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___ (three _ characters) or BlankNullSequence[]

is a pattern object that can stand for any sequence of zero or more Wolfram Language expressions.

___h or BlankNullSequence[h]

can stand for any sequence of expressions, all of which have head h.

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BlankNullSequence

___ (three _ characters) or BlankNullSequence[]

is a pattern object that can stand for any sequence of zero or more Wolfram Language expressions.

___h or BlankNullSequence[h]

can stand for any sequence of expressions, all of which have head h.

Details

  • Blank sequences work slightly differently depending on whether or not the head of the expression in which they appear is a symbol with the attribute Flat.
  • Consider matching the pattern f[a1,a2,…,___,c1,…] against the expression f[a1,a2,…,b1,…,c1,…]. If f is a symbol with attribute Flat, then the ___ will be taken to stand for the expression f[b1,…]. If f is not a symbol with attribute Flat, then ___ will be taken to stand for the sequence of expressions b1, …. With a named pattern, such as x___, x can be used only as an element in an expression. The sequence of expressions b1, … is "spliced in" to replace x, thereby usually increasing the length of the expression.
  • If ___ matches a sequence of length more than one, then the sequence will be represented by a Sequence object. In most uses of ___, however, the Sequence object will automatically be spliced into another expression, and will never appear explicitly.

Examples

Basic Examples  (3)

A function that works with any number of arguments:

Wolfram Language code: f[x___] := p[x, x]
Wolfram Language code: {f[], f[1], f[1, a]}

A function that works with any number of integer arguments:

Wolfram Language code: f[x___Integer] := p[x, Plus[x]]
Wolfram Language code: {f[], f[1], f[1, 2, 3], f[1, b, 3]}

A function that works with an integer followed by any number of arguments:

Wolfram Language code: f[x_Integer, y___] := Plus[y] ^ x
Wolfram Language code: {f[1], f[1, 2.], f[1, 2., x], f[x, 1, y]}
Wolfram Research (1988), BlankNullSequence, Wolfram Language function, https://reference.wolfram.com/language/ref/BlankNullSequence.html.

Text

Wolfram Research (1988), BlankNullSequence, Wolfram Language function, https://reference.wolfram.com/language/ref/BlankNullSequence.html.

CMS

Wolfram Language. 1988. "BlankNullSequence." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BlankNullSequence.html.

APA

Wolfram Language. (1988). BlankNullSequence. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BlankNullSequence.html

BibTeX

@misc{reference.wolfram_2026_blanknullsequence, author="Wolfram Research", title="{BlankNullSequence}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/BlankNullSequence.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_blanknullsequence, organization={Wolfram Research}, title={BlankNullSequence}, year={1988}, url={https://reference.wolfram.com/language/ref/BlankNullSequence.html}, note=[Accessed: 13-June-2026]}