### Abstract

Demonic refinement algebras are variants of Kleene algebras. Introduced by von Wright as a light-weight variant of the refinement calculus, their intended semantics are positively disjunctive predicate transformers, and their calculus is entirely within first-order equational logic. So, for the first time, off-the-shelf automated theorem proving (ATP) becomes available for refinement proofs. We used ATP to verify a toolkit of basic refinement laws. Based on this toolkit, we then verified two classical complex refinement laws for action systems by ATP: a data refinement law and Back's atomicity refinement law. We also present a refinement law for infinite loops that has been discovered through automated analysis. Our proof experiments not only demonstrate that refinement can effectively be automated, they also compare eleven different ATP systems and suggest that program verification with variants of Kleene algebras yields interesting theorem proving benchmarks. Finally, we apply hypothesis learning techniques that seem indispensable for automating more complex proofs.

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

Pages (from-to) | 35-62 |

Number of pages | 28 |

Journal | Annals of Mathematics and Artificial Intelligence |

Volume | 55 |

Issue number | 1-2 |

DOIs | |

State | Published - Oct 2009 |

### Fingerprint

### Keywords

- Action systems
- Automated deduction
- Kleene algebras
- Refinement calculus

### ASJC Scopus subject areas

- Artificial Intelligence
- Applied Mathematics

### Cite this

*Annals of Mathematics and Artificial Intelligence*,

*55*(1-2), 35-62. https://doi.org/10.1007/s10472-009-9151-8

**Automated verification of refinement laws.** / Höfner, Peter; Struth, Georg; Sutcliffe, Geoffrey.

Research output: Contribution to journal › Article

*Annals of Mathematics and Artificial Intelligence*, vol. 55, no. 1-2, pp. 35-62. https://doi.org/10.1007/s10472-009-9151-8

}

TY - JOUR

T1 - Automated verification of refinement laws

AU - Höfner, Peter

AU - Struth, Georg

AU - Sutcliffe, Geoffrey

PY - 2009/10

Y1 - 2009/10

N2 - Demonic refinement algebras are variants of Kleene algebras. Introduced by von Wright as a light-weight variant of the refinement calculus, their intended semantics are positively disjunctive predicate transformers, and their calculus is entirely within first-order equational logic. So, for the first time, off-the-shelf automated theorem proving (ATP) becomes available for refinement proofs. We used ATP to verify a toolkit of basic refinement laws. Based on this toolkit, we then verified two classical complex refinement laws for action systems by ATP: a data refinement law and Back's atomicity refinement law. We also present a refinement law for infinite loops that has been discovered through automated analysis. Our proof experiments not only demonstrate that refinement can effectively be automated, they also compare eleven different ATP systems and suggest that program verification with variants of Kleene algebras yields interesting theorem proving benchmarks. Finally, we apply hypothesis learning techniques that seem indispensable for automating more complex proofs.

AB - Demonic refinement algebras are variants of Kleene algebras. Introduced by von Wright as a light-weight variant of the refinement calculus, their intended semantics are positively disjunctive predicate transformers, and their calculus is entirely within first-order equational logic. So, for the first time, off-the-shelf automated theorem proving (ATP) becomes available for refinement proofs. We used ATP to verify a toolkit of basic refinement laws. Based on this toolkit, we then verified two classical complex refinement laws for action systems by ATP: a data refinement law and Back's atomicity refinement law. We also present a refinement law for infinite loops that has been discovered through automated analysis. Our proof experiments not only demonstrate that refinement can effectively be automated, they also compare eleven different ATP systems and suggest that program verification with variants of Kleene algebras yields interesting theorem proving benchmarks. Finally, we apply hypothesis learning techniques that seem indispensable for automating more complex proofs.

KW - Action systems

KW - Automated deduction

KW - Kleene algebras

KW - Refinement calculus

UR - http://www.scopus.com/inward/record.url?scp=70350381800&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350381800&partnerID=8YFLogxK

U2 - 10.1007/s10472-009-9151-8

DO - 10.1007/s10472-009-9151-8

M3 - Article

AN - SCOPUS:70350381800

VL - 55

SP - 35

EP - 62

JO - Annals of Mathematics and Artificial Intelligence

JF - Annals of Mathematics and Artificial Intelligence

SN - 1012-2443

IS - 1-2

ER -