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brainfuck.md

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 # Brainfuck
 
-Brainfuck is an extremely simple [esoteric programming language](esoland.md); simple by its specification (consisting only of 8 commands) but intentionally very hard to program in. It works similarly to a pure [Turing machine](turing_machine.md). In a way it is kind of [beautiful](beauty.md) by its [simplicity](minimalism.md). It is very easy to write your own brainfuck [interpreter](interpreter.md).
+Brainfuck is an extremely simple, untyped [esoteric programming language](esoland.md); simple by its specification (consisting only of 8 commands) but intentionally very hard to program in. It works similarly to a pure [Turing machine](turing_machine.md). In a way it is kind of [beautiful](beauty.md) by its [simplicity](minimalism.md). It is very easy to write your own brainfuck [interpreter](interpreter.md).
 
-There exist [self-hosted](self_hosting.md) brainfuck interpreters which is pretty fucked up.
+There exist [self-hosted](self_hosting.md) brainfuck interpreters which is pretty fucked up.
+
+The language is based on a 1964 language P´´ which was published in a mathematical paper; it is very similar to brainfuck except for having no [I/O](io.md).
+
+Brainfuck has seen tremendous success in the [esolang](esolang.md) community as the **lowest common denominator language**: just as mathematicians use [Turing machines](turing_machine.md) in proofs, esolang programmers use brainfuck in similar ways -- many esolangs just compile to brainfuck or use brainfuck in proofs of [Turing completeness](turing_complete.md) etc. This is thanks to brainfuck being an actual, implemented and working language reflecting real computers, not just a highly abstract mathematical model with many different variants. For example if one wants to encode a program as an integer number, we can simply take the binary representation of the program's brainfuck implementation.
+
+In [LRS](lrs.md) program brainfuck may be seriously used as a super simple [scripting language](script.md).
+
+## Specification
+
+The "vanilla" brainfuck operates as follows:
+
+We have a linear memory of **cells** and a **data pointer** which initially points to the 0th cell. The size and count of the cells is implementation-defined, but usually a cell is 8 bits wide and there is at least 30000 cells.
+
+A program consists of these possible commands:
+
+- `+`: increment the data cell under data pointer
+- `-`: decrement the data cell under data pointer
+- `>`: move the data pointer to the right
+- `<`: move the data pointer to the left
+- `[`: jump after corresponding `]` if value under data pointer is zero
+- `]`: jump after corresponding `[` if value under data pointer is zero
+- `.`: output value under data pointer as an ASCII character
+- `,`: read value and store it to the cell under data pointer
+
+## Variations
+
+TODO