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arXiv · 1602.06420

A Probabilistic Dependent Type System based on Non-Deterministic Beta Reduction

Jonathan H. Warrell
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Abstract

We introduce Probabilistic Dependent Type Systems (PDTS) via a functional language based on a subsystem of intuitionistic type theory including dependent sums and products, which is expanded to include stochastic functions. We provide a sampling-based semantics for the language based on non-deterministic beta reduction. Further, we derive a probabilistic logic from the PDTS introduced as a direct result of the Curry-Howard isomorphism. The probabilistic logic derived is shown to provide a universal representation for finite discrete distributions.

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Jonathan H. Warrell. 2016-02-20. A Probabilistic Dependent Type System based on Non-Deterministic Beta Reduction. https://arxiv.org/abs/1602.06420

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