Is a subscript to an indexed array an arithmetic expansion?

Question

Quoting from the Bash manual:

An indexed array is created automatically if any variable is assigned to using the syntax

name[subscript]=value

The subscript is treated as an arithmetic expression that must evaluate to a number.

Is subscript

• an arithmetic expression, or
• an arithmetic expansion where $(( and )) are ignored and only an arithmetic expression is there?

In other words, is there a step of arithmetic expansion here, just like when interpreting a command with arithmetic expansion?

For example,

$ declare -p myarr
declare -a myarr='([0]="0" [2]="3" [3]="9999")'

$ echo ${myarr[1+2]}
9999
$ echo ${myarr[$((1+2))]}
9999

Answer 1

Is there a step of arithmetic expansion [with array subscripts], just like when interpreting a command with arithmetic expansion?

Yes.

Variable expansion:

$ unset -v a
$ declare -p a
-bash: declare: a: not found
$ x=4
$ a[x]=4
$ declare -p a
declare -a a='([4]="4")'

Parameter expansion:

$ six=six
$ a[${#six}]=3
$ declare -p a
declare -a a='([3]="3" [4]="4")'

Command substitution:

$ a[$(echo 9)]=9
$ declare -p a
declare -a a='([3]="3" [4]="4" [9]="9")'

Quote removal:

$ a["5"]=5
$ declare -p a
declare -a a='([3]="3" [4]="4" [5]="5" [9]="9")'
$ a['6']=6
$ declare -p a
declare -a a='([3]="3" [4]="4" [5]="5" [6]="6" [9]="9")'
$ a[\7]=7
$ declare -p a
declare -a a='([3]="3" [4]="4" [5]="5" [6]="6" [7]="7" [9]="9")'

Reference

3.5.5 Arithmetic Expansion

All tokens in the expression undergo parameter and variable expansion, command substitution, and quote removal.

Answer 2

• Is a subscript to an indexed array an arithmetic expansion?

To be precise: No, it is an "arithmetic expression", identical to what is inside an "arithmetic expansion" but lacks the $(( )).

Both evaluate the expression till it becomes a number (or a null).