Abstract debugging of higher-order imperative languages
PLDI '93 Proceedings of the ACM SIGPLAN 1993 conference on Programming language design and implementation
Guarded commands, nondeterminacy and formal derivation of programs
Communications of the ACM
Extended static checking for Java
PLDI '02 Proceedings of the ACM SIGPLAN 2002 Conference on Programming language design and implementation
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Apron: A Library of Numerical Abstract Domains for Static Analysis
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Sufficient preconditions for modular assertion checking
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Precondition inference from intermittent assertions and application to contracts on collections
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
Symbolic methods to enhance the precision of numerical abstract domains
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Understanding the origin of alarms in ASTRÉE
SAS'05 Proceedings of the 12th international conference on Static Analysis
Inferring definite counterexamples through under-approximation
NFM'12 Proceedings of the 4th international conference on NASA Formal Methods
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In this article, we discuss the automatic inference of sufficient pre-conditions by abstract interpretation and sketch the construction of an under-approximating backward analysis. We focus on numeric domains and propose transfer functions, including a lower widening, for polyhedra, without resorting to disjunctive completion nor complementation, while soundly handling non-determinism. Applications include the derivation of sufficient conditions for a program to never step outside an envelope of safe states, or dually to force it to eventually fail. Our construction is preliminary and essentially untried, but we hope to convince that this avenue of research is worth considering.