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FreeQ[expr,form]

yields True if no subexpression in expr matches form, and yields False otherwise.

FreeQ[expr,form,levelspec]

tests only those parts of expr on levels specified by levelspec.

FreeQ[form]

represents an operator form of FreeQ that can be applied to an expression.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
Possible Issues  
See Also
Tech Notes
Related Guides
History
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FreeQ

FreeQ[expr,form]

yields True if no subexpression in expr matches form, and yields False otherwise.

FreeQ[expr,form,levelspec]

tests only those parts of expr on levels specified by levelspec.

FreeQ[form]

represents an operator form of FreeQ that can be applied to an expression.

Details and Options

  • form can be a pattern.
  • FreeQ uses standard level specifications:
  • nlevels 1 through n
    Infinitylevels 1 through Infinity
    {n}level n only
    {n1,n2}levels n1 through n2
  • The default value for levelspec in FreeQ is {0, Infinity}.
  • A positive level n consists of all parts of expr specified by n indices.
  • A negative level -n consists of all parts of expr with depth n.
  • Level -1 consists of numbers, symbols and other objects that do not have subparts.
  • Level 0 corresponds to the whole expression.
  • With the default option setting Heads->True, FreeQ looks at heads of expressions, and their parts.
  • FreeQ works on associations, testing values but not keys.
  • FreeQ[form][expr] is equivalent to FreeQ[expr,form].
  • Parallelize[FreeQ[expr,form]] computes FreeQ[expr,form] in parallel on all subkernels. »

Examples

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Basic Examples  (3)

Test whether a list is free of 0:

Wolfram Language code: FreeQ[{1, 2, 4, 1, 0}, 0]

FreeQ normally tests all levels in an expression:

Wolfram Language code: FreeQ[{{1, 1, 3, 0}, {2, 1, 2, 2}}, 0]

Test whether an association does not contain a value:

Wolfram Language code: FreeQ[<|a -> 1|>, 1]
Wolfram Language code: FreeQ[<|a -> 1|>, a]

Scope  (5)

FreeQ works with patterns:

Wolfram Language code: FreeQ[{a, b, b, a, a, a}, _Integer]
Wolfram Language code: FreeQ[{x ^ 2, y ^ 3, x ^ 5, x ^ 6}, y ^ _]

Use Verbatim to test for a literal blank:

Wolfram Language code: FreeQ[f[_], Verbatim[_]]

Test whether an association contains a specific rule:

Wolfram Language code: FreeQ[<|a -> 1|>, KeyValuePattern[{a -> 1}]]
Wolfram Language code: FreeQ[<|a -> 1|>, KeyValuePattern[{b -> 1}]]

Test whether a list of rules contains a specific rule:

Wolfram Language code: FreeQ[{a -> 1}, KeyValuePattern[{a -> 1}]]

Test whether an association contains a specific key:

Wolfram Language code: FreeQ[<|a -> b|>, KeyValuePattern[{a -> _}]]

Applications  (2)

Define a function that factors out "constants":

Wolfram Language code: f[c_ x_, x_] := c f[x, x] /; FreeQ[c, x]
Wolfram Language code: {f[3x, x], f[a x, x], f[(1 + x)x, x]}

Test which integrals are free of logarithms:

Wolfram Language code: Table[FreeQ[Integrate[x ^ n, x], Log], {n, -5, 5}]

Properties & Relations  (1)

Compute FreeQ in parallel:

Wolfram Language code: Parallelize[FreeQ[Range[10 ^ 6], 5]]

Possible Issues  (2)

For associations, FreeQ tests only values:

Wolfram Language code: FreeQ[<|a -> 1|>, 1]
Wolfram Language code: FreeQ[<|a -> 1|>, a]

KeyValuePattern tests for the entire rule:

Wolfram Language code: FreeQ[<|a -> 1|>, KeyValuePattern[{a -> _}]]
Wolfram Language code: FreeQ[<|a -> 1|>, KeyValuePattern[{b -> _}]]
Wolfram Research (1988), FreeQ, Wolfram Language function, https://reference.wolfram.com/language/ref/FreeQ.html (updated 2014).

Text

Wolfram Research (1988), FreeQ, Wolfram Language function, https://reference.wolfram.com/language/ref/FreeQ.html (updated 2014).

CMS

Wolfram Language. 1988. "FreeQ." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/FreeQ.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_freeq, author="Wolfram Research", title="{FreeQ}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/FreeQ.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_freeq, organization={Wolfram Research}, title={FreeQ}, year={2014}, url={https://reference.wolfram.com/language/ref/FreeQ.html}, note=[Accessed: 13-June-2026]}