以下是如何测试参数是否未设置、是否为空（“Null”）或是否设置了值：

+--------------------+----------------------+-----------------+-----------------+
|   Expression       |       parameter      |     parameter   |    parameter    |
|   in script:       |   Set and Not Null   |   Set But Null  |      Unset      |
+--------------------+----------------------+-----------------+-----------------+
| ${parameter:-word} | substitute parameter | substitute word | substitute word |
| ${parameter-word}  | substitute parameter | substitute null | substitute word |
| ${parameter:=word} | substitute parameter | assign word     | assign word     |
| ${parameter=word}  | substitute parameter | substitute null | assign word     |
| ${parameter:?word} | substitute parameter | error, exit     | error, exit     |
| ${parameter?word}  | substitute parameter | substitute null | error, exit     |
| ${parameter:+word} | substitute word      | substitute null | substitute null |
| ${parameter+word}  | substitute word      | substitute word | substitute null |
+--------------------+----------------------+-----------------+-----------------+

来源：POSIX：参数扩展：

在所有显示为“替换”的情况下，表达式将替换为显示的值。在所有显示为“assign”的情况下，参数都被指定该值，该值也会替换表达式。

要在操作中显示此内容，请执行以下操作：

+--------------------+----------------------+-----------------+-----------------+
|   Expression       |  When FOO="world"    |  When FOO=""    |    unset FOO    |
|   in script:       |  (Set and Not Null)  |  (Set But Null) |     (Unset)     |
+--------------------+----------------------+-----------------+-----------------+
| ${FOO:-hello}      | world                | hello           | hello           |
| ${FOO-hello}       | world                | ""              | hello           |
| ${FOO:=hello}      | world                | FOO=hello       | FOO=hello       |
| ${FOO=hello}       | world                | ""              | FOO=hello       |
| ${FOO:?hello}      | world                | error, exit     | error, exit     |
| ${FOO?hello}       | world                | ""              | error, exit     |
| ${FOO:+hello}      | hello                | ""              | ""              |
| ${FOO+hello}       | hello                | hello           | ""              |
+--------------------+----------------------+-----------------+-----------------+

case "$1" in
 "") echo "blank";;
 *) echo "set"
esac

为了明确回答OP关于如何确定变量是否已设置的问题，Lionel的回答是正确的：

if test "${name+x}"; then
    echo 'name is set'
else
    echo 'name is not set'
fi

这个问题已经有很多答案，但没有一个提供真正的布尔表达式来明确区分变量值。

以下是我得出的一些明确表达：

+-----------------------+-------------+---------+------------+
| Expression in script  | name='fish' | name='' | unset name |
+-----------------------+-------------+---------+------------+
| test "$name"          | TRUE        | f       | f          |
| test -n "$name"       | TRUE        | f       | f          |
| test ! -z "$name"     | TRUE        | f       | f          |
| test ! "${name-x}"    | f           | TRUE    | f          |
| test ! "${name+x}"    | f           | f       | TRUE       |
+-----------------------+-------------+---------+------------+

顺便说一下，这些表达式是等价的：测试＜表达式＞＜＝＞〔＜表达式＞〕

其他需谨慎使用的歧义表达：

+----------------------+-------------+---------+------------+
| Expression in script | name='fish' | name='' | unset name |
+----------------------+-------------+---------+------------+
| test "${name+x}"     | TRUE        | TRUE    | f          |
| test "${name-x}"     | TRUE        | f       | TRUE       |
| test -z "$name"      | f           | TRUE    | TRUE       |
| test ! "$name"       | f           | TRUE    | TRUE       |
| test ! -n "$name"    | f           | TRUE    | TRUE       |
| test "$name" = ''    | f           | TRUE    | TRUE       |
+----------------------+-------------+---------+------------+

在Bash中，可以在[[]]内置函数中使用-v：

#! /bin/bash -u

if [[ ! -v SOMEVAR ]]; then
    SOMEVAR='hello'
fi

echo $SOMEVAR

if [[ ${!xx[@]} ]] ; then echo xx is defined; fi

if [[ ${1:+isset} ]]
then echo "It was set and not null." >&2
else echo "It was not set or it was null." >&2
fi

if [[ ${1+isset} ]]
then echo "It was set but might be null." >&2
else echo "It was was not set." >&2
fi