The hierarchical non-linear planner, AbNLP, is introduced and its main features described, including the novel mechanisms by which abstraction is encapsulated within abstract operators, and possible interactions between developing levels of plan description are resolved. AbNLP has been developed in the rigorous tradition of STRIPS and TWEAK, and is therefore proposed as a foundation for the development of more powerful hierarchical planners. The main objective of the paper is to present a complete formal specification of the operational behaviour of the goal achievement functions and of the hierarchical refinement strategy employed by AbNLP. AbNLP is presented as a correct foundation for the construction of hierarchical planners. It is proposed that the refinement strategy used constitutes a powerful heuristic weapon against the inherent complexity of planning.