## Experiments on supporting interactive proof using resolution

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Venue: | In Basin and Rusinowitch [4 |

Citations: | 28 - 8 self |

### BibTeX

@INPROCEEDINGS{Meng_experimentson,

author = {Jia Meng and Lawrence C. Paulson},

title = {Experiments on supporting interactive proof using resolution},

booktitle = {In Basin and Rusinowitch [4},

year = {},

pages = {372--384}

}

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### Abstract

Abstract. Interactive theorem provers can model complex systems, but require much effort to prove theorems. Resolution theorem provers are automatic and powerful, but they are designed to be used for very different applications. This paper reports a series of experiments designed to determine whether resolution can support interactive proof as it is currently done. In particular, we present a sound and practical encoding in first-order logic of Isabelle’s type classes. 1

### Citations

717 |
Isabelle/HOL — A Proof Assistant for Higher-Order Logic, volume 2283 of LNCS
- Nipkow, Paulson, et al.
- 2002
(Show Context)
Citation Context ...oof as it is currently done. In particular, we present a sound and practical encoding in first-order logic of Isabelle’s type classes. 1 Introduction Interactive proof tools such as HOL [4], Isabelle =-=[8]-=- and PVS [10] have been highly successful. They have been used for verifying hardware, software, protocols, and so forth. Unfortunately, interactive proof requires much effort from a skilled user. Man... |

500 |
T.: Introduction to HOL: A Theorem Proving Environment for Higher Order Logic: Cambridge
- Melham
- 1993
(Show Context)
Citation Context ...interactive proof as it is currently done. In particular, we present a sound and practical encoding in first-order logic of Isabelle’s type classes. 1 Introduction Interactive proof tools such as HOL =-=[4]-=-, Isabelle [8] and PVS [10] have been highly successful. They have been used for verifying hardware, software, protocols, and so forth. Unfortunately, interactive proof requires much effort from a ski... |

406 | The inductive approach to verifying cryptographic protocols. Journal of computer security
- Paulson
- 1998
(Show Context)
Citation Context ...ent of multisets – Comb.thy: combinatory logic formalized in higher-order logic – List Prefix.thy: a prefixing relation on lists – Message.thy: a theory of messages for security protocol verification =-=[12]-=-sTheory Number of Lemmas Number of Goals Number of Goals Proved Multiset 3 3 3 Comb 18 29 24 List Prefix 7 8 8 Message 28 68 62 Table 1. Number of Goals Proved for Typed Lemmas Around 70 to 130 axiom ... |

206 | PVS: Combining specification, proof checking, and model checking
- Owre, Rajan, et al.
- 1996
(Show Context)
Citation Context ... currently done. In particular, we present a sound and practical encoding in first-order logic of Isabelle’s type classes. 1 Introduction Interactive proof tools such as HOL [4], Isabelle [8] and PVS =-=[10]-=- have been highly successful. They have been used for verifying hardware, software, protocols, and so forth. Unfortunately, interactive proof requires much effort from a skilled user. Many other tools... |

127 |
The TPTP Problem Library: CNF Release v1.2.1
- G, Suttner
- 1998
(Show Context)
Citation Context ...ic tools. One of our findings is that even the best resolution provers sometimes founder when given large sets of irrelevant axioms. We have been able to add several hard problems to the TPTP library =-=[19]-=-. 1 We hope that the engineers of resolution provers will make progress on the problem of relevance, and we have already had excellent cooperation from the Vampire team. We have also developed a way o... |

90 | Computing small clause normal forms
- Nonnengart, Weidenbach
(Show Context)
Citation Context ...ere chosen, each of them usually presenting more than one goal to Vampire. The combination of the six setting files was used. The time limit for each proof attempt was 60sec. We used formula renaming =-=[9]-=- before the CNF transformation in order to minimize the number of clauses. For typed Isabelle/HOL formulas, the inclusion of type information also helps to cut down the search space significantly. For... |

88 | Combining superposition, sorts and splitting
- Weidenbach
- 2001
(Show Context)
Citation Context ...he proof script to run without the automatic tool. Another use of the resolution proof is to identify the relevant Isabelle lemmas; that information might be valuable to users.sVampire [16] and SPASS =-=[20]-=- are the provers we have used for our experiments. These are leading resolution provers that have done well in recent CADE ATP System Competitions. Our objective to support integration with any resolu... |

70 | Type classes and overloading in higher-order logic
- Wenzel
- 1997
(Show Context)
Citation Context ...support higher-order logic, which in turn requires a sound modelling of the intricacies of Isabelle’s type system. 4.1 Types and Sorts in Isabelle/HOL Isabelle/HOL [8] supports axiomatic type classes =-=[21]-=-. A type class is a set of types for which certain operations are defined. An axiomatic type class has a set of axioms that must be satisfied by its instances: types belonging to that class. If a type... |

42 | Integrating Gandalf and HOL
- Hurd
- 1999
(Show Context)
Citation Context ... contain errors, even if the provers themselves are sound. Therefore, we would like possible to translate the resolution proof back into a native one, as Hurd has already done between Gandalf and HOL =-=[5]-=-. This could be done by implementing Isabelle versions of the rules used in automatic proofs, such as resolution and paramodulation. Isabelle could then re-play the proof found by the automatic tool. ... |

38 | A Generic Tableau Prover and its Integration with Isabelle
- Paulson
- 1999
(Show Context)
Citation Context ...ther code, including a decision procedure for linear arithmetic. – blast is a sort of generic tableaux theorem prover. It performs forward and backwards chaining using any lemmas supplied by the user =-=[13]-=-. – auto is a naive combination of the previous two tactics. It interleaves rewriting and chaining. However, this treatment of equality is primitive compared with that provided by a good resolution pr... |

37 |
Vampire 1.1 (system description
- Riazanov, Voronkov
- 2001
(Show Context)
Citation Context ...executions of the proof script to run without the automatic tool. Another use of the resolution proof is to identify the relevant Isabelle lemmas; that information might be valuable to users.sVampire =-=[16]-=- and SPASS [20] are the provers we have used for our experiments. These are leading resolution provers that have done well in recent CADE ATP System Competitions. Our objective to support integration ... |

32 | An LCF-style interface between HOL and first-order logic
- Hurd
- 2002
(Show Context)
Citation Context ...s have attempted to combine interactive and automatic theorem provers. The HOL system has for many years included a model elimination theorem prover, which recently Hurd has attempted to improve upon =-=[6]-=-. The Coq system has also been interfaced with an automatic first-order prover [2]. These approaches expect the user to pick relevant lemmassmanually. Another attempt, using the KIV system [1], includ... |

31 | Integrating automated and interactive theorem proving
- Ahrendt, Beckert, et al.
- 1998
(Show Context)
Citation Context ...ve upon [6]. The Coq system has also been interfaced with an automatic first-order prover [2]. These approaches expect the user to pick relevant lemmassmanually. Another attempt, using the KIV system =-=[1]-=-, includes an automatic mechanism for discarding irrelevant lemmas. This approach has attractions, and the overall performance might be improved by using a more powerful automatic prover. Closest to o... |

26 | Generic automatic proof tools
- Paulson
- 1997
(Show Context)
Citation Context ... ∈ B) An equation between Boolean terms is obviously not first-order. Moreover, Isabelle represents the left-to-right implication in a peculiar fashion related to its encoding of the sequent calculus =-=[11]-=-. Our translation has to recognize this encoding and translate it to the corresponding implication, which in this case is ∀c A B [c ∈ A ∩ B → (c ∈ A ∧ c ∈ B)] We also need to remove ZF terms, such as ... |

10 |
de Nivelle. Automatic proof construction in type theory using resolution
- Bezem, Hendriks, et al.
- 2002
(Show Context)
Citation Context ...tem has for many years included a model elimination theorem prover, which recently Hurd has attempted to improve upon [6]. The Coq system has also been interfaced with an automatic first-order prover =-=[2]-=-. These approaches expect the user to pick relevant lemmassmanually. Another attempt, using the KIV system [1], includes an automatic mechanism for discarding irrelevant lemmas. This approach has attr... |

5 | Integration of interactive and automatic provers
- Meng
(Show Context)
Citation Context ...s. We convert Isabelle’s formalisms into untyped first-order logic rather than expecting the resolution prover to support them. 3 Formalising Untyped Isabelle/ZF in FOL As Meng has reported elsewhere =-=[7]-=-, our first experiments concerned translating Isabelle/ZF formulas into first-order logic (FOL) in order to examine whether the use of resolution was practial. These experiments consisted of taking ex... |

4 | Isabelle’s logics: FOL and ZF
- Paulson
- 2003
(Show Context)
Citation Context ...generic: it supports a multiplicity of logics. The most important of these is higher-order logic, which is also the basis of the HOL system and PVS. Isabelle also supports Zermelo-Fraenkel set theory =-=[14]-=-, which is an untyped formalism based upon first-order logic. Isabelle provides substantial automation. Its reasoning tactics include the following: 1 SET787-1.p, SET787-2.p, COL088-1.p to COL0100-2.p... |

4 | Efficient checking of term ordering constraints
- Riazanov, Voronkov
- 2004
(Show Context)
Citation Context ...dences to functions and predicates to indicate which literals should be eliminated sooner; this information gives an ordering on literals, which Vampire computes using the Knuth-Bendix Ordering (KBO) =-=[15]-=-. However, since the resulting KBO is a partial ordering on terms with variables, it does not match our requirements exactly. The Vampire developers gave us a new version of Vampire (v6.03), with synt... |