Enforcing Termination of Interprocedural Analysis

TL;DR

This paper introduces a new local solver for abstract equation systems that guarantees termination of interprocedural analysis in non-recursive programs, addressing issues of non-termination in infinite domains.

Contribution

The paper presents a novel local solver for abstract equation systems that ensures termination for non-recursive programs regardless of domain finiteness.

Findings

The solver terminates for all non-recursive programs.

It is sound in the computed results.

Termination is guaranteed even with infinite domains.

Abstract

Interprocedural analysis by means of partial tabulation of summary functions may not terminate when the same procedure is analyzed for infinitely many abstract calling contexts or when the abstract domain has infinite strictly ascending chains. As a remedy, we present a novel local solver for general abstract equation systems, be they monotonic or not, and prove that this solver fails to terminate only when infinitely many variables are encountered. We clarify in which sense the computed results are sound. Moreover, we show that interprocedural analysis performed by this novel local solver, is guaranteed to terminate for all non-recursive programs --- irrespective of whether the complete lattice is infinite or has infinite strictly ascending or descending chains.