On Randomised Strategies in the $λ$-Calculus

Description

In this work we study randomised reduction strategies-a notion already known in the context of abstract reduction systems-for the λ-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 λ-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 the affine λ-calculus, where duplication is syntactically forbidden.

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