Formal Models of Operating System Kernels by Iain D. Craig

By Iain D. Craig

Working structures kernels are principal to the functioning of desktops. safety of the general method, in addition to its reliability and responsiveness, rely on the right kind functioning of the kernel. This special approach – providing a proper specification of a kernel – starts off with easy constructs and develops a collection of kernels; proofs are integrated as a part of the textual content.

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4 Hardware Model 33 InitCLOCK CLOCK timenow = 0 The length of the clock tick often needs to be converted into some other unit. For example, a 60Hz “tick” might be converted into seconds. ticklength : TIMEVAL The clock updates itself on every hardware “tick”: UpdateCLOCKOnTick ∆CLOCK timenow = timenow + ticklength When the current time is required, the following operation is used: TimeNow ΞCLOCK now ! : TIMEVAL now ! = timenow When a process needs to set an alarm, it sends the clock driver a message of the following type: TIMERRQ == PREF × TIMEVAL The message contains the identifier of the requesting process (here, of type PREF , the most general process reference type) plus the time by which it expects to receive the alarm.

Of the registers, the most important is the instruction pointer. Context switches are expensive because they copy the contents of all hardware registers into the current process descriptor. They occur when the scheduler determines that another process should be allocated to the processor. They are also required for the specification of semaphores. There are two main operations involved in context switching: one to copy state data from the process descriptor to the hardware and one to copy data in the opposite direction.

Elts = tail elts = tail ( x ! = y elts y elts ) Note that, even if x ! = y, we can consider them to be different instances of x !. ✷ 26 2 Standard and Generic Components Proposition 9. If, for some element, x , of elts, if elts(n) = x for some n, such that 1 ≤ n ≤ #elts, then RemoveNext n [X ] removes x from the queue, where: RemoveNext n ≡ (RemoveNext o 9 ... o 9 RemoveNext) n times Proof. , the elements elts(1) . . elts(n − 1)). The length is denoted by k . The predicate of RemoveNext is (changing the name of the output variable): elts = y!

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