Not so. I'm trying to figure out how to find the maximum entropy distribution for simple types, and recursively defined types are a part of that. This does not only apply to strings, it applies to sequences of all sorts, and I'm attempting to allow the possibility of error correction in these techniques. What is the point of doing statistics on coin flips? Once you learn something about the flip result, you basically just know it.
Well, in the coin flip case, the thing you care about learning about isn't the value in {Heads, Tails} of a coin flip, but the value in [0,1] of the underlying probability that the coin comes up heads. We can then put an improper prior on that underlying probability, with the idea that after a single coin flip, we update it to a proper prior.
Similarly, you could define here a family of distributions of string lengths, and have a prior (improper or otherwise) about which distribution in the family you're working with. For example, you could assume that the ...
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