# Universal Semantics for the Stochastic Lambda-Calculus

arXiv: https://arxiv.org/abs/2011.13171 · HTML: https://mlsanity.com/paper/2011.13171/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2020.

## Built on by (most cited first, 2 of 2)

- [Checking Trustworthiness of Probabilistic Computations in a Typed Natural Deduction System](https://mlsanity.com/paper/2206.12934/) (2022)
- [Trustworthiness Preservation by Copies of Machine Learning Systems](https://mlsanity.com/paper/2506.05203/) (2025)

## Abstract (arXiv)

We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build on previous work that used similar techniques to reason about higher-order probabilistic programs, but for the first time admit an adequacy theorem relating the operational and denotational views. This resolves the main issue left open in (Bacci et al. 2018).