internal languages for probabilistic programming

Last updated Dec 7, 2024

Categorical semantics of probabilistic programming

has traditionally been restricted to a few semantic universes: standard borel space via the Giry monad, quasiborel spaces for higher-order probability, or ωPAP spaces for differentiable probability theory. However, the synthetic approach to probability theory promises a more algebraic and general approach to program semantics, less focused on the particular analytic aspects of these models.

While the internal languages of complex categorical structures have moved large amounts of research effort — consider topos theory with its Mitchell-Bénabou language, or ∞-toposes via homotopy type theory — arguably, the internal languages of simpler and more general categorical structures (Markov categories, restriction categories, duoidal categories) have received considerably less attention.

The development of a probabilistic programming language with exact observations based on the internal language of traced distributive partial Markov categories.

Tags: probabilistic programming

, internal languages.