A computational interpretation of open induction

We study the proof-theoretic and computational properties of open induction, a principle which is classically equivalent to Nash-Williams' minimal-bad-sequence argument and also to (countable) dependent choice (and hence contains full classical analysis). We show that, intuitionistically, open induction and dependent choice are quite different: Unlike dependent choice, open induction is closed tinder negative- and A-translation, and therefore proves the same Pi(2)(0)-jormulas (over not necessarily decidable, basic predicates) with classical or intuitionistic arithmetic. Via modified realizability we obtain a new direct method for extracting programs from classical proofs of Pi(2)(0)-formulas using open induction. We also show that the computational interpretation of classical countable choice given by Berardi, Bezem and Coquand [2] can be derived from our results.