What does \$$1 mean in this shell function?

I saw this function definition from "Linux Shell Scripting Cookbook", I wonder why there needs two $ sign is needed in the last part of eval $1=\"$2\$\{$1:+':'\$$1\}\". How to understand each of the $ sign in entire eval condition? Thanks!

prepend() { [ -d "$2" ] && eval $1=\"$2\$\{$1:+':'\$$1\}\" && export $1 ; }

In addition to @tripleee's correct answer, I want to suggest you to try this at command line:

set -- foo bar
echo $1=\"$2\$\{$1:+':'\$$1\}\"

foo="bar${foo:+:$foo}"

Alternatively

As eval is evil, here is an alternative (but care evil is in details read further!):

prepend() {
    [[ -d $2 ]] &&
        printf -v "$1" '%s' "$2" "${!1+:}" "${!1}" &&
        export "$1"
}

which could be written as oneliner:

prepend() { [[ -d $2 ]]&&printf -v "$1" '%s' "$2" "${!1+:}" "${!1}"&&export "$1";}

Tests:

mkdir /tmp/foo /tmp/bar
prepend myVar /tmp/foo 
echo ${myVar@A}

declare -x myVar='/tmp/foo'

prepend myVar /tmp/bar 
echo ${myVar@A}

declare -x myVar='/tmp/bar:/tmp/foo'

prepend myVar /tmp/baz
echo ${myVar@A}

declare -x myVar='/tmp/bar:/tmp/foo'

Sanitizing:

Regarding @jhnc's comment, you could want to sanitize submitted variable name:

Let's try (again):

prepend 'h[`date +%c.%N>/dev/tty`]' /tmp/foo

Mon Nov 25 08:04:26 2024.549285838
Mon Nov 25 08:04:26 2024.552602686
Mon Nov 25 08:04:26 2024.554057179
bash: export: `h[`date +%c.%N>/dev/tty`]': not a valid identifier

Where date command was exectuted by prepand function (3 times)!!

To avoid this you may add a little test if stringContain ... in your command:

prepend() {
    case $1 in
        *[\`\$]* )
            return 1
        ;;
    esac
    [[ -d $2 ]] &&
        printf -v "$1" '%s' "$2" "${!1+:}" "${!1}" &&
        export "$1"
}

In one line:

prepend() { case $1 in *[\`\$]* ) return 1;;esac;[[ -d $2 ]]&&printf -v "$1" '%s' "$2" "${!1+:}" "${!1}"&&export "$1";}

Or two lines:

prepend() { case $1 in *[\`\$]* ) return 1;;esac
  [[ -d $2 ]] && printf -v "$1" '%s' "$2" "${!1+:}" "${!1}" && export "$1" ;}

Then

unset myVar
prepend myVar /tmp/foo 
echo ${myVar@A}

declare -x myVar='/tmp/foo'

prepend myVar /tmp/bar 
echo ${myVar@A}

declare -x myVar='/tmp/bar:/tmp/foo'

prepend myVar /tmp/baz
echo ${myVar@A}

declare -x myVar='/tmp/bar:/tmp/foo'

Upto there, everything look fine. Then finally:

prepend 'h[`date>/dev/tty`]' /tmp/foo

prepend 'h[$(date>/dev/tty)]' /tmp/foo

Nothing! but:

echo $?

1