Term rewriting and all that
A general framework to build contextual cover set
Journal of Symbolic Computation - Calculemus-99: integrating computation and deduction
Incorporating decision procedures in implicit induction
Journal of Symbolic Computation - Integrated reasoning and algebra systems
Mechanical Verification of an Ideal Incremental ABR Conformance
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Mechanical Verification of an Ideal Incremental ABR Conformance Algorithm
Journal of Automated Reasoning
'Descente Infinie' Induction-Based Saturation Procedures
SYNASC '07 Proceedings of the Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
Certification of Automated Termination Proofs
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
Combining Rewriting with Noetherian Induction to Reason on Non-orientable Equalities
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Annals of Mathematics and Artificial Intelligence
seL4: formal verification of an operating-system kernel
Communications of the ACM
Validation of the JavaCard platform with implicit induction techniques
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
A tactic language for the system Coq
LPAR'00 Proceedings of the 7th international conference on Logic for programming and automated reasoning
Integrating implicit induction proofs into certified proof environments
IFM'10 Proceedings of the 8th international conference on Integrated formal methods
Automatic 'descente infinie' induction reasoning
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
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Theorem proving is crucial for the formal validation of properties about user specifications. With the help of the Coq proof assistant, we show how to certify properties about conditional specifications that are proved using automated proof techniques like those employed by the Spike prover, a rewrite-based implicit induction proof system. The certification methodology is based on a new representation of the implicit induction proofs for which the underlying induction principle is an instance of Noetherian induction governed by an induction ordering over equalities. We propose improvements of the certification process and show that the certification time is reasonable even for industrial-size applications. As a case study, we automatically prove and certify more than 40% of the lemmas needed for the validation of a conformance algorithm for the ABR protocol.