Backslash Calculus

Backslash Calculus is a programming language invented by User:Tailcalled after reading this reddit comment.

Syntax

Backslash Calculus is based on lambda calculus, but it only uses two characters: backslash and space. This is the basic syntax:

```   E = \ \ E    - abstraction
| \ \\ E E - application
| \\       - innermost variable
| \\\      - the variable one level more out
| ...      - ...
```

Computational Class

Backslash Calculus is clearly Turing-complete, even if one ignores its simple translation to lambda calculus. Here are the SKI combinators:

```   S = \ \ \ \ \ \ \ \\ \ \\ \\\\ \\ \ \\ \\\ \\
K = \ \ \ \ \\\
I = \ \ \\
```

Alternative alphabets

Tailcalled imagined a few alternative alphabets for Backslash Calculus.

One can replace backslash with ' and space with ". The SKI combinators will look like this with that alphabet:

```   S = '"'"'"'"'"'"'"''"'"''"''''"''"'"''"'''"''
K = '"'"'"'"'''
I = '"'"''
```

Brainfuck

One can change the syntax a bit to make Backslash Calculus look more like brainfuck:

```   E0 = + E1 -
| [ E0 E0 ]
| .
| ,.
| ,,. <- unary-ish
| ...
E1 = > E0 <
| [ E1 E1 ]
| .
| ,.
| ,,. <- unary-ish
| ...
```

The SKI combinators will look like this:

```   S = +>+[[,,..][,..]]-<-
K = +>[,.]<-
I = +.-
```