Refined program extraction from classical proofs Original Research Article

The paper presents a refined method of extracting reasonable and sometimes unexpected programs from classical proofs of formulas of the form ∀x∃yB. We also generalize previously known results, since B no longer needs to be quantifier-free, but only has to belong to a strictly larger class of so-called “goal formulas”. Furthermore we allow unproven lemmas D in the proof of ∀x∃yB, where D is a so-called “definite” formula.