Light monotone Dialectica methods for proof mining
Mircea‐Dan Hernest · Mathematical logic quarterly · 2009
Abstract In view of an enhancement of our implementation on the computer, we explore the possibility of an algorithmic optimization of the various proof‐theoretic techniques employed by Kohlenbach for the synthesis of new (and better) effective uniform bounds out of established qualitative proofs in Numerical Functional Analysis. Concretely, we prove that the method (developed by the author in his thesis, as an adaptation to Dialectica interpretations of Berger's original technique for modified realizability and A‐translation) of “colouring” some of the quantifiers as “non‐computational” extends well toε‐arithmetization, elimination‐of‐extensionality and model‐interpretation (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)