In this paper we present the foundations of Rapids ("Replicated Ada Partitions In Distributed Systems"), an implementaion of the PCS supporting the transparent replication of partitions in distributed Ada 95 using semi-active replication. The inherently non-deterministic executions of multi-tasked partitions are modeled as piecewise deterministic histories. I discuss the validity and correctness of this model of computation and show how it can be used for efficient semi-active replication. The Rapids prototype ensures that replicas of a partition all go through the same history and are hence consistent.