# On the Taylor Expansion of Probabilistic $\lambda$-Terms (Long Version)

## TL;DR

This paper extends the Taylor expansion framework to probabilistic lambda calculus, establishing its adequacy as a semantic tool and linking it to probabilistic B"ohm trees, thus advancing the understanding of probabilistic computation semantics.

## Contribution

It generalizes the Taylor expansion to probabilistic lambda-terms and proves its adequacy and correspondence with probabilistic B"ohm trees, providing a new semantic perspective.

## Key findings

- Taylor expansion is adequate for probabilistic lambda-terms
- Established a correspondence with probabilistic B"ohm trees
- Extended resource calculus to probabilistic settings

## Abstract

We generalise Ehrhard and Regnier's Taylor expansion from pure to probabilistic $\lambda$-terms through notions of probabilistic resource terms and explicit Taylor expansion. We prove that the Taylor expansion is adequate when seen as a way to give semantics to probabilistic $\lambda$-terms, and that there is a precise correspondence with probabilistic B\"ohm trees, as introduced by the second author.