Chapter 5: Languages and Grammar 1 Compiler Designs and Constructions ( Page 92-158 ) Chapter 5: Languages and Grammar Objectives: Definition of Languages

Chapter 5: Languages and Grammar

1

Compiler Designs and Constructions (Page 92-158)

Chapter 5: Languages and Grammar

Objectives:Definition of LanguagesTypes of Languages

Dr. Mohsen Chitsaz

Chapter 5: Languages and Grammar 2

Languages

Def:Set of words

Set of Strings

Elements of a language Alphabet Word (Token) (Vocabulary) Grammar Sentence Semantic


Natural LanguagesExample: They run a store

Formal LanguagesExample: If (Total > Max)

Types of Languages


Def:G={, R, P, S}

G={Vt, Vn, P, S}

Vt Vn=

Grammars


Example

SimpleDatatype = {Integer, Real, Char, Boolean}

Datatype SimpleDatatype

SimpleDatatype Integer

SimpleDatatype Real

SimpleDatatype Boolean

SimpleDatatype Char


Example

Vt: Terminal Symbols (word, vocabulary, token}Integer, Char, Real, Boolean

Vn: Datatype, SimpleDatatype P: Datatype SimpleDatatype

SimpleDatatype IntegerSimpleDatatype RealSimpleDatatype BooleanSimpleDatatype Char

S: Datatype


Types of Grammars (Chomsky Hierarchy)

LHS RHS

Type Zero: UnrestrictedABC aa CaaF

Type One: Context Sensitive|| <= |B| A -- > aA BcAB aBCa abc


Types of Grammars (Chomsky Hierarchy)

Type Two: Context Free|| = 1 Vn

Type Three: Regular Grammar is a CFG with Right linear

Right LinearA wb

A w Left Linear

A Bw

A w


Context Free Grammar

Context Free Grammar G Context Free Language of Grammar L(G) Example:

<START> var <REST><REST> id: <SIMPLEDATATYPE>;<SIMPLEDATATYPE> integer<SIMPLEDATATYPE> real<SIMPLEDATATYPE> char<SIMPLEDATATYPE> Boolean


Example

S -->oS1 S o1 Vn={S}

Vt={0,1}

S={S} P={S oS1

S o1}


Language

Def: Language of a grammar: is a set of all sentences accepted by that grammar.L(G) = {w|S ->w}

Notation: Kleene Closure(*) Zero or more Positive Closure(+) One or more String Concatenation (.) Union (U)


Language

Example: L(Digit) = {0,1,2,3,4,5,6,7,8,9} L(Alpha) = {a,b, …, z} L(Digit)+ = 2 , 24 L(Alpha)* =a , , ab, abc L(Alpha) U (Digit) =a2, b6

Identifier: L(Alpha).( L(Alpha) U L(Digit) )*


Derivation

000111

S OS1 00S11 000111 Each of the forms is called Sentential

Form of this CFG L(G) = {On 1n; n >= 1}


Example

Write a grammar that produces a set of 0’s & 1’s in any order. It must start with a zero and end with a one. 01 0101 0011 011


Example

S 0A1 S 01 A 0A A 1A A 1 A 0

S 0A1 S 01 A BA B 0 B 1

S A A 01 A

oB1 B oB B 1B B 0 B 1


Example

What is the language of this grammar?S cSS bDS cD cDD bSD b


Example

Write a grammar which produces odd numbers of *’s

L(G) = { *n; n>=1; n MOD 2 <>0}


Example

S (S) S () S b

Write a grammar for the language L(G) = {bm Cn

dn em fp (gh*)p | m>=2, n>=0, p>=1}

Write a grammar for the languageL(G) = {bm Cn | 1<= n <= m <= 2n}


Tree

Definition: Node Edge Root Children Leaf(Terminal Node)

Level Height (Depth)Internal NodeExternal NodePreorder TraversalInorder TraversalPostorder Traversal

Implementation of Tree?


Context Free Grammar

Derivation: How an input sentence can be recognized.

Parsing: Process of finding derivation

Parser: Automation of parsing.- Left Derivation (Leftmost derivation) - Right Derivation (Rightmost derivation)


Example

Derive String of 01001 Left Derivation: Right Derivation:

1 S ----> 0AB2 A ----> 1A3 B ----> 0S4 S ----> 0S5 S ----> 16 A ----> 0


Example

<Expression> ----> <Term> <Term> ----> <Term> + <Factors> <Term> ----> <Factors> <Factors> ----> Id

Sentence id + id


Derivation tree:

Leftmost Derivation: Rightmost Derivation:


Ambiguous Grammar

Example <E> ----> <E> <OP> <E> <E> ----> Id <OP> ----> + <OP> ----> *

Sentence a+b*c Is this ambiguous?

Definition


Finite State Machine (Automata) FSM (FSA)

Simplified model for digital system Memory Input Output

FSM is used as a language recognizer

Example: Real Number + 2.44


BNF (Bachus-Naus Form)

+

-


FSM

q1


Grammar

<S> -------> + <q1> <S> -------> - <q1> <q1> ------> d <q2> <S> -------> d <q2> <q2> ------> d <q2> <q2> ------> . <q3> <q3> ------> d <q4> <q4> ------> d <q4> <q4> ------>


Language

-21.000

000.12-

Recognizer

Head

State = S

Memory

INPUT


Language

Lex: Translate regular expression into lexical analyzer program

Grammar:Write a grammar to recognize the traffic lights


Traffic Light

D ----> g DD ----> r SS ----> g DS ----> r SS ---->Language? gggrrggrrg…….


Push Down Machine

CFG is accepted by a FSM controlling a Push-down stack

Formal Definition:


Deterministic Finite State Machine (Q, , ,q0, F)

(Every move is absolutely determined by the current state and next input)

Where: Q: Finite Set of State

: Alphabet q0: Starting State (q)

F: Final States (Q) : State Transition Function


Deterministic Finite State Machine

Example of a Real Number

Q = {S, q1, q2, q3, q4}

q0 = {S} F = {q4} = {+, -, d, . }


= State Transition:(S,+) = q1(S,-) = q1(S, d) = q2(q1, d) = q2(q2, d) = q2(q2, . ) = q3(q3, d) = q4(q4, d) = q4


Transition Table input token

DFSM: Deterministic Finite State Machine No state with the same outgoing label.No state has more than one transition with the same label.

+ - . d S q1 q1 q2

q1 q2 q2 q3 q2 q3 q4 q4 q4 Acc

STATE

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Chapter 5: Languages and Grammar 1 Compiler Designs and Constructions ( Page 92-158 ) Chapter 5: Languages and Grammar Objectives: Definition of Languages