represents the combinator.
CombinatorY
represents the combinator.
Details
- The combinator has the property that TemplateBox[{}, CombinatorY]x is equal to x(TemplateBox[{}, CombinatorY]x).
- No transformations for CombinatorY are applied automatically.
- CombinatorY is output in StandardForm or TraditionalForm as . This typeset form can be input using cY.
Examples
open all close allBasic Examples (1)
Apply the standard reduction rules of combinatory logic:
These reduction rules do not terminate:
Properties & Relations (1)
The TemplateBox[{}, CombinatorY] combinator can be expressed in terms of TemplateBox[{}, CombinatorS], TemplateBox[{}, CombinatorK] and TemplateBox[{}, CombinatorI] in many ways:
See Also
Application CombinatorS CombinatorK FixedPoint
Function Repository: CombinatorConvert CombinatorTraditionalForm
Related Guides
History
Text
Wolfram Research (2020), CombinatorY, Wolfram Language function, https://reference.wolfram.com/language/ref/CombinatorY.html.
CMS
Wolfram Language. 2020. "CombinatorY." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CombinatorY.html.
APA
Wolfram Language. (2020). CombinatorY. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CombinatorY.html
BibTeX
@misc{reference.wolfram_2025_combinatory, author="Wolfram Research", title="{CombinatorY}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/CombinatorY.html}", note=[Accessed: 08-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_combinatory, organization={Wolfram Research}, title={CombinatorY}, year={2020}, url={https://reference.wolfram.com/language/ref/CombinatorY.html}, note=[Accessed: 08-January-2026]}