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Note: Below algorithms turns out to be not sufficient. The edit script for the following case is incomplete. Given S constructed from an empty tree

S = +/s:{} +/t:{}

obtain T from S by

T = S +/s/a:{} >/s:/t/s

Running below algorithm on S and T will result in an edit script which, when applied to S, will not create child node a. I.e. it will result in

S >/s:/t/s

An algorithm for creating edit scripts (in JSOP format) from two trees. See this GitHub repository for a proof of concept implementation and the related discussion on oak-dev@

// Global variable holding the JSOP journal after the diffTree below returns.
jsop = ""
  Create a JSOP journal, which when applied to tree S will transform
  it to tree T.
diffTrees(S, T) {
  // Create a location (trash) which will temporarily hold removed nodes.
  // This is necessary since these (or child nodes thereof) might still be
  // needed in move operations occurring only later in the differencing process.
  X = S.addNode(createUniqueName)

  // The main differencing process starts at the roots of the trees and
  // progresses recursively level by level.
  diffNodes(X, S, T)

  // Remove the trash location and all its content
  jsop += "-" + X.path

  Recursively create JSOP operations for the differences of the children
  of trees S and T. Tree X serves as trash.
diffNode(X, S, T) {
  deleted = S.childNames \ T.childNames   // set difference
  added   = T.childNames \ S.childNames

  // Need to take care of deleted nodes first in order to avoid
  // name clashes when adding new nodes later.
  for (d : deleted) {
    t = S.child(d)

    // Deleted nodes are moved to trash.
    op = ">" + t.path + ":" + X.path + "/" + createUniqueName
    jsop += op
    S.apply(op)               // Transform S according to the single op

  for (a : added) {
    t = T.child(a)

    // assume we can detect a copied node and know its source node
    if (isCopied(t)) {
      op = "*" + t.sourceNode.path + ":" + t.path

    // assume we can detect a moved node and know its source node
    else if (isMoved(t)) {
      op = ">" + t.sourceNode.path + ":" + t.path

    // this is an added node
    else {
      op = "+" + t.path

    jsop += op
    S.apply(op)               // Transform S according to the single op

  // assert S.childNames == T.childNames
  for (c : T.childNames) {
    diffNode(X, S.child(c), T.child(c))