User blog comment:Mh314159/FOX notation/@comment-39585023-20191205111828/@comment-35470197-20191206053136

> [a]‹S››α(n)(x) = [a]‹T›α(n-1)(x), α(j) = [a]‹T›α(j-1)(x), α(0) = [a]‹T›(x)

It is quite ambiguous, because the value of α refers not only to the input n but also a and T. For example, when I need to compute [a]‹(2,2)›_{α(3)}(x), I should compute [a]<(2,1)>_{α(2)}(x). Then the value has two candidates: If you want to define α as a function, then you need to substitue all data which are used in the definition. If you want to set α just as a symbol, then you need to specify it, and to clarify what the equality α(j) = … means.
 * 1) [a]<(2,0)>_{α(1)}(x) (Using the rule for S = (2,1))
 * 2) [a]<(2,1)>_{[a]<2,1>_{α(1)}(x)}(x) (Using the rule for α(j) and T = (2,1))
 * 3) [[a]<(2,1)>_{α(2)-1}(x)]<(2,1)>(x) (Using the rule for S = (2,1) and n = α(2))