Algorithmic solution of higher type equations

@article{Escard2013AlgorithmicSO,
  title={Algorithmic solution of higher type equations},
  author={Mart{\'i}n H{\"o}tzel Escard{\'o}},
  journal={J. Log. Comput.},
  year={2013},
  volume={23},
  pages={839-854}
}
  • M. Escardó
  • Published 1 August 2013
  • Mathematics
  • J. Log. Comput.
In recent work we developed the notion of exhaustible set as a higher-type computational counter-part of the topological notion of compact set. In this paper we give applications to the computation of solutions of higher-type equations. Given a continuous functional f : X → Y and y ∈ Y , we wish to compute x ∈ X such that f(x) = y, if such an x exists. We show that if x is unique and X and Y are subspaces of Kleene– Kreisel spaces of continuous functionals with X exhaustible, then x is… 

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