On Randomised Strategies in the λ-Calculus (Long Version)
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In this work we introduce randomised reduction strategies, a notion already studied in the context of abstract reduction systems, for the λ-calculus. We develop a simple framework that allows us to prove if a probabilistic strategy is positive almost-surely normalising. Then we propose a simple example of probabilistic 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 two classical sub-λ-calculi, namely those in which duplication and erasure are syntactically forbidden.
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