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.)