Broadening the applicability of local completeness analysis with intensional and extensional guarantees

Abstract

Local Completeness Logic (LCL) is a proof system for program analysis rooted in abstract interpretation. The program semantics is under-approximated by any provable postcondition, like incorrectness logic does, but it is also over-approximated by a (locally) complete abstraction of such a postcondition, like Hoare logic does. Therefore, any derivable triple will either prove the program to be correct or unveil true bugs. While the completeness of a program's function with respect to an abstract domain is inherently extensional, LCL's rules demand the preservation of local completeness throughout the abstract interpreter's computations. This characteristic renders LCL analysis intensional, meaning it depends on the way the program is written. Consequently, LCL proof system may not derive all the valid triples. This paper addresses this discrepancy by: 1) designing new rules that allow one to perform part of the intensional analysis in different (complete) abstract domains whenever necessary; and 2) to compare their expressiveness. Notably, some of these new rules enable the derivation of all extensionally valid triples, thereby decoupling the set of provable properties from the way the program is written.