Somebody asked me, how do we represent the state of a sequential device in HOL? 
And I am not quite sure. Mike himself wrote that it is simply about 
incorporating time into the model, so that if we have a counter then we can 
describe it by C(t+1) = C(t)+1, where C is its (visible) output and t 
represents time. 

But what if we have a primitive that doesn't expose its full state to the 
outside? Imagine a device that contains a counter that increments with every 
clock tick, but the counter value is hidden and the output is only a single bit 
to tell us whether the value of the counter is a prime number or not. Surely in 
such a case the counter itself would have to be visible in the formalisation 
even if no device was allowed to connect to it?

Larry Paulson




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