How do I determine whether a variable is already defined? Or a function?

There are several ways to test for a defined or non-empty variable or function depending upon the requirements.

"Declared", "Defined", and "Undefined"

Like in many languages, declaration and definition can be independent steps. To declare an object is to give it a name and datatype, whereas a definition associates it with a value, which may be empty. In Unix shell terminology, "unset", "set", and "null" are often used to mean "undefined", "defined", and "empty" respectively. Since "string" is very nearly the only common datatype, "null" usually means the empty string. With arrays, things become less consistent between shells.

Testing for a defined, non-empty variable / parameter.

Since the most common goal is to distinguish between an empty and non-empty variable or parameter, we'll discuss it first. These are the most common solutions arranged from most to least portable.

test x"$var" != x

Only needed for ancient Bourne shells. Don't use this in modern scripts.

test -n "$var"

POSIX sh plus some older Bourne shells which lacked [.

[ -n "$var" ]

POSIX sh and most Bourne shells including Heirloom. Best overall choice for new scripts requiring POSIX compatibility.

test "$var"

POSIX sh. POSIX specifies that for one argument, non-null is always true while null is always false.

[ "$var" ]

POSIX sh. As above. Still very portable.

[[ -n $var ]]

Here and below is Bash/Ksh/Zsh only. This is compatible with some buggy shell versions which didn't process the implicit -n correctly.

[[ $var ]]

Best overall choice for Bash/Ksh/Zsh where POSIX isn't a requirement. Usually best performance.

(( ${#var} ))

About as portable as the above. Almost always slower. Don't use this to test for empty strings.

To check the converse, whether a variable is empty (unset or zero-length), invert the above logic.

test x"$var" = x
test -z "$var"
[ -z "$var" ]
test ! "$var"
[ ! "$var" ]
[[ -z $var ]]
[[ ! $var ]]

Testing that a variable has been declared

Distinguishing between a variable that is undefined and one that is defined but empty is somewhat trickier, but possible.

# POSIX
${var+:} false
! ${var+false}
[ -n "${var+_}" ]

Which of the above performs best varies from shell to shell. If POSIX isn't a requirement, the following [[ solution usually performs best.

# Bash/ksh/zsh
[[ ${var+_} ]]

Another method that's occasionally seen is to check the status of typeset -p. The above method should be preferred over this.

# Bash/ksh/zsh
typeset -p var >/dev/null 2>&1
# returns 0 if var exists, error otherwise

Bash 4.2 adds a -v test:

# Bash 4.2 / ksh93
if [[ -v var ]]; then echo "var is defined"; fi

ksh93 additionally supports array indices with the -v test, while Bash so far does not. This should be the preferred method when targeting ksh93 specifically.

Testing that a function has been defined

For determining whether a function with a given name is already defined, there are several answers, all of which require Bash (or at least, non-Bourne) commands. Testing that a function is defined should rarely be necessary.

# Bash
[[ $(declare -f foo) ]]     # it prints nothing, if undefined
declare -f foo >/dev/null   # it also sets the exit status
[[ $(type -t f) == function ]]