A probabilistic theory of designs based on distributions

We present a theory of designs based on functions from the state space to real numbers, which we term distributions. This theory uses predicates, in the style of UTP, based on homogeneous relations between distributions, and is richer than the standard UTP theory of designs as it allows us to reason about probabilistic programs; the healthiness conditions H1{H4 of the standard theory are implicitly accounted for in the distributional theory we present. In addition we propose a Galois connection linkage between our distribution-based model of probabilistic designs, and the standard UTP model of (non-probabilistic) designs