We introduce a general static analysis framework to reason about program properties at an infinite number of runtime control points, called instances. Infinite sets of instances are represented by rational languages. Based on this instancewise framework, we extend the concept of induction variables to recursive programs. For a class of monoid-based data structures, including arrays and trees, induction variables capture the exact memory location accessed at every step of the execution. This compile-time characterization is computed in polynomial time as a rational function.