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# On the Expressivity of Minimal Generic Quantification

Abstract : We come back to the initial design of the $\nabla$ quantifier by Miller and Tiu, which we call minimal generic quantification. In the absence of fixed points, it is equivalent to seemingly stronger designs. However, several expected theorems about (co)inductive specifications can not be derived in that setting. We present a refinement of minimal generic quantification that brings the expected expressivity while keeping the minimal semantic, which we claim is useful to get natural adequate specifications. We build on the idea that generic quantification is not a logical connective but one that is defined, like negation in classical logics. This allows us to use the standard (co)induction rule, but obtain much more expressivity than before. We show classes of theorems that can now be derived in the logic, and present a few practical examples.
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Cited literature [17 references]

https://hal.inria.fr/inria-00284186
Contributor : David Baelde Connect in order to contact the contributor
Submitted on : Monday, June 2, 2008 - 1:49:42 PM
Last modification on : Thursday, March 5, 2020 - 6:24:27 PM
Long-term archiving on: : Friday, September 28, 2012 - 3:11:40 PM

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• HAL Id : inria-00284186, version 1

### Citation

David Baelde. On the Expressivity of Minimal Generic Quantification. International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice, Andreas Abel, Christian Urban, Jun 2008, Pittsburgh, United States. ⟨inria-00284186⟩

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