Probabilistic non-determinism
Set theory for verification. I: from foundations to functions
Journal of Automated Reasoning
Stochastic lambda calculus and monads of probability distributions
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
WinBUGS – A Bayesian modelling framework: Concepts, structure, and extensibility
Statistics and Computing
Set Theory, Higher Order Logic or Both?
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
Applicative programming with effects
Journal of Functional Programming
Semantics of probabilistic programs
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
A probabilistic language based on sampling functions
ACM Transactions on Programming Languages and Systems (TOPLAS)
Composable probabilistic inference with b(laise)
Composable probabilistic inference with b(laise)
Mixed deterministic and probabilistic networks
Annals of Mathematics and Artificial Intelligence
BLOG: probabilistic models with unknown objects
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Monolingual probabilistic programming using generalized coroutines
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Effective Bayesian inference for stochastic programs
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Refining syntactic sugar: tools for supporting macro development
Refining syntactic sugar: tools for supporting macro development
Computing in cantor's paradise with λZFC
FLOPS'12 Proceedings of the 11th international conference on Functional and Logic Programming
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Bayesian practitioners build models of the world without regarding how difficult it will be to answer questions about them. When answering questions, they put off approximating as long as possible, and usually must write programs to compute converging approximations. Writing the programs is distracting, tedious and error-prone, and we wish to relieve them of it by providing languages and compilers. Their style constrains our work: the tools we provide cannot approximate early. Our approach to meeting this constraint is to 1) determine their notation's meaning in a suitable theoretical framework; 2) generalize our interpretation in an uncomputable, exact semantics; 3) approximate the exact semantics and prove convergence; and 4) implement the approximating semantics in Racket (formerly PLT Scheme). In this way, we define languages with at least as much exactness as Bayesian practitioners have in mind, and also put off approximating as long as possible. In this paper, we demonstrate the approach using our preliminary work on discrete (countably infinite) Bayesian models.