A domain theory for statistical probabilistic programming
We give an adequate denotational semantics for languages with recursive higher-order
types, continuous probability distributions, and soft constraints. These are expressive …
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
Metareasoning can be achieved in probabilistic programming languages (PPLs) using
agent models that recursively nest inference queries inside inference queries. However, the …
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 …
probability theory is a general, axiomatic formalism to describe their underlying structures …
Affine monads and lazy structures for Bayesian programming
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 …
infinite-dimensional Bayesian methods such as Poisson processes, Gaussian processes …
Probabilistic programming semantics for name generation
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 …
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 …
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 …
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 …
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 …
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 …
Our family of sheaf models is a generalization of many examples from the literature, such as …