Semi-decidability of May, Must and Probabilistic Testing in a Higher-type Setting

We show that, in a fairly general setting including higher-types, may, must and probabilistic testing are semi-decidable. The case of must testing is perhaps surprising, as its mathematical definition involves universal quantification over the infinity of possible outcomes of a non-deterministic program. The other two involve existential quantification and integration. We also perform first steps towards the semi-decidability of similar tests under the simultaneous presence of non-deterministic and probabilistic choice.