User blog comment:B1mb0w/The S Function Version 2/@comment-5529393-20160710173738/@comment-10262436-20160712123745

I take your point. The 'definition' section is assuming a little bit. I have done this to cut to the chase and define the restricted and generalised versions of the S function which I rely upon to build a well ordered sequence.

If we ignore these sections and allow any values for the inputs to S or T then all you will need is to apply the sub and dec procedures to manipulate the functions and evaluate some equivalent strings or strings of higher or lower ordinal value.

Therefore the sub and dec procedures should probably constitute the defining ruleset. The 'defintion' section on this blog could be renamed to a something like 'normal form'...

Does this make sense ?