NONDETERMINACY AND RECURSION VIA STACKS AND GAMES

The weakest-precondition interpretation of recursive procedures is developed for a language with a combination of unbounded demonic choice and unbounded angelic choice. This compositional formal semantics is proved to be equal to a game-theoretic operational semantics. Two intermediate stages are exploited. One step consists of unfolding the declaration of the recursive procedures. Fixpoint induction is used to prove the validity of this step. The compositional semantics of the unfolded declaration is proved to be equal to a formal semantics of a stack implementation of the recursive procedures. After an introduction to boolean two-person games, this stack semantics is shown to correspond to a game-theoretic operational semantics.