How to use double or single brackets, parentheses, curly braces

I am confused by the usage of brackets, parentheses, curly braces in Bash, as well as the difference between their double or single forms. Is there a clear explanation?

In Bash, test and [ are builtins.

The double bracket enables additional functionality. For example, you can use && and || instead of -a and -o and there's a regular expression matching operator =~ .

The braces, in addition to delimiting a variable name are used for parameter expansion so you can do things like:

Also, brace expansions create lists of strings which are typically iterated over in loops:

$ echo f{oo,ee,a}d
food feed fad

$ mv error.log{,.OLD}
(error.log is renamed to error.log.OLD because the brace expression
expands to "mv error.log error.log.OLD")

$ for num in {000..2}; do echo "$num"; done
000
001
002

$ echo {00..8..2}
00 02 04 06 08

$ echo {D..T..4}
D H L P T

Note that the leading zero and increment features weren't available before Bash 4.

Thanks to gboffi for reminding me about brace expansions.

Double parentheses are used for arithmetic operations:

((a++))

((meaning = 42))

for ((i=0; i<10; i++))

echo $((a + b + (14 * c)))

and they enable you to omit the dollar signs on integer and array variables and include spaces around operators for readability.

Single brackets are also used for array indices:

array[4]="hello"

element=${array[index]}

Curly brace are required for (most/all?) array references on the right hand side.

ephemient's comment reminded me that parentheses are also used for subshells. And that they are used to create arrays.

array=(1 2 3)
echo ${array[1]}
2

$ VARIABLE=abcdef
$ if [ $VARIABLE == abcdef ] ; then echo yes ; else echo no ; fi
yes

$ VARIABLE=abcdef
$ if [[ $VARIABLE == 123456 ]] ; then echo yes ; else echo no ; fi
no

$ pwd
/home/user 
$ (cd /tmp; pwd)
/tmp
$ pwd
/home/user

4a. Braces ( {} ) are used to unambiguously identify variables. Example:

    $ VARIABLE=abcdef
    $ echo Variable: $VARIABLE
    Variable: abcdef
    $ echo Variable: $VARIABLE123456
    Variable:
    $ echo Variable: ${VARIABLE}123456
    Variable: abcdef123456

4b. Braces are also used to execute a sequence of commands in the current shell context, eg

    $ { date; top -b -n1 | head ; } >logfile 
    # 'date' and 'top' output are concatenated, 
    # could be useful sometimes to hunt for a top loader )

    $ { date; make 2>&1; date; } | tee logfile
    # now we can calculate the duration of a build from the logfile

There is a subtle syntactic difference with ( ) , though (see bash reference) ; essentially, a semicolon ; after the last command within braces is a must, and the braces { , } must be surrounded by spaces.

Brackets

if [ CONDITION ]    Test construct  
if [[ CONDITION ]]  Extended test construct  
Array[1]=element1   Array initialization  
[a-z]               Range of characters within a Regular Expression
$[ expression ]     A non-standard & obsolete version of $(( expression )) [1]

[1] http://wiki.bash-hackers.org/scripting/obsolete

Curly Braces

${variable}                             Parameter substitution  
${!variable}                            Indirect variable reference  
{ command1; command2; . . . commandN; } Block of code  
{string1,string2,string3,...}           Brace expansion  
{a..z}                                  Extended brace expansion  
{}                                      Text replacement, after find and xargs

Parentheses

( command1; command2 )             Command group executed within a subshell  
Array=(element1 element2 element3) Array initialization  
result=$(COMMAND)                  Command substitution, new style  
>(COMMAND)                         Process substitution  
<(COMMAND)                         Process substitution 

Double Parentheses

(( var = 78 ))            Integer arithmetic   
var=$(( 20 + 5 ))         Integer arithmetic, with variable assignment   
(( var++ ))               C-style variable increment   
(( var-- ))               C-style variable decrement   
(( var0 = var1<98?9:21 )) C-style ternary operation

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