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On randomised strategies in the $λ$-calculus (long version) (1805.03934v2)

Published 10 May 2018 in cs.LO

Abstract: In this work we study randomised reduction strategies,a notion already known in the context of abstract reduction systems, for the $\lambda$-calculus. We develop a simple framework that allows us to prove a randomised strategy to be positive almost-surely normalising. Then we propose a simple example of randomised strategy for the $\lambda$-calculus that has such a property and we show why it is non-trivial with respect to classical deterministic strategies such as leftmost-outermost or rightmost-innermost. We conclude studying this strategy for two sub-$\lambda$-calculi, namely those where duplication and erasure are syntactically forbidden, showing some non-trivial properties.

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