Lambda calculus (ConceptTopic, 3)
From Hi.gher. Space
Basic
Identity, "Idiot"
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Always returns its parameter.
- Symbol: I
Mockingbird
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Gives the same result as applying its parameter to itself.
- Symbol: ω
- ωω = Ω
Omega
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The result of applying the Mockingbird to itself. Note that this can't take any parameter, since its evaluation results in an infinite loop. Usually treated as "undefined" and is said to be related to infinity.
- Symbol: Ω
Why
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A fixed-point combinator. Returns a value which remains the same when transformed under the original parameter.
- Symbol: Y
- YI = Ω
Kestrel
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Always returns the first of two parameters (and ignores the second). Usually treated as "true".
- Symbol: K
Kite
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Always returns the second of two parameters (and ignores the first). Usually treated as "false".
- Symbol: KI (because it is the result of applying the Kestrel to the Identity).
Identity once removed
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By definition, it gives the same result as applying the first parameter to the second. Alternatively, when called with one parameter it returns that parameter... unless I'm missing something. So what would make it any more worthwhile using than the ordinary Identity bird?
- Symbol: I* or CT (because it is technically the crossed Thrush, see below).
Thrush
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- Symbol: T
Konstant Mocker
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- Symbol: Kω
Crossed Konstant Mocker
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- Symbol: C(Kω)
Lark
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- Symbol: L
Owl
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- Symbol: O
Warbler
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- Symbol: W
Crossed Warbler
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- Symbol: CW
