A Theory of Termination via Indirection

Abstract

Step-indexed models provide approximations to a class of domain
equations and can prove type safety, partial correctness, and program
equivalence; however, a common misconception is that they
are inapplicable to liveness problems. We disprove this by applying
step-indexing to develop the first Hoare logic of total correctness
for a language with function pointers and semantic assertions.
In fact, from a liveness perspective, our logic is stronger: we verify
explicit time resource bounds. We apply our logic to examples containing
nontrivial "higher-order" uses of function pointers and we
prove soundness with respect to a standard operational semantics.
Our core technique is very compact and may be applicable to other
liveness problems. Our results are machine checked in Coq.