Practical probabilistic programming with monads

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Design and Implementation of Probabilistic Programming Language Anglican (2016, background): “Probabilistic programming languages are often implemented as pure functional languages [6, 9, 21] in the sense that they do not allow mutable states.”
Probabilistic Inference by Program Transformation in Hakaru (System Description) (2016, background): “[11] both embed a probabilistic language in a general-purpose functional language, respectively OCaml and Haskell.”
Bayesian Probabilistic Numerical Methods (2017, methodology): “For instance, a method node in a pipeline can be related to a monad aggregating several distributions into a single output distribution (Ścibior et al., 2015).”
Deep Probabilistic Programming (2017, methodology): “Moreover, it enables us to simplify both de- terministic and stochastic operations in the graph, before executing any code (Ścibior et al., 2015; Zinkov & Shan, 2016).”
A lambda-calculus foundation for universal probabilistic programming (2015, background): “Scibior et al. (2015) deﬁne a monadic embedding of probabilistic programming in Haskell along the lines of Kozen’s semantics; their paper describes various inference algorithms but has no formal correctness results.”
Denotational validation of higher-order Bayesian inference (2017, methodology): “In previous work with Gordon [Ścibior et al. 2015], we manipulated a free monad representation to obtain an implementation of SMC.”