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Con
text
-Fre
eA
naly
sis
Lect
ure
Com
pile
rsS
S20
09
Dr.-
Ing.
Ina
Sch
aefe
r
Sof
twar
eTe
chno
logy
Gro
upTU
Kai
sers
laut
ern
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s1
Con
tent
ofLe
ctur
e
1.In
trodu
ctio
n:O
verv
iew
and
Mot
ivat
ion
2.S
ynta
x-an
dTy
peA
naly
sis
2.1
Lexi
calA
naly
sis
2.2
Con
text
-free
Syn
tax
Ana
lysi
s2.
3C
onte
xt-s
ensi
tive
Syn
tax
Ana
lysi
s3.
Tran
slat
ion
toTa
rget
Lang
uage
3.1
Tran
slat
ion
ofIm
pera
tive
Lang
uage
Con
stru
cts
3.2
Tran
slat
ion
ofO
bjec
t-Orie
nted
Lang
uage
Con
stru
cts
4.S
elec
ted
Asp
ects
ofC
ompi
lers
4.1
Inte
rmed
iate
Lang
uage
s4.
2O
ptim
izat
ion
4.3
Com
man
dS
elec
tion
4.4
Reg
iste
rAllo
catio
n4.
5C
ode
Gen
erat
ion
5.G
arba
geC
olle
ctio
n6.
XM
LP
roce
ssin
g(D
OM
,SA
X,X
SLT
)
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s2
Out
line
ofC
onte
xt-F
ree
Ana
lysi
s
1.S
peci
ficat
ion
ofPa
rser
s
2.Im
plem
enta
tion
ofPa
rser
sTo
p-D
own
Syn
tax
Ana
lysi
sR
ecur
sive
Des
cent
LL(k
)Par
sing
Theo
ryLL
Pars
erG
ener
atio
nB
otto
m-U
pS
ynta
xA
naly
sis
Prin
cipl
esof
LRPa
rsin
gLR
Pars
ing
Theo
ryS
LR,L
ALR
,LR
(k)P
arsi
ngLA
LR-P
arse
rGen
erat
ion
3.E
rror
Han
dlin
g
4.C
oncr
ete
and
Abs
tract
Syn
tax
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s3
Con
text
-Fre
eS
ynta
xA
naly
sis
Task
s•
Che
ck,i
fTok
enS
tream
(from
Sca
nner
)mat
ches
cont
ext-f
ree
synt
axof
lang
uage
s!
Err
orC
ase:
Err
orha
ndlin
g!
Cor
rect
ness
:Con
stru
ctio
nof
Syn
tax
Tree
Par
ser
Toke
n S
trea
m
Abst
ract
/ C
oncr
ete
Synta
x T
ree
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s4
Con
text
-Fre
eS
ynta
xA
naly
sis
(2)
Rem
arks
:•
Pars
ing
can
bein
terle
aved
with
othe
ract
ions
proc
essi
ngth
epr
ogra
m(e
.g.a
ttrib
utat
ion)
.•
Syn
tax
tree
cont
rols
impo
rtan
tpar
tsof
trans
latio
n.H
ence
,we
dist
ingu
ish
!C
oncr
ete
synt
axtre
eco
rres
pond
sto
cont
ext-f
ree
gram
mar
!A
bstra
ctsy
ntax
tree
aim
sat
furt
herp
roce
ssin
gst
eps,
com
pact
repr
esen
tatio
nof
esse
ntia
linf
orm
atio
n.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s5
Spe
cific
atio
nof
Pars
ers
Spe
cific
atio
nof
Pars
ers
2ge
nera
lspe
cific
atio
nte
chni
ques
•S
ynta
xD
iagr
ams
•C
onte
xt-F
ree
Gra
mm
ars
(ofte
nin
exte
nded
form
)
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s6
Spe
cific
atio
nof
Pars
ers
Con
text
-Fre
eG
ram
mar
s
Defi
nitio
nLe
tNan
dT
betw
oal
phab
ets,
with
N!
T="
and
!a
finite
subs
etof
N#
(N$
T)!
and
S%
N.T
hen
"=
(N,T
,!,S
)is
aco
ntex
t-fre
egr
amm
ar(C
FG)w
here
•N
isth
ese
tofn
on-te
rmin
als
•T
isth
ese
toft
erm
inal
s•
!is
the
seto
fpro
duct
ions
rule
s•
Sis
the
star
tsym
bol(
axio
m)
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s7
Spe
cific
atio
nof
Pars
ers
Con
text
-Fre
eG
ram
mar
s(2
)
Not
atio
ns:
•A
,B,C
,...
deno
teno
n-te
rmin
als
•a,
b,c,
...de
note
term
inal
s•
x,y,
z,..
.de
note
strin
gsof
term
inal
s,i.e
.x%
T!
•!,"
,#,$
,%,&
,'ar
est
rings
ofte
rmin
als
and
non-
term
inal
s,i.e
.!%
(N$
T)!
Pro
duct
ions
are
deno
ted
byA&
!.
The
nota
tion
A&
!|"|#|.
..is
anab
brev
iatio
nfo
rA&
!,A
&"
,A&
#,.
..
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s8
Spe
cific
atio
nof
Pars
ers
Der
ivat
ion
Let"
=(
N,T
,!,S
)be
aC
FG:
•$
isdi
rect
lyde
rivab
lefro
m%
in",%
prod
uces
$di
rect
ly,%'
$,i
fth
ere
exis
ts&
A'
=%
and
&!'
=$
and
A&
!%
!
•$
isde
rivab
lefro
m%
in",%'
!$
,ift
here
exis
ts%
0,..
.,%
nw
ith%
=%
0an
d$
=%
nan
dfo
rall
i%{0
,...
,n(
1}it
hold
sth
at%
i'
%i+
1.%
0,..
.,%
nis
the
deriv
atio
nof
$fro
m%
.•'
!is
the
refle
xive
,tra
nsiti
vecl
osur
eof'
.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s9
Spe
cific
atio
nof
Pars
ers
Der
ivat
ion
(2)
•Th
ede
rivat
ion
%0,
...,
%n
isa
left
deriv
atio
n(r
ight
deriv
atio
n),i
fin
%ith
ele
ft-m
ost(
right
-mos
t)no
n-te
rmin
alis
repl
aced
.Lef
tde
rivat
ion
step
sar
ede
note
dby
%'
lm$
.Rig
htde
rivat
ion
step
sar
ede
note
dby
%'
rm$
.
•Th
etre
e-lik
ere
pres
enta
tion
ofa
deriv
atio
nis
asy
ntax
tree.
•L(
")
={z%
T!|S'
!z}
isth
ela
ngua
gege
nera
ted
by".
•x%
L(")
isa
sent
ence
of".
•%%
(N$
T)!
with
S'
!%
isa
sent
entia
lfor
mof
".
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s10
Spe
cific
atio
nof
Pars
ers
Am
bigu
ityin
Gra
mm
ars
•A
sent
ence
isun
ambi
guou
sif
itha
sex
actly
one
synt
axtre
e.A
sent
ence
isam
bigu
ous
ifit
has
mor
eth
anon
esy
ntax
tree.
•Fo
reac
hsy
ntax
tree,
ther
eex
ists
exac
tlyon
left
deriv
atio
nan
dex
actly
one
right
deriv
atio
n.•
Thus
itho
lds:
Ase
nten
ceis
unam
bigu
ous
if-an
d-on
ly-if
itha
sex
actly
one
left
(rig
ht)d
eriv
atio
n.•
Agr
amm
aris
ambi
guou
sif
itco
ntai
nsan
ambi
guou
sse
nten
ce,
else
itis
unam
bigu
ous.
•Fo
rpro
gram
min
gla
ngua
ges,
unam
bigu
ous
gram
mar
sar
ees
sent
ial,
asth
ese
man
tics
and
the
trans
latio
nar
ede
fined
byth
esy
ntac
ticst
ruct
ure.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s11
Spe
cific
atio
nof
Pars
ers
Am
bigu
ityin
Gra
mm
ars
(2)
Exa
mpl
e1:
Gra
mm
arfo
rExp
ress
ions
"0
•S&
E•
E&
E+
E•
E&
E)
E•
E&
(E)
•E&
ID
Con
side
rthe
inpu
tstri
ng(a
v+
av))
bv+
cv+
dv
whi
chis
the
follo
win
gin
putt
oth
eco
ntex
t-fre
ean
alys
is(I
D+
ID))
ID+
ID+
ID
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s12
Spe
cific
atio
nof
Pars
ers
Am
bigu
ityin
Gra
mm
ars
(3)
Syn
tax
tree
for(
ID+
ID))
ID+
ID+
ID
54
© A
. P
oe
tzsch
-Heff
ter,
TU
Kais
ers
laute
rn25.04.2007
Be
isp
iele
: (
Me
hrd
eu
tigke
it)
1. B
eis
pie
l e
iner
Ausdru
cksgra
mm
atik:
!0:
S
E
, E
E
+ E
, E
E
* E
, E
(
E )
, E
ID
Betr
achte
die
Ein
gab
e: (a
v+
av)
*b
v +
cv +
dv)
Ein
ga
be z
ur
kf-
Analy
se: (
ID
+ ID
) *
ID
+ ID
+ ID
S "
"
"
"
"
E E
E
E
E
( ID
+
ID
)
*
ID
+
ID
+
ID
-S
ynta
xb
aum
ents
pri
cht nic
ht d
en ü
blic
hen
Rechenre
geln
.
-E
s g
ibt m
ehre
re S
ynta
xbäum
e g
em
äß
!0,
insbeson
dere
ist die
Gra
mm
atik m
ehrd
eutig.
•S
ynta
xtre
edo
esno
tmat
chco
nven
tiona
lrul
esof
arith
met
ic.
•Th
ere
are
seve
rals
ynta
xtre
esac
cord
ing
to"
0fo
rthi
sin
put,
henc
e"
0is
ambi
guou
s.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s13
Spe
cific
atio
nof
Pars
ers
Am
bigu
ityin
Gra
mm
ars
(4)
Exa
mpl
e2:
Am
bigu
ityin
if-th
en-e
lse
cons
truct
ifB1
then
ifB2
then
A:=
9el
seA:
=7
Firs
tDer
ivat
ion
55
© A
. P
oe
tzsch
-Heff
ter,
TU
Kais
ers
laute
rn25.04.2007
2.
Me
hrd
eu
tig
ke
it b
eim
if-t
he
n-e
lse
-Ko
nstr
ukt:
ifB
1th
en
if
B2
the
n
A:=
8e
lse
A
:= 7
IFT
HE
NE
LS
E
AN
W
IFT
HE
N
AN
W
AN
W
ZW
Z
W
IF I
D T
HE
N
IF I
D T
HE
N
ID E
Q C
O E
LS
E I
D E
Q C
O
ZW
Z
W
AN
W
AN
W
IFT
HE
NE
LS
E
AN
W
IFT
HE
N
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s14
Spe
cific
atio
nof
Pars
ers
Am
bigu
ityin
Gra
mm
ars
(5)
Sec
ond
Der
ivat
ion
55
© A
. P
oe
tzsch
-Heff
ter,
TU
Kais
ers
laute
rn25.04.2007
2. M
ehrd
eutigkeit b
eim
if-t
hen-e
lse-K
onstr
ukt:
ifB
1th
en
if B
2th
en
A:=
8e
lse A
:= 7
IFT
HE
NE
LS
E
AN
W
IFT
HE
N
AN
W
AN
W
ZW
ZW
IF ID
TH
EN
IF
ID
TH
EN
ID
EQ
CO
ELS
E ID
EQ
CO
ZW
ZW
AN
W
AN
W
IFT
HE
NE
LS
E
AN
W
IFT
HE
N
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s15
Spe
cific
atio
nof
Pars
ers
Am
bigu
ityin
Gra
mm
ars
(6)
Rem
arks
:•
Eac
hde
rivat
ion
corr
espo
nds
toex
actly
one
synt
axtre
e.In
reve
rse,
fore
ach
synt
axtre
e,th
ere
can
bese
vera
lder
ivat
ions
.•
Inst
ead
ofth
ete
rm"s
ynta
xtre
e"of
ten
also
the
term
s"s
truct
ure
tree"
or"d
eriv
atio
ntre
e"ar
eus
ed.
•Fo
reac
hla
ngua
ge,t
here
can
bese
vera
lgen
erat
ing
gram
mar
s,i.e
.th
em
appi
ngL:
Gra
mm
ar&
Lang
uage
isin
gene
raln
otin
ject
ive.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s16
Spe
cific
atio
nof
Pars
ers
Am
bigu
ityas
Gra
mm
arP
rope
rty
Am
bigu
ityis
agr
amm
arpr
oper
ty.T
hegr
amm
arfo
rexp
ress
ions
"0
isan
exam
ple
ofan
ambi
guou
sgr
amm
ar.
"0: •
S&
E•
E&
E+
E•
E&
E)
E•
E&
(E)
•E&
ID
57
© A
. P
oe
tzsch
-Heff
ter,
TU
Kais
ers
laute
rn25.04.2007
Be
isp
iel: (
Me
hrd
eu
tigke
it a
ls G
ram
ma
tike
ig.)
Die
ob
ige
Au
sd
rucksg
ram
ma
tik
!0:
S
E
, E
E
+ E
| E
* E
| E
(
E )
| E
ID
iste
in B
eis
pie
l fü
r e
ine
me
hrd
eu
tig
e G
ram
ma
tik:
S E
E
E
E
E
ID
+
ID
*ID
E
E
E
E
E S
Me
hrd
eu
tig
ke
it ist
zu
nä
ch
st
ein
ma
l e
ine
Gra
mm
atik-
eig
en
sch
aft
.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s17
Spe
cific
atio
nof
Pars
ers
Am
bigu
ityas
Gra
mm
arP
rope
rty
(2)
But
ther
eex
ists
anun
ambi
guou
sgr
amm
arfo
rthe
sam
ela
ngua
ge:
"1: •
S&
E•
E&
T+
E|T
•T&
F)
T|F
•F&
(E)|ID
58
© A
. P
oe
tzsch
-Heff
ter,
TU
Kais
ers
laute
rn25.04.2007
Aber
es g
ibt
ein
ee
indeutig
e G
ram
matik f
ür
die
Spra
che:
!1:
S
E,
E
T +
E | T
, T
F
* T
| F
, F
(
E )
| I
D
S
E
E
E
E
F
F
F
F
T
T
T
T
( ID
+ ID
)
*
ID
+
IDFT
Le
se
n S
ie z
u A
bsch
nitt 2
.2.1
:
Wilh
elm
, M
aure
r:
•aus K
ap. 8, S
ynta
ktische A
naly
se, d
ie S
. 2
71 -
283
App
el:
•aus
Cha
p. 3, S
. 40 -
47
(Es g
ibt
ab
er
au
ch
ko
nte
xtf
reie
Sp
rach
en
, d
ie n
ur
du
rch
me
hrd
eu
tig
e G
ram
ma
tiken
besch
rie
be
n w
erd
en
.)In
aS
chae
fer
Con
text
-Fre
eA
naly
sis
18
Spe
cific
atio
nof
Pars
ers
Lite
ratu
re
Rec
omm
ende
dR
eadi
ng:
•W
ilhel
m,M
aure
r:C
hapt
er8,
pp.2
71-2
83(S
ynta
ctic
Ana
lysi
s)•
App
el:C
hapt
er3,
pp.4
0-47
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s19
Impl
emen
tatio
nof
Pars
ers
Impl
emen
tatio
nof
Pars
ers
Ove
rvie
w•
Top-
Dow
nPa
rsin
g!
Rec
ursi
veD
esce
nt!
LL-P
arsi
ng!
LL-P
arse
rGen
erat
ion
•B
otto
m-U
pPa
rsin
g!
LR-P
arsi
ng!
LALR
,SLR
,LR
(k)-
Pars
ing
!LA
LR-P
arse
rGen
erat
ion
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s20
Impl
emen
tatio
nof
Pars
ers
Met
hods
forC
onte
xt-F
ree
Ana
lysi
s
•M
anua
llyde
velo
ped,
gram
mar
-spe
cific
impl
emen
tatio
n(e
rror
-pro
ne,i
nflex
ible
)•
Bac
ktra
ckin
g(s
impl
e,bu
tine
ffici
ent)
•C
ocke
-You
nger
-Kas
ami-A
lgor
ithm
(196
7):
!fo
rall
CFG
sin
Cho
msk
yN
orm
alfo
rm!
base
don
idea
ofdy
nam
icpr
ogra
mm
ing
!Ti
me
Com
plex
ityO
(n3 )
,how
ever
linea
rcom
plex
ityde
sire
d•
Top-
Dow
n-M
etho
ds:f
rom
Axi
omto
Toke
nst
ream
•B
otto
m-u
p-M
etho
ds:f
rom
Toke
nst
ream
toA
xiom
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s21
Impl
emen
tatio
nof
Pars
ers
Exa
mpl
e:To
p-D
own
Ana
lysi
sA
ccor
ding
to"
1:R
esul
tis
ale
ftde
rivat
ion.
60
© A
. P
oe
tzsch
-Heff
ter,
TU
Kais
ers
laute
rn25.04.2007
Be
isp
iel:
(To
p-d
ow
n-A
na
lyse
)
S E
=>
T
+
E
=
>
F
*
T
+
E
=
>
(
E
)
*
T
+
E
=
>
(
T
+
E
)
*
T
+
E
=>
(
F
+
E
)
*
T
+
E
=>
(
ID
+
E
)
*
T
+
E
=>
(
ID
+
T
)
*
T
+
E
=>
(
ID
+
F
)
*
T
+
E
=>
(
ID
+
ID
)
*
T
+
E
=>
(
ID
+
ID
)
*
F
+
E
=>
(
ID
+
ID
)
*
ID
+
E
=>
(
ID
+
ID
)
*
ID
+
T
=>
(
ID
+
ID
)
*
ID
+
F
=>
(
ID
+
ID
)
*
ID
+
ID
Erg
eb
nis
de
rtd
-An
aly
se
ist
ein
e L
inksa
ble
itu
ng
.
Gem
äß
!1
:
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s22
Impl
emen
tatio
nof
Pars
ers
Exa
mpl
e:B
otto
m-U
pA
naly
sis
Acc
ordi
ngto
"1:
Res
ulti
sa
right
deriv
atio
n.
61
© A
. P
oe
tzsch
-Heff
ter,
TU
Kais
ers
laute
rn25.04.2007
Be
isp
iel:
(Bott
om
-up
-An
aly
se
)
(
ID
+
ID
)
*
ID
+
ID
<=
(
F
+
I
D
)
*
I
D
+
I
D
<
=
(
T
+
I
D
)
*
I
D
+
I
D
<
=
(
T
+
F)
*
ID
+
ID
<=
(
T
+
T
)
*
I
D
+
I
D
<
=
(
T
+
E
)
*
I
D
+
I
D
<
=
(
E
)
*
ID
+
ID
<=
F
*
ID
+
I
D
<
=
F
*
F
+
ID
<=
F
*
T
+
ID
<=
T
+
ID
<=
T
+
F
<=
T
+
T
<=
T
+
E
<=
E
<=
S
<=
Erg
eb
nis
de
rb
u-A
na
lyse
ist
ein
e R
ech
tsa
ble
itu
ng
.
Gem
äß
!1 :
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s23
Impl
emen
tatio
nof
Pars
ers
Con
text
-free
Ana
lysi
sw
ithlin
earc
ompl
exity
•R
estri
ctio
nson
Gra
mm
ar(n
otev
ery
CFG
has
alin
earp
arse
r)•
Use
ofpu
sh-d
own
auto
mat
aor
syst
ems
ofre
curs
ive
proc
edur
es•
Usa
geof
look
ahea
dto
rem
aini
ngin
puti
nor
dert
ose
lect
next
prod
uctio
nru
leto
beap
plie
d
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s24
Impl
emen
tatio
nof
Pars
ers
Syn
tax
Ana
lysi
sM
etho
dsan
dPa
rser
Gen
erat
ors
•B
asic
Kno
wle
dge
ofS
ynta
xA
naly
sis
ises
sent
ialf
orus
eof
Pars
erG
ener
ator
s.•
Pars
erge
nera
tors
are
nota
lway
sap
plic
able
.•
Ofte
n,er
rorh
andl
ing
has
tobe
done
man
ually
.•
Met
hods
unde
rlyin
gpa
rser
gene
ratio
nis
ago
odex
ampl
efo
rage
neric
tech
niqu
e(a
nda
high
light
ofco
mpu
ters
cien
ce!).
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s25
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Top-
Dow
nS
ynta
xA
naly
sis
Edu
catio
nalO
bjec
tives
•G
ener
alP
rinci
ple
ofTo
p-D
own
Syn
tax
Ana
lysi
s•
Rec
ursi
veD
esce
ntPa
rsin
g(a
tan
Exa
mpl
e)•
Exp
ress
iven
ess
ofTo
p-D
own
Pars
ing
•B
asic
Con
cept
sof
LL(k
)Par
sing
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s26
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Rec
usiv
eD
esce
nt
Bas
icId
ea
•E
ach
non-
term
inal
Ais
asso
ciat
edw
itha
proc
edur
e.Th
ispr
oced
ure
acce
pts
apa
rtia
lsen
tenc
ede
rived
from
A.
•Th
epr
oced
ure
impl
emen
tsa
finite
auto
mat
onco
nstru
cted
from
the
prod
uctio
nsst
artin
gfro
mA
•R
ecur
sion
ofgr
amm
aris
map
ped
tom
utua
lrec
ursi
vepr
oced
ures
such
that
stac
kof
high
erpr
ogra
min
gla
ngua
ges
can
beus
edfo
rim
plem
enta
tion.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s27
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Con
stru
ctio
nof
Rec
ursi
veD
esce
ntPa
rser
Let"
" 1be
aC
FG(li
ke"
1)w
itha
term
inal
#de
notin
gth
een
dof
the
inpu
t.
"" 1: •
S&
E#
•E&
T+
E|T
•T&
F)
T|F
•F&
(E)|ID
Con
stru
ctite
mau
tom
aton
fore
ach
non-
term
inal
A.T
heite
mau
tom
aton
desc
ribes
the
anal
ysis
ofth
epr
oduc
tions
with
left
side
A.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s28
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Item
Auto
mat
a
S&
E#
64
© A
. P
oe
tzsch
-Heff
ter,
TU
Kais
ers
laute
rn25.04.2007
Ko
nstr
uktio
n e
ine
s P
ars
ers
mit d
er
Me
tho
de
de
s r
eku
rsiv
en
Ab
stie
gs (
exe
mp
larisch
):
Se
i !
‘
wie
!1, aber
mit R
and
zeic
hen #
, d.h
.
S
E #
, E
T
+ E
| T
, T
F
* T
| F
, F
(
E )
| I
D
Konstr
uie
re f
ür
jedes N
ichtt
erm
inal A
den s
og
ena
nnte
n
Item-Automaten
. E
r beschre
ibt d
ie A
naly
se d
erj
en
ige
n
Pro
duktion
en, d
ere
n lin
ke S
eite A
ist:
1
[S .E
#]
[S
E.#
][S
E
#.]
[E.T
+E
]
[E.T
]
[T.F
*T]
[ T
.F
]
[F.(
E)]
[F.I
D ]
[ET
+.E
][E
T+
E.]
[ET.+
E]
[ET.]
[ T
F.]
[TF.*
T]
[TF
*.T
][T
F*T.]
[FID.]
[F(.
E)]
[F(E.)
][F
(E).
]
E#
T+
E
F*
T
( ID
E)
E&
T+
E|T
64
© A
. P
oe
tzsch
-Heff
ter,
TU
Kais
ers
laute
rn25.04.2007
Ko
nstr
uktio
n e
ine
s P
ars
ers
mit d
er
Me
tho
de
de
s r
eku
rsiv
en
Ab
stie
gs (
exe
mp
larisch
):
Se
i !
‘
wie
!1, aber
mit R
and
zeic
hen #
, d.h
.
S
E #
, E
T
+ E
| T
, T
F
* T
| F
, F
(
E )
| I
D
Konstr
uie
re f
ür
jedes N
ichtt
erm
inal A
den s
og
ena
nnte
n
Item-Automaten
. E
r beschre
ibt d
ie A
naly
se d
erj
en
ige
n
Pro
duktion
en, d
ere
n lin
ke S
eite A
ist:
1
[S .E
#]
[S
E.#
][S
E
#.]
[E.T
+E
]
[E.T
]
[T.F
*T]
[ T
.F
]
[F.(
E)]
[F.I
D ]
[ET
+.E
][E
T+
E.]
[ET.+
E]
[ET.]
[ T
F.]
[TF.*
T]
[TF
*.T
][T
F*T.]
[FID.]
[F(.
E)]
[F(E.)
][F
(E).
]
E#
T+
E
F*
T
( ID
E)
T&
F)
T|F
64
© A
. P
oe
tzsch
-Heff
ter,
TU
Kais
ers
laute
rn25.04.2007
Ko
nstr
uktio
n e
ine
s P
ars
ers
mit d
er
Me
tho
de
de
s r
eku
rsiv
en
Ab
stie
gs (
exe
mp
larisch
):
Se
i !
‘
wie
!1, aber
mit R
and
zeic
hen #
, d.h
.
S
E #
, E
T
+ E
| T
, T
F
* T
| F
, F
(
E )
| I
D
Konstr
uie
re f
ür
jedes N
ichtt
erm
inal A
den s
og
ena
nnte
n
Item-Automaten
. E
r beschre
ibt d
ie A
naly
se d
erj
en
ige
n
Pro
duktion
en, d
ere
n lin
ke S
eite A
ist:
1
[S .E
#]
[S
E.#
][S
E
#.]
[E.T
+E
]
[E.T
]
[T.F
*T]
[ T
.F
]
[F.(
E)]
[F.I
D ]
[ET
+.E
][E
T+
E.]
[ET.+
E]
[ET.]
[ T
F.]
[TF.*
T]
[TF
*.T
][T
F*T.]
[FID.]
[F(.
E)]
[F(E.)
][F
(E).
]
E#
T+
E
F*
T
( ID
E)
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s29
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Item
Auto
mat
a(2
)
F&
(E)|ID
64
© A
. P
oe
tzsch
-Heff
ter,
TU
Kais
ers
laute
rn25.04.2007
Ko
nstr
uktio
n e
ine
s P
ars
ers
mit d
er
Me
tho
de
de
s r
eku
rsiv
en
Ab
stie
gs (
exe
mp
larisch
):
Se
i !
‘
wie
!1, aber
mit R
and
zeic
hen #
, d.h
.
S
E #
, E
T
+ E
| T
, T
F
* T
| F
, F
(
E )
| I
D
Konstr
uie
re f
ür
jedes N
ichtt
erm
inal A
den s
og
ena
nnte
n
Item-Automaten
. E
r beschre
ibt d
ie A
naly
se d
erj
en
ige
n
Pro
duktion
en, d
ere
n lin
ke S
eite A
ist:
1
[S .E
#]
[S
E.#
][S
E
#.]
[E.T
+E
]
[E.T
]
[T.F
*T]
[ T
.F
]
[F.(
E)]
[F.I
D ]
[ET
+.E
][E
T+
E.]
[ET.+
E]
[ET.]
[ T
F.]
[TF.*
T]
[TF
*.T
][T
F*T.]
[FID.]
[F(.
E)]
[F(E.)
][F
(E).
]
E#
T+
E
F*
T
( ID
E)
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s30
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Rec
ursi
veD
esce
ntPa
rsin
gP
roce
dure
s
•Ite
mAu
tom
ata
can
bem
appe
dto
recu
rsiv
epr
oced
ures
.•
The
inpu
tis
ato
ken
stre
amte
rmin
ated
by#.
•Th
eva
riabl
ecu
rrSy
mbol
cont
ains
one
toke
nlo
okah
ead,
i.e.t
hefir
stsy
mbo
loft
hest
ream
.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s31
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Rec
ursi
veD
esce
ntPa
rsin
gP
roce
dure
s(2
)
Pro
duct
ion:
S&
E#
void
S(){
E();
if(currSymbol==
’#’){
accept();
}else
{error();
}}
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s32
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Rec
ursi
veD
esce
ntPa
rsin
gP
roce
dure
s(3
)P
rodu
ctio
n:E&
T+
E|T
void
E(){
T(); if(currSymbol==
’+’){
readSymbol();
E();
}} P
rodu
ctio
n:T&
F)
T|F
void
T(){
F(); if(currSymbol==
’*’){
readSymbol();
T();
}}
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s33
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Rec
ursi
veD
esce
ntPa
rsin
gP
roce
dure
s(4
)
Pro
duct
ion:
F&
(E)|ID
void
F(){
if(currSymbol==
’(’){
readSymbol();
E();
if(currSymbol==
’)’){
readSymbol();
} else
error();
} else
if(currSymbol==
ID){
readSymbol();
} else
error();
}
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s34
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Rec
ursi
veD
esce
ntPa
rsin
gP
roce
dure
s(5
)
Rem
arks
:•
Rec
ursi
veD
esce
nt!
isre
lativ
ely
easy
toim
plem
ent
!ca
nea
sily
beus
edw
ithot
hert
asks
(see
follo
win
gex
ampl
e)!
isa
typi
cale
xam
ple
fors
ynta
x-di
rect
edm
etho
ds(s
eeal
sofo
llow
ing
exam
ple)
•E
xam
ple
uses
one
toke
nlo
okah
ead.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s35
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Rec
ursi
veD
esce
ntan
dE
valu
atio
n
Exa
mpl
e:In
terp
rete
rfor
Exp
ress
ions
usin
gre
curs
ive
desc
ent
intenv(Ident);//
ID->
int
//localvariable
int_result
stores
intermediate
results
intS(){
intint_result
:=E();
if(currSymbol==
’#’)
{return
int_result;
}else
{error();
return
error_result;
}}
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s36
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Rec
ursi
veD
esce
ntan
dE
valu
atio
n(2
)
intE(){
intint_result
:=T();
if(currSymbol==
’+’){
readSymbol();
return
int_result
+E();
}} intT(){
intint_result
:=F();
if(currSymbol==
’*’){
readSymbol();
return
int_result
*T();
}}
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s37
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Rec
ursi
veD
esce
ntan
dE
valu
atio
n(3
)
intF(){
intint_result;
if(currSymbol==
’(’){
readSymbol();
int_result
:=E();
if(currSymbol==
’)’){
readSymbol();
return
int_result;
}else
{error();
return
error_result;}
} else
if(currSymbol==
ID){
readSymbol();
return
env(code(ID));
}else
{error();
return
error_result;}
}In
aS
chae
fer
Con
text
-Fre
eA
naly
sis
38
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Rec
ursi
veD
esce
ntan
dE
valu
atio
n(4
)
•E
xten
sion
ofPa
rser
with
Act
ions
/Com
puta
tions
can
easi
lybe
impl
emen
ted,
butm
ixin
gof
conc
eptu
ally
diffe
rent
task
san
dca
uses
prog
ram
sha
rdto
mai
ntai
n.•
Forw
hich
gram
mar
sdo
esth
ere
curs
ive
desc
entt
echn
ique
wor
k?&
LL(k
)Par
sing
Theo
ry
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s39
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
LLPa
rsin
g
•B
asis
forT
own-
Dow
nS
ynta
xA
naly
sis
•Fi
rstL
:Rea
dIn
putf
rom
Left
toR
ight
•S
econ
dL:
Sea
rch
forL
eftD
eriv
atio
ns
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s40
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
LL(k
)Gra
mm
ars
Defi
nitio
n(L
L(k)
Gra
mm
ar)
Let"
=(
N,T
,!,S
)be
aC
FGan
dk%
N.
"is
anLL
(k)g
ram
mar
,iff
oran
ytw
ole
ftde
rivat
ions
S'
! lmuA
!'
lmu"
!'
! lmux
and
S'
! lmuA
!'
lmu#
!'
! lmuy
itho
lds
that
ifpr
efix(
k,x)
=pr
efix(
k,y)
then
"=
#.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s41
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
LL(k
)Gra
mm
ars
(2)
Rem
arks
:•
Agr
amm
aris
anLL
(k)g
ram
mar
iffo
rale
ftde
rivat
ion
with
kto
ken
look
ahea
dth
eco
rrec
tpro
duct
ion
fort
hene
xtde
rivat
ion
step
can
befo
und.
•A
Lang
uage
L*
#!
isLL
(k)i
fthe
reex
ists
LL(k
)gra
mm
ar"
with
L(")
=L.
•Th
ede
finiti
onof
LL(k
)gra
mm
ars
prov
ides
nom
etho
dto
test
ifa
gram
mar
has
the
LL(k
)pro
pert
y.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s42
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Non
LL(k
)Gra
mm
ars
Exa
mpl
e1:
Gra
mm
arw
ithLe
ftR
ecur
sion
"2:
•S&
E#
•E&
E+
T|T
•T&
T)
F|F
•F&
(E)|ID
Elim
inat
ion
ofLe
ftR
ecur
sion
:R
epla
cepr
oduc
tions
offo
rmA&
A!|"
whe
re"
does
nots
tart
with
Aby
A&
"A"an
dA"&
!A" |(
.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s43
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Non
LL(k
)Gra
mm
ars
(2)
Elim
inat
ion
ofLe
ftR
ecur
sion
:Fr
om"
2w
eob
tain
"3.
"2: •
S&
E#
•E&
E+
T|T
•T&
T)
F|F
•F&
(E)|ID
"3
•S&
E#
•E&
TE"
•E"&
+TE
" |(•
T&
FT"
•T"&)F
T|(
•F&
(E)|ID
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s44
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Non
LL(k
)Gra
mm
ars
(3)
Exa
mpl
e2:
Gra
mm
ar"
4w
ithun
limite
dlo
okah
ead
•S
TM&
VAR
:=VA
R|ID
(ID
LIS
T)
•VA
R&
ID|ID
(ID
LIS
T)
•ID
LIS
T&
ID|ID
,ID
LIS
T
"4
isno
tan
LL(k
)gra
mm
arfo
rany
k.(P
roof
:cf.
Wilh
elm
,Mau
rer,
Exa
mpl
e8.
3.4,
p.31
9)
Tran
sfor
mat
ion
toLL
(2)g
ram
mar
"" 4:
•S
TM&
AS
S_C
ALL
|ID:=
VAR
•A
SS
_CA
LL&
ID(I
DLI
ST
)AS
S_C
ALL
_RE
ST
•A
SS
_CA
LL_R
ES
T&
:=VA
R|(
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s45
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Non
LL(k
)Gra
mm
ars
(4)
Rem
ark:
The
trans
form
edgr
amm
ars
acce
ptth
esa
me
lang
uage
,but
prov
ide
othe
rsyn
tax
trees
.
From
ath
eore
tical
poin
tofv
iew
,thi
sis
acce
ptab
le.
From
apr
ogra
mm
ing
lang
uage
impl
emen
tatio
npe
rspe
ctiv
e,th
isis
inge
nera
lnot
acce
ptab
le.
Ther
ear
ela
ngua
ges
Lfo
rwhi
chno
LL(k
)gra
mm
ar"
exis
tsth
atge
nera
tes
the
lang
uage
,i.e
.L("
)=
L.(E
xam
ple:
Gra
mm
ar"
5)
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s46
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Non
LL(k
)Gra
mm
ars
(5)
Exa
mpl
e3:
ForL
("5)
,the
reex
ists
noLL
(k)g
ram
mar
.
•S&
A|B
•A&
aAb|
0•
B&
aBbb
|1
We
show
that
ther
eis
nok
such
that
"5
isan
LL(k
)gr
amm
ar.
Pro
of.
Letk
bear
bitra
rybu
tfixe
d.C
hoos
etw
ode
rivat
ions
acco
rdin
gto
the
LL(k
)defi
nitio
nan
dsh
owth
atde
sipi
teof
equa
lpre
fixes
ofle
ngth
kth
ere
suts
from
"an
d#
are
note
qual
:
S'
! lmS'
Alm'
! lmak
0bk
S'
! lmS'
lmB'
! lmak
1b2k
Then
:pre
fix(k
,ak0b
k)
=pr
efix(
k,ak
1b2k
)=
ak,b
ut"
=A+=
B=
#.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s47
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
FIR
ST
and
FOLL
OW
Set
s
Defi
nitio
nLe
t"=
(N
,T,!
,S)
bea
CFG
,k%
N.T
#k
={u%
T!|le
ngth
(u),
k}de
note
sal
lpre
fixes
ofle
ngth
atle
astk
.
We
defin
e:•
FIR
ST k
:(N$
T)!&
P(T
#k)
with
FIR
ST k
(!)
={p
refix
(k,u
)|!'
!u}
whe
repr
efix(
n,u)
=u
fora
llu
with
leng
th(U
),
n.•
FOLL
OW
k:(N$
T)!&
P(T
#k)
with
FOLL
OW
k(!
)=
{w|S'
!"!#-
w%
FIR
ST k
(#)}
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s48
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
FIR
ST
and
FOLL
OW
Set
sin
Pars
eTr
ees
XS
FIRSTk(X)
FOLLOWk(X)
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s49
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Cha
ract
eriz
atio
nof
LL(1
)Gra
mm
ars
Defi
nitio
n(R
educ
edC
FG)
AC
FG"
=(N
,T,!
,S)
isre
duce
dif
each
non-
term
inal
occu
rsin
ade
rivat
ion
and
each
non-
term
inal
deriv
esat
leas
tone
wor
d.
Lem
ma
Are
duce
dC
FGis
LL(1
)if-a
nd-o
nly-
iffo
rany
two
prod
uctio
nsA&
"an
dA&
#it
hold
sth
at
FIR
ST 1
(").
1FO
LLO
W1(
A)!
FIR
ST 1
(#).
1FO
LLO
W1(
A)
="
whe
reL 1.
1L 2
={p
refix
(1,v
w)|v%
L 1,w
%L 2
}
Rem
ark:
FIR
ST
and
FOLL
OW
sets
are
com
puta
ble,
such
this
crite
rion
can
bech
ecke
dau
tom
atic
ally.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s50
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Exa
mpl
es:F
IRS
T kan
dFO
LLO
Wk
Che
ckth
atm
odifi
edex
pres
sion
gram
mar
"3
isLL
(1).
•S&
E#
•E&
TE"
•E"&
+TE
" |(•
T&
FT"
•T"&)F
T|(
•F&
(E)|ID
Com
pute
FIR
ST 1
and
FOLL
OW
1fo
reac
hno
n-te
rmin
al.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s51
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Exa
mpl
es:F
IRS
T kan
dFO
LLO
Wk
(2)
•F&
(E)|ID
:FI
1((E
)).
1FO
LLO
W1(
F)!
FIR
ST 1
(ID
).
FOLL
OW
1(F
)=
{(}.
1FO
LLO
W1(
F)!{I
D}.
FOLL
OW
1(F
)=
"•
E"&
+TE
" |(:
FIR
ST 1
(+TE
" ).
1FO
LLO
W1(
E" )!
FIR
ST 1
(().
FOLL
OW
1(E" )
={+
}.
1FO
LLO
W1(
E" )!{(}.
FOLL
OW
1(E" )
={+
}!{
#,)}
="
•T"&)F
T|(
:FI
RS
T 1()
FT" ).
1FO
LLO
W1(
T" )!
FIR
ST 1
(().
FOLL
OW
1(T" )
={)
}.
1FO
LLO
W1(
T" )!{(}.
FOLL
OW
1(T" )
={)
}!{+
,#,)}
="
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s52
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Pro
ofof
LLC
hara
cter
izat
ion
Lem
ma
•Le
ft-T
o-R
ight
Dir
ectio
n:"
isLL
(1)i
mpl
ies
FIR
ST
and
FOLL
OW
char
acte
rizat
ion.
Pro
ofby
Con
trad
ictio
n:S
uppo
setw
opr
oduc
tions
A&
"an
dA&
#w
ith"+=
#an
d$
=FI
RS
T 1("
).
1FO
LLO
W1(
A)!
FIR
ST 1
(#).
1FO
LLO
W1(
A)+=".
Then
ther
eex
ists
z%
$w
ithle
ngth
(z)
=1.
As
"is
redu
ced,
ther
ear
etw
ode
rivat
ions
:
S'
!$
A!'
$"!'
!$
zxS'
!$
A!'
$#!'
!$
zy
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s53
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Pro
ofof
LLC
hara
cter
izat
ion
Lem
ma
(2)
Thus
,we
can
cons
truct
the
follo
win
gle
ftde
rivat
ions
:
S'
! lmuA
!'
lmu"
!'
! lmuz
xS'
! lmuA
!'
lmu#
!'
! lmuz
y
with
prefi
x(1,
zx)
=z
=pr
efix(
1,zy
)w
hich
cont
radi
cts
the
LL(1
)pr
oper
tyof
".
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s54
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Pro
ofof
LLC
hara
cter
izat
ion
Lem
ma
(3)
•R
ight
-To-
Left
Dir
ectio
n:FI
RS
Tan
dFO
LLO
Wch
arac
teriz
atio
nim
plie
s"
isLL
(1).
Pro
ofby
Con
trad
ictio
n:S
uppo
se"
isno
tLL(
1).T
hen
ther
ear
etw
odi
ffere
ntde
rivat
ions
with
leng
th(z
)=
1:
S'
!$
A!'
$"!'
!$
zxS'
!$
A!'
$#!'
!$
zy
But
z%
FIR
ST 1
(").
1FI
RS
T 1(#
)w
hich
isa
cont
radi
ctio
n.
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s55
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Pars
erG
ener
atio
nfo
rLL(
k)La
ngua
ges
LL(k
) Par
ser
Gen
erat
or
Gra
mm
ar
Table
for
Push
-Dow
n A
uto
mat
on/
Par
ser
Pro
gram
Err
or:
G
ram
mar
is
not
LL(k
)
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s56
Impl
emen
tatio
nof
Pars
ers
Top-
Dow
nS
ynta
xA
naly
sis
Pars
erG
ener
atio
nfo
rLL(
k)La
ngua
ges
(2)
Rem
arks
:•
Use
ofpu
sh-d
own
auto
mat
aw
ithlo
okah
ead
•S
elec
tPro
duct
ion
from
Tabl
es•
Adv
anta
ges
over
botto
m-u
pte
chni
ques
iner
rora
naly
sis
and
erro
rha
ndlin
g
Exa
mpl
eS
yste
m:
AN
TLR
(htt
p://
www.
antl
r.or
g/)
Rec
omm
ende
dR
eadi
ngfo
rTo
p-D
own
Ana
lysi
s:•
Wilh
elm
,Mau
rer:
Cha
pter
8,S
ectio
ns8.
3.1.
toS
ectio
ns8.
3.4,
pp.
312
-329
Ina
Sch
aefe
rC
onte
xt-F
ree
Ana
lysi
s57
