Getting results from programs extracted from classical proofs

Abstract

AbstractWe present a new method to extract from a classical proof of ∀x(I[x]→∃y(O[y]∧S[x,y])) a program computing y from x. This method applies when O is a data type and S is a decidable predicate. Algorithms extracted this way are often far better than a stupid enumeration of all the possible outputs and this is verified on a nontrivial example: a proof of Dickson's lemma