User blog comment:Mh314159/new YIP notation/@comment-39585023-20190714235606/@comment-35470197-20190718145926

> So that Is that what I need to declare?

Not exactly. What you need to declare is the order of the definition of variables. If you define \(n\) as \([a-1]\), then you take \(a\) first and \(n\) depends on \(a\). On the other hand, if you define \(a\) as a unique positive integer (if exists) satisfying \(n = [a-1]\), then you take \(n\) first and \(a\) depends on \(n\).

> The rule for Y is used to reduce a string that has an initial zero,

The problem is that it is not clear what lines are rules applicable to \([a,b,\ldots,\alpha,\beta]\). In order to clarify the argument, I enumerate the lines. Then since you distinguished line 1, we can guess that every symbol (or at least \(a\) and \(\beta\)) in line 2 is positive. Of course, it is ambiguous, and hence it is better to declare the range (cf. ambguity by the lack of declaration). Since \(n\) is defined by using \(\beta\), we can guess that line 3 is a portion of line 2. On the other hand, line 4 can make sense independently of line 2. Since the same expression, e.g. \(\underline{0}_0(x)\), can mean distinct values in your rules, it is impossible for us to determine whether the expressions in the right hand sides take values depending on parameters in line 2. Namely, we have two reasonable guess: Permitting the abbreviation of the dependency causes multiple use of the same symbol whose value heavily depends on parameters outside the expression itself. If you intend something like "this value can be determined by the expression, while that value is not", others do not have a way to guess it before you write additional descriptions.
 * 1) \([a,b,\ldota,\alpha,0] = \cdots\)
 * 2) \([a,b,\ldota,\alpha,\beta] = \cdots\)
 * 3) \(n = \cdots\)
 * 4) If \(Y = \cdots\)
 * 5) \(\underline{0}_0(x) = \cdots\)
 * Line 4 is just a rule to compute an expression, which is independent of line 2. (Similar to line 1)
 * Line 4 is a portion of line 2. Therefore the values of the right hand sides are not determined by the expressions, i.e. depend on parameters in line 2. (Similar to line 5)