## Certification of automated termination proofs (2007)

Venue: | In Proc. 6th FroCoS |

Citations: | 18 - 4 self |

### BibTeX

@INPROCEEDINGS{Contejean07certificationof,

author = {Evelyne Contejean and Pierre Courtieu and Julien Forest and Olivier Pons and Xavier Urbain},

title = {Certification of automated termination proofs},

booktitle = {In Proc. 6th FroCoS},

year = {2007},

pages = {148--162}

}

### OpenURL

### Abstract

2 CÉDRIC – Conservatoire national des arts et métiers Abstract. Nowadays, formal methods rely on tools of different kinds: proof assistants with which the user interacts to discover a proof step by step; and fully automated tools which make use of (intricate) decision procedures. But while some proof assistants can check the soundness of a proof, they lack automation. Regarding automated tools, one still has to be satisfied with their answers Yes/No/Donotknow, the validity of which can be subject to question, in particular because of the increasing size and complexity of these tools. In the context of rewriting techniques, we aim at bridging the gap between proof assistants that yield formal guarantees of reliability and highly automated tools one has to trust. We present an approach making use of both shallow and deep embeddings. We illustrate this approach with a prototype based on the CiME rewriting toolbox, which can discover involved termination proofs that can be certified by the COQ proof assistant, using the COCCINELLE library for rewriting. 1

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Citation Context ... they are proven to be terminating. We restrict here to first order. The last decade has been very fertile w.r.t. automation of termination proofs, and yielded many efficient tools (APROVE [15], CiME =-=[7]-=-, JAMBOX [13], TPA [19], TTT [17] and others) referenced on the Termination Competition’s web site [21], some of which display nice output for human reading. However, there is still a clear gap betwee... |

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Citation Context ...n a small example in our prototype, namely CiME 2.99. While being based on the CiME 2 tool box, this prototype does not certify all its predecessor’s termination power. For instance, modular criteria =-=[25]-=- and termination modulo equational theories are not supported yet. In the following, we restrict to (marked/unmarked) Dependency Pairs [1] 6 the transitive closure ofone_step is defined asrwr in COCCI... |

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Citation Context ...hese systems do not tackle the problem of termination proofs. To our knowledge the only other approach to generate termination certificates for rewriting systems relies on the CoLoR/Rainbow libraries =-=[4]-=-. In this approach, term algebras and TRSs are handled via an embedding even deeper than in COCCINELLE, since a TRS is given by a set of pairs of terms. Notice that the RPO in CoLoR is weaker than the... |

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Citation Context ...ng. We restrict here to first order. The last decade has been very fertile w.r.t. automation of termination proofs, and yielded many efficient tools (APROVE [15], CiME [7], JAMBOX [13], TPA [19], TTT =-=[17]-=- and others) referenced on the Termination Competition’s web site [21], some of which display nice output for human reading. However, there is still a clear gap between proof assistants that provide f... |

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Citation Context ...n automated provers and COQ. Amongst them, the theorem-prover ZÉNON [12], based on tableaux, produces COQ proof terms as certificates. ELAN enjoys techniques to produce COQ certificates for rewriting =-=[22]-=-. Bezem describes an approach regarding resolution [3]. However, these systems do not tackle the problem of termination proofs. To our knowledge the only other approach to generate termination certifi... |

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Citation Context ...prover ZÉNON [12], based on tableaux, produces COQ proof terms as certificates. ELAN enjoys techniques to produce COQ certificates for rewriting [22]. Bezem describes an approach regarding resolution =-=[3]-=-. However, these systems do not tackle the problem of termination proofs. To our knowledge the only other approach to generate termination certificates for rewriting systems relies on the CoLoR/Rainbo... |

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Citation Context ...or does not deal with AC nor C symbols, hence in this work all symbols have an arityFree n. However, AC/C symbols are used in other parts of COCCINELLE, in particular the formalisation of AC matching =-=[5]-=-. A term algebra is a module defined from its signatureFand the set of variablesX. Module Type Term. Declare Module Import F : Signature. Declare Module Import X : decidable_set.S. Terms are defined a... |

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Citation Context ...g work in the A3PAT group is to define a more general language that can even tackle proofs of various rewriting properties such as termination, confluence (which needs termination), equational proofs =-=[6]-=-, etc. We think that a good candidate could be based on the tree structure we explained on Section 4.1. One particularly interesting follow-up of this work is the possibility to plug automated termina... |

3 | The termination competition 2006
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Citation Context ...tile w.r.t. automation of termination proofs, and yielded many efficient tools (APROVE [15], CiME [7], JAMBOX [13], TPA [19], TTT [17] and others) referenced on the Termination Competition’s web site =-=[21]-=-, some of which display nice output for human reading. However, there is still a clear gap between proof assistants that provide formal guarantees of reliability and highly automated tools one has to ... |

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Citation Context ...irs is the following and fits in the general structure we explained on section 4.1: Lemma wfR_if_wfDPR: well_founded DPR -> well_founded (one_step R). The proof follows a general scheme due to Hubert =-=[18]-=-. It involves several nested inductions instantiating the proof of the criterion in the particular setting of DPR and one_step R. Marked symbols A refinement of the DP criterion consists in marking he... |