The document discusses parsing and context-free grammars. It defines parsing as constructing a parse tree from a stream of tokens using the rules of a context-free grammar. It provides examples of parse trees being built from both top-down and bottom-up parsing approaches. Key aspects of context-free grammars like non-terminals, terminals, production rules, and the start symbol are also summarized.

2.  Parsing is a process that constructs a syntactic
structure (i.e. parse tree) from the stream of
tokens.
 Breaks the data into smaller units for easy
translation
 Used to determine if input data may be derived
from the start symbol of the grammer

4.  Identifies lexical units in a source statement
 Classifies units into different classes e.g. id’s,
constants, reserved ids etc and enters them into
different tables
 Token contains Class code and number in class
Syntax :Code #no eg : id#10
Example
Statement a := b + I;
a := b + I ;
id#2 op#5 id#3 op#3 id#1 op#10

5.  Determines the statement class such as
assignment statement, if stmt etc.
 Eg: a,b : real ; and a:=b +I ;

6.  Determines the meaning of the expression
 Results in addition of information such as type,
length
 Determines the meaning of subtree

7. Stmt a:= b + I ; proceeds as
1. Type is added to tree
2. Rules of assignment indicate expression on
RHS should be evaluated first
3. Rules of addition indicate I should be converted
before addition

8.  A context-free grammar (CFG) G is a quadruple
(N, Σ, P, S) where
 N: a set of non-terminal symbols
 Σ: a set of terminals ( N ∩ Σ = Ǿ)
 P: a set of rules (P: N → (N U Σ)*)
 S: a start symbol.

9. N = {Q, F,}
Σ = {0, 1}
P = {Q → 11Q, Q→ 00F,
F → 11F, F→ ε }
S = q
to generate 110011
Q →11Q →1100F →110011F →110011ε

10.  They provide a precise mathematical definition
that clearly rules out certain types of language.
 The formal definition means that context free
grammars are computationally TRACTABLE--it is
possible to write a computer program which
determines whether sentences are
grammatical or not.
 They provide a convenient visual notation for
the structure of sentences (the tree).

12.  Goal of parser : build a derivation
 Top-down parser : build a derivation by working from
the start symbol towards the input.
 Builds parse tree from root to leaves
 Builds leftmost derivation
 Bottom-up parser : build a derivation by working
from the input back toward the start symbol
 Builds parse tree from leaves to root
 Builds reverse rightmost derivation

13.  Consider the grammar:
S → c A d
A → ab | a
The input string is “cad”

14. Given the grammar :
E → TE’
E’ → +TE’ | λ
T → FT’
T’ → *FT’ | λ
F → (E) | id
The input: id + id * id

16. STACK INPUT BUFFER ACTION
$ num1+num2*num3$ shift
$num1 +num2*num3$ reduc
$F +num2*num3$ reduc
$T +num2*num3$ reduc
$E +num2*num3$ shift
$E+ num2*num3$ shift
$E+num2 *num3$ reduc
$E+F *num3$ reduc
$E+T *num3$ shift
E+T* num3$ shift
E+T*num3 $ reduc
E+T*F $ reduc
E+T $ reduc
E $ accept
E -> E+T
| T
| E-T
T -> T*F
| F
| T/F
F -> (E)
| id
| -E
num

17. Parsing 17
 A parse tree is created from
root to leaves
 The traversal of parse trees
is a preorder traversal
 Tracing leftmost derivation
 Two types:
 Backtracking parser
 Predictive parser
 A parse tree is created from
leaves to root
 The traversal of parse trees
is a reversal of post order
traversal
 Tracing rightmost derivation
 More powerful than top-
down parsing
 LR parserBacktracking: Try different
structures and backtrack if it
does not matched the input Predictive: Guess the
structure of the parse tree
from the next input