A domain theory for statistical probabilistic programming

M Vákár, O Kammar, S Staton - … of the ACM on Programming Languages, 2019 - dl.acm.org
We give an adequate denotational semantics for languages with recursive higher-order
types, continuous probability distributions, and soft constraints. These are expressive …

Reasoning about “reasoning about reasoning”: semantics and contextual equivalence for probabilistic programs with nested queries and recursion

Y Zhang, N Amin - Proceedings of the ACM on Programming …, 2022 - dl.acm.org
Metareasoning can be achieved in probabilistic programming languages (PPLs) using
agent models that recursively nest inference queries inside inference queries. However, the …

Structural foundations for probabilistic programming languages

DM Stein - 2021 - ora.ox.ac.uk
Probability theory and statistics are fundamental disciplines in a data-driven world. Synthetic
probability theory is a general, axiomatic formalism to describe their underlying structures …

Affine monads and lazy structures for Bayesian programming

S Dash, Y Kaddar, H Paquet, S Staton - Proceedings of the ACM on …, 2023 - dl.acm.org
We show that streams and lazy data structures are a natural idiom for programming with
infinite-dimensional Bayesian methods such as Poisson processes, Gaussian processes …

Probabilistic programming semantics for name generation

M Sabok, S Staton, D Stein, M Wolman - Proceedings of the ACM on …, 2021 - dl.acm.org
We make a formal analogy between random sampling and fresh name generation. We show
that quasi-Borel spaces, a model for probabilistic programming, can soundly interpret the ν …

Concrete categories and higher-order recursion: With applications including probability, differentiability, and full abstraction

C Matache, S Moss, S Staton - Proceedings of the 37th Annual ACM …, 2022 - dl.acm.org
We study concrete sheaf models for a call-by-value higher-order language with recursion.
Our family of sheaf models is a generalization of many examples from the literature, such as …

A domain-theoretic approach to statistical programming languages

J Goubault-Larrecq, X Jia, C Théron - Journal of the ACM, 2023 - dl.acm.org
We give a domain-theoretic semantics to a statistical programming language, using the plain
old category of dcpos, in contrast to some more sophisticated recent proposals. Remarkably …

Deterministic stream-sampling for probabilistic programming: semantics and verification

F Dahlqvist, A Silva, W Smith - 2023 38th Annual ACM/IEEE …, 2023 - ieeexplore.ieee.org
Probabilistic programming languages rely fundamentally on some notion of sampling, and
this is doubly true for probabilistic programming languages which perform Bayesian …

Synthetic topology in Homotopy Type Theory for probabilistic programming

ME Bidlingmaier, F Faissole, B Spitters - Mathematical Structures in …, 2021 - cambridge.org
The ALEA Coq library formalizes measure theory based on a variant of the Giry monad on
the category of sets. This enables the interpretation of a probabilistic programming language …

Concrete categories and higher-order recursion

C Matache, S Moss, S Staton - Proceedings of the 37th Annual ACM …, 2022 - ora.ox.ac.uk
We study concrete sheaf models for a call-by-value higher-order language with recursion.
Our family of sheaf models is a generalization of many examples from the literature, such as …