### Abstract

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.

Original language | English (US) |
---|---|

Title of host publication | POPL 2013 - Proceedings of 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages |

Pages | 537-548 |

Number of pages | 12 |

DOIs | |

State | Published - 2013 |

Event | 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2013 - Rome, Italy Duration: Jan 23 2013 → Jan 25 2013 |

### Other

Other | 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2013 |
---|---|

Country | Italy |

City | Rome |

Period | 1/23/13 → 1/25/13 |

### Fingerprint

### Keywords

- craig interpolants
- crdecision procedures
- crsatisfiability module theories
- data structures
- program analysis

### ASJC Scopus subject areas

- Software

### Cite this

*POPL 2013 - Proceedings of 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages*(pp. 537-548) https://doi.org/10.1145/2429069.2429132

**Complete instantiation-based interpolation.** / Totla, Nishant; Wies, Thomas.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*POPL 2013 - Proceedings of 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages.*pp. 537-548, 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2013, Rome, Italy, 1/23/13. https://doi.org/10.1145/2429069.2429132

}

TY - GEN

T1 - Complete instantiation-based interpolation

AU - Totla, Nishant

AU - Wies, Thomas

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - craig interpolants

KW - crdecision procedures

KW - crsatisfiability module theories

KW - data structures

KW - program analysis

UR - http://www.scopus.com/inward/record.url?scp=84874129799&partnerID=8YFLogxK

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U2 - 10.1145/2429069.2429132

DO - 10.1145/2429069.2429132

M3 - Conference contribution

AN - SCOPUS:84874129799

SN - 9781450318327

SP - 537

EP - 548

BT - POPL 2013 - Proceedings of 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

ER -