Type-based termination of recursive definitions

@article{Barthe2004TypebasedTO,
  title={Type-based termination of recursive definitions},
  author={Gilles Barthe and Maria Jo{\~a}o Frade and Eduardo Gim{\'e}nez and Lu{\'i}s Pinto and Tarmo Uustalu},
  journal={Mathematical Structures in Computer Science},
  year={2004},
  volume={14},
  pages={97-141}
}
This paper introduces λ̂ , a simply typed lambda calculus supporting inductive types and recursive function definitions with termination ensured by types. The system is shown to enjoy subject reduction, strong normalisation of typable terms and to be stronger than a related system λG in which termination is ensured by a syntactic guard condition. The system can, at will, be extended to support coinductive types and corecursive function definitions also. 
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