Mendler-style Iso-(Co)inductive predicates: a strongly normalizing approach

@inproceedings{MirandaPerea2012MendlerstyleIP,
  title={Mendler-style Iso-(Co)inductive predicates: a strongly normalizing approach},
  author={Favio Ezequiel Miranda-Perea and Lourdes Del Carmen Gonz{\'a}lez-Huesca},
  booktitle={Workshop on Logical and Semantic Frameworks with Applications},
  year={2012}
}
We present an extension of the second-order logic AF2 with iso-style inductive and coinductive definitions specifically designed to extract programs from proofs a la Krivine-Parigot by means of primitive (co)recursion principles. Our logic includes primitive constructors of least and greatest fixed points of predicate transformers, but contrary to the common approach, we do not restrict ourselves to positive operators to ensure monotonicity, instead we use the Mendler-style, motivated here by… 

A realizability interpretation of Church's simple theory of types

A realizability interpretation of an intuitionistic version of Church's Simple Theory of Types which can be viewed as a formalization of intuitionistic higher-order logic and includes operators for monotone induction and coinduction and simple realizers for them.

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