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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:

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

Applications  (1)

Prove an identity among combinators:

Properties & Relations  (3)

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

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

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

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

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_2025_combinatori, author="Wolfram Research", title="{CombinatorI}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/CombinatorI.html}", note=[Accessed: 26-October-2025]}

BibLaTeX

@online{reference.wolfram_2025_combinatori, organization={Wolfram Research}, title={CombinatorI}, year={2020}, url={https://reference.wolfram.com/language/ref/CombinatorI.html}, note=[Accessed: 26-October-2025]}