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Noncanonical Parsing
Sylvain Schmitz
[email protected]
16 mai 2006
Sylvain Schmitz (Laboratoire I3S)
EJC06 (LaBRI)
1 / 22
Context-Free Grammars
The Java Programming Language
Java Declarations
Gosling et al. [1996]
Example
public class Declarations {
public final static int FIELD = 10;
public static int method (int i) {
// ...
}
}
EJC06 (LaBRI)
3 / 22
Java Grammar
Example
// ...
}
}
<FDecl >→ <FModS > <Type > <VDeclS > ;
<FModS >→<FModS ><FMod >| ε
<FMod >→public | final | static | transient | . . .
<Type >→ <NonVoidType >
<MHead >→<MModS ><ResType ><MDecl ><Throws >
<MModS >→<MModS ><MMod >| ε
<MMod >→public | final | static | abstract | . . .
<ResType >→ <NonVoidType >| void
EJC06 (LaBRI)
3 / 22
Java Grammar
Example
// ...
}
}
EJC06 (LaBRI)
3 / 22
Java Grammar
Example
// ...
}
}
EJC06 (LaBRI)
3 / 22
Java Grammar
Example
// ...
}
}
EJC06 (LaBRI)
3 / 22
Java Grammar
Example
// ...
}
}
EJC06 (LaBRI)
3 / 22
Java Grammar
Example
// ...
}
}
EJC06 (LaBRI)
3 / 22
Java Grammar
Example
// ...
}
}
EJC06 (LaBRI)
3 / 22
Java Grammar
Example
// ...
}
}
EJC06 (LaBRI)
3 / 22
Java Grammar
Example
// ...
}
}
EJC06 (LaBRI)
3 / 22
Java Grammar
Example
// ...
}
}
EJC06 (LaBRI)
3 / 22
Java Grammar
Example
// ...
}
}
EJC06 (LaBRI)
3 / 22
Java Grammar
Example
// ...
}
}
EJC06 (LaBRI)
3 / 22
Java Grammar
Example
// ...
}
}
EJC06 (LaBRI)
3 / 22
Java Grammar
Example
// ...
}
}
EJC06 (LaBRI)
3 / 22
Java Grammar
Example
// ...
}
}
EJC06 (LaBRI)
3 / 22
Bottom-Up Parsing
Nondeterminism
Example
MModS
public
final
static
int
FIELD = 10 ;
$ k public final static int FIELD = 10;$
EJC06 (LaBRI)
4 / 22
Bottom-Up Parsing
Nondeterminism
Example
MModS
ε
|=
reduce
public
final
static
int
FIELD = 10 ;
$ε k public final static int FIELD = 10;$
$<MModS > k public final static int FIELD = 10;$
EJC06 (LaBRI)
4 / 22
Bottom-Up Parsing
Nondeterminism
Example
MModS
ε
public
final
static
int
FIELD = 10 ;
$ <MModS > k public final static int FIELD = 10;$
|=
$ <MModS > public k final static int FIELD = 10;$
shift
EJC06 (LaBRI)
4 / 22
Bottom-Up Parsing
Nondeterminism
Example
MModS
FMod
ε
public
|=
reduce
final
static
int
FIELD = 10 ;
$ <MModS > <FMod > k final static int FIELD = 10;$
EJC06 (LaBRI)
4 / 22
Bottom-Up Parsing
Nondeterminism
Example
error!
MModS
FMod
ε
public
final
static
int
FIELD = 10 ;
$ <MModS ><FMod > k final static int FIELD = 10;$
EJC06 (LaBRI)
4 / 22
Bottom-Up Parsing
LR(0) Parsing
Example
MModS
MMod
ε
public
|=
reduce
final
static
int
FIELD = 10 ;
$ <MModS > <MMod > k final static int FIELD = 10;$
EJC06 (LaBRI)
4 / 22
Bottom-Up Parsing
LR(0) Parsing
Example
MModS
MModS
MMod
ε
public
|=
reduce
final
static
int
FIELD = 10 ;
$<MModS ><MMod > k final static int FIELD = 10;$
$<MModS > k final static int FIELD = 10;$
EJC06 (LaBRI)
4 / 22
Bottom-Up Parsing
LR(0) Parsing
Example
MModS
MModS
MMod
ε
public
final
static
int
FIELD = 10 ;
$ <MModS > k final static int FIELD = 10;$
|=
$ <MModS > final k static int FIELD = 10;$
shift
EJC06 (LaBRI)
4 / 22
Bottom-Up Parsing
LR(0) Parsing
Example
MModS
MModS
MMod
ε
public
|=
reduce
MMod
final
static
int
FIELD = 10 ;
$ <MModS > final k static int FIELD = 10;$
$ <MModS > <MMod > k static int FIELD = 10;$
EJC06 (LaBRI)
4 / 22
Bottom-Up Parsing
LR(0) Parsing
Example
MModS
MModS
MModS
MMod
ε
public
|=
reduce
MMod
final
static
int
FIELD = 10 ;
$<MModS ><MMod > k static int FIELD = 10;$
$<MModS > k static int FIELD = 10;$
EJC06 (LaBRI)
4 / 22
Bottom-Up Parsing
LR(k) Parsing
Why Determinism Matters
+ Performance
+ Safety
− Generality
EJC06 (LaBRI)
5 / 22
Bottom-Up Parsing
LR(k) Parsing
LR(k) Parsing
Knuth [1965]
I
complete stack information
I
k symbols of lookahead
EJC06 (LaBRI)
6 / 22
Bottom-Up Parsing
LR(k) Parsing
LR(k) Parsing
Knuth [1965]
I
complete stack information: regular language
I
EJC06 (LaBRI)
6 / 22
Bottom-Up Parsing
LR(k) Parsing
LR(k) Parsing
Knuth [1965]
I
complete stack information: regular language
I
Example
MMod
MModS
[$]
[$ MModS]
[$ MModS MMod]
static
[$ MModS
static ]
EJC06 (LaBRI)
6 / 22
Bottom-Up Parsing
LR(k) Parsing
Nondeterminism
Example
MModS
MModS
MModS
MMod
ε
public
|=
reduce
MMod
final
static
int
FIELD = 10 ;
[$][$ <MModS >][$ <MModS ><MMod >] k static int FIELD
[$][$ <MModS >] k static int FIELD = 10;$
EJC06 (LaBRI)
7 / 22
Bottom-Up Parsing
LR(k) Parsing
Nondeterminism
Example
MModS
MModS
MModS
MMod
ε
public
MMod
final
static
int
FIELD = 10 ;
[$][$ <MModS >] k static int FIELD = 10;$
|=
[$][$ <MModS >] [$ <MModS > static] k int FIELD = 10;$
shift
EJC06 (LaBRI)
7 / 22
Bottom-Up Parsing
LR(k) Parsing
Nondeterminism
Example
MModS
MModS
MModS
MMod
ε
public
|=
reduce
MMod
MMod
final
static
int
FIELD = 10 ;
[$][$ <MModS >][$ <MModS > static] k int FIELD = 10;$
[$][$ <MModS >][$ <MModS ><MMod >] k int FIELD = 10;$
EJC06 (LaBRI)
7 / 22
Bottom-Up Parsing
LR(k) Parsing
Nondeterminism
Example
MModS
MModS
MModS
MModS
MMod
ε
public
|=
reduce
MMod
MMod
final
static
int
FIELD = 10 ;
[$][$ <MModS >][$ <MModS ><MMod >] k int FIELD = 10;$
[$][$ <MModS >] k int FIELD = 10;$
EJC06 (LaBRI)
7 / 22
Bottom-Up Parsing
LR(k) Parsing
Nondeterminism
Example
MModS
MModS
MModS
MModS
MMod
ε
public
MMod
MMod
final
static
int
FIELD = 10 ;
[$][$ <MModS >] k int FIELD = 10;$
|=
[$][$ <MModS >] [$ <MModS > int] k FIELD = 10;$
shift
EJC06 (LaBRI)
7 / 22
Bottom-Up Parsing
LR(k) Parsing
Nondeterminism
Example
MModS
MModS
MModS
MModS
MMod
ε
public
|=
reduce
MMod NonVoidType
MMod
final
static
int
FIELD = 10 ;
[$][$ <MModS >]int k FIELD = 10;$
[$][$ <MModS >][$ <MModS ><NonVoidType >] k FIELD = 10
EJC06 (LaBRI)
7 / 22
Bottom-Up Parsing
LR(k) Parsing
Nondeterminism
Example
MModS
MModS
MModS
MModS
MMod
ε
public
|=
reduce
ResType
MMod NonVoidType
MMod
final
static
int
FIELD = 10 ;
[$][$ <MModS >][$ <MModS ><NonVoidType >] k FIELD = 10
[$][$ <MModS >][$ <MModS ><ResType >] k FIELD = 10;$
EJC06 (LaBRI)
7 / 22
Bottom-Up Parsing
LR(k) Parsing
Nondeterminism
Example
MModS
MModS
MModS
MModS
MMod
ε
public
ResType
MMod NonVoidType
MMod
final
static
int FIELD = 10
;
[$] . . . k FIELD = 10;$
|=
[$] . . . [$ <MModS ><ResType > FIELD] k = 10;$
shift
EJC06 (LaBRI)
7 / 22
Bottom-Up Parsing
LR(k) Parsing
Nondeterminism
Example
MModS
MModS
MModS
MModS
MMod
ε
public
ResType
MMod NonVoidType
MMod
final
static
int FIELD = 10
;
[$] . . . [$ <MModS ><ResType > FIELD] k = 10;$
|=
[$] . . . [$ <MModS ><ResType > FIELD =] k 10;$
shift
EJC06 (LaBRI)
7 / 22
Bottom-Up Parsing
LR(k) Parsing
Nondeterminism
Example
MModS
MModS
MModS
MModS
MMod
ε
public
ResType
MMod NonVoidType
MMod
error!
final
static
int FIELD = 10
;
[$] . . . [<MModS ><ResType > FIELD =] k 10;$
EJC06 (LaBRI)
7 / 22
Bottom-Up Parsing
LR(k) Parsing
Nondeterminism
Example
FModS
ε
|=
reduce
public
final
static
int
FIELD = 10 ;
[$]ε k public final static int FIELD = 10;$
[$][$ <FModS >] k public final static int FIELD = 10;$
EJC06 (LaBRI)
7 / 22
Bottom-Up Parsing
LR(k) Parsing
LR(k) Parsing
I
I
Example
Choice between reductions <FModS > →ε and <MModS > →ε:
[$]εkpublic static final . . . final static int l =
[$]εkpublic static final . . . final static int l (
I
Unbounded lookahead needed for better generality
EJC06 (LaBRI)
8 / 22
Bottom-Up Parsing
LR(k) Parsing
LR(k) Parsing
I
I
Example
I
EJC06 (LaBRI)
8 / 22
Bottom-Up Parsing
LR(k) Parsing
LR(k) Parsing
I
I
Example
I
EJC06 (LaBRI)
8 / 22
Why Noncanonical Parsing?
Parsing a Program Source
I
Good generality
I
Determinism
I
O(n) time complexity
EJC06 (LaBRI)
9 / 22
Why Noncanonical Parsing?
Parsing a Program Source
I
Good generality
I
Determinism
I
Noncanonical parsing
EJC06 (LaBRI)
9 / 22
Parsing Example
Colmerauer [1970], Szymanski and Williams [1976], Tai [1979]
Example
FModS
public
final
static
int
FIELD = 10 ;
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
FModS
public
final
static
int
FIELD = 10 ;
|=
$ public k final static int FIELD = 10;$
shift
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
FModS
public
final
static
int
FIELD = 10 ;
$public k final static int FIELD = 10;$
|=
$public final k static int FIELD = 10;$
shift
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
FModS
public
final
static
int
FIELD = 10 ;
$public final k static int FIELD = 10;$
|=
$public final static k int FIELD = 10;$
shift
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
FModS
public
final
static
int
FIELD = 10 ;
$public final static k int FIELD = 10;$
|=
$public final static int k FIELD = 10;$
shift
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
NonVoidType
FModS
public
|=
reduce
final
static
int
FIELD = 10 ;
$public final static int k FIELD = 10;$
$public final static k <NonVoidType > FIELD = 10;$
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
NonVoidType
FModS
public
final
static
int
;
FIELD = 10
$public final static k <NonVoidType > FIELD = 10;$
|=
$public final static <NonVoidType > k FIELD = 10;$
shift
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
NonVoidType
FModS
public
final
static
int
;
FIELD = 10
$public final static <NonVoidType > k FIELD = 10 ;$
|=
$public final static <NonVoidType > FIELD = 10 k ;$
shift
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
VDeclS
NonVoidType
FModS
public
|=
reduce
final
static
int
FIELD = 10
;
$public final static <NonVoidType > FIELD = 10 k ;$
$public final static <NonVoidType > k <VDeclS > ;$
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
Type
VDeclS
NonVoidType
FModS
public
|=
reduce
final
static
int
;
FIELD = 10
$public final static <NonVoidType > k <VDeclS > ;$
$public final static k <Type > <VDeclS > ;$
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
Type
VDeclS
FMod NonVoidType
FModS
public
|=
reduce
final
static
int
FIELD = 10
;
$public final static k <Type ><VDeclS > ;$
$public final k <FMod > <Type ><VDeclS > ;$
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
Type
VDeclS
FMod NonVoidType
FMod
FModS
public
|=
reduce
final
static
int
FIELD = 10
;
$public final k <FMod ><Type ><VDeclS > ;$
$public k <FMod > <FMod ><Type ><VDeclS > ;$
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
Type
VDeclS
FMod NonVoidType
FMod
FModS
FMod
public
|=
reduce
final
static
int
;
FIELD = 10
$ public k <FMod ><FMod ><Type ><VDeclS > ;$
$ k <FMod > <FMod ><FMod ><Type ><VDeclS > ;$
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
Type
VDeclS
FMod NonVoidType
FMod
FModS
FMod
ε
public
|=
reduce
final
static
int
FIELD = 10
;
$ ε k <FMod ><FMod ><FMod ><Type ><VDeclS > ;$
$ k <FModS > <FMod ><FMod ><FMod ><Type ><VDeclS >
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
Type
VDeclS
FMod NonVoidType
FMod
FModS
FMod
ε
public
final
static
int
FIELD = 10
;
$ k <FModS > <FMod ><FMod ><FMod ><Type ><VDeclS >
|=
$ <FModS > k <FMod ><FMod ><FMod ><Type ><VDeclS >
shift
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
Type
VDeclS
FMod NonVoidType
FMod
FModS
FMod
ε
public
final
static
int
FIELD = 10
;
$ <FModS > k <FMod > <FMod ><FMod ><Type ><VDeclS
|=
$ <FModS > <FMod > k <FMod ><FMod ><Type ><VDeclS
shift
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
Type
VDeclS
FMod NonVoidType
FModS
FModS
FMod
ε
public
|=
reduce
FMod
final
static
int
FIELD = 10
;
$ <FModS ><FMod > k <FMod ><FMod ><Type ><VDeclS >
$ k <FModS > <FMod ><FMod ><Type ><VDeclS > ;$
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
Type
VDeclS
FMod NonVoidType
FModS
FModS
FMod
ε
public
FMod
final
static
int
;
FIELD = 10
$ k <FModS > <FMod ><FMod ><Type ><VDeclS > ;$
|=
$ <FModS > k <FMod ><FMod ><Type ><VDeclS > ;$
shift
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
Type
VDeclS
FMod NonVoidType
FModS
FModS
FMod
ε
public
FMod
final
static
int
;
FIELD = 10
$ <FModS > k <FMod > <FMod ><Type ><VDeclS > ;$
|=
$ <FModS > <FMod > k <FMod ><Type ><VDeclS > ;$
shift
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
Type
FModS
FModS
FModS
FMod
ε
public
|=
reduce
VDeclS
FMod NonVoidType
FMod
final
static
int
;
FIELD = 10
$ <FModS ><FMod > k <FMod ><Type ><VDeclS > ;$
$ k <FModS > <FMod ><Type ><VDeclS > ;$
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
Type
FModS
FModS
FModS
FMod
ε
public
VDeclS
FMod NonVoidType
FMod
final
static
int
FIELD = 10
;
$ k <FModS > <FMod ><Type ><VDeclS > ;$
|=
$ <FModS > k <FMod ><Type ><VDeclS > ;$
shift
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
Type
FModS
FModS
FModS
FMod
ε
public
VDeclS
FMod NonVoidType
FMod
final
static
int
FIELD = 10
;
$ <FModS > k <FMod > <Type ><VDeclS > ;$
|=
$ <FModS > <FMod > k <Type ><VDeclS > ;$
shift
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
FModS
FModS
FModS
FModS
FMod
ε
public
|=
reduce
Type
VDeclS
FMod NonVoidType
FMod
final
static
int
FIELD = 10
;
$ <FModS ><FMod > k <Type ><VDeclS > ;$
$ k <FModS > <Type ><VDeclS > ;$
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
FModS
FModS
FModS
FModS
FMod
ε
public
Type
VDeclS
FMod NonVoidType
FMod
final
static
int
FIELD = 10
;
$ k <FModS > <Type ><VDeclS > ;$
|=
$ <FModS > k <Type ><VDeclS > ;$
shift
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
FModS
FModS
FModS
FModS
FMod
ε
public
Type
VDeclS
FMod NonVoidType
FMod
final
static
int
FIELD = 10
;
$ <FModS > k <Type > <VDeclS > ;$
|=
$ <FModS > <Type > k <VDeclS > ;$
shift
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
FModS
FModS
FModS
FModS
FMod
ε
public
Type
VDeclS
FMod NonVoidType
FMod
final
static
int
FIELD = 10
;
$ <FModS ><Type > k <VDeclS > ;$
|=
$ <FModS ><Type > <VDeclS > k ;$
shift
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
FModS
FModS
FModS
FModS
FMod
ε
public
Type
VDeclS
FMod NonVoidType
FMod
final
static
int
FIELD = 10 ;
$ <FModS ><Type ><VDeclS > k ; $
|=
$ <FModS ><Type ><VDeclS > ; k $
shift
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
FDecl
FModS
FModS
FModS
FModS
FMod
ε
public
|=
reduce
Type
VDeclS
FMod NonVoidType
FMod
final
static
int
FIELD = 10 ;
$ <FModS ><Type ><VDeclS > ; k $
$ k <FDecl > $
EJC06 (LaBRI)
10 / 22
Parsing Example
Example
FDecl
FModS
FModS
FModS
FModS
FMod
ε
public
Type
VDeclS
FMod NonVoidType
FMod
final
static
int
FIELD = 10 ;
$ k <FDecl > $
|=
$ <FDecl > k $
shift
EJC06 (LaBRI)
10 / 22
Noncanonical Parsers Generation
Noncanonical Lookaheads
Example
FModS
FDecl
FModS
ε
;
transient
EJC06 (LaBRI)
11 / 22
Example
FModS
FModS
FDecl
FMod
ε
;
transient
EJC06 (LaBRI)
11 / 22
Example
FModS
FModS
FMod
ε
public
FDecl
;
transient
EJC06 (LaBRI)
11 / 22
Example
FModS
FModS
FMod
ε
public
final
FDecl
;
transient
EJC06 (LaBRI)
11 / 22
Example
FModS
FModS
FMod
ε
public
final
static
transient
FDecl
;
EJC06 (LaBRI)
11 / 22
Example
FModS
FModS
FMod
ε
public
final
static
transient
FDecl
;
EJC06 (LaBRI)
11 / 22
Example
FModS
FDecl
FModS
ε
;
transient
EJC06 (LaBRI)
11 / 22
Example
FDecl
FModS
Type
VDeclS
ε
;
transient
EJC06 (LaBRI)
11 / 22
Example
FDecl
FModS
Type
VDeclS
NonVoidType
ε
;
transient
EJC06 (LaBRI)
11 / 22
Example
FDecl
FModS
Type
VDeclS
NonVoidType
ε
int
;
transient
EJC06 (LaBRI)
11 / 22
Notation
<FModS > → ε
{public, final, static, int,
transient, <FMod >, <Type >,
<NonVoidType >}
EJC06 (LaBRI)
11 / 22
Comparison
<FModS > → ε
<NonVoidType >}
<MModS > → ε
abstract, <MMod >, <ReturnType >,
<NonVoidType >}
EJC06 (LaBRI)
11 / 22
Conflicts
<FModS > → ε
<NonVoidType >}
<MModS > → ε
<NonVoidType >}
EJC06 (LaBRI)
11 / 22
Decisions
<FModS > → ε
<NonVoidType >}
<MModS > → ε
<NonVoidType >}
EJC06 (LaBRI)
11 / 22
Noncanonical LALR(1)
DeRemer and Pennello [1982], Schmitz [2006]
Example
[$ MModS MMod]
MMod
MModS [$ MModS]
[$]
ε
FModS
static
FMod
[$ FModS]
static
FMod
int
[$ MModS
static ]
[$ FModS FMod]
[$ MModS
static ]
[$ FModS Type]
[$ FModS
static ]
EJC06 (LaBRI)
12 / 22
Example
[$ MModS MMod]
MMod
MModS [$ MModS]
[$]
ε
FModS
static
FMod
[$ FModS]
static
FMod
int
[$ MModS
static ]
[$ FModS FMod]
[$ MModS
static ]
[$ FModS Type]
[$ FModS
static ]
EJC06 (LaBRI)
12 / 22
Example
[$ MModS MMod]
MMod
MModS [$ MModS]
[$]
ε
FModS
static
FMod
[$ FModS]
static
lookback
FMod
int
[$ MModS
static ]
[$ FModS FMod]
[$ MModS
static ]
[$ FModS Type]
[$ FModS
static ]
EJC06 (LaBRI)
12 / 22
Example
[$ MModS MMod]
MMod
MModS [$ MModS]
[$]
ε
FModS
static
FMod
[$ FModS]
directly
reads
static
FMod
int
[$ MModS
static ]
[$ FModS FMod]
[$ MModS
static ]
[$ FModS Type]
[$ FModS
static ]
EJC06 (LaBRI)
12 / 22
Valid Covers
Schmitz [2006]
Example
FModS
public
final
static
int
FIELD = 10 ;
EJC06 (LaBRI)
13 / 22
Valid Covers
Schmitz [2006]
Example
FModS
FModS
FModS
FMod
ε
public
FMod
final
static
int
FIELD = 10
;
EJC06 (LaBRI)
13 / 22
Valid Covers
Schmitz [2006]
Example
FModS
FModS
public
final
static
int
FIELD = 10
;
EJC06 (LaBRI)
13 / 22
Noncanonical States
Schmitz [2006]
Example
[$ MModS MMod]
MMod
MModS [$ MModS]
[$]
static
[$static ]
FModS
[$ FModS]
static
FMod
static
[$ MModS
static ]
[$ FModS FMod]
[$ MModS
static ]
J$ staticK = {[$ static], [$ <FModS > static],
[$ <MModS > static]}
EJC06 (LaBRI)
14 / 22
End Comments
Closing Comments
I
I
I
Good generality
Determinism
NLALR(1)
I
I
Simple & fast computations on LR(0) automaton
Other prefix equivalences possible
Improvements
Better generality: no preset lookahead length
EJC06 (LaBRI)
15 / 22
LR(0) Construction
Valid0($ <MModS > )
MModS
MModS
MMod
Throws
int
<MModS>→ <MModS >
· <MMod >
EJC06 (LaBRI)
16 / 22
LR(0) Construction
Valid0($ <MModS > )
MModS
MModS
MMod
Throws
public
int
·
<MMod>→ public
EJC06 (LaBRI)
16 / 22
LR(0) Construction
Valid0($ <MModS > )
MModS
MModS
MMod
Throws
static
int
·
<MMod>→ static
EJC06 (LaBRI)
16 / 22
LR(0) Construction
Valid0($ <MModS > )
MModS
MModS
MMod
Throws
final
int
·
<MMod>→ final
EJC06 (LaBRI)
16 / 22
LR(0) Construction
Valid0($ <MModS > )
MModS
MModS
MMod
Throws
abstract
int
·
<MMod>→ abstract
EJC06 (LaBRI)
16 / 22
LR(0) Construction
Valid0($ <MModS > )
MHead
MModS
ResType
MDecl
Throws
int
<MHead>→ <MModS >
· <ResType ><MDecl ><Thro
EJC06 (LaBRI)
16 / 22
LR(0) Construction
Valid0($ <MModS > )
MHead
MModS
ResType
MDecl
Throws
void
int
·
<ResType>→ <NonVoidType >
EJC06 (LaBRI)
16 / 22
LR(0) Construction
Valid0($ <MModS > )
MHead
MModS
ResType
MDecl
Throws
NonVoidType
int
·
<ResType>→ void
EJC06 (LaBRI)
16 / 22
LR(0) Construction
Valid0($ <MModS > )
MHead
MModS
ResType
MDecl
Throws
NonVoidType
int
·
<NonVoidType>→ int
EJC06 (LaBRI)
16 / 22
LR(0) Construction
Valid0($ <MModS > )
·
<MModS>→ <MModS > <MMod >
<MMod >→ public
<MMod >→ static
<MMod >→ final
<MMod >→ abstract
<MHead >→ <MModS > <ResType ><MDecl ><
<ResType >→ <NonVoidType >
<ResType >→ void
<NonVoidType >→ int
·
·
·
·
·
·
·
·
EJC06 (LaBRI)
16 / 22
LR(0) Construction
Valid0($ <MModS > static)
MModS
MModS
MMod
Throws
static
int
·
<MMod>→static
EJC06 (LaBRI)
16 / 22
LR(0) Construction
Valid0($ <MModS > <MMod >)
MModS
MModS
MMod
Throws
int
<MModS>→ <MModS ><MMod >
·
EJC06 (LaBRI)
16 / 22
LR(0) Construction
Valid0($ <MModS > )
MMod
MModS
[$]
[$ MModS]
[$ MModS MMod]
static
[$ MModS
static ]
EJC06 (LaBRI)
16 / 22
Syntactic Predicates
Parr and Quong [1995]
I
User defined lookahead pattern
Example
((MMod)* ResType MDecl)?
I
Error-prone
I
Exponential time complexity
EJC06 (LaBRI)
18 / 22
I
Example
I
Error-prone
I
EJC06 (LaBRI)
18 / 22
I
Example
I
Error-prone
I
EJC06 (LaBRI)
18 / 22
I
Example
I
Error-prone
I
EJC06 (LaBRI)
18 / 22
LR-Regular Parsing
Baker [1981], Bermudez and Schimpf [1990], Farré and Fortes Gálvez [2001]
I
Finite State lookahead discrimination
I
O(n2 ) time complexity
I
Only considers terminal symbols
EJC06 (LaBRI)
19 / 22
LR-Regular Parsing
I
Example
abstract void
int
(
MModS
= , ;
FModS
IDENT
public static ...
transient
I
I
EJC06 (LaBRI)
19 / 22
LR-Regular Parsing
I
Example
abstract void
int
(
MModS
= , ;
FModS
IDENT
public static ...
transient
I
I
EJC06 (LaBRI)
19 / 22
LR-Regular Parsing
I
Example
abstract void
int
(
MModS
= , ;
FModS
IDENT
public static ...
transient
I
I
EJC06 (LaBRI)
19 / 22
T. P. Baker. Extending lookahead for LR parsers.
J. Comput. Syst. Sci., 22(2):243–259, 1981. doi:
10.1016/0022-0000(81)90030-1.
M. E. Bermudez and K. M. Schimpf. Practical arbitrary
lookahead LR parsing. J. Comput. Syst. Sci., 41(2):
230–250, 1990. doi: 10.1016/0022-0000(90)90037-L.
A. Colmerauer. Total precedence relations. J. ACM, 17
(1):14–30, Jan. 1970. doi: 10.1145/321556.321559.
F. DeRemer and T. Pennello. Efficient computation of
LALR(1) look-ahead sets. ACM Trans. Prog. Lang.
Syst., 4(4):615–649, 1982. doi:
10.1145/69622.357187.
J. Farré and J. Fortes Gálvez. A bounded-connect
construction for LR-regular parsers. In R. Wilhelm,
editor, CC’01, volumeNoncanonical
2027 Parsing
of Lecture Notes
in
EJC06 (LaBRI)
20 / 22
J. Gosling, B. Joy, and G. Steele. The JavaTM Language
Specification. Addison-Wesley Longman Publishing
Co., Inc., first edition, Aug. 1996. ISBN
0-201-63451-1. URL
http://java.sun.com/docs/books/jls/.
D. E. Knuth. On the translation of languages from left
to right. Information and Control, 8:607–639, 1965.
T. J. Parr and R. W. Quong. ANTLR: A
predicated-LL(k) parser generator. Software, Practice
and Experience, 25(7):789–810, 1995. ISSN
0038-0644. URL
http://citeseer.nj.nec.com/12770.
EJC06 (LaBRI)
21 / 22
S. Schmitz. Noncanonical LALR(1) parsing. In Z. Dang
and O. H. Ibarra, editors, DLT’06, volume 4036 of
Lecture Notes in Computer Science, pages 95–107.
Springer, 2006.
T. G. Szymanski and J. H. Williams. Noncanonical
extensions of bottom-up parsing techniques. SIAM J.
Comput., 5(2):231–250, June 1976. URL
http://locus.siam.org/SICOMP/volume-05/
art 0205019.html.
K.-C. Tai. Noncanonical SLR(1) grammars. ACM Trans.
Prog. Lang. Syst., 1(2):295–320, 1979. ISSN
0164-0925. doi: 10.1145/357073.357083.
EJC06 (LaBRI)
22 / 22

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