Conflicting accounts of λ-definability

© 2016 A function on some domain is λ-definable if the corresponding function of λ-terms is so definable. However, the correspondence is parametrized by a representation of the domain. Often there is a natural choice of representation, but when the domain consists of λ-terms then they can be represented by either themselves or by the Church numeral of their Gödel number. This choice determines whether or not all computable functions are λ-definable