I want to check the type of the input argument in bash.

Here is the test function:

my_fun() {
    local -A var_map
    local -a var_list
    local var_string=""
    
    check_type "var_map"
    check_type "var_list"
    check_type "var_string"
}

check_type() {
    local -n test_name="$1"
    
    # How to check the type of "test_name" is a "map", "list", or "string" here?
    
    local type="$(what_command_to_check_type "$test_name")
    
    if [[ "$type" == "-A (map)" ]]
    then
        echo "this is a map"
    elif [[ "$type" == "-a (list)" ]]
    then
        echo "this is a list"
    elif [[ "$type" == "string" ]]
    then
        echo "this is a string"
    fi
}

How to check the type in the “check_type()“?