1.
Each expression has a type. 

(A) e -- If the static type of e is t1 
	if t1 is a subtype of A then ignore the type cast.
	if A is a subtype of t1 then the type of (A) e is A.
	else type error

Rest of the type rules are standard.

Code generation:
Each class has a special field classID (could be String containing the
fully qualified name); we will instead store a unique integer for each
class. We assign the classIDs such that, if class B extends class A, then
A.classID < B.classID.

new A() -- If size of class A is n bytes, we allocate n+4 bytes (for the
additional classID) and set classID to A.classID.

(A) e -- t1 = [e]; if (t1.classID > A.classID) error.

2. 
A flow graph is reducible iif when we remove all the back edges the
resulting flow graph is acyclic:

Proof by contradiction: Say the graph is reducible, we remove the backedges and the resulting
flow graph has a cycle. Add the backedges. Do T1/T2 transformation
repeatedly -- would not lead to a single node.


3.
See Section 18.10 Muchnick

4. 
At each program point, maintain the set of copies:

Intraprocedural copy propagation:

CPin (i) = meet CPout(j) // for all predecessor j of i

CPout (i) = COPY(i) + (CPin (i) - Kill (i))

Context insensitive analysis:

CPin (p) = meet CPout (all calls to p)

CPout (call p) = CPout (p)

CPin, CPout: for each statement i return a set of variable names.