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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 and compilers (i.e. themselves written in brainfuck) which is pretty fucked up. The smallest one is probably the one called [dbfi](dbfi.md) which has only slightly above 400 characters, that's incredible!!! (Esolang wiki states that it's one of the smallest self interpreters among imperative languages).
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).