Abstract
We investigate the degree of parallelism (or modularity) in the hyperbalanced λ-calculus, λH, a subcalculus of λ-calculus containing all simply typable terms (up to a restricted η-expansion). In technical terms, we study the family relation on redexes in λH, and the contribution relation on redex-families, and show that the latter is a forest (as a partial order). This means that hyperbalanced λ-terms allow for maximal possible parallelism in computation. To prove our results, we use and further refine, for the case of hyperbalanced terms, some well known results concerning paths, which allow for static analysis of many fundamental properties of β-reduction.
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Kennaway, R., Khasidashvili, Z., Piperno, A. (2002). Static Analysis of Modularity of β-Reduction in the Hyperbalanced λ-Calculus. In: Tison, S. (eds) Rewriting Techniques and Applications. RTA 2002. Lecture Notes in Computer Science, vol 2378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45610-4_5
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DOI: https://doi.org/10.1007/3-540-45610-4_5
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