# Savage Operator

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**Savage Operator** is a esolang created by User:Yayimhere inspired by Unlambda

## syntax form

a operator is applied with Prefix notation like in Unlambda and brackets around a string `e`

:

(e)

## operators

some of these are represented with Lambda calculus expressions. also all these expressions have input `x`

, and if there is a second input that is `y`

:

**e**: a lambda expression with no body. can't be the final result nor be applied to something**v**:`λx.v`

**E**:`λx.x (λx. )`

which can also not be the final result**i**:`λx.x`

**ε**:`λx.ε x`

**w**:`(λx.(x))`

**∞**: evaluate`x`

**∞'**: evaluate`x`

for a single iteration**a**:`λx.λy.x y`

without evaluating it**a'**:**a**but goes into brackets, without evaluating it**b'**:**a'**but prepend**d**: rename all instances of`x`

(including in input) in expression`y`

as`z`

**[(**:*x*)(*y*)(*z*)]`x=λz.y`

or`x=y`

if`z`

is empty

### exclusions

**∞**and**∞'**cant be applied to:**[(**,*x*)(*y*)(*z*)]**e**, and**E****b'**,**a'**,**d**, and**a**cant be applied to:**∞**,**∞'**,**a'**,**b'**,**[(**,*x*)(*y*)(*z*)]**d**

## Turing-completeness

Savage Operator is turing complete since we can define SKI combinator calculus operators:

[(S)(a’ (a’ (w (a g x) ) (a f x) (a’ (d x e f) (d x e g))) )(f)] [(K)(a’ (d x e y) y)(x)] and I is just... i

now any expression in SKI calculus is valid in Savage operator. these work by creating functions that are equal to the `S and K`

operators