A Realizability Interpretation for Classical Analysis

We present a realizability interpretation for classical analysis–an association of a term to every proof so that the terms assigned to existential formulas represent witnesses to the truth of that formula. For classical proofs of Π2 sentences ∀x∃yA(x, y), this provides a recursive type 1 function which computes the function given by f(x) = y iff y is the least number such that A(x, y).