is an attribute that can be assigned to a symbol f to indicate that the elements ei in expressions of the form f[e1,e2,…] should automatically be sorted into canonical order. This property is accounted for in pattern matching.
Orderless
is an attribute that can be assigned to a symbol f to indicate that the elements ei in expressions of the form f[e1,e2,…] should automatically be sorted into canonical order. This property is accounted for in pattern matching.
Details
- The Orderless attribute for a function corresponds to the mathematical property of commutativity.
- Functions with the Orderless attribute use canonical order as described in the notes for Sort .
- For an object that represents a matrix or a tensor, the Orderless attribute represents symmetry among indices.
- Functions like Plus and Times are Orderless .
- In matching patterns with Orderless functions, all possible orders of arguments are tried.
- The Orderless attribute must be assigned before defining any values for an Orderless function.
Examples
open all close allBasic Examples (3)
Properties & Relations (2)
All possible argument orderings are tried to match a definition for an orderless function:
Elements of an expression whose head is orderless are sorted into standard order:
This sorting occurs as part of the standard evaluation process:
Possible Issues (1)
Pattern matching with orderless functions can lead to a large number of possible cases:
See Also
Tech Notes
Related Guides
History
Introduced in 1988 (1.0)
Text
Wolfram Research (1988), Orderless, Wolfram Language function, https://reference.wolfram.com/language/ref/Orderless.html.
CMS
Wolfram Language. 1988. "Orderless." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Orderless.html.
APA
Wolfram Language. (1988). Orderless. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Orderless.html
BibTeX
@misc{reference.wolfram_2025_orderless, author="Wolfram Research", title="{Orderless}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Orderless.html}", note=[Accessed: 16-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_orderless, organization={Wolfram Research}, title={Orderless}, year={1988}, url={https://reference.wolfram.com/language/ref/Orderless.html}, note=[Accessed: 16-November-2025]}