@article{Escardo01082013,
    Abstract = {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 article, 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 computable uniformly in f, y and the exhaustibility condition. We also establish a version of this for computational metric spaces X and Y, where is X computationally complete and has an exhaustible set of Kleene--Kreisel representatives. Examples of interest include evaluation functionals defined on compact spaces X of bounded sequences of Taylor coefficients with values on spaces Y of real analytic functions defined on a compact set. A corollary is that it is semi-decidable whether a function defined on such a compact set fails to be analytic, and that the Taylor coefficients of an analytic function can be computed extensionally from the function.},
    Author = {Escard{\'o}, Mart{\'\i}n},
    EPrint = {http://logcom.oxfordjournals.org/content/23/4/839.full.pdf+html},
    File = {Algorithmic solution of higher type equations - Escardó (0) (0) - a - a - y.pdf},
    Journal = {Journal of Logic and Computation},
    Number = {4},
    Pages = {839-854},
    Title = {Algorithmic solution of higher type equations},
    URL = {http://logcom.oxfordjournals.org/content/23/4/839.abstract},
    Volume = {23},
    Year = {2013},
    bdsk-url-1 = {http://logcom.oxfordjournals.org/content/23/4/839.abstract},
    bdsk-url-2 = {http://dx.doi.org/10.1093/logcom/exr048},
    date-added = {2013-12-28 08:42:55 +0000},
    date-modified = {2013-12-28 08:42:55 +0000},
    doi = {10.1093/logcom/exr048}
}

@article{Escardo01082013, Abstract = {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 article, 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 computable uniformly in f, y and the exhaustibility condition. We also establish a version of this for computational metric spaces X and Y, where is X computationally complete and has an exhaustible set of Kleene--Kreisel representatives. Examples of interest include evaluation functionals defined on compact spaces X of bounded sequences of Taylor coefficients with values on spaces Y of real analytic functions defined on a compact set. A corollary is that it is semi-decidable whether a function defined on such a compact set fails to be analytic, and that the Taylor coefficients of an analytic function can be computed extensionally from the function.}, Author = {Escard{\'o}, Mart{\'\i}n}, EPrint = {http://logcom.oxfordjournals.org/content/23/4/839.full.pdf+html}, File = {Algorithmic solution of higher type equations - Escardó (0) (0) - a - a - y.pdf}, Journal = {Journal of Logic and Computation}, Number = {4}, Pages = {839-854}, Title = {Algorithmic solution of higher type equations}, URL = {http://logcom.oxfordjournals.org/content/23/4/839.abstract}, Volume = {23}, Year = {2013}, bdsk-url-1 = {http://logcom.oxfordjournals.org/content/23/4/839.abstract}, bdsk-url-2 = {http://dx.doi.org/10.1093/logcom/exr048}, date-added = {2013-12-28 08:42:55 +0000}, date-modified = {2013-12-28 08:42:55 +0000}, doi = {10.1093/logcom/exr048} }