Great expectations: Unifying Statistical Theory and Programming
Computation
2025-10-14 v1
Abstract
Beginning in the 1970s, statistician-cum-logician Per Martin-L\"of wrote a series of papers developing what became Martin-L\"of type theory, realizing a system where the distinction between mathematics and programming disappears. Inspired by this vision, this paper introduces dependent type theory (of which Martin-L\"of type theory is an example) to a statistical audience. Examples from statistics and probability theory demonstrate how dependent type theory and an algebraic perspective can unify the theoretical and computational concerns of statistics, ensuring rigorous, machine-checked proofs and executable software.
Keywords
Cite
@article{arxiv.2510.09853,
title = {Great expectations: Unifying Statistical Theory and Programming},
author = {Bradley Saul},
journal= {arXiv preprint arXiv:2510.09853},
year = {2025}
}