BinFlak is a language a lot like BrainFlak, but compressed so that programs are a lot shorter, and any sequence of bytes is a unique syntactially-valid program.

Encoding a BrainFlak program into BinFlak is a two-step process:

First, the program is encoded as a base-five number (with the end of the program going in the high bits). Since only one closing-bracket is valid at any given position in a program, all closing-brackets are mapped to 0.

Second, the numbers are "compacted," by subtracting the number of invalid programs (with more closing than opening braces) are less than it. Currently, this is calculated by brute-force, but I'm sure there's a clean(er) mathematical way to find this.

Finally, this number (as a sequence of extended-ASCII characters or whatnot) is your program.

Decoding a BinFlak program into BrainFlak follows this process in reverse.

As an example, let's translate the BrainFlak program [()()] into BinFlak.

• To convert it to a base-5 number, we reverse it and follow the table above to get 001012, or 132.
• Compacting this, we subtract 30, because there are 30 invalid programs less than 1012:
  • 10, 20, 30, 40, 100, 110, 120, 130, 140, 200, 210, 220, 230, 240, 300, 310, 320, 330, 340, 400, 410, 420, 430, 440, 1000, 1001, 1002, 1003, 1004, and 1010 are all invalid because they attempt to close a bracket they never open.
• Finally, the program is 102, or read as ASCII f.