Λ-HELL

This is still a work in progress. It may be changed in the future.

λ-HELL is an esolang made by User:Yetyetty1234567890.

The goal of the language is not to be as "reduced" as possible, but rather as unconcise as possible, without adding any bloat. Bloat in this case means any unnecessary things, such as "add 200 million a's to the end of the program" or something more subtle, like in INTERCAL where you need a certain ratio of "PLEASE" to "DO" at the start of every line.

Definiton

λ-HELL is an extremely stripped down version of Lambda calculus. First, the output of λ-HELL MUST be determenistic. However, the execution order of the Lambdas in an expression in λ-HELL are still indeterministic. Secondly, there is only 1 type of variable; x. Therefore, all Lambdas are assumed to be λx.. Other than that, Lambdas only have two inputs: λx. (_ _).

Turing-completeness proof

To start with the Turing-completeness proof of this language, we must first talk about state machines.

Expressions as labels

Simply speak, let's say we have some combination of expressions, (A B). (The letters are placeholders for lambda expressions) To represent a completed reduction, we can write A[B]. Now, we must build from a few key assumptions: A[B][C] = A[B[C]]

Something idk

TODO: Finish this proof