You are right, of course. By "sensible properties" I simply meant the
list of (Path, Value) is assumed to represent a tree (eg. it has been
generated by a traversal of some original tree). By "ordered" I meant
Path(s) segments are lexicographically ordered and (Path, Value) are
enumerated from a tree using depth-first traversal.
Thanks,
Arnaud
On Wed, Apr 11, 2012 at 2:15 AM, Richard O'Keefe
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"]]) ==> [([1,1],"zabbo"),([2,1],"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.)