Proof Theory and Computational Analysis
Ulrich Kohlenbach November 1997 |

## Abstract:In this survey paper we start with a discussion how functionals of finite type can be used for the proof-theoretic extraction of numerical data (e.g. effective uniform bounds and rates of convergence) from non-constructive proofs in numerical analysis.
We focus on the case where the extractability of
polynomial bounds is guaranteed. This leads to the
concept of hereditarily polynomial bounded analysis
Finally we discuss the relationship between
In a sequel of appendices to this paper we indicate the
expressive power of
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