CSC 8505 Compiler Construction Context-Free Grammars
description
Transcript of CSC 8505 Compiler Construction Context-Free Grammars
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CFG 1
CSC 8505Compiler Construction
- Context Free Grammars Using grammars in parsers
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CFG 2
Parsing Process Call the scanner to get tokens Build a parse tree from the stream of to
kens A parse tree shows the syntactic structure
of the source program. Add information about identifiers in the
symbol table Report error, when found, and recover f
rom thee error
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CFG 3
Grammar a tuple ( V, T, P, S ) where
V is a finite set of nonterminals, containing S, T is a finite set of terminals, P is a set of production rules in the form of β wh
ere and β are strings over V U T , and S is the start symbol.
Example G= ({S, A, B, C}, {a, b, c}, P, S)
P= { SSABC, BA AB, CB BC, CA AC, SA a, aA aa, aB ab, bB bb, bC bc, cC cc}
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CFG 4
- Context Free Grammar a tuple ( V, T, P, S ) where
V is a finite set of nonterminals, containingS,
T is a finite set of terminals, P is a set of production rules in the form of
β where is in V and β is in (V U T )*, and S is the start symbol.
Any string in (V U T)* is called a sententi al form.
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CFG 5
Examples E E O E E (E) E id O + O - O * O /
S SS S (S)S S () S
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CFG 6
- Backus Naur Form (BNF) Nonterminals are in < >. Terminals are any other symbols. ::= means . | means or. Examples:
<E> ::= <E><O><E>| (<E>) | ID <O> ::= - + | | * | /
<S> ::= <S><S> | (<S>)<S> | () |
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CFG 7
Derivation A sequence of replacement of a substri
ng in a sentential form.Definition Let G = (V , T , P , S ) be a CFG, , , be
strings in (V ( T)* and A is in V.A G if A is in P.
*G denotes a derivation in zero step ormore.
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CFG 8
Examples S SS | (S)S | () | S
SS (S)SS (S)S(S)S (S)S(())S ((S)S)S(())S ((S)())S(())S ((())())S(())S ((())()) (())S ((())())(())
E E O E | (E) | id O - *+ | | | / E
E O E (E) O E (E O E) O E* ((E O E) O E) O E ((id O E)) O E) O E ((id + E)) O E) O E ((id + id)) O E) O E * ((id + id)) * id) + id
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CFG 9
Leftmost Derivation Rightmost Derivation Each step of the derivati
on is a replacement of t he leftmost nonterminal
s in a sentential form.E E O E (E ) O E (E O E) O E (id O E) O E (id + E ) O E (id + id) O E (id + id) * E (id + id) * id
Each step of the derivati on is a replacement of th
e rightmost nonterminal s in a sentential form.
E E O E E O id E * id (E *) id (E O E *) id (E O *id) id (E (( + ) * (id + id) * id
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CFG 10
Language Derived from Grammar Let G = (V , T , P , S ) be a CFG. A string w in T * is derived from G if S *
Gw. A language generated by G , denoted by
L(G ), is a set of strings derived from G. L(G) = {w| S *
Gw}.
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CFG 11
Right/Left Recursive A grammar is a left r
ecursive if its produc tion rules can gener
ate a derivation of th e form A * A X.
Examples: E E O id | (E) | id E F + id | (E) | id
F E * id | id E F + id
E * id + id
A grammar is a rightrecursive if its produ
ction rules can gener ate a derivation of th
e form A * X A. Examples:
E id O E | (E) | id E id + F | (E) | id
F id * E | id E id + F
id + id * E
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CFG 12
Parse Tree A labeled tree in which
the interior nodes are labeled by nonterminals
leaf nodes are labeled by terminals the children of an interior node represent a
replacement of the associated nonterminal in a derivation
corresponding to a derivationE(id
EF
*id i
d
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CFG 13
Parse Trees and Derivations E E + E 1( ) id + E (2 ) id + E * E (3 ) id + id * E (4 ) id + id * id (5 )
E E + E 1( ) E + E * E 2( ) E + E * id 3( ) E + id * id 4( ) id + id * id 5( )
Preorder numbering
Reverse or postorder numbering
(
E 1
E 2 E 5
E 3
* E4
id
id
id
(
E 1
E 5 E 3
E 2
* E4
id
id
id
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CFG 14
Grammar: ExampleList of parameters in: Function definition
function sub(a,b,c) Function call
sub(a,1,2)
<Fdef> function id ( <argList> )<argList> id , <arglist> | id<Fcall> id ( <parList> )<parList> <par> ,<parlist>| <par><par> id | const
<Fdef> function id ( <argList> )<argList> <arglist> , id | id<Fcall> id ( <parList> )<parList> <parlist> ,<par>| <par><par> id | const
<argList> id , <arglist> id, id , <arglist> … (id ,)* id<argList> <arglist> , id<arglist> , id, id … id (, id )*
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CFG 15
Grammar: ExampleList of parameters If zero parameter is
allowed, then ?
<Fdef> function id ( <argList> )| function id ( )
<argList> id , <arglist> | id<Fcall> id ( <parList> ) | id ( )<parList> <par> ,<parlist>| <par><par> id | const
<Fdef> function id ( <argList> )<argList> id , <arglist> | id | <Fcall> id ( <parList> )<parList> <par> ,<parlist>| <par><par> id | const
Work ?
NO! Generateid , id , id ,
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CFG 16
Grammar: ExampleList of statements: No statement One statement:
s; More than one
statement: s; s; s;
A statement can be a block of statements. {s; s; s;}
Is the following correct?{ {s; {s; s;} s; {}} s; }
<St> ::= | s; | s; <St> | { <St> } <St><St> { <St> } <St> { <St> } { { <St> } <St>} { { <St> } s; <St>} { { <St> } s; } { { s; <St> } s;} { { s; { <St> } <St> } s;} { { s; { <St> } s; <St> } s;} { { s; { <St> } s; { <St> } <St> } s;} { { s; { <St> } s; { <St> } } s;} { { s; { <St> } s; {} } s;} { { s; { s; <St> } s; {} } s;} { { s; { s; s;} s; {} } s;}
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CFG 17
Abstract Syntax Tree Representation of actual source tokens Interior nodes represent operators. Leaf nodes represent operands.
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CFG 18
Abstract Syntax Tree for Expression
( E
E E
E
*E
id3
id2
id1
(
id1id3
*id2
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CFG 19
Abstract Syntax Tree for If Statement
st
ifStatement
)exptrue
(if
else st
st elsePart
return
if
true
st return
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CFG 20
Ambiguous Grammar A grammar is ambiguous if it can gener
ate two different parse trees for one string.
Ambiguous grammars can cause incons istency in parsing.
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CFG 21
Example: Ambiguous Grammar E E + E E - E E E E * E E E / E E ((
+
E
E
E
E
*E
id3
id2
id1
*
E
E
id2
E
E
+E
id1
id3
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CFG 22
Ambiguity in Expressions Which operation is to be done first?
solved by precedence An operator with higher precedence is done bef
ore one with lower precedence. An operator with higher precedence is placed in
a rule (logically) further from the start symbol. solved by associativity
- -If an operator is right associative (or left associa tive), an operand in between2 operators is asso ciated to the operator to the right (left).
- Right associated : W + ( X+(Y+Z)) ((((-(((((((((( ( ((( ( (( ( (( ( (
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CFG 23
Precedence E E + E E - E E E E * E E E / E E id E E + E E - E E E F F F * F
F F / FF id
+
E
E
E
E
*E
id3
id2
id1
*
E
E
id2
E
E
+E
id1
id3
E
+ E E
*F
id3id2
id1 F
F F
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CFG 24
Precedence (cont’d) E - E + E | E E | F F F * F | F / F | X X ( E ) | id
(id1 + id2) * id3* id4
* F
X
F
+E id4
id3
E
X
E X
E
F
) (
*F F
id1
X
F
id2
X
F
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CFG 25
Associativity - Left associative operato
rs E - E + F | E F | F F F * X | F / X | X X ( E ) | id
(id1 + id2) * id3 / id4 = (( (id1 + id2) * id3) / id4)
/ F X
(E
id3 X E
E F
) (
*F X
id1XF
id4
XF
id2
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CFG 26
Ambiguity in Dangling Else St IfSt | ...
IfSt if ( E ) St | if ( E ) St else St E 0 | 1 | …
IfSt
)if ( elseE StSt
IfSt
)if ( E St
0
1
0 IfSt
)if ( elseE StSt
IfSt
)if ( E St
1
0{ if ( ) { (1) }if St
SS S} 0{ if ( ) 1{ if ( ) St else St } }
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CFG 27
Disambiguating Rules for Dangling El se
St MatchedSt | UnmatchedSt
UnmatchedSt if (E) St | if (E) MatchedSt else Unmatched
St MatchedSt
if (E) MatchedSt else MatchedSt| ...
E 0 | 1
if (0) if (1) St else St= if (0)
if (1) St else St
UnmatchedSt
)if ( E
MatchedSt
)if ( elseE MatchedStMatchedSt
St
St
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CFG 28
- Extended Backus Naur Form (EBNF) Kleene’s Star/ Kleene’s Closure
Seq ::= St {; St} Seq ::= {St ;} St
Optional Part IfSt ::= if ( E ) St [else St] - E ::= F [+ E ] | F [ E]
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CFG 29
Syntax Diagrams Graphical representation of EBNF rules
nonterminals: terminals: sequences and choices:
Examples X ::= ( E) | id
Seq ::= {St ;} St
E ::= F [+ E ]
IfStid
( )Eid
StSt;
F ( E