Syntax Analysis Part I: Understanding Parsing and Context-Free Grammars, Study Guides, Projects, Research of Electrical and Electronics Engineering

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Syntax Analysis

– Part I

EECS 483 – Lecture 4 University of Michigan Monday, September 15, 2003

• 1 -

Announcements^ Y

My office hours

» Move ahead 30 mins do don’t overlap with

EECS 496 so much

» Now 3:30 – 5:30 on Wednes

Y

Project 1

• 3 -

Parsing Analogy^ • Syntax analysis for natural languages

• Recognize whether a sentence is grammatically correct • Identify the function of each word

sentence

subject

verb

indirect object

object

I^

gave

him

noun phrase article

nounbook

the

“I gave him the book”

• 4 -

Syntax Analysis Overview^ Y

Goal – determine if the input token streamsatisfies the syntax of the program

Y

What do we need to do this?

» An expressive way to describe the syntax » A mechanism that determines if the input

token stream satisfies the syntax description

Y

For lexical analysis

» Regular expressions describe tokens » Finite automata = mechanisms to generate

tokens from input stream

• 6 -

Context-Free Grammars^ Y

Consist of 4 components:

» Terminal symbols = token or

ε

» Non-terminal symbols = syntactic variables » Start symbol S = special non-terminal » Productions of the form LHS

Æ

RHS

y^

LHS = single non-terminal y^

RHS = string of terminals and non-terminals y^

Specify how non-terminals may be expanded

Y

Language generated by a grammar is the set ofstrings of terminals derived from the start symbolby repeatedly applying the productions

» L(G) = language generated by grammar G

S^

Æ

a S a S^

Æ

T

T

Æ

b T b T

Æ

• 7 -

CFG - Example^ Y

Grammar for balanced-parentheses language

» S

Æ

( S ) S

» S

Æ

ε y^

1 non-terminal: S y^

2 terminals: “)”, “)” y^

Start symbol: S y^

2 productions

Y

If grammar accepts a string, there is a derivation ofthat string using the productions

» “(())” » S = (S)

ε

= ((S) S)

ε

ε)

ε

)^

ε^

? Why is the final S required?

• 9 -

A Parser

Context free grammar, G

Yes, if s in L(G) No, otherwise

Parser

Token stream, s (from lexer)

Error messages

Syntax analyzers (parsers) = CFG acceptors which also output the corresponding derivation when the token stream is accepted

Various kinds: LL(k), LR(k), SLR, LALR

• 10 -

RE is a Subset of CFG^ Can inductively build a grammar for each RE

ε^

S

Æ

a^

S

Æ

a

R1 R

S

Æ

S1 S

R1 | R

S

Æ

S1 | S

R1*

S

Æ

S1 S |

Where

G1 = grammar for R1, with start symbol S1 G2 = grammar for R2, with start symbol S

• 12 -

Constructing a Derivation^ Y

Start from S (the start symbol)

Y

Use productions to derive a sequence oftokens

Y

For arbitrary strings

,^

,^

γ^

and for a

production: A

Æ

» A single step of the derivation is»^

A

(substitute

for A)

Y

Example

» S

Æ

E + S

» (S + E) + E

Æ

(E + S + E) + E

• 13 -

Class Problem

»^

S^

Æ

E + S | E

»^

E^

Æ

number | (S)

Y^

Derive: (1 + 2 + (3 + 4)) + 5

• 15 -

Parse Tree vs Abstract Syntax Tree

S

E

+^

S

( S )

E

E + S

E + S

E

( S )E + S

E

Parse tree also called “concrete syntax”

AST discards (abstracts) unneeded information – more compact format

• 16 -

Derivation Order^ Y

Can choose to apply productions in any order,select non-terminal and substitute RHS ofproduction

Y

Two standard orders: left and right-most

Y

Leftmost derivation

» In the string, find the leftmost non-terminal and apply

a production to it » E + S

Æ

1 + S

Y

Rightmost derivation

» Same, but find rightmost non-terminal » E + S

Æ

E + E + S

• 18 -

Class Problem

»^

S^

Æ

E + S | E

»^

E^

Æ

number | (S) | -S

Y^

Do the rightmost derivation of : 1 + (2 + -(3 + 4)) + 5

• 19 -

Ambiguous Grammars^ Y

In the sum expression grammar, leftmostand rightmost derivations producedidentical parse trees

Y

+ operator associates to the right in parsetree regardless of derivation order