Characterizing lambda-terms with equal reduction behavior
Fairouz Kamareddine, CJ Roel Bloo, RP Rob Nederpelt · TU/e Research Portal · 2000
We define an equivalence relation on lambda-terms called shuffle-equivalence which attempts to capture the notion of reductional equivalence on strongly normalizing terms. The aim of reductional equivalence is to characterize the evaluation behavior of programs. The shuffle-equivalence classes are shown to divide the classes of beta-equal strongly normalising terms (programs which lead to the same final value/output) into smaller ones consisting of terms with similar evaluation behavior. We refine beta-reduction from a relation on terms to a relation on shuffle-equivalence classes, called shuffle-reduction, and show that this refinement captures existing generalisations of lambda-reduction. Shuffle-reduction allows one to make more redexes visible and to contract these newly visible redexes. Moreover, it allows more freedom in choosing the reduction path of a term, which can result in smaller terms along the reduction path if a clever reduction strategy is used. This can benefit both programming language...