The Apprentice Challenge J Strother Moore Department of Computer - - PowerPoint PPT Presentation

The Apprentice Challenge

J Strother Moore Department of Computer Sciences University of Texas at Austin

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A Class Involving Multiple Threads

class Container { public int counter; } class Job extends Thread { Container objref; public void setref(Container o) {

• bjref = o; }

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public Job incr () { synchronized(objref) {

• bjref.counter = objref.counter + 1; }

return this; } public void run() { for (;;) {incr(); } } }

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class Apprentice { public static void main(String[] args){ Container container = new Container(); for (;;) {Job job = new Job(); job.setref(container); job.start(); } } }

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Theorem The value of the counter never decreases. This has to be formulated more carefully to account for Java’s 32-bit int arithmetic.

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Theorem (let* ((s1 (run sched *a0*)) (s2 (step th s1))) (or (equal (counter s1) nil) (equal (counter s1) (counter s2)) (equal (int-fix (+ 1 (counter s1))) (counter s2))))

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It’s Obvious...

class Container {public int counter; } class Job extends Thread { Container objref; public void setref(Container o) {objref = o; } public Job incr () { synchronized(objref){

• bjref.counter = objref.counter + 1;}

return this; } public void run() { for (;;) {incr(); } } } class Apprentice { public static void main(String[] args){ Container container = new Container(); for (;;) {Job job = new Job(); job.setref(container); job.start(); } } }

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class Container {public int counter; } class Job extends Thread { Container objref; public void setref(Container o) {objref = o; } public Job incr () { synchronized(objref) {objref.counter = objref.counter + 1; } return this; } public void run() { for (;;) {incr(); } } } class Apprentice { public static void main(String[] args){ Container container = new Container(); Container bogus = new Container(); for (;;) {Job job = new Job(); job.setref(bogus); job.start(); job.setref(container); } } }

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Heap Thread Table Class Table

Thread 0 Job incr() synchronized(objref) {objref.counter = objref.counter + 1;} Apprentice main() Container container = new Container(); Container bogus = new Container() for (;;) { Job job = new Job(); job.setref(bogus); job.start(); job.setref(container);}

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Heap Class Table

Thread 0 −−− −−− container counter: monitor: container counter: monitor:

Thread Table

Job incr() synchronized(objref) {objref.counter = objref.counter + 1;} Apprentice main() Container container = new Container(); Container bogus = new Container() for (;;) { Job job = new Job(); job.setref(bogus); job.start(); job.setref(container);}

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• Heap

Thread Table Class Table

Thread 1 Thread 0 −−− −−− container counter: monitor: container counter: monitor: Job1

• bjref:

Job job = new Job(); Job incr() synchronized(objref) {objref.counter = objref.counter + 1;} Apprentice main() Container container = new Container(); Container bogus = new Container() job.setref(bogus); job.start(); job.setref(container);} for (;;) {

u n s c h e d u l e d

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• Heap

Thread Table Class Table

Thread 1 Thread 0 −−− −−− container counter: monitor: container counter: monitor: Job1

• bjref:

Job job = new Job(); Job incr() synchronized(objref) {objref.counter = objref.counter + 1;} Apprentice main() Container container = new Container(); Container bogus = new Container() job.setref(bogus); job.start(); job.setref(container);} for (;;) {

u n s c h e d u l e d

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Heap Thread Table Class Table

Thread 1 Thread 0 −−− −−− container counter: monitor: container counter: monitor: Job1

• bjref:

Job job = new Job(); Job incr() synchronized(objref) {objref.counter = objref.counter + 1;} Apprentice main() Container container = new Container(); Container bogus = new Container() job.setref(bogus); job.start(); job.setref(container);} for (;;) {

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Heap Thread Table Class Table

Thread 1 Thread 0 −−− container counter: monitor: container counter: monitor: Job1

• bjref:

Job job = new Job(); −−− Job incr() synchronized(objref) {objref.counter = objref.counter + 1;} Apprentice main() Container container = new Container(); Container bogus = new Container() job.setref(bogus); job.start(); for (;;) { job.setref(container);}

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Heap Thread Table Class Table

Thread 1 Thread 0 −−− container counter: monitor: container counter: monitor: Job1

• bjref:

Job job = new Job(); Thread 1

• bjref.counter + 1;}

Job incr() synchronized(objref) Apprentice main() Container container = new Container(); Container bogus = new Container() job.setref(bogus); job.start(); job.setref(container);} for (;;) { {objref.counter =

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Heap Thread Table Class Table

Thread 1 Thread 0 −−− container counter: monitor: container counter: monitor: Job1

• bjref:

Job job = new Job(); Thread 1

• bjref.counter + 1;}

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Job incr() synchronized(objref) {objref.counter = Apprentice main() Container container = new Container(); Container bogus = new Container() job.setref(bogus); job.start(); job.setref(container);} for (;;) {

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Heap Thread Table Class Table

Thread 1 Thread 0 −−− container counter: monitor: container counter: monitor: Job1

• bjref:

Job job = new Job(); Thread 1

• bjref.counter + 1;}

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Job incr() synchronized(objref) {objref.counter = Apprentice main() Container container = new Container(); Container bogus = new Container() job.setref(bogus); job.start(); job.setref(container);} for (;;) {

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Heap Thread Table Class Table

Thread 1 Thread 0 −−− container counter: monitor: container counter: monitor: Job1

• bjref:

Job job = new Job(); Thread 1

• bjref.counter + 1;}

1

Job incr() synchronized(objref) {objref.counter = Apprentice main() Container container = new Container(); Container bogus = new Container() job.setref(bogus); job.start(); job.setref(container);} for (;;) {

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Heap Thread Table Class Table

Thread 1 Thread 0 −−− container counter: monitor: container counter: monitor: Job job = new Job(); Thread 1

• bjref.counter + 1;}

1

Thread 2 Job1

• bjref:

Job2

• bjref:

Job incr() synchronized(objref) {objref.counter = Apprentice main() Container container = new Container(); Container bogus = new Container() job.setref(bogus); job.start(); job.setref(container);} for (;;) {

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Heap Thread Table Class Table

Thread 1 Thread 0 1000000 container counter: monitor: container counter: monitor: Thread 1

1

Thread 2 Job1

• bjref:

Job2

• bjref:

Thread 2

• bjref.counter + 1;}

Job incr() synchronized(objref) {objref.counter =

• bjref.counter + 1;}

Job incr() synchronized(objref) {objref.counter =

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Heap Thread Table Class Table

Thread 1 Thread 0 1000000 container counter: monitor: container counter: monitor: Thread 1 Thread 2 Job1

• bjref:

Job2

• bjref:

Thread 2

• bjref.counter + 1;}

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Job incr() synchronized(objref) {objref.counter =

• bjref.counter + 1;}

Job incr() synchronized(objref) {objref.counter =

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Heap Thread Table Class Table

Thread 1 Thread 0 1000000 container counter: monitor: container counter: monitor: Thread 1 Thread 2 Job1

• bjref:

Job2

• bjref:

Thread 2

• bjref.counter + 1;}

Job incr() synchronized(objref) {objref.counter =

• bjref.counter + 1;}

Job incr() synchronized(objref) {objref.counter =

1

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class Container { public int counter; } class Job extends Thread { Container objref; public void setref(Container o) {objref = o; } public Job incr () { synchronized(objref) {objref.counter = objref.counter + 1; } return this; } public void run() { for (;;) {incr(); } } } class Apprentice { public static void main(String[] args){ Container container = new Container(); for (;;) {Job job = new Job(); job.setref(container); job.start(); } } }

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Theorem (let* ((s1 (run sched *a0*)) (s2 (step th s1))) (rel (counter s1) (counter s2)))

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(defthm Lemma-1 (good-state *a0*)) (defthm Lemma-2 (implies (good-state s) (good-state (step th s)))) (defthm Lemma-3 (implies (good-state s) (rel (counter s) (counter (step th s)))))

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