Synopsis: Indirection theory gives a clean interface to higher-order step indexing. Many different semantic features of programming languages can be modeled in indirection theory. The models of indirection theory use dependent types to stratify quasirecursive predicates, thus avoiding paradoxes of self-reference. Lambda calculus with mutable references serves as a case study to illustrate the use of indirection theory models.

When defining both Indirection and Separation one must take extra care to ensure that aging commutes over separation. We demonstrate how to build an axiomatic semantics with using higher-order separation logic, for the pointer/continuation language introduced in the case study of Part II.