Bar recursion is not computable via iteration

@article{Longley2018BarRI,
  title={Bar recursion is not computable via iteration},
  author={John Longley},
  journal={CoRR},
  year={2018},
  volume={abs/1804.07277}
}
We show that the bar recursion operators of Spector and Kohlenbach, considered as third-order functionals acting on total arguments, are not computable in Gödel’s System T plus minimization, which we show to be equivalent to a programming language with a higher-order iteration construct. The main result is formulated so as to imply the non-definability of… CONTINUE READING