On Randomised Strategies in the $λ$-Calculus

Ugo Dal Lago (1, 2) , Gabriele Vanoni (2, 1)

1 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna
2 FOCUS - Foundations of Component-based Ubiquitous Systems

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.

Domaines: Logique en informatique [cs.LO]; Langage de programmation [cs.PL]

Ugo Dal Lago, Gabriele Vanoni. On Randomised Strategies in the $λ$-Calculus. 19th Italian Conference on Theoretical Computer Science, Sep 2018, Urbino, Italy. ⟨hal-01926512⟩