Classical Logic with Mendler Induction - A Dual Calculus and Its Strong Normalization

@inproceedings{Campos2016ClassicalLW,
  title={Classical Logic with Mendler Induction - A Dual Calculus and Its Strong Normalization},
  author={Marco Devesas Campos and Marcelo P. Fiore},
  booktitle={LFCS},
  year={2016}
}
We investigate (co-)induction in Classical Logic under the propositions-as-types paradigm, considering propositional, second-order, and (co-)inductive types. Specifically, we introduce an extension of the Dual Calculus with a Mendler-style (co-)iterator that remains strongly normalizing under head reduction. We prove this using a non-constructive realizability argument.