward sequential representations of a function, based on cons- and snoc-lists, respectively, there is also a representation as a homomorphism. Our contribution is a mechanizable method to extract the homomorphism representation from a pair of sequential representations. The method is decomposed to a generalization problem and an inductive claim, both solvable by term rewriting techniques. To solve the former we present a sound generalization procedure which yields the required representation, and terminates under reasonable assumptions. We illustrate the method and the procedure by the parallelization of the scan-function (parallel prefix). The inductive claim is provable automatically.
Partially supported by grant Ku 996/3-l of the DFG within the Schwerpunkt Deduktion at the University of Tübingen.
Partially supported by the DFG project RecuR2 and by the DAAD exchange programs ARC and PROCOPE.
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Geser, A., Gorlatch, S. (1997). Parallelizing functional programs by generalization. In: Hanus, M., Heering, J., Meinke, K. (eds) Algebraic and Logic Programming. ALP HOA 1997 1997. Lecture Notes in Computer Science, vol 1298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027002
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DOI: https://doi.org/10.1007/BFb0027002
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