Deterministic Semantics for Probabilistic Programs

In this talk I will review two semantics for probabilistic programs. The first is measure-theoretic and defined in a monoidal closed category of Banach spaces. The second is based on streams of samples and defined in a Cartesian closed category of topological spaces. Both are purely deterministic.  I will briefly describe these semantics, compare them with standard approaches and with each other, and discuss what they can teach us about probabilistic programs. This is joint work with Dexter Kozen, Alexandra Silva and Billy Smith.