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 and brug, and the english word hell

commands

these are the commands of Brugtiohell:

x10, notated as Ex, (z)x00y notated as λz x y, and 1, from Jot

ʎ̥, and ɤ̞, from FROSTWIRE-666

I the identity function

` from Unlambda

w, from Savage Operator



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

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

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

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

all output capabilities are ignored. 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 wut ever
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,z'x00y ,  and 1 only)

so the operators defined by other operators would be:

∀ = λq.ʎ̥(q`(`)U)
ω = λq.01qʎ̥ (BLC binary)
E = λq.q10 (jot binary)
∄ = λq.L(J`(`)(`))qʎ̥
⁂ = 1(ʎ̥(`))1ɤ̞x10y01(Y)1(∄z) #binary is Jot binary