Interpreting weak Kőnig's lemma in theories of nonstandard arithmetic

We show how to interpret weak König’s lemma in some recently defined theories of nonstandard arithmetic in all finite types. Two types of interpretations are described, with very different verifications. The celebrated conservation result of Harvey Friedman about weak König’s lemma can be proved using these interpretations. We also address some issues concerning the collecting of witnesses in herbrandized functional interpretations.