In scalar-oriented languages an efficient way to solve this 
problem can be described in 3 words:  depth first search.
That is:

treesum(x) is
- value(x) if x is a leaf
- value(x) + +/ treesum"0 (sons of x) if not

The time and space should be within a small factor
of the time and space to do +/\values , which none of the
solutions mentioned so far comes near.

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