Test if a variable is unset

For scalar variables, in standard (POSIX) sh syntax:

if [ "${var+set}" != set ]; then
  echo var is not set
fi

Or fancier albeit less legible things like

if [ -z "${var++}" ]; then
  echo var is unset
fi

Or:

if ${var+false}; then
  echo var is unset
fi

For array variables (not that arrays are portable), in zsh or yash, that would return unset unless the array is assigned any list including the empty list, while in bash or ksh that would return unset unless the element of index 0 is set. Same for associative arrays (for key "0").

Note that except in zsh (when not in sh emulation), export var or readonly var declares the variable but doesn't give it any value, so shells other than zsh will report var as unset there (unless var had been assigned a value before the call to export/readonly).