Contracts, Games and Reenement

We consider the notion of a contract that governs the behavior of a collection of agents. In particular, we study the question of whether a group among these agents can achieve a given goal by following the contract. We show that this can be reduced to studying the existence of winning strategies in a two-person game. We deene a weakest precondition semantics for contract statements that permits us to compute the initial states from which a group of agents has a winning strategy to reach their goal. This semantics generalizes the traditional predicate transformer semantics for program statements to contracts and games. Ordinary programs and interactive programs are special kinds of contracts. A notion of correctness and reenement is introduced for contracts. Contracts are shown to form a complete lattice with respect to the reenement ordering.