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arXiv · 1901.02853

Lambda Calculus and Probabilistic Computation

Claudia Faggian·Simona Ronchi della Rocca
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Abstract

We introduce two extensions of the $\lambda$-calculus with a probabilistic choice operator, $\Lambda_\oplus^{cbv}$ and $\Lambda_\oplus^{cbn}$, modeling respectively call-by-value and call-by-name probabilistic computation. We prove that both enjoys confluence and standardization, in an extended way: we revisit these two fundamental notions to take into account the asymptotic behaviour of terms. The common root of the two calculi is a further calculus based on Linear Logic, $\Lambda_\oplus^!$, which allows for a fine control of the interaction between choice and copying, and which allows us to develop a unified, modular approach.

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Claudia Faggian, Simona Ronchi della Rocca. 2019-01-09. Lambda Calculus and Probabilistic Computation. https://arxiv.org/abs/1901.02853

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