Enforcing Termination of Interprocedural Analysis

Frielinghaus, Stefan Schulze; Seidl, Helmut; Vogler, Ralf

doi:10.1007/978-3-662-53413-7_22

Cited by 3 publications

(4 citation statements)

References 25 publications

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“…Assume further that for all . Then by the results of Frielinghaus et al (2016), also holds. Accordingly, the pair can then be understood as a sound description of the least partial post-solution of the concrete system for x .…”

Section: Correctness Of Tdtermmentioning

confidence: 81%

“…Let denote the least total solution of some concrete system which is described by . In Frielinghaus et al (2016), it has been proven that then also holds. Moreover, let denote the least -closed subset containing some initial unknown x .…”

Section: Correctness Of Tdtermmentioning

confidence: 99%

“…Since for different values in for , different unknowns are queried, this function cannot be monotonic. In order to deal with such non-monotonicities, Frielinghaus et al (2016) have introduced the concept of a lower monotonization of the abstract system .…”

Section: Correctness Of Tdtermmentioning

confidence: 99%

“…Systems for interprocedural analysis, however, are not necessarily monotonic. The problems concerning termination as encountered by the non-standard local iteration strategy from Amato et al (2016) were resolved in Frielinghaus et al (2016) where the switch from a widening to a narrowing iteration for an unknown was carefully redesigned.…”

Section: Introductionmentioning

confidence: 99%

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Three improvements to the top-down solver

Seidl

Vogler

2021

Math. Struct. Comp. Sci.

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The local solver TD is a generic fixpoint engine which explores a given system of equations on demand. It has been successfully applied to the interprocedural analysis of procedural languages. The solver TD gains efficiency by detecting dependencies between unknowns on the fly. This algorithm has been recently extended to deal with widening and narrowing as well. In particular, it has been equipped with an automatic detection of widening and narrowing points. That version, however, is only guaranteed to terminate under two conditions: only finitely many unknowns are encountered, and all right-hand sides are monotonic. While the first condition is unavoidable, the second limits the applicability of the solver. Another limitation is that the solver maintains the current abstract values of all encountered unknowns instead of a minimal set sufficient for performing the iteration. By consuming unnecessarily much space, interprocedural analyses may not succeed on seemingly small programs. In the present paper, we therefore extend the top-down solver TD in three ways. First, we indicate how the restriction to monotonic right-hand sides can be lifted without compromising termination. We then show how the solver can be tuned to store abstract values only when their preservation is inevitable. Finally, we also show how the solver can be extended to side-effecting equation systems. Right-hand sides of these may not only provide values for the corresponding left-hand side unknowns but at the same time produce contributions to other unknowns. This practical extension has successfully been used for a seamless combination of context-sensitive analyses (e.g., of local states) with flow-insensitive analyses (e.g., of globals).

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