JML and Class Specifications

• Class invariant• JML definitions• Queue example• Running JML in Eclipse

Review JML Language1. JML specs are comments:/*@ …. @*/

2. The Hoare triple{P} s1; s2; …; sn {Q} is written in JML/Java as:

/*@ requires P ; ensures Q ;@*/type method (parameters) { locals s1; s2; …; sn

}

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Class SpecificationsA class C is formally specified if:

1. Every constructor and public method M in the class has

preconditions and postconditions, and2. C has a special predicate called its class invariant INV

which, for every object o in C, argument x and call o.M(x), must be true both before and after the call.

Note: During a call, INV may temporarily become false.

Why are we doing this???• Formal specifications provide a

foundation for rigorous OO system design (e.g., “design by contract”).

• They enable static and dynamic assertion checking of an entire OO system.

• They enable formal correctness proof of an OO system.

Example: A Simple Queue Class

public class Queue { /* A first-in-first-out queue looks like this:

Node Node |val | |val | |prior| --> |prior| --> ... First

last ... <-- |next | <-- |next | */

private class Node { } private Node first = null;private Node last = null;private int n = 0; public void enqueue(Object v) { }public Object dequeue( ) {}public Object front() {}public boolean isEmpty() {}public int size() {}public void display() {}

}

state variableshelp us defineINVpublicmethods M

public constructor C = Queue()

internal “helper” class

Adding Class-Level Specifications

/*@ public model Node H, T; private represents H <- first; private represents T <- last; public invariant n == size(); @*/private /*@ spec_public @*/ Node first = null;private /*@ spec_public @*/ Node last = null;private /*@ spec_public @*/ int n = 0;

more JML

JML model variablesclass invariant INV

Notes: 1) JML model variables allow a specification to distance itself from the class’s implementation details.2) “spec_public” allows JML specifications to treat a Java variable as public without forcing the code to do the same.

Adding Method Specifications

/*@ ensures T.prior == \old(T) && H.prior == null && T.val.equals(v) ;

@*/public void enqueue(Object v) {

last = new Node(v, last, null);if (first == null) first = last;else (last.prior).next = last;n = n+1;

}

Notes: 1) \old denotes the value of T at entry to enqueue.2) The ensures clause specifies that enqueue adds v to the tail T, and that the head H is not affected.

What specifications for dequeue?

/*@

@*/public Object dequeue( ) {

Object result = first.val;first = first.next;if (first != null) first.prior = null ;else last = null;n = n-1;return result;

}

“Pure” methods

/*@ requires n > 0; ensures \result == H.val && H == \old(H);@*/public /*@ pure @*/ Object front() { return first.val; }

Note: A method is pure if:1) it has no non-local side effects, and2) it is provably non-looping.

Design by Contract Concretized

Obligations Benefits

Client(caller)

Arguments for eachmethod/constructor callmust satisfy its requiresclause

The call delivers correctresult, and the object keepsits integrity

Class(object)

Result for each call mustsatisfy both its ensuresclause and INV

Called method/constructordoesn’ t need extra code tocheck argument validity

Note: Blame can be assigned if obligations aren’ t met!

The contract for the Queue class

Obligations Benefits

Client(caller)

Arguments for every call toQueue(), enqueue,dequeue, front,isEmpty, size, anddisplay

must satisfy its requiresclause

Every call to Queue(), enqueue, dequeue,, front, isEmpty, size, and displaydelivers a correct result,and the object keeps itsintegrity

Class(object)

Result from each call mustsatisfy both its ensuresclause and the class invariantn == size()

No method orconstructor needs extracode to check argumentvalidity

Test driving the Queue class

public class QueueTest { public static void main(String[] args) { Queue q = new Queue(); int val; int n = Integer.parseInt(args[0]); for (int i=1; i <= n; i++) q.enqueue(args[i]); System.out.print("Queue contents = "); q.display(); System.out.println("Is Queue empty? " + q.isEmpty()); System.out.println("Queue size = " + q.size()); while (! q.isEmpty()) { System.out.print(" dequeue " + q.dequeue()); System.out.print(" Queue contents = "); q.display(); } System.out.println("Is Queue empty now? " + q.isEmpty()); }}

Contract test 1: normal run

% jmlrac QueueTest 5 1 2 3 4 5Queue contents = last --> 5 4 3 2 1 <-- firstIs Queue empty? falseQueue size = 5 dequeue 1 Queue contents = last --> 5 4 3 2 <-- first dequeue 2 Queue contents = last --> 5 4 3 <-- first dequeue 3 Queue contents = last --> 5 4 <-- first dequeue 4 Queue contents = last --> 5 <-- first dequeue 5 Queue contents = last --> <-- firstIs Queue empty now? true%

Contract test 2: precondition violation

Queue contents = last --> 1 2 3 4 5 <-- first…dequeue 4 Queue contents = last --> 5 <-- firstdequeue 5 Queue contents = last --> <-- firstException in thread "main" org.jmlspecs.jmlrac.runtime.JMLEntryPreconditionError: by method Queue.dequeue regarding specifications at File "../../home/allen/Desktop/workspace/myQueueTest/myqueuetest/

Queue.java", line 36, character 29 when'this' is myqueuetest.Queue@b166b5at myqueuetest.Queue.checkPre$dequeue$Queue(Queue.java:626)at myqueuetest.Queue.dequeue(Queue.java:771)at myqueuetest.QueueTest.main(QueueTest.java:16)

Note: blame is likely to be with the caller QueueTest, since a precondition has been violated.

Contract test 3: postcondition violation

Note: blame is likely to be with the callee Queue, since a postcondition has been violated.

Queue contents = last --> 5 4 3 2 1 <-- firstIs Queue empty? FalseException in thread "main" org.jmlspecs.jmlrac.runtime.

JMLNormalPostconditionError: by method Queue.dequeue regarding specifications at File "../../home/allen/Desktop/workspace/myQueueTest/myqueuetest/Queue.java", line 37, character 52 when

'\old(H)' is myqueuetest.Queue$Node@b166b5'\result' is 5'this' is myqueuetest.Queue@cdfc9c…

Contract test 4: invariant error

% jmlrac QueueTest 5 1 2 3 4 5Exception in thread "main" org.jmlspecs.jmlrac.runtime.JMLInvariantError: by method Queue.enqueue@post<File "../../home/allen/Desktop/workspace/

myQueueTest/myqueuetest/Queue.java", line 28, character 24> regardingspecifications at File

"../../home/allen/Desktop/workspace/myQueueTest/myqueuetest/Queue.java", line 22, character 38 …

Note: blame is again likely to be with the callee Queue, since an invariant has been violated.

Class and System Correctness

So far, we have only done testing!What about formal verification?

1. A class C is (formally) correct if:a. It is formally specified, andb. For every object o and every constructor and public

method M in the class, the Hoare triple

is valid for every argument x.

2. A system is correct if all its classes are correct.

€

{P∧INV} o.M(x) {Q∧INV}

E.g., Correctness of dequeue()

/*@ requires n > 0; ensures \result.equals(\old(H).val) && H == \old(H).next;

@*/public Object dequeue( ) {

Object result = first.val;first = first.next;if (first != null) first.prior = null ; To prove:else last = null;n = n-1; where:return result;

}

€

{P∧INV}dequeue(){Q∧INV}

P ≡ n > 0

Q ≡ \result = \old( first).val∧ first = \old( first).next

INV ≡ n = size()

Note: We again use rules of inference and reason through the code, just like we did with Factorial.

1.2.3.4.5.6.7.

A “loose” correctness proof for dequeue()

1. “Loose” because a. We assume the validity of size(), andb. We omit some details.

2. The assignments in dequeue(), together with ,ensure the validity of :1. Steps 1 and 7 establish \result = \old(first).val2. Steps 2-5 establish first = \old(first).next3. Step 6 and our assumption establish n = size():

a. I.e., n = \old(n) -1b. and size() = \old(size()) -1c. So, n = size(), since \old(n) = \old(size())

€

P∧INV

€

Q∧INV

More Observations

1. Formal verification:a. is an enormous task for large

programs.b. only proves that specifications and

code agree.c. only proves partial correctness

(assumes termination).

2. Tools exist for:a. Statically checking certain run-time properties of Java

programs (ESC/Java2)b. formally verifying Ada programs (Spark)

3. Tools are being developed to help with formal verificationof Java programs (Diacron, LOOP)

4. What is the cost/benefit of formal methods???