Widening for Control-Flow

We present a parameterized widening operator that determines the control-flow sensitivity of an analysis, i.e., its flow-sensitivity, context-sensitivity, and path-sensitivity. By instantiating the operator’s parameter in different ways, the analysis can be tuned to arbitrary sensitivities without changing the abstract semantics of the analysis itself. Similarly, the analysis can be implemented so that its sensitivity can be tuned without changing the analysis implementation. Thus, the sensitivity is an independent concern, allowing the analysis designer to design and implement the analysis without worrying about its sensitivity and then easily experiment with different sensitivities after the fact. Additionally, we show that the space of control-flow sensitivities induced by this widening operator forms a lattice. The lattice meet and join operators are the product and sum of sensitivities, respectively. They can be used to automatically create new sensitivities from existing ones without manual effort. The sum operation in particular is a novel construction, which creates a new sensitivity less precise than either of its operands but containing elements of both.