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I was reading Alan Turing's paper "On Computable Numbers with an Application to the Entscheidungsproblem".

I was reading well until I encountered "4. Abbreviated Tables", page 235-236, where Turing uses a new way of writing a computation table for a machine. I am totally lost here. I don not understand the examples he gives (starting from page 236) to explain the idea of skeleton tables.

I need help with understanding how skeleton tables are to be read, and what they mean.

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m-functions are quite similar to what we call today "macros". $f(\dots)$ is just the name of a supplementary m-configuration, that can be parameterized (like a macro). The trick is to not overthink it.

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  • $\begingroup$ Where can I read about macros? $\endgroup$
    – Sidd
    May 15, 2015 at 11:23
  • $\begingroup$ Well, if you don't know what a macro is, then my answer was not of great help. Check this out: en.m.wikipedia.org/wiki/Macro_(computer_science). $\endgroup$
    – André Souza Lemos
    May 15, 2015 at 11:43
  • $\begingroup$ I understand macros, but still having trouble with m-functions. Does the parametrization mean that the m-function $f(...)$ is a m-configuration, which depends on the arguments on the function? If so, what is the format of the arguments? Does the m-function take in an m-configuration as argument and return another m-configuration? $\endgroup$
    – Sidd
    May 16, 2015 at 5:35
  • $\begingroup$ The answers are: 1) yes, 2) the arguments are m-configurations or other m-functions (capital fraktur letters), or symbols (lowercase letters), 3) it takes what it takes [see 2)] and yes, returns itself, rewritten. $\endgroup$
    – André Souza Lemos
    May 16, 2015 at 6:14
  • $\begingroup$ Suggestion: work out a complete example, a simple one, and edit your question adding it. I'll edit my answer accordingly, if necessary. $\endgroup$
    – André Souza Lemos
    May 16, 2015 at 6:17

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