 Kleene and Vesley’s [1965] gives a careful axiomatic treatment of intuitionistic analysis, a proof of its consistency relative to a classically correct subtheory, and an extended application to Brouwer’s theory of real number generators. Kleene’s [1969] formalizes the theory of partial recursive functionals, enabling precise formalizations of the function-realizability interpretation used in [1965] and of a related q-realizability interpretation which gives the Church-Kleene Rule for intuitionistic analysis.