Brugtiohell

Brugtiohell is a esolang created by User:Yayimhere. its a jumble of other esolangs put together for some reason. the name is a pun of the danish words funktionel(functional) and brug(use), and the english word hell.

commands

these are the commands of Brugtiohell:

x10, notated as E, (z)x00y notated as µ, and 1 written that exact way, from Jot

ʎ̥, and ɤ̞, from FROSTWIRE-666

I the identity function

` from Unlambda

w, from Savage Operator

while here are the ones defined in terms of other operators:

01xʎ̥, notated as ω, with the binary from BLC, and ʎ̥ from FROSTWIRE-666

ʎ̥(x`(`)U), notated as ∀, with ` from Unlambda, and U from ()

L(J`(`)(`))xʎ̥, notated as ∄, with ` from Unlambda, L and J(jay) from CZTOLJDEFGKJSKI calculus, U from (), and ʎ̥ from FROSTWIRE-666

λx.λy.λz.1(ʎ̥(`))1ɤ̞x10y01(λ(`) (01) z)1(∄z) notated as ⁂, with the binary from Jot, ɤ̞ and ʎ̥ from FROSTWIRE-666, ` from unlambda,
and ∄ from well... this

all output capabilities are ignored. All these notatio. here are all the commands from seperate langs in lambda calculus and the already defined operators:

----
S = λf.λg.λx. f x (g x)
K = λx.λy.x
B = λx.λy.λz.x (y z)
U = λx.x(S)(K)
01x y = `x y (BLC)
L = λa.λb.a (b b)
J = λa.λb.λc.λd.a b (a d c)
ᶑ̊ = λx.λy.y x
ꞎ = λx.λy.λz.B (ᶑ̊ x y) x z #spesifically for λx.λy.S (B x x x) (ꞎ y) not how it works in FROSTWIRE-666
^^^not commands^^^
----
ʎ̥ = λx.B (K) x (S)
ɤ̞ = λx.λy.S (B x x x) (ꞎ y)
` = λx.λy.x y #not how it is in Unlambda but wutever
w = λx.(x)
since Jot is already defined in lambda calculus it works, and does not have to be defined
(although we have the subset x10,zx00y,  and 1 only)

so:

E = λx.x10
µ = λx.λy.λz.(z)x00y
ω = λx.01xʎ̥
∀ = λx.ʎ̥(x`(`)U)
∄ = λx.L(J`(`)(`))xʎ̥
⁂ = λx.λy.λz.1(ʎ̥(`))1ɤ̞x10y01(λ(`) (01) z)1(∄z)