Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Elements of functional programming
Elements of functional programming
Selected papers of international conference on Fifth generation computer systems 92
Probabilistic frame-based systems
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Semantics and Inference for Recursive Probability Models
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Probabilistic reasoning for complex systems
Probabilistic reasoning for complex systems
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
SPOOK: a system for probabilistic object-oriented knowledge representation
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Object-oriented Bayesian networks
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
Network fragments: representing knowledge for constructing probabilistic models
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
Context-specific independence in Bayesian networks
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Bucket elimination: a unifying framework for probabilistic inference
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Fuzzy-Probabilistic logic for common sense
AGI'12 Proceedings of the 5th international conference on Artificial General Intelligence
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There is increasing interest within the research community in the design and use of recursive probability models. There remains concern about computational complexity costs and the fact that computing exact solutions can be intractable for many nonrecursive models. Although inference is undecidable in the general case for recursive problems, several research groups are actively developing computational techniques for recursive stochastic languages. We have developed an extension to the traditional λ calculus as a framework for families of Turing complete stochastic languages. We have also developed a class of exact inference algorithms based on the traditional reductions of the λ calculus. We further propose that using the deBruijn notation (a λ-calculus notation with nameless dummies) supports effective caching in such systems, as the reuse of partial solutions is an essential component of efficient computation. Finally, our extension to the λ-calculus offers a foundation and general theory for the construction of recursive stochastic modeling languages as well as promise for effective caching and efficient approximation algorithms for inference.