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The + operator in Bash is a context-dependent token whose behavior is strictly dictated by the syntactic construct in which it is evaluated. It functions as an arithmetic operator, an assignment/append operator, a parameter expansion modifier, an attribute toggler, a directory stack index indicator, and a pattern-matching quantifier.

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Arithmetic Evaluation

Within arithmetic expansion, the + token functions as a standard binary addition operator or a unary positive operator. Bash arithmetic is restricted to integers; floating-point operations are not natively supported. Syntax: 
$(( operand1 + operand2 ))
let "result = operand1 + operand2"
$(( +operand ))

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Append and Assignment Operator (+=)

The += token is a compound assignment operator that performs context-dependent appending or arithmetic addition. Syntax: 
variable+="string"
array+=(element1 element2)
(( variable += integer ))
  • String Concatenation: When applied to a standard scalar variable, it appends the right-hand string to the existing value.
  • Array Appending: When applied to an indexed or associative array using compound assignment syntax (), it appends new elements to the array.
  • Arithmetic Assignment: Within an arithmetic evaluation context (( )) or let, it performs integer addition and assigns the computed sum back to the variable.
  • Integer Attribute Assignment: If a scalar variable has the integer attribute set (via declare -i), using += on it performs arithmetic addition rather than string concatenation, even outside of an explicit arithmetic context like (( )) or let.

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Parameter Expansion (Alternate Value)

In brace-enclosed parameter expansion, the + operator tests the state of a variable and substitutes an alternate string based on whether the variable is set or null. It does not modify the original variable. Syntax: 
${parameter+word}
${parameter:+word}
  • ${parameter+word}: If parameter is declared/set (even if its value is null), the expansion evaluates to word. If unset, it evaluates to nothing.
  • ${parameter:+word}: The inclusion of the colon (:) enforces a strict non-null test. If parameter is set and not null, it evaluates to word. If unset or null, it evaluates to nothing.

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Shell Option and Attribute Toggling

When used as an argument prefix with the set builtin or variable declaration builtins (declare, typeset, local), the + operator disables shell options or removes variable attributes. This is the inverse of standard POSIX conventions where - enables options or sets attributes. Note: The export builtin does not accept + flags to remove attributes. To remove the export attribute from a variable, you must use export -n or declare +x. Syntax: 
set +[short-option-flag]
set +o [long-option-name]
declare +[attribute-flag] variable_name
typeset +[attribute-flag] variable_name

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Directory Stack Indexing

Builtins that manipulate the directory stack (pushd, popd, dirs) use the + prefix followed by an integer to reference a specific directory index. The +N notation specifies the Nth directory from the left of the directory stack, starting with zero. Syntax: 
pushd +N
popd +N
dirs +N

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Extended Globbing Quantifier

When the extglob shell option is enabled (shopt -s extglob), the + operator functions as a pattern-matching quantifier. It evaluates strings against a delimited list of patterns. Syntax: 
+(pattern1|pattern2|...)
This construct matches one or more occurrences of any of the patterns specified within the parentheses.

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Regular Expression Quantifier

Within the conditional test construct [[ ]] utilizing the =~ binary operator, the right-hand side is evaluated as a POSIX Extended Regular Expression (ERE). Here, + retains its standard regex definition. Syntax: 
[[ $string =~ pattern+ ]]
The + quantifies the preceding regex token, requiring it to match one or more times consecutively.
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