Temporal Preconditions of Recursive Procedures

The meaning of an imperative program is defined to be the precondition of the executions as a function of proposed behaviour. In the case of Dijkstra's weakest precondition, the proposed behaviour is termination in a state with a given postcondition. For the temporal predicate transformers of Lukkien, the proposed behaviour is specified in terms of predicates on the intermediate states. For example, for a command c and predicates p, q and r, the predicate wto.p.q.c.r is the precondition such that, for every execution sequence of c, a state in which p holds is eventually followed by a state in which q holds or by termination in a state in which r holds.