compiler construction · 6 precedence these two derivations point out a problem with the grammar it...

Compiler Construction

LECTURE # 7

The CourseCourse Code: CS-4141

Course Title: Compiler Construction

Instructor: JAWAD AHMAD◦ Email Address: [email protected]

Web Address: http://csandituoslahore.weebly.com/cc.html

Term (Semester): FALL 2017

Duration: 15/16 Weeks

mailto:[email protected]

3

Parse TreesG

E

E op E

E op Ex –

2 * y

Leftmost derivation

4

Parse TreesG

E

E op E

E op Ex –

2 * y

evaluation order

x – ( 2 * y )

5

Parse TreesG

E

op

evaluation order

(x – 2 ) * y

E

x –

E

E op E

2

* y

Rightmost

derivation

6

Precedence

These two derivations pointout a problem with thegrammar

It has no notion of precedence,or implied order of evaluation

7

Precedence

To add precedence

Create a non-terminal for each level of precedence

Isolate corresponding part of grammar

8

Precedence

To add precedence

Force parser to recognize high precedence subexpressions first.

9

Precedence

For algebraic expressions

Multiplication and division, first. (level one)

Subtraction and addition, next (level two)

12

Precedence

This grammar is larger

Takes more rewriting to reach some of the terminal symbols

But it encodes expected precedence

13

Precedence

Produces same parse tree under leftmost and rightmost derivations

Let’s see how it parses x – 2 * y

14

Precedence

Rule Sentential Form

- Goal

1 expr

3 expr – term

5 expr – term factor

9 expr – term

7 expr – factor

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Derivations & Precedence

Rule Sentential Form

8 expr –

4 term –

7 factor –

9 –

The rightmost derivation

16

Parse Trees G

E

F

T

T F

–

*

T

E

T

evaluation orderx – ( 2 * y )

17

Precedence

Both leftmost and rightmost derivations give the sameexpression

Because the grammar directly encodes the desired precedence.

18

Ambiguous Grammars

If a grammar has more than one leftmost derivation for a single sentential form, the grammar is ambiguous

19

Ambiguous Grammars

If a grammar has more than one rightmost derivation for a single sentential form, the grammar is ambiguous

20

Ambiguous Grammars

The leftmost and rightmost derivations for a sentential form may differ, even in an unambiguous grammar

Let’s consider the classic if-then-else example

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Ambiguous Grammars

if-then-else problem

Stmt → if Expr then Stmt

| if Expr then Stmt else Stmt

| … other stmts ….

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Ambiguous Grammars

The following sentential form has two derivations:

if E1 then if E2 then S else S2

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Ambiguity

Production 1,

then

Production 2:

if E1 thenif E2 then S1

else S2

E1

if

then

if

then

else

S1

S2

E2

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Ambiguity

E1

if

then

if

then else

S1 S2

E2

Production 2,

then

Production 1:

if E1 thenif E2 then S1else S2

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Ambiguity

E1

if

then

if

then

else

S1

S2

E2

E1

if

then

if

then else

S1 S2

E2

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Removing Ambiguity

Must rewrite grammar to avoid generating the problem

Match each else to innermost umatched if

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Removing Ambiguity

1. Stmt → If E then Stmt

2. | If E then WithElse else Stmt

3. | Assignment

4. WithElse → If E then WithElse else WithElse

5. | Assignment

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Removing Ambiguity

Let derive the following using the rewritten grammar:

if E1 then if E2 then A1 else A2

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E1

Stmt

then

else

A1 A2E2

if Expr Stmt

Stmtthenif Expr Withelse

This binds the else controlling A2 to inner if

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Context-Free Grammars

We have been using the term context-free without explaining why such rules are in fact “free of context”.

31


The simple reason is that nonterminals appear by themselves to the left of the arrow in context-free rules:

A → a

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The rule A → a says that A may be replaced by a anywhere, regardless of where A occurs.

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On the other hand, we could define a context as pair of strings b, g, such that a rule would apply only if b occurs before and g occurs after the nonterminal A.

34

Context-Sensitive Grammars

We would write this as

b A g → b a g

Such a rule in which a ≠ e is called a context-sensitive grammar rule

Parsing Techniques

36

Parsing Techniques

Top-down parsers

Start at the root of the parse tree and grow towards leaves.

Pick a production and try to match the input

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Parsing Techniques

Top-down parsers

Bad “pick” may need to backtrack

Some grammars are backtrack-free.

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Parsing Techniques

Bottom-up parsers

Start at the leaves and grow toward root

As input is consumed, encode possibilities in an internal state.

compiler construction · 6 precedence these two derivations point out a problem with the grammar it...

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