User blog comment:Wythagoras/Dollar function formal definition/@comment-5529393-20130620080327

Nice changes, however it looks like rule 6 and rule 9 conflict now.

It seems like the rules are still incomplete, for example a$[[0,1],1] doesn't seem to satisfy any of the rules.  Presumably you just reduce [0,1] and sub it in the expression, but it has to satisfy some rule.

My first quibble with your comparison with FGH is

a$[[[[0,1],1],1],1] ~ f_e_(gamma_0)+1(a)

it appears that

a$[[[0,1],1],1] ~ f_gamma_0^2(a)

a$[[[1,1],1],1] ~ f_gamma_0^3(a)

a$[[[2,1],1],1] ~ f_gamma_0^4(a)

a$[[[[0,1],1],1],1] ~ f_gamma_0^gamma_0(a) = f_w^w^(Gamma_0 * 2) (a)

Similarly,

a$[[[[[0,1],1],1],1],1] ~ f_w^w^w^(Gamma_0 * 2) (a)

a$[[[[[[0,1],1],1],1],1],1] ~ f_w^w^w^w^(Gamma_0 * 2) (a)

and so on.