Compiler Designs and Constructions Page 92158

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Compiler Designs and Constructions (Page 92-158)

• Chapter 5 Languages and Grammar
• Objectives
• Definition of Languages
• Types of Languages
• Dr. Mohsen Chitsaz

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Languages

• Def
• Set of words
• Set of Strings
• Elements of a language
•  Alphabet ? Word (Token) (Vocabulary)
• Grammar ? Sentence
• Semantic

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Types of Languages

• Natural Languages
• Example They run a store
• Formal Languages
• Example If (Total gt Max)

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Grammars

• Def
• G?, R, P, S
• GVt, Vn, P, S
• Vt ? Vn ?

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Example

• SimpleDatatype Integer, Real, Char, Boolean
• Datatype ? SimpleDatatype
• SimpleDatatype ? Integer
• SimpleDatatype ? Real
• SimpleDatatype ? Boolean
• SimpleDatatype ? Char

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Example

• Vt Terminal Symbols (word, vocabulary, token
• Integer, Char, Real, Boolean
• Vn Datatype, SimpleDatatype
• P Datatype ? SimpleDatatype
• SimpleDatatype ? Integer
• SimpleDatatype ? Real
• SimpleDatatype ? Boolean
• SimpleDatatype ? Char
• S Datatype

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Types of Grammars (Chomsky Hierarchy)

• ? ? ?
• LHS RHS 
• Type Zero Unrestricted
• ABC ? a
• a ? CaaF 
• Type One Context Sensitive
• ? lt B
•  A -- gt a
• A ? Bc
• AB ? aB
• Ca ? abc

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Types of Grammars (Chomsky Hierarchy)

• Type Two Context Free
• ? 1
• ? ? Vn
• Type Three Regular Grammar is a CFG with Right
  linear
• Right Linear
• A ? wb
• A ? w
• Left Linear
• A ? Bw
• A ? w

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Context Free Grammar

• Context Free Grammar G
• Context Free Language of Grammar L(G)
• Example
• ltSTARTgt ? var ltRESTgt
• ltRESTgt ? id ltSIMPLEDATATYPEgt
• ltSIMPLEDATATYPEgt ? integer
• ltSIMPLEDATATYPEgt ? real
• ltSIMPLEDATATYPEgt ? char
• ltSIMPLEDATATYPEgt ? Boolean

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Example

• S --gtoS1
• S ? o1
• VnS
• Vt0,1
• SS
• PS ? oS1
• S ? o1

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Language

• Def Language of a grammar is a set of all
  sentences accepted by that grammar.
• L(G) wS -gtw
• Notation
• Kleene Closure() Zero or more
• Positive Closure() One or more
• String Concatenation (.)
• Union (U)

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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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Derivation

• 000111
• S ? OS1 ? 00S11 ? 000111
• Each of the forms is called Sentential Form of
  this CFG
• L(G) On 1n n gt 1

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Example

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

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Example

• S ? A
• A ? 01
• A ? oB1
• B ? oB
• B ? 1B
• B ? 0
• B ? 1

• S ? 0A1
• S ? 01
• A ? 0A
• A ? 1A
• A ? 1
• A ? 0

• S ? 0A1
• S ?01
• A ? BA
• B ? 0
• B ? 1

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Example

• What is the language of this grammar?
• S ? cS
• S ? bD
• S ? c
• D ? cD
• D ? bS
• D ?b

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Example

• Write a grammar which produces odd numbers of s
  
• L(G) n ngt1 n MOD 2 ltgt0 

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Example

• S? (S)
• S ? ()
• S ? b
• Write a grammar for the language
• L(G) bm Cn dn em fp (gh)p mgt2, ngt0, pgt1
• Write a grammar for the language
• L(G) bm Cn 1lt n lt m lt 2n

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Tree

• Level
• Height (Depth)
• Internal Node
• External Node
• Preorder Traversal
• Inorder Traversal
• Postorder Traversal

• Definition
• Node
• Edge
• Root
• Children
• Leaf(Terminal Node)

Implementation of Tree?
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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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Example

• 1 S ----gt 0AB
• 2 A ----gt 1A
• 3 B ----gt 0S
• 4 S ----gt 0S
• 5 S ----gt 1
• 6 A ----gt 0

• Derive String of 01001
• Left Derivation
• Right Derivation

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Example

• ltExpressiongt ----gt ltTermgt
• ltTermgt ----gt ltTermgt ltFactorsgt
• ltTermgt ----gt ltFactorsgt
• ltFactorsgt ----gt Id
• Sentence id id

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• Derivation tree
• Leftmost Derivation
• Rightmost Derivation

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Ambiguous Grammar

• Example
• ltEgt ----gt ltEgt ltOPgt ltEgt
• ltEgt ----gt Id
• ltOPgt ----gt
• ltOPgt ----gt
• Sentence abc Is this ambiguous?
• Definition

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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

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BNF (Bachus-Naus Form)
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FSM
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Grammar

• ltSgt -------gt ltq1gt
• ltSgt -------gt - ltq1gt
• ltq1gt ------gt d ltq2gt
• ltSgt -------gt d ltq2gt
• ltq2gt ------gt d ltq2gt
• ltq2gt ------gt . ltq3gt
• ltq3gt ------gt d ltq4gt
• ltq4gt ------gt d ltq4gt
• ltq4gt ------gt

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Language
-21.000
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Language

• Lex Translate regular expression into lexical
  analyzer program
• GrammarWrite a grammar to recognize the traffic
  lights

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Traffic Light

• D ----gt g DD ----gt r SS ----gt g DS ----gt r SS
  ----gtLanguage? gggrrggrrg.

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Push Down Machine

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

Formal Definition
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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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Deterministic Finite State Machine

• Example of a Real Number
• Q S, q1, q2, q3, q4q0 S F q4 ?
  , -, d, .

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• ? 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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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.