Where does the modern canonical version of the Turing machine come from? Turing's original 1936 description of his a-machine differs in several respects from the Turing machine I studied at university, leading me to questions:


The Turing machine I learned about was essentially a recognizer: it would either accept or reject input having specified characteristics.  It has an accept or halt final state.  By contrast, Turing describes a computing machine proper--his model computations involve producing and outputting numbers--without any particular halt state--although, for the proof that the Entscheidungsproblem has no solution, he does propose a machine D that would mark as "s" or "u" some other machine based on whether it is circular ("u").  Where does the recognizer view of the Turing machine come from?  Is it the result of later theorists focusing in on the imaginary machine D in Section 8 of Turing's paper?
The version of the Turing machine I got--e.g., from Sipser--required a definition of language as a "set of strings," where a Turing machine would recognize a given input string as belonging or not to some language L.  Where does this idea come from?  Turing's model of computation makes no reference to this concept of "language."  Is it due to Sipser?  Or Penrose?
Turing defines "circular" in a way that seems surprising and counterintuitive today:  "If a computing machine never writes down more than a finite number of symbols of the first kind [i.e., symbols from {0, 1}], it will be called circular."  Suppose you want the machine to compute a + b, where a and b are integers.  This sounds as if a machine that halts when finished computing a number with a finite representation is circular.  Moreover, Turing never explains what is circular in the common sense of the word about such a machine.  Is he just leaving out an argument that the reader is supposed to infer?  Presumably, the argument would go thus:  if we assume (but why?) that the machine should compute a number whose representation is infinite, then, if the machine halts, this can only result from a circularity in the state diagram--either one state leads to itself, without any motion or change of written symbol, or the states follow in a circular sequence with an equivalent result.  That seems to me to presuppose a lot--for instance, that the circularity does not result in any motion beyond the squares already written and that the written symbols remain the same as before.


Was there published work leading up to Turing's 1936 paper already introducing the concept of circularity, so that he could merely allude to it?

Thanks!
Is it due to Sipser? Or Penrose?

Sorry, that made me laugh out loud.  Penrose?

Today's notion of formal language (a language is a set of words or strings) can be traced at least as far back as Frege in the late 1800's and Thue in the early 1900's.  Chomsky's 1956 paper was very influential, and definitely uses the term "language" for a set of strings.

There is also the 1961 paper of Bar-Hillel, Perles, and Shamir.  I would check that.  

This 1963 paper by Evey (https://www.computer.org/csdl/proceedings/afips/1963/5063/00/50630215.pdf ) uses the term "language" in the modern sense in relation to machines.  Perhaps earlier explicit references can be found in the work of Emil Post.