Let me suggest the following corrections to your cube language
message. If any of these are not actual errors, but are actually
misunderstandings on my part, then I apologize for causing undue
confusion, but I thought it would be helpfull to people trying to
understand you system to have these corrected as soom as possible.

ACW@MIT-AI 07/19/80 01:42:56
...

One more piece of notation: For any manipulations M and N, I write
M'NM as N[M], reading this as if N were a function: "N of M".

I think you must intend N[M] to mean M N M' .
    ...

T[I] T'[I'] J' means "Rotate the floor-parallel center-slice a
quarter turn counter-clockwise as seen from above."

T[I] and T'[I'] don't touch the floor-parallel center-slice at all and
J' rotates it clockwise (as seen from above), my guess is that the
description should simply read: "Rotate the floor-parallel
center-slice a quarter turn clockwise as seen from above."
...

Set Q= (TT)[J] (TT)[ZJ] "Half turn body-slicing center-slice."

This must be a typo or some discarded notation. My guess is that this
should read Q= (TT)[J] (TT)[J']. I don't think that the description
here ("Half turn body-slicing center-slice") fits, but it works in
producing the pattern anyway. If you had said Q= (TT)[J] (TT)[J'] II
then you could get the pattern and fit the description too!