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Parallel Beta Reduction is Not Elementary Recursive (1998)  (Make Corrections)  (9 citations)
Andrea Asperti, Harry G. Mairson
Symposium on Principles of Programming Languages



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Abstract: We analyze the inherent complexity of implementing Lévy's notion of optimal evaluation for the lambda-calculus, where similar redexes are contracted in one step via so-called parallel lambda-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 ... (Update)

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...paths. A strong normalization proof for simply typed l calculus using a similar idea (but completely different technically) appears in [2]. Arrow decoration of hyperbalanced terms is useful for other purposes too. For example, it allows us to develop a static garbage...

.... reduction does not say that such optimal reduction is inecient only that the parallel reduction cannot be considered a unit cost operation [3]. In summary, all of the translations we outline possess a simple graph reduction on translated terms (cut elimination for linear logic)...

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BibTeX entry:   (Update)

Andrea Asperti and Harry Mairson. Parallel beta reduction is not elementary recursive. In Conference Record of POPL '98: The 25th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, San Diego, California, 1998. http://citeseer.ist.psu.edu/asperti98parallel.html   More

@inproceedings{ asperti98parallel,
    author = "Andrea Asperti and Harry G. Mairson",
    title = "Parallel Beta Reduction is not Elementary Recursive",
    booktitle = "Symposium on Principles of Programming Languages",
    pages = "303--315",
    year = "1998",
    url = "citeseer.ist.psu.edu/asperti98parallel.html" }
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