COP 4020 Lecture 5 Overview
			        Syntax 1/23/02

syntax is the specification of what is valid in a language, while
semantics is the meaning of expressions in a language.

Strings in a language are called sentences or statements.
The smallest unit of a language is called a lexeme.
lexemes can be combined to make statements.
A token is a category of lexemes.

For example, 24 is a lexeme that is an integer literal token.

A language recognizer is a tool that can read in a statement and decide
whether it belongs in a language L or not.

A language generator is a tool that can simply generate valid statements
in a language L.

It turns out that most programming languages are context free grammars.
(In the book it is also referred to as Backus-Naur form.)

A CFG has four components:

1) an alphabet
2) a start symbol
3) a list of variables
4) a list or productions or rules.

The alphabet is the set of valid lexemes. A language is simply a set of
strings, where a string is the concatenation of 0 or more elements of the
alphabet.

Here is an example grammar:

alphabet = {a, b}
Start symbol = S
Variables = {A, B}

Rules:

S -> aA | Bb
A -> Ab | a
B -> Ba | b

Now, this set or rules is essentially a generator of the grammer. You 
follow the rules like so:

S -> aA -> aAb -> aAbb -> aabb

Every time you have a variable in a production, you can substitute for it
using all the given rules. Eventually you'll get rid of all the variables.
What is left is a string in the language. If there exists a method to 
follow the given rules and come up with a string w, then w is in the 
language described by the grammar.

Based upon the derivation of a string, a parse tree for that derivation
can be drawn. (This was done in class.)

If a string in a grammar has two different parse trees, then the grammar
is ambiguous. This is because the semantics of a grammar come from the 
parse tree of an expression in the grammar. If the expression has two
different parse trees, that means it can be interpreted in two different
ways.

Several ambiguous grammars can be turned into equivalent unambiguous
grammars. Examples are in the text.