Kleene's Church–Turing Thesis: In the years 1939-1952, Stephen Kleene would go on to overtly name, after switching from presenting his work in the mathematical terminology of the lambda calculus to his own theory of partial recursive functions or Gödel-Kleene recursiveness, both Church's thesis and Turing's thesis. Finally coining the term the "Church-Turing thesis" in a section from his graduate textbook on logic. In which he was helping to give clarifications to concepts, demanded in a critique from William Boone on Alan Turing's paper "The Word Problem in Semi-Groups with Cancellation", defend, and express the two "theses" and then "identify" them (show equivalence) by use of his Theorem XXX: