Time Bounds for General Function Pointers

We develop a logic of explicit time resource bounds for a language with function pointers and semantic assertions. 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 resource bounding problems, and is the first application of step-indexed models in which the outermost quantifier is existential instead of universal. Our results are machine checked in Coq.