Nested Brace Expansion

Nested brace expansion is the recursive evaluation of Bash brace expressions ({...}) embedded within one another. The Bash parser evaluates these structures strictly outside-in using top-down recursive descent. It identifies the outermost brace expression, splits the contents by commas at the current nesting level (level 0), and recursively expands each resulting part left-to-right, preserving strict ordering without applying implicit sorting.

Syntax and Lexical Parsing

During the parsing phase, Bash identifies unescaped braces and commas to determine the hierarchical depth of the expression. Brace expansion occurs strictly before variable, command, and arithmetic expansions.

# General syntax structure
{element1,prefix{inner1,inner2}suffix,element3}

When an outer brace expression is evaluated, Bash splits it into its constituent elements. If an element contains further nested braces, the parser recursively expands them, distributing any literal prefix or suffix characters across the generated inner strings.

Expansion Mechanics

1. Hierarchical Comma Separation

Commas define the boundaries of elements at the current nesting level. An element can be a literal string, a sequence, or another brace expression.

$ echo {A,B{C,D}}
A BC BD

Execution flow:

1. The parser identifies the outermost brace and splits it by the level-0 comma into two elements: A and B{C,D}.
2. The first element A contains no further braces and remains A.
3. The second element B{C,D} is recursively evaluated. The parser splits {C,D} into C and D.
4. The prefix B is distributed to both, yielding BC and BD.

2. Deep Nesting

Nesting can occur at arbitrary depths. Because evaluation is strictly outside-in, the parser resolves the outermost structure first and recursively descends into deeper levels.

$ echo {1,2{3,4{5,6}}}
1 23 245 246

Execution flow:

1. The parser splits the outermost level into 1 and 2{3,4{5,6}}.
2. The element 1 is fully resolved.
3. The element 2{3,4{5,6}} is recursively expanded. The parser splits the next brace {3,4{5,6}} into 3 and 4{5,6}, yielding 23 and 24{5,6}.
4. The element 23 is fully resolved.
5. The element 24{5,6} is recursively expanded. The parser splits {5,6} into 5 and 6, yielding 245 and 246.

3. Adjacent Nesting (Left-to-Right Expansion)

If multiple brace expressions are nested adjacently within a single outer element, Bash evaluates them left-to-right, outside-in.

$ echo {A,B{1,2}{X,Y}}
A B1X B1Y B2X B2Y

Execution flow:

1. The outermost brace is split into A and B{1,2}{X,Y}.
2. The element A is fully resolved.
3. In B{1,2}{X,Y}, the leftmost brace {1,2} is expanded first, yielding B1{X,Y} and B2{X,Y}.
4. The parser then recursively expands {X,Y} in each resulting string.
5. B1{X,Y} expands to B1X and B1Y.
6. B2{X,Y} expands to B2X and B2Y.

4. Nested Sequences

Sequence expressions ({x..y}) can be nested within comma-separated brace lists. The sequence is generated as a standard element during the recursive descent.

$ echo {X,Y{1..3},Z}
X Y1 Y2 Y3 Z

Edge Cases and Limitations

• Malformed Sequence Bounds: Sequence expressions require hardcoded integers or single characters at the time of lexical analysis. Nesting a sequence inside a sequence bound (e.g., {1..{2..5}}) does not throw a syntax error or halt execution. Instead, the parser fails to identify the outer structure as a valid sequence. It falls back to standard expansion, evaluating the inner sequence and treating the outer characters as literals.

$ echo {1..{2..5}}
{1..2} {1..3} {1..4} {1..5}

• Empty Elements: An empty element within a nested brace is treated as a null string. It is a valid token and will be concatenated as an empty value during recursive expansion.

$ echo {A,B{C,}}
A BC B

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