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Ropes and rope-like functional extensible vectors with O(1) prepend/append.
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Date: -- (:)
From: Mauricio Fernandez <mfp@a...>
Subject: Re: [Caml-list] Ropes and rope-like functional extensible vectors with O(1) prepend/append.
On Mon, Jul 30, 2007 at 02:47:23PM +0100, Jon Harrop wrote:
> On Monday 30 July 2007 12:51:29 Mauricio Fernandez wrote:
> > > I'd like metadata in every node, so I can provide a constructor that
> > > combines the metadata of child nodes and a cull function to accelerate
> > > searches.
> >
> > If I understand it correctly, that scheme could in the limit turn some O(n)
> > searches into O(log n)?), right?
> 
> Something like that, yes.
> 
> > Unlike Vec, Vect uses "compact" leaves (Leaf of 'a array) of bounded size
> > (leaf_size, typically 16-64), which might not fit very well.
> 
> I can think of two solutions:
> 
> 1. Linear search.
> 
> 2. Store an array of metadata corresponding to a binary search of the array of 
> elements in a leaf.
> 
> The latter sounds sexy but the former would probably suffice. :-)

Yes, linear search over <100 elements should be acceptable if the
structure is to hold several orders of magnitude more...

> > something like this maybe?
> >
[...]
> >       | Leaf of ('meta -> 'meta -> meta) * 'meta array * 'a array
> >
> > 		(* maybe also  * 'meta  to cache the last computation? *)
> >
> > or even without the ('meta -> 'meta -> 'meta) part, forcing the user to
> > pass the function on each modification?  Just thinking out loud.
> 
> I would use a functor to pass it the "combine" and "cull" functions, rather 
> than putting them in the tree itself. This is analogous to the Set.Make 
> functor accepting a comparison function.

You're very right, a functor makes so much more sense here: it saves one word
per node and allows stronger typing (the alternative would be ugly, lots
of  if mycombine != hiscombine then invalid_arg "operation" and errors found at
run-time).

So combine would be  combine : 'meta -> 'meta -> 'meta; commutative and
associative, so that it can be used in leaves as  
  Array.fold_left combine arr default
which shows that a default value for the metadata would have to be provided
too.

What about cull? a  control_cull : 'meta -> bool  that tells the vect whether
the search goes on recursively for each node (so the search is carried out by
a function in Vect) , or a function that handles recursion itself, using some
get_metadata : ('a, 'meta) t -> 'meta ? It seems the latter could lead to a
leaky abstraction though. Which type would it have anyway? Both
('a, 'meta) t -> 'a  and say  ('a, 'meta) t -> 'a list  could be useful (the
former can be used for find and the latter e.g. for select).

> > At any rate, it'd be better to provide it as a separate structure, any
> > suggestions for the name?.
> 
> You could just call it Tree and try to make it as generic as possible.
> 
> You could then reimplement the Set module on top of your data structure by 
> searching for the index of the given element and inserting it if it is new. 

For the sake of better space efficiency? Set uses 5 words per element, but it
could be brought down to 3.5 words by adding a new constructor. Still, Vect's
~1.125 to ~2.0 would remain considerably better.
It'd be great to find a way to make good use of the O(1) append to improve
on Set's logarithmic bounds, but I can't see how right now (again, it's late :)

> > > The usual HOFs, like map.
> >
> > I just pushed a patch with filter and map. The former is trivially
> > implemented with fold + append (thanks to the O(1) append). I was going to
> > code map the same way but I ended up making one that returns an isomorphic
> > vect and is faster (since there's no need to rebalance).
> 
> Yes. You could also use recursive subdivision to create a perfectly balanced 
> result.

The problem is that the obvious implementation, using Array, would run against
the max_array_length limit. Avoiding it is pretty easy but there are still 
a few more interesting things to be done :)

> > So Vect currently has iter, iteri, rangeiter, fold, map and filter. I'm
> > considering renaming fold to fold_left and providing fold_right too.
> 
> I'd definitely provide both folds, yes.
> 
> I'd also like specialized rewrite functions that avoid allocations when the 
> outputs are the same as the inputs. So I'd make the set function bail via an 
> exception when the element is left unchanged, returning the original Vect and 
> doing no allocation in this case. I'd also like an id_map function that did a 
> map but reused old branches whenever they were left unchanged.

I've renamed fold to fold_left and added fold_right as well as 
id_map : ('a -> 'a) -> 'a t -> 'a t.

Last but not least, I've added destructive_set : int -> 'a -> 'a t -> unit.
It's evil but so much faster...
http://eigenclass.org/repos/oropes/head/set-balanced.png
It brings Vect one order of magnitude closer to Array for ephemeral usage.

-- 
Mauricio Fernandez  -   http://eigenclass.org