Not all function spaces are equally easy to search. If you're looking for a continuous, possibly even monotonic, real map that approximates a given data set, fi

Not all function spaces are equally easy to search. If you're looking for a continuous, possibly even monotonic, real map that approximates a given data set, fine, just perform a regression. If you want to attach one of finitely many tags to every element of a data set, fine, just use a clustering algorithm or perform a correspondence analysis. But, can you find higher-order functions using these techniques? Or can you find arbitrary computable functions on the integers using these techniques? Note that the integers don't have a very good notion of “sufficiently near”, unlike the reals.