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CombinatorI

represents the TemplateBox[{}, CombinatorI] combinator.

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CombinatorI

CombinatorI

represents the TemplateBox[{}, CombinatorI] combinator.

Details

Examples

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Basic Examples  (2)

Apply the standard reduction rules of combinatory logic:

Wolfram Language code: CombinatorIx //. {CombinatorSx_y_z_ :> xz(yz), CombinatorIx_ :> x}

Use the axioms of combinatory logic to prove the TemplateBox[{}, CombinatorI] identity:

Wolfram Language code: FindEquationalProof[CombinatorI == , "CombinatorAxioms"]

Applications  (1)

Prove an identity among combinators:

Wolfram Language code: thm = CombinatorS(CombinatorK(CombinatorSCombinatorI))(CombinatorS(CombinatorKCombinatorK)CombinatorI) == ;
Wolfram Language code: proof = FindEquationalProof[thm, "CombinatorAxioms"]

Properties & Relations  (3)

The TemplateBox[{}, CombinatorI] combinator is equivalent to the term :

Wolfram Language code: Function[x, x][]

The TemplateBox[{}, CombinatorI] combinator is equivalent to the identity function:

Wolfram Language code: Identity[x]

The TemplateBox[{}, CombinatorI] combinator can be expressed in terms of TemplateBox[{}, CombinatorS] and TemplateBox[{}, CombinatorK] as TemplateBox[{}, CombinatorS]TemplateBox[{}, CombinatorK]TemplateBox[{}, CombinatorK]:

Wolfram Language code: CombinatorSCombinatorKCombinatorK //. {CombinatorSx_y_z_ :> xz(yz), CombinatorKx_y_ :> x}

The expression for TemplateBox[{}, CombinatorI] is not unique:

Wolfram Language code: CombinatorSCombinatorKCombinatorS //. {CombinatorSx_y_z_ :> xz(yz), CombinatorKx_y_ :> x}
Wolfram Research (2020), CombinatorI, Wolfram Language function, https://reference.wolfram.com/language/ref/CombinatorI.html.

Text

Wolfram Research (2020), CombinatorI, Wolfram Language function, https://reference.wolfram.com/language/ref/CombinatorI.html.

CMS

Wolfram Language. 2020. "CombinatorI." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CombinatorI.html.

APA

Wolfram Language. (2020). CombinatorI. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CombinatorI.html

BibTeX

@misc{reference.wolfram_2026_combinatori, author="Wolfram Research", title="{CombinatorI}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/CombinatorI.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_combinatori, organization={Wolfram Research}, title={CombinatorI}, year={2020}, url={https://reference.wolfram.com/language/ref/CombinatorI.html}, note=[Accessed: 12-June-2026]}