User:Alemagno12/AM12 Array Notation/Dimensional

Dimensional Array Notation, or DAN for short, is the third part of my array notation.

WIP!

Definition
The limit of linear arrays in LAN is 1,1,1,1,....,1,1,1,2.

But wait! We have more separators.

The separator after the comma is {2}, which is the limit of linear arrays. The comma is a shorthand for {1}.

The limit is 1{n}2.

Rules
Expressions are of the form n(x,y|A1{n}A2), where x, y and n are positive integers, and A1 and A2 are any arrays with the highest separator of a level lower than {n}. Comma is a shorthand for {1}.

x is the base, and y is the nester.

Case 1: If there is no |, replace the array with xy

Case 2: If there is a |:
 * Search for the highest separator level.
 * Case 2a: If the separator is a comma (linear array), then:
 * Search for the last entry.
 * Case 2aa: If the last entry is a 1, delete it.
 * Else, search for the first entry.
 * Case 2ab: If there isn't anything after the first entry, decrease it by 1 and nest the nester the nester times
 * Case 2ac: If there's something after the first entry, and the first entry is 1:
 * Case 2aca: If the second entry is 1, ignore the rest of the expression and solve the array like normal
 * Case 2acb: If the second entry is not 1, decrease it by 1 and nest the first entry the nester times

The process ends.

Levels
In LAN, the base and the nester do not count as part of the expression. Nor does the |.

There is only one separator, the comma, which has the lowest level.

Subfunctions
There are no subfunctions in LAN.