[Haskell-cafe] Best bit LIST data structure

[Ryan Newton]

Hi Cafe,

We are lucky to have a plethora of data structures out there.  But it does
make choosing one off hackage difficult at times.  In this case I'm *not*
looking for a O(1) access bit vector (Data.Vector.Unboxed seems to be the
choice there), but an efficient representation for a list of bits
(cons,head,tail).

Let's say that you want to represent tree indices as you walk down a binary
tree.  [Bool] is a simple choice, you only add to the front of the list (0/1
= Left/Right), sharing the tails.  But [Bool] is quite space inefficient.

Something like [Int] would allow packing the bits more efficiently.  A Lazy
ByteString could amortize the space overhead even more... but in both cases
there's a tiny bit of work to do in wrapping those structures for per-bit
access.  That's probably the right thing but I wanted to check to see if
there's something else recommended, perhaps more off-the-shelf.

What about just using the Data.Bits instance of Integer?  Well, presently,
the setBit instance for very large integers creates a whole new integer,
shifts, and xors:

http://haskell.org/ghc/docs/latest/html/libraries/base/src/Data-Bits.html#setBit
(I don't know if it's possible to do better.  From quick googling GMP seems
to use an array of "limbs" rather than a chunked list, so maybe there's no
way to treat large Integers as a list and update only the front...)

Advice appreciated!

Thanks,
  -Ryan
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