Section 3 with Remik (rz33@cornell.edu) 
Meeting #5 Notes
********************************************************
Administrivia:  Evaluate your TAs with www.engineering.cornell.edu/taeval/survey.cfm
		Check the cs212 website for Assignment #2 errata
Review:		Type-safety in languages
		Type checking a program

Why Type-Safety?
****************************
Types act as an attribute on values.  Therefore we can ensure
that we use only specific operations defined for certain
categories of types.  Although this adds security to our
code, some argue against this restriction since it may limit
the capabilities of a language.

If we are interested in ensuring types are used properly,
we need to type check our programs.  There are 2 ways about
it:

	Static (Compile time): Pascal
		vs.
	Dynamic (Run-time): Visual Basic, ML

Static checking is typically a pre-processing step for
compiling, but it can also been done inline.
Languages employing type-checking are called "Strongly Typed",
such as Java and Pascal.  Those that don't are "Weakly Typed",
such as C and LISP.  

Here is an example that won't compile by Java:
	int x = 0;
	...
	x = x + true;	// mixing addition with boolean; undefined

A Simple Type-Checker
****************************
Let's write a method to type check this simple language su:
EXP	 ::= INTEXP | BOOL
INTEXP	 ::= (INTEXP + INTEXP) | n
BOOL	 ::= "true" | "false"

static final int INTEGER = 0;	// types in our language
static final int BOOLEAN = 1;

bool typeCheck(CS211In f) {
	try {
		getType(f);
	} catch (Exception e) {
		return false;	// type checking failed	
	}
	return true;		// no exception, it passed
}
int getType(CS211In f) {
	switch( f.peekAtKind() ) {
		case f.INTEGER:	return INTEGER;
		case f.WORD:	if (f.check("true") ||
				    f.check("false"))
					return 	BOOLEAN;	
				else
					throw new Exception("Type error");
		case f.OPERATOR:
		  f.check('(');
		  int type1 = getType(f);	// use recursion
		  f.check('+');
		  int type2 = getType(f);

		  if (type1 == INTEGER) {	// adding integers?
			if(type1 == type2) 	
				return INTEGER; // yes
			else
				throw new Exception("Adding non-integer");
		  } else
			throw new Exception("Adding non-integer");
	}

	return 0;	// shouldn't be able to get to this line
}