Section: New Results

Abstract domains

Abstract domains and solvers for set reasoning

Participants : Arlen Cox, Bor-Yuh Evan Chang [University of Colorado, Boulder, USA] , Huisong Li, Xavier Rival [correspondant] .

In [15] , we studied the abstraction and inferrence of set properties.

When constructing complex program analyses, it is often useful to reason about not just individual values, but collections of values. Symbolic set abstractions provide building blocks that can be used to partition elements, relate partitions to other partitions, and determine the provenance of multiple values, all without knowing any concrete values. To address the simultaneous challenges of scalability and precision, we formalized and implemented an interface for symbolic set abstractions and constructed multiple abstract domains relying on both specialized data structures and off-the-shelf theorem provers. We developed techniques for lifting existing domains to improve performance and precision. We evaluated these domains on real-world data structure analysis problems.

Abstraction of optional numerical values

Participants : Jiangchao Liu, Xavier Rival [correspondant] .

In [20] , we designed a functor to lift a numerical abstract domain into an abstract domain that accounts for optional numerical values.

We proposed 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 described the general form of abstract states, and propose sound and automatic static analysis algorithms. We evaluated our construction in the case of an array abstract domain.