Parametric shape analysis via 3-valued logic
ACM Transactions on Programming Languages and Systems (TOPLAS)
Verifying reachability invariants of linked structures
POPL '83 Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Proving Pointer Programs in Hoare Logic
MPC '00 Proceedings of the 5th International Conference on Mathematics of Program Construction
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
An interpolating theorem prover
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2004)
Interpolation for data structures
Proceedings of the 14th ACM SIGSOFT international symposium on Foundations of software engineering
Back to the future: revisiting precise program verification using SMT solvers
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Ground Interpolation for the Theory of Equality
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Complete Instantiation for Quantified Formulas in Satisfiabiliby Modulo Theories
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Incremental Instance Generation in Local Reasoning
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Ground Interpolation for Combined Theories
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Constraint solving for interpolation
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
The Why/Krakatoa/Caduceus platform for deductive program verification
CAV'07 Proceedings of the 19th international conference on Computer aided verification
On local reasoning in verification
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Quantified invariant generation using an interpolating saturation prover
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
To goto where no statement has gone before
VSTTE'10 Proceedings of the Third international conference on Verified software: theories, tools, experiments
Beyond quantifier-free interpolation in extensions of Presburger arithmetic
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
The reduced product of abstract domains and the combination of decision procedures
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Efficient interpolant generation in satisfiability modulo linear integer arithmetic
TACAS'11/ETAPS'11 Proceedings of the 17th international conference on Tools and algorithms for the construction and analysis of systems: part of the joint European conferences on theory and practice of software
An efficient decision procedure for imperative tree data structures
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Interpolation-based software verification with WOLVERINE
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
An Interpolating Sequent Calculus for Quantifier-Free Presburger Arithmetic
Journal of Automated Reasoning
Playing in the grey area of proofs
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Lazy abstraction with interpolants
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Hierarchic reasoning in local theory extensions
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
A combination method for generating interpolants
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
SLAB: a certifying model checker for infinite-state concurrent systems
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Interpolation and symbol elimination in vampire
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
A practical and complete approach to predicate refinement
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Lazy abstraction with interpolants for arrays
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
From strong amalgamability to modularity of quantifier-free interpolation
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Automating separation logic using SMT
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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Craig interpolation has been a valuable tool for formal methods with interesting applications in program analysis and verification. Modern SMT solvers implement interpolation procedures for the theories that are most commonly used in these applications. However, many application-specific theories remain unsupported, which limits the class of problems to which interpolation-based techniques apply. In this paper, we present a generic framework to build new interpolation procedures via reduction to existing interpolation procedures. We consider the case where an application-specific theory can be formalized as an extension of a base theory with additional symbols and axioms. Our technique uses finite instantiation of the extension axioms to reduce an interpolation problem in the theory extension to one in the base theory. We identify a model-theoretic criterion that allows us to detect the cases where our technique is complete. We discuss specific theories that are relevant in program verification and that satisfy this criterion. In particular, we obtain complete interpolation procedures for theories of arrays and linked lists. The latter is the first complete interpolation procedure for a theory that supports reasoning about complex shape properties of heap-allocated data structures. We have implemented this procedure in a prototype on top of existing SMT solvers and used it to automatically infer loop invariants of list-manipulating programs.