Stochastic lambda calculus and monads of probability distributions
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A probabilistic language based upon sampling functions
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Machine Learning
FUNCTIONAL PEARLS: Probabilistic functional programming in Haskell
Journal of Functional Programming
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Embedded Probabilistic Programming
DSL '09 Proceedings of the IFIP TC 2 Working Conference on Domain-Specific Languages
PRISM: a language for symbolic-statistical modeling
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
IBAL: a probabilistic rational programming language
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
BLOG: probabilistic models with unknown objects
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
All of Statistics: A Concise Course in Statistical Inference
All of Statistics: A Concise Course in Statistical Inference
Measure transformer semantics for Bayesian machine learning
ESOP'11/ETAPS'11 Proceedings of the 20th European conference on Programming languages and systems: part of the joint European conferences on theory and practice of software
Automating mathematical program transformations
PADL'10 Proceedings of the 12th international conference on Practical Aspects of Declarative Languages
Proofs of randomized algorithms in CoQ
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
On the formalization of the lebesgue integration theory in HOL
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Dynamic symbolic computation for domain-specific language implementation
LOPSTR'11 Proceedings of the 21st international conference on Logic-Based Program Synthesis and Transformation
A model-learner pattern for bayesian reasoning
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Deriving probability density functions from probabilistic functional programs
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Uncertain: a first-order type for uncertain data
Proceedings of the 19th international conference on Architectural support for programming languages and operating systems
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There has been great interest in creating probabilistic programming languages to simplify the coding of statistical tasks; however, there still does not exist a formal language that simultaneously provides (1) continuous probability distributions, (2) the ability to naturally express custom probabilistic models, and (3) probability density functions (PDFs). This collection of features is necessary for mechanizing fundamental statistical techniques. We formalize the first probabilistic language that exhibits these features, and it serves as a foundational framework for extending the ideas to more general languages. Particularly novel are our type system for absolutely continuous (AC) distributions (those which permit PDFs) and our PDF calculation procedure, which calculates PDF s for a large class of AC distributions. Our formalization paves the way toward the rigorous encoding of powerful statistical reformulations.