Chapter 4
Lexical and Syntax Analysis
Chapter 4 Topics
4.1
4.2
4.3
4.4
4.5
Introduction
Lexical Analysis
The Parsing Problem
Recursive-Descent Parsing
Bottom-Up Parsing
4-2
4.1 Introduction
• Language
implementation systems
must analyze source
code, regardless of the
specific implementation
approach
• Nearly all syntax analysis
is based on a formal
description of the syntax
of the source language
(BNF)
4-3
Syntax Analysis
• The syntax analysis portion of a language
processor nearly always consists of two
parts:
– A low-level part called a lexical analyzer
(mathematically, a finite automaton based on a
regular grammar)
– A high-level part called a syntax analyzer, or
parser (mathematically, a push-down
automaton based on a context-free grammar,
or BNF)
1-4
Advantages of Using BNF to Describe Syntax
• BNF provides a clear and concise syntax
description, both for human and for software
system that uses them.
• BNF description can be used as the direct basis for
the syntax analyzer.
• Implementations based on BNF are relatively easy
to maintain because of their modularity.
1-5
Reasons to Separate Lexical and Syntax Analysis
• Simplicity - less complex approaches can be used
for lexical analysis; separating them simplifies the
parser
• Efficiency - separation allows optimization of the
lexical analyzer
• Portability - parts of the lexical analyzer may not
be portable, but the parser always is portable
1-6
4.2 Lexical Analysis
• A lexical analyzer is a pattern matcher for character strings.
• A lexical analyzer is a “front-end” for the parser. It is a part
of syntax analyzer, and performs syntax analysis at the
lowest level of program structure.
An input program appears to a compiler as a single string of
character. It collects characters into logical groupings and
assigned internal codes to the groupings.
• Logical groupings are named lexemes. Internal codes for
categories of these groupings are named tokens.
1-7
Example: result = oldsum – value / 100;
Token
IDENT
ASSIGN_OP
IDENT
SUB_OP
IDENT
DIV_OP
INT_LIT
SEMICOLON
Lexeme
Result
=
oldsum
–
value
/
100
;
4-8
Lexical Analysis (continued)
• The lexical analyzer is usually a function that is
called by the parser when it needs the next token.
• Three approaches to building a lexical analyzer:
– Write a formal description of the tokens and use a
software tool that constructs table-driven lexical
analyzers given such a description
– Design a state diagram that describes the tokens and
write a program that implements the state diagram
– Design a state diagram that describes the tokens and
hand-construct a table-driven implementation of the
state diagram
1-9
Lexical Analysis (cont’d): State Diagram
Design
– A naïve state diagram would have a transition
from every state on every character in the
source language - such a diagram would be
very large!
1-10
Lexical Analysis (cont.)
• In many cases, transitions can be combined
to simplify the state diagram
– When recognizing an identifier, all uppercase
and lowercase letters are equivalent
• Use a character class that includes all 52 letters
– When recognizing an integer literal, all digits are
equivalent - use a digit class for 10 integral
literal.
1-11
Lexical Analysis (cont.)
• Reserved words and identifiers can be
recognized together (rather than having a
part of the diagram for each reserved word)
– Use a table lookup to determine whether a
possible identifier is in fact a reserved word
1-12
Lexical Analysis (cont.)
• Convenient utility subprograms:
– getChar - gets the next character of input, puts
it in nextChar, determines its class and puts
the class in charClass
– addChar - puts the character from nextChar
into the place the lexeme is being accumulated,
lexeme
– lookup - determines whether the string in
lexeme is a reserved word (returns a code)
1-13
State Diagram for Recognizing
Arithmetic Expressions
1-14
Lexical Analyzer
Implementation:
 SHOW front.c (pp. 176-181)
- Following is the output of the lexical analyzer of
front.c when used on (sum + 47) / total
Next
Next
Next
Next
Next
Next
Next
Next
token
token
token
token
token
token
token
token
is:
is:
is:
is:
is:
is:
is:
is:
25
11
21
10
26
24
11
-1
Next
Next
Next
Next
Next
Next
Next
Next
lexeme
lexeme
lexeme
lexeme
lexeme
lexeme
lexeme
lexeme
is
is
is
is
is
is
is
is
(
sum
+
47
)
/
total
EOF
1-15
4.3 The Parsing Problem
• Goals of the parser, given an input
program:
– Find all syntax errors; for each, produce an
appropriate diagnostic message and recover
quickly
– Produce the parse tree, or at least a trace of the
parse tree, for the program
1-16
4.3.1 Introducing to Parsing
• Two categories of parsers
– Top down - produce the parse tree, beginning
at the root
• Order is that of a leftmost derivation
• Traces or builds the parse tree in preorder
– Bottom up - produce the parse tree, beginning
at the leaves
• Order is that of the reverse of a rightmost derivation
• Useful parsers look only one token ahead in
the input
1-17
A set of notational conventions for grammar
symbols
1. Terminals : lowercase letters at the beginning of the
alphabet (a, b, …)
2. Nonterminals: uppercase letters at the beginning of the
alphabet (A, B, …)
3. Terminals or nonterminals: uppercase letters at the end of
the alphabet (W, X, Y, Z)
4. Strings of terminals: lowercase letters at the end of the
alphabet (w, x, y, z)
5. Mixed strings (terminals and/or nonterminals):lowercase
Greek letters (α, β, δ, γ)
4-18
4.3.2 Top-Down Parsers
• Top-down Parsers
– Top-down parsing is a type of parsing strategy
wherein one first looks at the highest level of the
parse tree and works down the parse tree by
using the rewriting rules of a formal grammar.
For example, if the current sentential form is:
xAα
and the A-rules are AbB, AcBb, and Aa,
a top-down parser must choose among three
rules to get the next sentential form, which
could be xbBα, xcBbα, or xaα
1-19
Top-Down Parsers (cont’d)
• The most common top-down parsing
algorithms:
– Recursive descent parser - a coded
implementation based directly on BNF
description of syntax language.
– Most common alternative to recursive descent
parser is to use parsing table to implement BNF
rules.
Both are LL parsers (left-to-right leftmost
derivation)
1-20
4.3.3 Bottom-Up Parsers
• Bottom-up parsers
– A bottom-up parser constructs a parse tree by beginning
at the leaves and processing toward the root.
In term of derivation, it can described as follows: Given a
right sentential form, , determine what substring of  is
the right-hand side of the rule in the grammar that must
be reduced to produce the previous sentential form in the
right derivation
– The most common bottom-up parsing algorithms are in
the LR (left-to-right scan, rightmost derivation) family
(such as LALR, canonical LR parser (LR(1) parser) , LR(0)
parser)
1-21
4.3.4 The Complexity of Parsing
• The Complexity of Parsing
– Parsers that work for any unambiguous
grammar are complex and inefficient ( O(n3),
where n is the length of the input )
– All algorithms used for the syntax analyzers of
commercial compilers have complexity O(n).
1-22
4.4 Recursive-Descent Parsing
4.4.1 Recursive-Descent Parsing Process
• A recursive-descent parsing is so named because
it consists of collection of subprograms, many of
which are recursive, and it produce a parse tree in
top-down order.
• EBNF is ideally suited for being the basis for a
recursive-descent parser, because EBNF
minimizes the number of nonterminals
1-23
Recursive-Descent Parsing (cont.)
• A grammar for simple arithmetic expressions:
<expr>  <term> {(+ | -) <term>}
<term>  <factor> {(* | /) <factor>}
<factor>  id | int_constant | ( <expr> )
Note: Inf EBNF, additional metacharacters
– { } for a series of zero or more
– ( ) for a list, must pick one
– [ ] for an optional list; pick none or one
1-24
Recursive-Descent Parsing (cont.)
• Assume we have a lexical analyzer named
lex, which puts the next token code in
nextToken
• The coding process:
– For each terminal symbol in the RHS, compare it
with the nextToken. If they match, continue,
else there is a syntax error
– For each nonterminal symbol in the RHS, call its
associated parsing subprogram
1-25
Recursive-Descent Parsing (cont.)
/* Function expr
Parses strings in the language
generated by the rule:
<expr> → <term> {(+ | -) <term>}
*/
void expr() {
/* Parse the first term */
term();
/* As long as the next token is + or -, call
lex to get the next token and parse the
next term */
while (nextToken = = ADD_OP ||
nextToken = = SUB_OP){
lex();
term();
}
}
1-26
Recursive-Descent Parsing (cont.)
• This particular routine does not detect errors
• Convention: Every parsing routine leaves the next
token in nextToken
1-27
Recursive-Descent Parsing (cont.)
• A nonterminal that has more than one RHS
requires an initial process to determine which RHS
it is to parse.
– The correct RHS is chosen on the basis of the next token
of input (the lookahead)
– The next token is compared with the first token that can
be generated by each RHS until a match is found
– If no match is found, it is a syntax error
1-28
Recursive-Descent Parsing (cont.)
/* term
Parses strings in the language generated by the rule:
<term> -> <factor> {(* | /) <factor>)
*/
void term() {
printf("Enter <term>\n");
/* Parse the first factor */
factor();
/* As long as the next token is * or /,
next token and parse the next factor */
while (nextToken == MULT_OP || nextToken == DIV_OP) {
lex();
factor();
}
printf("Exit <term>\n");
} /* End of function term */
1-29
Recursive-Descent Parsing (cont.)
/* Function factor
Parses strings in the language
generated by the rule:
<factor> -> id | (<expr>) */
void factor() {
/* Determine which RHS */
if (nextToken) == ID_CODE || nextToken == INT_CODE)
/* For the RHS id, just call lex */
lex();
/* If the RHS is (<expr>) – call lex to pass over the left parenthesis,
call expr, and check for the right parenthesis */
else if (nextToken == LP_CODE) {
lex();
expr();
if (nextToken == RP_CODE)
lex();
else
error();
} /* End of else if (nextToken == ... */
else error(); /* Neither RHS matches */
}
1-30
Recursive-Descent Parsing (cont.)
- Trace of the lexical and syntax analyzers on (sum + 47) / total
Next token is:
Enter <expr>
Enter <term>
Enter <factor>
Next token is:
Enter <expr>
Enter <term>
Enter <factor>
Next token is:
Exit <factor>
Exit <term>
Next token is:
Enter <term>
Enter <factor>
Next token is:
Exit <factor>
Exit <term>
Exit <expr>
Next token is:
Exit <factor>
25 Next lexeme is (
11 Next lexeme is sum
Next token is: 11 Next lexeme is total
Enter <factor>
Next token is: -1 Next lexeme is EOF
Exit <factor>
Exit <term>
Exit <expr>
21 Next lexeme is +
10 Next lexeme is 47
26 Next lexeme is )
24 Next lexeme is /
1-31
<expr>
<term>
<factor>
(
<expr>
<term>
<factor>
<id>
sum
+
/
)
<term>
<factor>
<id>
total
<factor>
int_constant
47
<expr>  <term>{(+|-)<term>}
<term>  <factor>{(*|/)<factor>}
<factor>  <id> | int_constant | (<expr>)4-32
4.4.2 The LL Grammar Class
The Left Recursion Problem
• If a grammar has left recursion, either direct or
indirect, it causes a catastrophic problem for LL
parsers.
e.g., A  A + B
•
A grammar can be modified to remove left recursion
For each nonterminal, A,
1. Group the A-rules as A → Aα1 | … | Aαm | β1 | β2 | … | βn
where none of the β’s begins with A
2. Replace the original A-rules with
A → β1A’ | β2A’ | … | βnA’
A’ → α1A’ | α2A’ | … | αmA’ | ε
(Note : ε specifies the empty string)
1-33
• Example Grammar with Left Recursion
E  E + T | T
T  T*F | F
F  (E) | id
Grammar 1
• Complete Replacement Grammar
E  T E’
E’  + T E’|ε
T  F T’
T’ *F T’| ε
F  (E) | id
Grammar 2
E-rules
α1=+T, β=T,
(m=1,n=1)
E-rules
α1=*F, β=F,
(m=1,n=1)
Grammar 2 generates the same language as
Grammar 1, but it is not left recursive.
4-34
• Indirect Left Recursion Problem
e.g., A  B a A
B  A b
To remove indirect left recursion => Paper (Aho et
al., 2006)
4-35
Left Recursion Problem (cont’d)
Two issues:
• Left recursion disallow top-down parsing;
• Whether the parser can always choose the correct RHS on the
basis of the next token of input, using only the first token
generated by the leftmost nonterminal in the current
sentential form.
Solution: To conduct a Pairwise Disjointness Test
• Pairwise Disjointness Test: a test of non-left recursive
grammar.
4-36
Pairwise disjointness test
• Define: FIRST(α) = { a | α =>* a β} (If α =>* ε, ε is in FIRST(α))
• For each nonterminal, A, that has more than one RHS, for
each pair of rules, A 
αi
and A 
αj,
if FIRST(αi)  FIRST(αj) = φ, this pair passes the
test; otherwise it fails the test.
4-37
Pairwise disjointness test
Example: Perform the pairwise disjointness test for the
following rules:
A  aB | bAb | Bb
B  cB | d
Sol: FIRST(aB)={a}, FIRST(bAb)={b}, FIRST(Bb)={c,d}
FIRST(aB) FIRST(bAb)= φ
FIRST(aB) FIRST(Bb)= φ
FIRST(bAb)  FIRST(Bb)= φ
4-38