FreeQ

Whether pattern matches nowhere in expr — itself, or any subexpression, at any depth.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageFreeQ✓↗

FreeQ(expr, pattern)True unless pattern matches expr or some subexpression

Typed signatures

Type	Package	Applies
(any, any) -> boolean	combinatorics	always

Domain: Collections

Details

• Searches the WHOLE tree, not just the top level — that's the difference from MatchQ, which only checks expr itself.
• An Association's keys are not parts: only its values are searched.
• Uses the same wildcard grammar as MatchQ — see its reference entry for what's supported.

Examples

Basic #

live ↗

In$\mathrm{FreeQ}(x^2+1, x)$Out$\mathrm{False}$

The pattern $0$ occurs in the list, so it is not free of it

live ↗

In$\mathrm{FreeQ}(\bigl\lbrack1, 2, 4, 1, 0\bigr\rbrack, 0)$Out$\mathrm{False}$

The search descends into sublists and finds the $0$

live ↗

In$\mathrm{FreeQ}(\bigl\lbrack\bigl\lbrack1, 1, 3, 0\bigr\rbrack, \bigl\lbrack2, 1, 2, 2\bigr\rbrack\bigr\rbrack, 0)$Out$\mathrm{False}$

Values inside an association count as parts, so $1$ is found

live ↗

In$\mathrm{FreeQ}(\mathrm{Association}(\operatorname{KeyValuePair}(a, 1)), 1)$Out$\mathrm{False}$

live ↗

In$\mathrm{FreeQ}(\mathrm{Association}(\mathrm{Rule}(a, 1)), a)$Out$\mathrm{True}$

Scope #

live ↗

In$\mathrm{FreeQ}(x^2+1, y)$Out$\mathrm{True}$

b is found two levels deep

live ↗

In$\mathrm{FreeQ}(\bigl\lbrack\bigl\lbrack a, b\bigr\rbrack\bigr\rbrack, b)$Out$\mathrm{False}$

About

Examples	7
Checked against	Wolfram Language 7 agree
Crosswalk	Wolfram Language

See also: MatchQ, Level