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Conference Papers Year : 2010

Integrating Implicit Induction Proofs into Certified Proof Environments


We give evidence of the direct integration and automated checking of implicit induction-based proofs inside certified reasoning en- vironments, as that provided by the Coq proof assistant. This is the first step of a long term project focused on 1) mechanically certifying im- plicit induction proofs generated by automated provers like Spike, and 2) narrowing the gap between automated and interactive proof tech- niques 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 induc- tion principles are separated and validated independently from the proof scripts that consist in a bunch of one-to-one translations of implicit in- duction proof steps. The translated steps can be checked independently, too, so the validation process fits well for parallelisation and for the man- agement of large proof scripts. Moreover, our approach is more general; any kind of implicit induction proof can be considered because the limi- tations 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.
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hal-00553070 , version 1 (06-01-2011)


  • HAL Id : hal-00553070 , version 1


Sorin Stratulat. Integrating Implicit Induction Proofs into Certified Proof Environments. Integrated Formal Methods, 2010, France. pp.320-335. ⟨hal-00553070⟩


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