Realizability for constructive theory of functions and classes and its application to program synthesis

This paper gives a q-realizability interpretation for Feferman´s constructive theory T₀ of functions and classes by using a set completion program without doubling variables, and proves its soundness. This result solves an open problem proposed by Feferman in 1979. Moreover by using this interpretation we can prove a program extraction theorem for T₀, which enables us to use constructive sets of T₀ for program synthesis