  This paper describes a new algorithm for exact Bayesian inference that is
based on a recently proposed compositional semantics of Bayesian networks in
terms of channels. The paper concentrates on the ideas behind this algorithm,
involving a linearisation (`stretching') of the Bayesian network, followed by a
combination of forward state transformation and backward predicate
transformation, while evidence is accumulated along the way. The performance of
a prototype implementation of the algorithm in Python is briefly compared to a
standard implementation (pgmpy): first results show competitive performance.
