  In this chapter, we explore how (Type-2) computable distributions can be used
to give both (algorithmic) sampling and distributional semantics to
probabilistic programs with continuous distributions. Towards this end, we
sketch an encoding of computable distributions in a fragment of Haskell and
show how topological domains can be used to model the resulting PCF-like
language. We also examine the implications that a (Type-2) computable semantics
has for implementing conditioning. We hope to draw out the connection between
an approach based on (Type-2) computability and ordinary programming throughout
the chapter as well as highlight the relation with constructive mathematics
(via realizability).
