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OneIdentity

is an attribute that can be assigned to a symbol f to indicate that f[x], f[f[x]], etc. are all equivalent to x for the purpose of pattern matching.

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OneIdentity

OneIdentity

is an attribute that can be assigned to a symbol f to indicate that f[x], f[f[x]], etc. are all equivalent to x for the purpose of pattern matching.

Details

Examples

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Basic Examples  (1)

The pattern matches, because Times has attribute OneIdentity:

Wolfram Language code: MatchQ[x, Times[n_., x_]]
Wolfram Language code: Attributes[Times]

Any function with attribute OneIdentity will match:

Wolfram Language code: SetAttributes[f, OneIdentity]
Wolfram Language code: MatchQ[a, f[x_ : 0, y_]]

Properties & Relations  (2)

OneIdentity allows defaults to apply to expressions that do not involve Times at all:

Wolfram Language code: Definition[Times]
Wolfram Language code: {x, 2x, -x} /. (n_.x) :> y ^ n

For Flat functions, any sequence of arguments will match Blank:

Wolfram Language code: SetAttributes[f, Flat];
Wolfram Language code: {f[a], f[b, c]} /. f[x_] :> x

When f is both Flat and OneIdentity, f[x_] will attempt to match x_ to a rather than f[a]:

Wolfram Language code: SetAttributes[f, {Flat, OneIdentity}]
Wolfram Language code: {f[a], f[b, c]} /. f[x_] :> x

Possible Issues  (1)

In order for f[a] to match a, you must use a pattern that includes Optional:

Wolfram Language code: SetAttributes[f, OneIdentity]
Wolfram Language code: MatchQ[x, f[_]]
Wolfram Language code: MatchQ[x, f[_ : 0]]

Similarly, the following pattern fails because f has no defined defaults:

Wolfram Language code: MatchQ[x, f[_.]]

Defining a default will resolve this issue:

Wolfram Language code: Default[f] = 1
Wolfram Language code: MatchQ[x, f[_.]]
Wolfram Research (1988), OneIdentity, Wolfram Language function, https://reference.wolfram.com/language/ref/OneIdentity.html (updated 2003).

Text

Wolfram Research (1988), OneIdentity, Wolfram Language function, https://reference.wolfram.com/language/ref/OneIdentity.html (updated 2003).

CMS

Wolfram Language. 1988. "OneIdentity." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2003. https://reference.wolfram.com/language/ref/OneIdentity.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_oneidentity, author="Wolfram Research", title="{OneIdentity}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/OneIdentity.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_oneidentity, organization={Wolfram Research}, title={OneIdentity}, year={2003}, url={https://reference.wolfram.com/language/ref/OneIdentity.html}, note=[Accessed: 12-June-2026]}