A Verified Compositional Algorithm for AI Planning

We report on our HOL4 verification of an AI planning algorithm. The algorithm is compositional
in the following sense: a planning problem is divided into multiple smaller abstractions, then each of
the abstractions is solved, and finally the abstractions’ solutions are composed into a solution for
the given problem. Formalising the algorithm, which was already quite well understood, revealed
nuances in its operation which could lead to computing buggy plans. The formalisation also revealed
that the algorithm can be presented more generally, and can be applied to systems with infinite
states and actions, instead of only finite ones.
Our formalisation extends an earlier model for slightly simpler transition systems, and demonstrates another step towards formal treatments of more and more of the algorithms and reasoning
used in AI planning, as well as model checking.