Draft:Plutonium hexafluoride
Plutonium hexafluoride (for a lack of a better name) is an esolang by User:KaleidoscopeFive in 2026. It is a combinatory logic language based on Lazy K and Crazy J with the main idea being to use the Phoenix combinator ф and its power in an aristocratic system.
Basis
The basis used is the IGф basis. Since there are no cancellative combinators, this is an aristocratic basis.
I x = x G x y z w = x w (y z) ф x y z w = x (y w) (z w)
The character used to represent the Phoenix in Plutonium hexafluoride is not the Greek letter phi, but instead the Cyrillic letter Ef. This was deliberately chosen to avoid inconsistencies between fonts.
Despite its great power however, the Phoenix has one major weakness that makes it necessary to insert another combinator into the Iф system, which is that it cannot re-order its arguments. Initially, the T combinator was used to remedy this problem but the G combinator was found to be far superior as it allowed changing grouping.
Table of combinators
| Combinator | Bird name | Expression (CC) | Expression (Unlambda) | Proof |
|---|---|---|---|---|
I
|
Identity bird | I
|
i
|
Check the basis again. |
M
|
Mockingbird | фIII
|
```фiii
|
фIIIx I(Ix)(Ix) I(x)(x) xx Q.E.D. |
M2
|
Double mockingbird | фI(фI)I
|
```фi`фii
|
фI(фI)Ixy I((фI)x)(Ix)y I(фIx)(x)y фIxxy I(xy)(xy) xy(xy) Q.E.D. |
O
|
Owl | фII
|
``фii
|
фIIxy I(Iy)(xy) I(y)(xy) y(xy) Q.E.D. |
S
|
Starling | фI
|
`фi
|
фIxyz I(xy)(xz) xy(xz) Q.E.D. |
S'
|
Converse starling | ф(GII)
|
`ф``gii
|
ф(GII)xyz GII(xz)(yz) I(yz)(I(xz)) I(yz)(xz) (yz)(xz) yz(xz) Q.E.D. |
T
|
Thrush | GII
|
``gii
|
GIIxy Iy(Ix) Iy(x) y(x) yx Q.E.D. |
ω
|
Omega bird | фIII(фIII)
|
````фiii```фiii
|
фIII(фIII) I(I(фIII))(I(фIII)) I(фIII)(фIII) фIII(фIII) Q.E.D. This is quite trivial thanks to the S and I combinators. |
Church numerals
| Number | Expresion (CC) | Expression (Unlambda) |
|---|---|---|
| 0 | Impossible | |
| 1 | TBA
|
TBA
|
Examples
Infinite loop
````фiii```фiii
