Control-Flow Analysis and Type Systems

We establish a series of equivalences between type systems and control-flow analyses. Specifically, we take four type systems from the literature (involving simple types, subtypes and recursion) and conservatively extend them to reason about control-flow information. Similarly, we take four standard control-flow systems and conservatively extend them to reason about type consistency. Our main result is that we can match up the resulting type and control-flow systems such that we obtain pairs of equivalent systems, where the equivalence is with respect to both type and control-flow information. In essence, type systems and control-flow analysis can be viewed as complementary approaches for addressing questions of type consistency and control-flow.