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, Appendix: Description of APE-plan

, APE-plan returns a refinement tree T for ?. It starts by creating a refinement tree with a single node n labeled ? and calls a sub-routine APE-plan-Task which builds a complete refinement tree for n. APE-plan has three main sub-procedures: APE-plan-Task, APE-plan-Method and APE-planCommand. APE-plan-Task looks at b method instances for refining a task ?. It calls APE-planMethod for each of the b method instances and returns the tree with the most optimal value. Every refinement tree has a value based on probability and cost. Once APE-plan-Task has chosen a method instance m for ? , it re-labels the node n from ? to m, in the current refinement tree T. Then it simulates the steps in m one by one by calling the sub-routine APE-plan-Method. APE-plan-Method first checks whether the search has reached the maximum depth, The main procedure of APE-plan is shown in Figure 5. b, b and d are global variables representing the search breadth, sample breadth and search depth respectively. APE-plan receives as input a task ? to be planned for, a set of methods M and the current state s