CombinatorY
combinator.
CombinatorY
represents the 
combinator.
Details
- The
combinator has the property that ![TemplateBox[{}, CombinatorY]x](Files/CombinatorY.en/7.png "TemplateBox[{}, CombinatorY]x")
is equal to ![x(TemplateBox[{}, CombinatorY]x)](Files/CombinatorY.en/8.png "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:
CombinatorYf /. AxiomaticTheory["CombinatorAxioms", "RewriteRules"]f(CombinatorYf)These reduction rules do not terminate:
Nest[ReplaceAll[CombinatorYf_ :> f(CombinatorYf)], CombinatorYf, 10]Properties & Relations (1)
The ![TemplateBox[{}, CombinatorY]](Files/CombinatorY.en/18.png "TemplateBox[{}, CombinatorY]"){kind=small}
combinator can be expressed in terms of ![TemplateBox[{}, CombinatorS]](Files/CombinatorY.en/19.png "TemplateBox[{}, CombinatorS]"){kind=small}
, ![TemplateBox[{}, CombinatorK]](Files/CombinatorY.en/20.png "TemplateBox[{}, CombinatorK]"){kind=small}
and ![TemplateBox[{}, CombinatorI]](Files/CombinatorY.en/21.png "TemplateBox[{}, CombinatorI]"){kind=small}
in many ways:
cU = CombinatorS(CombinatorK(CombinatorSCombinatorI))(CombinatorSCombinatorICombinatorI);
cY = cUcUNest[ReplaceAll[{CombinatorSx_y_z_ :> xz(yz), CombinatorKx_y_ :> x, CombinatorIx_ :> x}], cYf, 4 * 2]
Wolfram Research (2020), CombinatorY, Wolfram Language function, https://reference.wolfram.com/language/ref/CombinatorY.html.
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