  There is increasing interest within the research community in the design and
use of recursive probability models. Although there still remains concern about
computational complexity costs and the fact that computing exact solutions can
be intractable for many nonrecursive models and impossible 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 lambda-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
lambda-calculus. We further propose that using the deBruijn notation (a
lambda-calculus notation with nameless dummies) supports effective caching in
such systems (caching being an essential component of efficient computation).
Finally, our extension to the lambda-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.
