Ground Interpolation for Combined Theories

Goel, Amit; Krstić, Sava; Tinelli, Cesare

doi:10.1007/978-3-642-02959-2_16

Cited by 29 publications

(32 citation statements)

References 20 publications

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“…Furthermore, our scheme can deal with resolution steps where a mixed literal occurs in both antecedents, which are forbidden by other schemes [5,12].…”

Section: Discussionmentioning

confidence: 99%

Proof Tree Preserving Interpolation

Christ

Hoenicke

Nutz

2013

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Craig interpolation in SMT is difficult because, e. g., theory combination and integer cuts introduce mixed literals, i. e., literals containing local symbols from both input formulae. In this paper, we present a scheme to compute Craig interpolants in the presence of mixed literals. Contrary to existing approaches, this scheme neither limits the inferences done by the SMT solver, nor does it transform the proof tree before extracting interpolants. Our scheme works for the combination of uninterpreted functions and linear arithmetic but is extendable to other theories. The scheme is implemented in the interpolating SMT solver SMTInterpol.

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“…Furthermore, our scheme can deal with resolution steps where a mixed literal occurs in both antecedents, which are forbidden by other schemes [5,12].…”

Section: Discussionmentioning

confidence: 99%

Proof Tree Preserving Interpolation

Christ

Hoenicke

Nutz

2013

Tools and Algorithms for the Construction and Analysis of Systems

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“…Ground interpolation procedures for specific theories have been developed, e.g., for linear arithmetic over reals [23,38] and integers [8,9], uninterpreted functions with equality [19,38,50], functional lists [50], as well as, combinations of these theories [11,21,38,50]. These are the procedures that our approach builds on.…”

Section: Related Workmentioning

confidence: 99%

“…Modern SMT solvers implement ground interpolation procedures for the theories that are most commonly used in program verification. This includes theories such as linear arithmetic [8,9,23,38], the theory of uninterpreted function symbols with equality [19,38,50], and combinations of such theories [11,21,38,50]. However, many application-specific theories remain unsupported.…”

Section: Introductionmentioning

confidence: 99%

Complete instantiation-based interpolation

TotlaNishant

WiesThomas

2013

SIGPLAN Not.

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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 modeltheoretic 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.

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“…Such a restriction causes no loss of generality because any interpolation procedure for conjunctions of literals can be extended in a uniform way to arbitrary ground formulasand under the right conditions also combined with interpolation procedures for other theories [McM05b,CGS08,GKT09].…”

Section: Introductionmentioning

confidence: 99%

Ground interpolation for the theory of equality

Fuchs¹,

Goel²,

Grundy³

et al. 2012

Logical Methods in Computer Science

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Abstract. Given a theory T and two formulas A and B jointly unsatisfiable in T , a theory interpolant of A and B is a formula I such that (i) its non-theory symbols are shared by both A and B, (ii) it is entailed by A in T , and (iii) it is unsatisfiable with B in T . Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence graphs representing derivations in that theory. These graphs can be produced by conventional congruence closure algorithms in a straightforward manner. By working with graphs, rather than at the level of individual proof steps, we are able to derive interpolants that are pleasingly simple (conjunctions of Horn clauses) and smaller than those generated by other tools. Our interpolation method can be seen as a theory-specific implementation of a cooperative interpolation game between two provers. We present a generic version of the interpolation game, parametrized by the theory T , and define a general method to extract runs of the game from proofs in T and then generate interpolants from these runs.

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Ground Interpolation for Combined Theories

Cited by 29 publications

References 20 publications

Proof Tree Preserving Interpolation

Proof Tree Preserving Interpolation

Complete instantiation-based interpolation

Ground interpolation for the theory of equality

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