# m-functions in Turing's paper “On Computable Numbers and applications…”

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.

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.
• 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? – Sidd May 16 '15 at 5:35