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Parallelizing Functional Programs by Generalization
 Journal of Functional Programming
, 1997
"... List homomorphisms are functions that are parallelizable using the divideandconquer paradigm. We study the problem of finding a homomorphic representation of a given function, based on the BirdMeertens theory of lists. A previous work proved that to each pair of leftward and rightward sequential ..."
Abstract

Cited by 9 (1 self)
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List homomorphisms are functions that are parallelizable using the divideandconquer paradigm. We study the problem of finding a homomorphic representation of a given function, based on the BirdMeertens theory of lists. A previous work proved that to each pair of leftward and rightward sequential representations of a function, based on cons and snoclists, 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 scanfunction (parallel prefix). The inductive claim is provable automatically.
Parallelizing Functional Programs by Term Rewriting
, 1997
"... List homomorphisms are functions that can be computed in parallel using the divideandconquer paradigm. We study the problem of finding a homomorphic representation of a given function, based on the BirdMeertens theory of lists. A previous work proved that to each pair of leftward and rightward se ..."
Abstract

Cited by 2 (2 self)
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List homomorphisms are functions that can be computed in parallel using the divideandconquer paradigm. We study the problem of finding a homomorphic representation of a given function, based on the BirdMeertens theory of lists. A previous work proved that to each pair of leftward and rightward sequential representations of a function, based on cons and snoclists, 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 scanfunction (parallel prefix). The inductive claim is provable automatically. Keywords: P...