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Parallel Beta Reduction Is Not Elementary Recursive

2001
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Information and Computation
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We analyze the inherent complexity of implementing Lévy's notion of optimal evaluation for the λ-calculus, where similar redexes are contracted in one step via so-called parallel β-reduction. Optimal evaluation was finally realized by Lamping, who introduced a beautiful graph reduction technology for sharing evaluation contexts dual to the sharing of values. His pioneering insights have been modified and improved in subsequent implementations of optimal reduction. We prove that the cost of

doi:10.1006/inco.2001.2869
fatcat:ha4xzhxoq5ae3fjuj4zgshlblq