Scanning a tree is also known as tree traversal or tree search. ResourceFunction["AncestralTreeScan"] always visits vertices according to a depth-first traversal.

Scanning a tree is typically used to carry out an operation on subtrees where the operation has a "side effect", such as making an assignment.

ResourceFunction["AncestralTreeScan"][f,g,t] performs a depth-first scan of the tree t, where the following arguments are passed to the function f at the current vertex v: the list of computations made on the vertices of the tree on the path from the root to the parent of v (which will always be the empty list if v is the root), and the datum extracted from t at v. At v, this output of f is appended to the list of computations, before this updated list is passed as the lone argument to the output function g. In this way a sequence of values computed at the vertices of the tree can be output, where the value to be computed at a given vertex depends on the values computed at its ancestors, without repeating computations or storing more computed values than just those belonging to the ancestors of the given vertex.