Past exam of the computer science course of the University of Oxford / 2015 / Principles of programming languages / 2 / e / Solution

Represent a binary semaphore by a two-element list containing the addresses of its busy flag and its waiting FIFO queue. A blocked continuation belongs to the waiting FIFO queue, not the scheduler's runnable FIFO queue. These definitions extend the FunMem scheduler from the preceding part:

val semaphore() =
  let val busy = new() in
  let val waiting = new() in
    busy := false; waiting := nil; busy : waiting : nil;

val acquire(s) =
  let val busy = head(s) in
  let val waiting = head(tail(s)) in
    if !busy then
      callcc(lambda (blocked)
        waiting := append(!waiting,blocked:nil); dispatch())
    else (busy := true; nil);

val release(s) =
  let val busy = head(s) in
  let val waiting = head(tail(s)) in
    if !waiting = nil then (busy := false; nil)
    else let val next = head(!waiting) in
      waiting := tail(!waiting); enqueue(next); nil

A newly created semaphore is free. Acquiring it while free marks it busy and immediately returns nil. Acquiring it while busy captures the remainder of the caller, appends that continuation to the waiting FIFO queue, and dispatches a runnable computation. No runnable copy of the blocked caller is retained.

When a waiting caller exists, release keeps the busy flag true: the released permit is reserved for that caller. It removes exactly one waiting continuation and appends it to the scheduler's runnable FIFO queue. It does not invoke dispatch, so the releasing computation keeps running. A newcomer cannot steal the reserved permit during the interval before the released caller resumes. That caller's captured continuation resumes after acquire with nil, already possessing the permit.These are FIFO semaphores; the question only requires selecting one waiter, so choosing the oldest is a valid stronger discipline. The updates contain no suspension except at the explicit blocking point, making them atomic relative to this cooperative multitasking scheduler. As allowed in the paper, invalid releases and executions in which every remaining computation is blocked need no error handling; the latter are deadlocks, not a way to make progress.