Abstraction of optional numerical values

Abstract

We propose a technique to describe properties of numerical stores with optional values, that is, where some variables may have no value. Properties of interest include numerical equalities and inequalities. Our approach lifts common linear inequality based numerical abstract domains into abstract domains describing stores with optional values. This abstraction can be used in order to analyze languages with some form of option scalar type. It can also be applied to the construction of abstract domains to describe complex memory properties that introduce symbolic variables, e.g., in order to summarize unbounded sets of program variables, and where these symbolic variables may be undefined, as in some array or shape analyses. We describe the general form of abstract states, and propose sound and automatic static analysis algorithms. We evaluate our construction in the case of an array abstract domain.