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Reactive models such as that used by Fran [l] allow one to describe a system that changes with time, by describing the state of an object after an event in terms of the situation before the event. This approach has advantages over the action based approach taken by imperative languages and the monadic approach 121. Notably, the state of any behaviour is defined in only one place, and one does not need to worry about when things should be updated. Systems such as Fran [l] allow one to specify the state that the system should be in at an exact point in absolute time, however current machines are only capable of processing information at a finite speed, and so may be unable to set behaviours to the states specified at the times specified. We will usually need to have a lag between the time at which something is specified to take on a value, and the time at which the state actually changes. What is more, the length of this lag will generally be non-deterministic. This lag needs to be dealt with in some way. The convention has been for no objects to be allowed to lag with respect to others, causing everything to always lag by the same amount. This greatly restricts what one can do with the system. One cannot have behaviours that are allowed to update at different rates, or that update as quickly as possible. One also cannot have practical distributed systems, as the synchronisation overhead would be unworkable. In order to make the reactive approach as expressive as the imperative approach, and thus practically applicable to areas beyond those of realtime processing and animations, we need to introduce a degree of temporal non-determinism into our model.

Controlled temporal non-determinism for reasoning with a machine of finite speed