## The Problem

Cornelius needs to handle arbitrary exceptions and try/catch blocks. To do this in its entirety will be hard, so I’ve decide to start with something simpler: null pointer dereferencing.

## Null Pointer Dereferencing

Cornelius handles field writing and reading of objects, for instance:

int foo() {
int x = a.b;
return x;
}


Listing 1: A Java program that dereferences a class variable this.a

If we knew that a was never null then we could output something like:

(method-root
;; The returned value is the result of two reads.
;; 1. (rd (path (var this) (derefs a)) (heap 0)) reads this.a from
;;    (heap 0)
;; 2. The result of the above read is used as the base of the outer rd node,
;;    which dereferences variable name b in (heap 0)
(rd (path
(rd (path (var this) (derefs a)) (heap 0))
(derefs b))
(heap 0))
;; The returned heap
(heap 0))


Listing 2: The (incorrect) PEG produced by Cornelius currently...note that this doesn't handle null dereferences

I need to check the dereference of (this.a).b) for nullity; I can skip the null check for this since this is never null.

## Why is this tricky?

I’ll need to capture control flow somewhere. Consider the following method:

int derefAndAssign(Foo a) {
int x = 0;
try {
int y = a.value;  // Might throw NPE
x = 1;            // Doesn't execute if NPE is thrown.
} catch (NullPointerException e) {}
return x;  // This x shouldn't track assignment x = x + 1 when a is null
}


Listing 3: This method illustates the intersection of concerns between handling possible exceptional status and control flow.

If a is null, then the print statement and executed. The semantics for the print statement are implicitly handled because a.value is serialized to (rd (path (var a) (derefs value)) (heap 0)), which implicitly tracks the possibility that a might be null.

But in the case of x = 1, this is a simple assignment to a local variable and doesn’t involve the heap at all. Thus if we just update our context naively, x will always be 1 at there return statement.

## The solution

### The Heap

Heaps now track two things: heap state and exception status: (heap STATE STATUS). STATE is a chain of wr nodes, while STATUS is a chain of conditionals testing for conditions and resulting in unit if none of the conditions are met, or specific exception types if the corresponding condition is met.

For instance, (heap unit (phi (isnull? (var a) (exception java.lang.NullPointerException) unit))) represents a heap with a single possible NPE triggered by (var a) being null.

### Exit Conditions

Cornelius tracks exit conditions in its contexts:

    final public ImmutableSet<PegNode> exitConditions;


Listing 4: PegContext.exitConditions

During serialization, which is basically just a big AST visit, every time we encounter code that might throw an exception (for now, just NullPointerExceptions), we register it in the context:

    @Override
public ExpressionResult visit(FieldAccessExpr n, PegContext arg) {
final ExpressionResult scope = n.getScope().accept(this, arg);
final PegNode path = PegNode.path(scope.peg.id, n.getNameAsString());
// isnull: the exit condition for this dereference
final PegNode isnull = PegNode.isnull(scope.peg.id);
// the null pointer exception that is thrown when the 'scope' of the
// FieldAccessExpr is null (e.g., in a.x, 'a' is the scope)
final PegNode npe = PegNode.exception("java.lang.NullPointerException");
// nullCheck: the resulting context after a null check, with the
// corresponding exception condition
final PegContext nullCheck = scope.context.withExceptionCondition(isnull, npe);
return PegNode.rd(path.id, scope.context.heap.id).exprResult(nullCheck);
}


Listing 5: PegExprVisitor.visit(FieldAccessExpr, PegContext)

An ExpressionResult is just a wrapper around a PegContext and a PegNode, as well as some convenience methods.

Under the hood, PegContext.withExceptionCondition(PegNode cond, PegNode exception) copies the current PegContext with the following modifications

1. cond is added to the new PegContext’s exitConditions
2. the new context’s heap now tracks the possibility of this exceptional status. This is stored in context.heap.status. If there have been no exceptions thrown, then context.heap.status is unit (or something that is, in theory, rewritable to unit). If it is not unit, that means that an exception has been thrown already, which in turn means that the current exception is not thrown. Thus the new status is:
 (phi (unit? OLD-STATUS)
;; Old status is unit, so whenever the new exit condition is true,
;; the status should be the new exception. Otherwise, it's the old
;; exception status
(phi NEW-EXIT-CONDITION EXCEPTION OLD-STATUS)
;; The old statis is NOT unit, which means that an exception was
;; thrown that hasn't been caught. The old status should be used.
OLD-STATUS)


On subsequent assignment operations, instead of directly updating the context we now predicate that update on exit conditions:

    /**
* A helper method wrapping {@code setLocalVar} to predicate assignments on appropriate checks against
* exitConditions.
* @param key variable name we are assigning to
* @param val value we are assigning
* @return context resulting from assignment
*/
public PegContext performAssignLocalVar(final String key, final PegNode val) {
if (exitConditions.isEmpty()) {
return setLocalVar(key, val);
}
return setLocalVar(key, PegNode.phi(PegNode.exitConditions(exitConditions).id, getLocalVar(key).id, val.id));
}


Listing 6: PegContext.performLocalAssign(String, PegNode): this helper method performs a local assignment predicated on any possible exit conditions that occurred before this

This also needs to be tracked by context joins, but this is pretty straight forward…I just union the exitConditions and update heap state and status based on control flow:

    /**
* Combine two contexts, merging control flow.
* @param c1 the context resulting from the then branch that executes if {@code guardId} is true
* @param c2 the context resulting from the else branch that executes if {@code guardId} is false
* @param guardId the id of the branching condition
* @return combined contexts
*/
public static PegContext combine(PegContext c1, PegContext c2, Integer guardId) {
assert c1.fieldNames == c2.fieldNames;  // TODO: is this true? This should be true
final ImmutableSet<String> domain = c1.localVariableLookup.keySet().stream().filter(c2.localVariableLookup::containsKey)
.collect(Collectors.collectingAndThen(Collectors.toSet(), ImmutableSet::copyOf));

final PegNode.Heap combinedHeap = PegNode.heap(
PegNode.phi(guardId, c1.heap.state, c2.heap.state).id,
PegNode.phi(guardId, c1.heap.status, c2.heap.status).id
);

final ImmutableSet<PegNode> combinedExitConditions = (new ImmutableSet.Builder<PegNode>())