  We introduce Probabilistic Dependent Type Systems (PDTS) via a functional
language based on a subsystem of intuitionistic type theory including dependent
sums and products, which is expanded to include stochastic functions. We
provide a sampling-based semantics for the language based on non-deterministic
beta reduction. Further, we derive a probabilistic logic from the PDTS
introduced as a direct result of the Curry-Howard isomorphism. The
probabilistic logic derived is shown to provide a universal representation for
finite discrete distributions.
