Grammars (Specifying and deconstructing valid sentences)

1. Programming Languages
Building a Web Brower
Instructor : Westley Weimer
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3. 3
Grammar
how words and their component parts combine to form sentences
I think (O)
Sentence → Subject Verb
think think I (X)
exp → num + num
7 + 5 (O)
+ 2 5 (X)

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Grammar
G = ( VN, VT, P, S )
VN = A finite set of non-terminal symbols
VT = A finite set of terminal symbols
P = A finite set of production rules
S = S∈N, start symbol

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Grammar
S ⇒ aA (S → aA)
S ⇒ abS (A → bS)
S ⇒ abbB (S → bB)
S ⇒ abbaS (B → aS)
S ⇒ abba (S → E)
P : S → aA | bB | Epsilon
P : A → bS
P : B → aS
G = ({S, A}, {a, b}, P, S)
VN VT

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Grammar
 Unrestricted Grammar
 Context-Sensitive Grammar
 Context-Free Grammar
 Regular Grammar

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Regular Grammar
RLG(Right-Linear Grammar) : A → tB, A → t
OR
LLG(Left-Linear Grammar) : A → Bt, A → t
P : S → aA
P : A → bA | b
P : S → Aa
P : A → Ab | b

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Regular Grammar
P : S → aA | c
P : A → Sb
G = ({S, A}, {a, b, c}, P, S)
S ⇒ aA ⇒ aSb ⇒ acb
S ⇒ aA ⇒ aSb ⇒ aaAb
S ⇒ aaSbb ⇒ aacbb
L(G) = { ancbn | n ≥ 0 }
↔ r"a*cb*" (X)
P : S → aA | c
P : A → bS
G = ({S, A}, {a, b, c}, P, S)
S ⇒ aA ⇒ abS ⇒ abc
S ⇒ aA ⇒ abS ⇒ abaA
S ⇒ ababS ⇒ ababc
L(G) = { (ab)n c | n ≥ 0 }
↔ r "(?:ab)*c" (O)

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Regular Grammar
Regular
Expression
Finite
Automata
Regular
Grammar
“Regular Language”

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Context Free Grammar
doesn't care about the line above or below it
X = 1
X + 2 → 3
X = 3
X + 2 → 5
X + 2

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Context Free Grammar
P : A → α
V*
P : S → aA | c
P : A → Sb
V* = ( VN U VT )*, A string of variables and/or terminals

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Context Free Grammar
P : S → ( S )
P : S → EpsilonP :
G = ({S}, {( , )}, P, S)
S ⇒ ( S ) ⇒ ( )
S ⇒ ( S ) ⇒ (( S )) ⇒ (( ))
S ⇒ ( S ) ⇒ (( S )) ⇒ ((( S ))) ⇒ ((( )))
L(G) = { (n )n | n ≥ 1 } ↔ r"(*)*" (X)

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Relation between RL and CFL
Context Free Language
Regular Language
Every Regular Language is Context Free Language!

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Syntactical
Analysis
Lexical
Analysis
“Lexing” “Parsing”
Regular Grammar
(Word Rules)
Context Free Grammar
(Sentence Rules)
String
List of
Tokens
Lexing and Parsing

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