Savage Operator

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