λx.

λx. is a esolang version of lambda calculus created by User:Yayimhere. it's a 4 instruction esolang

how it works

λx. works like lambda calculus(written a little differently) but the only thing you can do is the λx. hence the name. its written like this:

λx. (A)

this creates a function A which can be used in other functions. now the only thing you can add is more λx.'s inside. so this is a valid expression:

λx. (λx. ) (A)

this is not:

λx. x (A)

other than that it evaluates normally. to reference a function A with input x:

λx(A)

there is a 3 extra rule for reduction:

1. two functions nested(so for example λx.λy. with nothing in the body will move together(so the example provided before becomes λxy.λ.)
2. a empty function with no arguments nor a body will simplify to nothing
3. a function with no body but a argument will just leave the argument(so λxy. becomes xy)

and a 2 changes:

if something encased by brackets and does not hold a function the bracket will no be lifted

beta reduction applies to the function inputs

also Ẏ is replaced with user input and ẋ will output the following expression. else than these changes nothing id diffrent from normal lambda calculus

a simple example

heres a simple example:

λx. (λy. (λx.λy.) (A) ) (B)
λλworld(A)hello(B)

this simplifies to:

(hello world.)

so that function reverses the input

examples

Cat program:

λinput. λinput. (cat)
ẋ λẎ(cat)

identity function:

λx. λx. (identity)