Term rewriting and all that
Automation inductive specification proofs
Fundamenta Informaticae - Special issue on symbolic computation and artificial intelligence
A general framework to build contextual cover set
Journal of Symbolic Computation - Calculemus-99: integrating computation and deduction
Efficient Reasoning about Executable Specifications in Coq
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Proceedings of the 10th International Conference on Automated Deduction
Mechanical Verification of an Ideal Incremental ABR Conformance Algorithm
Journal of Automated Reasoning
Formal design and verification of operational transformation algorithms for copies convergence
Theoretical Computer Science - Algebraic methodology and software technology
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
Zenon: an extensible automated theorem prover producing checkable proofs
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Automatic 'descente infinie' induction reasoning
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
A tool for automated theorem proving in agda
TYPES'04 Proceedings of the 2004 international conference on Types for Proofs and Programs
Automated certification of implicit induction proofs
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
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We give evidence of the direct integration and automated checking of implicit induction-based proofs inside certified reasoning environments, as that provided by the Coq proof assistant. This is the first step of a long term project focused on 1) mechanically certifying implicit induction proofs generated by automated provers like Spike, and 2) narrowing the gap between automated and interactive proof techniques inside proof assistants such that multiple induction steps can be executed completely automatically and mutual induction can be treated more conveniently. Contrary to the current approaches of reconstructing implicit induction proofs into scripts based on explicit induction tactics that integrate the usual proof assistants, our checking methodology is simpler and fits better for automation. The underlying implicit induction principles are separated and validated independently from the proof scripts that consist in a bunch of one-to-one translations of implicit induction proof steps. The translated steps can be checked independently, too, so the validation process fits well for parallelisation and for the management of large proof scripts. Moreover, our approach is more general; any kind of implicit induction proof can be considered because the limitations imposed by the proof reconstruction techniques no longer exist. An implementation that integrates automatic translators for generating fully checkable Coq scripts from Spike proofs is reported.