least power -- they deliberately use a computer language that is not quite fully Turing-complete, often a language that guarantees that all subroutines are guaranteed to finish, such as Coq . ^ In none of his work did Turing use the word "halting" or "termination". Turing's biographer Hodges does not have the word "halting" or words "halting problem" in his index. The earliest known use of the words "halting problem" is in a proof by Davis (1958, p. 70–71): "A related problem is the printing problem for a simple Turing machine Z with respect to a symbol S i ". Davis adds no attribution for his proof, so one infers that it is original with him. But Davis has pointed out that a statement of the proof exists informally in Kleene (1952, p. 382). Copeland (2004, p 40) states that: "The halting problem was so named (and it appears, first stated) by Martin Davis [cf Copeland footnote 61]... (It is often said that Turing stated and proved the halting theorem in 'On Computable Numbers', but strictly this is not true)." Alan Turing , On computable numbers, with an application to the Entscheidungsproblem , Proceedings of the London Mathematical Society, Series 2, 42 (1936), pp 230–265. online version This is the epochal paper where Turing defines Turing machines , formulates the halting problem, and shows that it (as well as the Entscheidungsproblem ) is unsolvable. Alfred North Whitehead and Bertrand Russell , Principia Mathematica to *56, Cambridge at the University Press,