[Haskell-cafe] Reconstructing a tree from a list of its paths (to leaves)
ok at cs.otago.ac.nz
Wed Apr 11 02:15:26 CEST 2012
On 10/04/2012, at 7:55 PM, Arnaud Bailly wrote:
> I am manipulating labeled multiway trees, some kind of "lightweight"
> XML notation. One thing I would like to be able to do is manipulating
> a tree as a list of (Path, Value). Generating such a list is easy but
> I am a little bit surprised to find it harder to reconstruct a tree,
> given such a list assuming some sensible properties (list is ordered,
> for example).
Given a tree, there is a unique set of (Path, Value) pairs.
Given a set of (Path, Value) pairs, there might be no trees,
one, or infinitely many.
For example, suppose we have
data XM = XE String [XM] | XL String
as a simplification of XML and
paths :: XM -> [([Int],String)]
paths (XL s) = [(, s)]
paths (XE _ ks) = [(i:p,v) | (i,k) <- zip [1..] ks, (p,v) <- paths k]
as the function to reduce a tree to a list of (path,value) pairs.
paths (XE "foo" [XE "bar" [XL "zabbo"], XE "ugh" [XL "troppo"]])
in which "foo", "bar", and "ugh" have been irretrievably lost.
So you need to be rather more explicit about your "sensible properties".
(The list being ordered is not one of them; sorting is a solved problem.)
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