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Chapter 5: Languages and Grammar 1 Compiler Designs and Constructions ( Page ) Chapter 5: Languages and Grammar Objectives: Definition of Languages Types of Languages Dr. Mohsen Chitsaz

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Chapter 5: Languages and Grammar2 Languages Def: Set of words Set of Strings Elements of a language Alphabet Word (Token) (Vocabulary) Grammar Sentence Semantic

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Chapter 5: Languages and Grammar3 Natural Languages Example: They run a store Formal Languages Example: If (Total > Max) Types of Languages

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Chapter 5: Languages and Grammar4 Def: G={ , R, P, S} G={V t, V n, P, S} V t V n = Grammars

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Chapter 5: Languages and Grammar5 Example SimpleDatatype = { Integer, Real, Char, Boolean } Datatype SimpleDatatype SimpleDatatype Integer SimpleDatatype Real SimpleDatatype Boolean SimpleDatatype Char

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Chapter 5: Languages and Grammar6 Example V t : Terminal Symbols ( word, vocabulary, token } Integer, Char, Real, Boolean V n : Datatype, SimpleDatatype P: Datatype SimpleDatatype SimpleDatatype Integer SimpleDatatype Real SimpleDatatype Boolean SimpleDatatype Char S: Datatype

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Chapter 5: Languages and Grammar7 Types of Grammars (Chomsky Hierarchy) LHS RHS Type Zero: Unrestricted ABC a a CaaF Type One: Context Sensitive | | <= |B| A -- > a A Bc AB aB Ca abc

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Chapter 5: Languages and Grammar8 Types of Grammars (Chomsky Hierarchy) Type Two: Context Free | | = 1 Vn Type Three: Regular Grammar is a CFG with Right linear Right Linear A w b A w Left Linear A B w A w

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Chapter 5: Languages and Grammar9 Context Free Grammar Context Free Grammar G Context Free Language of Grammar L(G) Example: var id: ; integer real char Boolean

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Chapter 5: Languages and Grammar10 Example S -->oS1 S o1 V n ={S} V t ={0,1} S={S} P={S oS1 S o1}

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Chapter 5: Languages and Grammar11 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)

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Chapter 5: Languages and Grammar12 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) )*

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Chapter 5: Languages and Grammar13 Derivation S OS1 00S11 Each of the forms is called Sentential Form of this CFG L(G) = {On 1n; n >= 1}

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Chapter 5: Languages and Grammar14 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

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Chapter 5: Languages and Grammar15 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

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Chapter 5: Languages and Grammar16 Example What is the language of this grammar? S cS S bD S c D cD D bS D b

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Chapter 5: Languages and Grammar17 Example Write a grammar which produces odd numbers of * ’ s L(G) = { *n; n>=1; n MOD 2 <>0}

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Chapter 5: Languages and Grammar18 Example S (S) S () S b Write a grammar for the language L(G) = {b m C n d n e m f p (gh*) p | m>=2, n>=0, p>=1} Write a grammar for the language L(G) = {b m C n | 1<= n <= m <= 2n}

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Chapter 5: Languages and Grammar19 Tree Definition: Node Edge Root Children Leaf(Terminal Node) Level Height (Depth) Internal Node External Node Preorder Traversal Inorder Traversal Postorder Traversal Implementation of Tree?

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Chapter 5: Languages and Grammar20 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)

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Chapter 5: Languages and Grammar21 Example Derive String of Left Derivation : Right Derivation: 1 S ----> 0AB 2 A ----> 1A 3 B ----> 0S 4 S ----> 0S 5 S ----> 1 6 A ----> 0

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Chapter 5: Languages and Grammar22 Example ----> ----> + ----> ----> Id Sentence id + id

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Chapter 5: Languages and Grammar23 Derivation tree: Leftmost Derivation: Rightmost Derivation:

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Chapter 5: Languages and Grammar24 Ambiguous Grammar Example ----> ----> Id ----> + ----> * Sentence a+b*c Is this ambiguous? Definition

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Chapter 5: Languages and Grammar25 Finite State Machine (Automata) FSM (FSA) Simplified model for digital system Memory Input Output FSM is used as a language recognizer Example: Real Number

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Chapter 5: Languages and Grammar26 BNF (Bachus-Naus Form) + -

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Chapter 5: Languages and Grammar27 FSM q1

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Chapter 5: Languages and Grammar28 Grammar > + > - > d > d > d >. > d >

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Chapter 5: Languages and Grammar29 Language Recognizer Head State = S Memory INPUT

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Chapter 5: Languages and Grammar30 Language Lex: Translate regular expression into lexical analyzer program Grammar: Write a grammar to recognize the traffic lights

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Chapter 5: Languages and Grammar31 Traffic Light D ----> g D D ----> r S S ----> g D S ----> r S S ----> Language? gggrrggrrg …….

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Chapter 5: Languages and Grammar32 Push Down Machine CFG is accepted by a FSM controlling a Push-down stack Formal Definition:

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Chapter 5: Languages and Grammar33 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

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Chapter 5: Languages and Grammar34 Deterministic Finite State Machine Example of a Real Number Q = {S, q1, q2, q3, q4} q0 = {S} F = {q4} = {+, -, d,. }

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Chapter 5: Languages and Grammar35 = State Transition: (S,+) = q1 (S,-) = q1 (S, d) = q2 (q1, d) = q2 (q2, d) = q2 (q2,. ) = q3 (q3, d) = q4 (q4, d) = q4

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Chapter 5: Languages and Grammar36 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 q2 q1 q2 q3q2 q3 q4 Acc STATESTATE

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