Unable to append to array using parallel

I can't append to an array when I use parallel, no issues using a for loop. ### Parallel example:

append() { arr+=("$1"); } 
export -f append

parallel -j 0 append ::: {1..4}
declare -p arr

### Output:

-bash: declare: arr: not found

### For loop:

for i in {1..4}; do arr+=("$i"); done
declare -p arr

### Output:

declare -a arr=(="1" ="2" ="3" ="4")

I thought the first example is a translation of the for loop in functional style, so what's going on?