• DOI:10.4204/EPTCS.81.3
• Corpus ID: 12724128

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}
}

• F. E. Miranda-Perea, Lourdes Del Carmen González-Huesca
• Published in
  Workshop on Logical and…
  27 March 2012
• Mathematics

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 the concept of monotonization of an arbitrary operator on a complete lattice. We prove an adequacy theorem with respect to a realizability semantics based on saturated sets and saturated-valued functions and as a consequence we obtain the strong normalization property for the proof-term reduction, an important feature which is absent in previous related work.