### Abstract

Most verification approaches assume a mathematical formalism in which functions are total, even though partial functions occur naturally in many applications. Furthermore, although there have been various proposals for logics of partial functions, there is no consensus on which is "the right" logic to use for verification applications. In this paper, we propose using a three-valued Kleene logic, where partial functions return the "undefined" value when applied outside of their domains. The particular semantics are chosen according to the principle of least surprise to the user; if there is disagreement among the various approaches on what the value of the formula should be, its evaluation is undefined. We show that the problem of checking validity in the three-valued logic can be reduced to checking validity in a standard two-valued logic, and describe how this approach has been successfully implemented in our tool, CVC Lite.

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

Pages (from-to) | 13-23 |

Number of pages | 11 |

Journal | Electronic Notes in Theoretical Computer Science |

Volume | 125 |

Issue number | 3 |

DOIs | |

State | Published - Jul 18 2005 |

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### Keywords

- CVC
- Kleene
- Partial functions
- Three-valued logic

### ASJC Scopus subject areas

- Computer Science (miscellaneous)

### Cite this

*Electronic Notes in Theoretical Computer Science*,

*125*(3), 13-23. https://doi.org/10.1016/j.entcs.2004.06.064

**A practical approach to partial functions in CVC lite.** / Berezin, Sergey; Barrett, Clark; Shikanian, Igor; Chechik, Marsha; Gurfinkel, Arie; Dill, David L.

Research output: Contribution to journal › Article

*Electronic Notes in Theoretical Computer Science*, vol. 125, no. 3, pp. 13-23. https://doi.org/10.1016/j.entcs.2004.06.064

}

TY - JOUR

T1 - A practical approach to partial functions in CVC lite

AU - Berezin, Sergey

AU - Barrett, Clark

AU - Shikanian, Igor

AU - Chechik, Marsha

AU - Gurfinkel, Arie

AU - Dill, David L.

PY - 2005/7/18

Y1 - 2005/7/18

N2 - Most verification approaches assume a mathematical formalism in which functions are total, even though partial functions occur naturally in many applications. Furthermore, although there have been various proposals for logics of partial functions, there is no consensus on which is "the right" logic to use for verification applications. In this paper, we propose using a three-valued Kleene logic, where partial functions return the "undefined" value when applied outside of their domains. The particular semantics are chosen according to the principle of least surprise to the user; if there is disagreement among the various approaches on what the value of the formula should be, its evaluation is undefined. We show that the problem of checking validity in the three-valued logic can be reduced to checking validity in a standard two-valued logic, and describe how this approach has been successfully implemented in our tool, CVC Lite.

AB - Most verification approaches assume a mathematical formalism in which functions are total, even though partial functions occur naturally in many applications. Furthermore, although there have been various proposals for logics of partial functions, there is no consensus on which is "the right" logic to use for verification applications. In this paper, we propose using a three-valued Kleene logic, where partial functions return the "undefined" value when applied outside of their domains. The particular semantics are chosen according to the principle of least surprise to the user; if there is disagreement among the various approaches on what the value of the formula should be, its evaluation is undefined. We show that the problem of checking validity in the three-valued logic can be reduced to checking validity in a standard two-valued logic, and describe how this approach has been successfully implemented in our tool, CVC Lite.

KW - CVC

KW - Kleene

KW - Partial functions

KW - Three-valued logic

UR - http://www.scopus.com/inward/record.url?scp=21644465814&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21644465814&partnerID=8YFLogxK

U2 - 10.1016/j.entcs.2004.06.064

DO - 10.1016/j.entcs.2004.06.064

M3 - Article

VL - 125

SP - 13

EP - 23

JO - Electronic Notes in Theoretical Computer Science

JF - Electronic Notes in Theoretical Computer Science

SN - 1571-0661

IS - 3

ER -