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arXiv · 2510.09853

Great expectations: Unifying Statistical Theory and Programming

Bradley Saul
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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.

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Bradley Saul. 2025-10-10. Great expectations: Unifying Statistical Theory and Programming. https://arxiv.org/abs/2510.09853

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