 After learning of Church’s 1936 proposal to identify effectiveness with lambda-definability (while preparing his own paper for publication) Turing quickly established that the concept of lambda-definability and his concept of computability are equivalent (by proving the “theorem that all … λ-definable sequences … are computable” and its converse; 1936: 88ff). Thus, in Church’s proposal, the words “λ-definable function of positive integers” (and equally the words “recursive function of positive integers”) can be replaced by “function of positive integers that is computable by Turing machine”. 