Como Construir um Compilador Utilizando Ferramentas Java€¦ · !0/ i i i i i i i i Como Construir...

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Como Construirum Compilador

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Como Construirum Compilador

UtilizandoFerramentas Java

Márcio Delamaro

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• ´ V'"µ=m• ´ V'"Vª$V /V Vªo$V V¼qV V V 7µ=m• ´ V BV V'C.C'C.V _µ=m• ´ V$BVLBVtµC4 ;^+M'+W<+e%: 5 ;$@RW\MH¦§L+: 5 ]FU9Wi; 5 ;$@RWi`M':878CØ= 5 :G+p E @Y%Rde E :G6 5 e%:G+g: 5

5 :8+78W 5 M.+:G7U):G+W RW E .e Ç +; 5 ;$'1+7 EG5 ;Y%R>M.3Y%R3 E :8W 5%E 5E :GRWi; 5E iR E 7^Y%Ra 5 ;$>7GK»:G+7d 5 W 5JE 'eÆe.W 5 M' 5 5 W 5 >7U :8+78 CB· E8E 'WV 5 Y%R7G: 5 M.¦§t: 5 5E8E R<M.+:G7U E NV³+V³b¶iù EGE E ;R E HM.:G'Wi E 5 W :87I E >7U:G+78 E ú C

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½^WibLMKI1%7U 5 R#>;$>' E5 7G»RW M.¦§t: 5Σ]»RWi:8RMK 5 78;$>e;;$»M':878 E ;$

ΣC

fZ5 7`+g>W<M 5

• 〈0, 1, 0, 1, 1, 0〉]RWi)MKI178 E5 78 ´ V'"µ&m

• 〈2, 1, 0, 8〉]RWi0LMKI1%7U E5 7G ´ V."V V /V LV oV Vªq$V V µ&m

• 〈c, o, m, p, i, l, e, r〉]RWi)MKI178 E5 78 ´ V BV.C'C'C.V$_µ&m

• 〈a, ab, b, abc〉]JRWi<M'I17U EG5 78 ´ VBVLBVtµC

?dW +7UMXVy 5 ;$>W 5E 78+78 E +e%:87»RWiäM'I17UÍt+eL E M.R$:8.eLe; 5 Vye 5 7U;$+W 5 7Gp78:8V E M':878 E Y%Rb< 5 W< È >WäC fZ5 7`g$+W<M 5 V$ 5 ;$+W 5E E +7G>1>7

• 〈0, 1, 0, 1, 1, 0〉 5 W 5 2&020&02­m

• 〈2, 1, 0, 8〉 5 W 5p· 0&2¸³m

• 〈c, o, m, p, i, l, e, r〉 5 W 5 !19tü± C

fZ5 78]+WV〈a, ab, b, abc〉

eLT 5 5 ;$ E >7078+7G E >e:U; E 'W)M. E W<+e%:8z 5 7&'+V6 5 E E8E 78+7G E >e:US>T 5 5 ;$>7GK(.e;'>7 5 R$:G7U E M'I17U E M']+W ;Y%R>M'Y%R^; E *vW 5%E 7G>7G+pE +e%:87>Vy 5 W 5 VP 5 7 +g$+W<M 5 V

〈a, a, b, abc〉C=» E8E <+ E5 Vt 5 ;$+W 5%E R$:8.M''_>7J E S 5%E +e%:87G

E M.+:G7U E 7U.eL;$'>7) 5 W 5 E +787*i E M':878 E ;&MKI178C·îMKI178〈a, ab, b, abc〉E +78'VL>e:UT 5 VL78+78 E +e%:U;i 5 W 5 p,¶3)iLMKI1%7U

〈a, a, b, abc〉Vt 5 W 5 #+C

= 5 :G+p E V$ 5 78]+WVY%R 5E E S 5%E eLT 5 ¦§_>+WîL7G:G;)MKI178Cû» Ç e+p E 5 :8Wie9 5 ;$FRWi(MKI178¥¹àù;$+e 5 :8; 5 5 7

|x|úZ 5 W 5 5 eXHW<+7 5 ;FM':878 E

;$"¹$Ck= 5%E g$+W<M 5E e:8+78 5 7G E V:G>7 â W 5%E

• |010110| = 6m

• |2108| = 4m

• |compiler| = 8m

• |a ab b abc| = 4C

m 5 7G)YRLMKYR+7»MH¦§L+: 5ΣVP;$ Ç ep E 3RWi¶He'>iM'I17Ui;$b:UWie9 5 ÍY%R3;+e 5 p

:8W 5E 5 7λCdû» Ç e+W)p E V$:8W3t]+WV 5%E 5 ev*Re%: 5E

• Σk º ´ M'I17U E ¹ E5 7GΣ | |x| = k

µ&m

• Σ∗ =

∞⋃

k=0

Σk = Σ0 ∪ Σ1 ∪ Σ2...m

• Σ+ = Σ∗ − λC

4 9+%W 5E Vy+e%:UT 5 V J ;$ Ç e'S>T 5 ; 5 Y%R0]<RWizM.'eR+W ;; 5ä5 MH¦§L+: 5ΣVBRWi

M'.eR+W¼» EG5 7GΣ]@RW E RP 5 ev*Re%: 5 Y%RM'Y%R>7Ø;$

Σ∗CÌök*vW 5EØ5E g$+W<M 5E E +R.7NC

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• ´ Vy"V V "Vy"N Vy""µ(]JRWi<M'.eR+W EG5 7G ´ V."µ(Y%Rb 5 e%:G]>W E > E LMKI1%7U E m• ´ x ∈ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9∗ | x

78+7G E >e:U3RWîeXHW<+7 5 ;$>+.WiM â W<7'µ]RWiM''eR>W E5 78 ´ V'"Vª$V /V Vªo$V V¼qV V 7µ» 5 WRW¨e=HW)>7 5 'e Ç e.: 5 ;$LMKI1%7U E m

•5 5 ev*Re%: 5 ;$(: 5 ; 5EF5E 7 5 78W< E °%I1b1­M''; 5E ù E .e%:U:GK+W<+e%:GJ 5 7G78: 5E úk]JRWiM''eR>W E5 78 RW«M.¦§t: 5

Σ 5 W< 5%E : 5 ;

ìM'I17U E 7G E >7G1; E 5 W 5#À VÁ#Â[µ Á LVµ À :UCì EGâ W0 5 M 5%E E LNK E 5 W 5 ÄÃ V:ÅtV5Æ +:8Cìe 5 W) E ;$178'­I1+ E V%W<]: 5 ; 5E VMK E8E E :8C

f 7U; Ç e'78W 5%E ¦ 5 78W<M.W<>e:8RWi-M''eR>W ;$7 5 78W<S+T 5 Vk;$+1+W 5E V@>e%:8T 5 V;$ Ç e'7JY%RM 5 MH¦§L+: 5E5 78 5 Y%RMZ E8E #M'.eR+Wæ])¦ 5 78Wi;Íi;$ Ç e.7Y%R EJE T 5 EM'I17U E 1­M.K; E 78» E8E M'.eR+WCØ= E 78¯Ig$.Wi E[E >S È E 1+78+W 5E M'RW< E Wie+'78 E;$J¦§_++7a EGEG5 C

2.2 Gramática livre de contexto?dW\>78MVNRWi^M''eR>Wê;$67 5 7UWiS+T 5 t+7G:G+eL6^RWi»MK E8E @;$@M''eR>e E U9W<p; E ;$dM''eR>e E M'.178 E ;@ 5 e:8g: 5 C̽^Wi ; E Wie+'78 E ;$ E @; Ç e'78+W :8 E M''eR>e E]F 5 7kW)> 5 ; E 78Wi­:GK+ E M'.178 E ;$` 5 e%:Gg: 5 Cؽ»Wi»78W<­:GK+»M.'17Ga;$` 5 e:8g: 5 ù¹JA 4 ú]JRWiiY%R­;$78RMK

〈Ω, Σ, S, P 〉V 5 e;$

ΣuÍ] 5 M.¦§t: 5<EG5 7G 5 Y%RMB)M'.eR+W];$ Ç eK;m

ΩuÍ]JRW« 5 ev*Re%: 5 eT 5 1_> 5 ;$ EGâ W3 5 M 5E eT 5 :8+78W)'e E m

Pu#]RW« 5 ev*Re%: 5 ;$7 5 ;$RS È E ;)¦ 5 78W<

A → αV 5 eL;$

A ∈ Ω

α ∈ (Σ ∪ Ω)∗m

Su#] 5iEGâ W0 5 M 5 'e'+'MB;)7UWi­:8'>V

S ∈ ΩC

¤Q 5 ev*Re%: 5Σ;FRW< 7UWi­:GK+`] 5 M.¦§t: 5JEG5 78 5 Y%RM$ E M'I17U E ;»M''eR>W

;$ E v; E T 5 ¦ 5 78Wi; E Cz= 5 5 e%:G+g%: 5 ;$z¹JA 4FE VZ 5E :GRW<p E iU9Wi7 5E >M.>W)>e%: 5E ;$Σ;$ EGâ W0 5 M 5%E :G>7GW<'e E C^¤ 5 ev*Re%: 5

Ω]b;$ E v*Re%: 5 ;$

ΣC m +R E +M'+W<+e%: 5E eT 5 +e%:G7UW

e0¦ 5 78WiS>T 5 ; E >;$>' E ;<M.'eRL>WC m T 5 R$:G'M'._N; 5%E 5 W 5iEGâ W0 5 M 5%E R$g$.M'K78 E 7U;$ Ç e'7G>W0p E J E 7 5 ;RS È E ;<78Wi­:GK+C· E 7 5 ;$RLS È E

PE T 5 78+78 E ;$ E R E :8H:8RKS+T 5 Y%R<:I+Wÿ; 5 M'; 5 E Y%R+7U; 5 ; 5

→RW

EGâ W0 5 M 5 eT 5 :G+78W<.eLMP ; 5 MK; 5 ;$.78+.: 5 VRWi0>;$>'b¦ 5 78W<; 5 7 EGâ W0 5 M 5%E :8+78W)'e E EGâ W0 5 M 5%E eT 5 :G>7GW<'e Ed5 R

λCd·Ê7G:G'76; 50EGâ W0 5 M 5 'eKKM

SV% E8E E 78+7U EkE T 5 M''>; E

E R E :G.:GR'e; 5 p E 5 eT 5 p:8+78W<.eM[Y%R<L78>0; 5 MK; 5 E Y%R+7U; 5 ;$0RW<z7 5 ;$RS+T 5 t+MKM'I17U)Y%R3 E :8­#; 5 M'; 5 ;$'7G>H: 5 ;$ E :8C m 3iLMKI1%7U 5 $:8';i 5%EGE R E5 W)>e%:G EGâ W0 5 M 5%E:G>7GW<'e E V@+e%:UT 5 E8E M'I17Ut+7G:G+eL J M.'eRL>W ;$ Ç e';L>M'7UWi­:GK+C m +;$+K 5 $:GK;ä 5 e:8]+W .e; EGâ W0 5 M 5%E eT 5 :G+78W<.eL E Vy>e:UT 5 e 5 1ù E ú E R E :8H:8R'S>T 5 ù È E ú;$>1ù§W#ú E +7»¦ +.:8ù E ú :8]0Y%R E )U9+R0ÍRWiÍ>;$>'#Y%R0:G>e9zt+e E EGâ W0 5 M 5%E :8+7GpW<.eL E CödW 5E : 5 Wi7^ 5 W 5 +g>W<M 5 <78W<­:GK+

G1 = 〈S, A, B, a, b, c, S, P 〉V 5 e;$

P]

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(1) S → AB(2) A → aAb(3) A → λ(4) B → cB(5) B → λ

· E8E 'WV$b7:8.7F; 50EGâ W0 5 M 5 .e'+'MS 5 ;$+W 5%E M.K+7@RWi E NY&kI+e+'b; 7 5 ;$RS È E

;$P:8]äY%RäRWi&>;$>'¹\Y%Rä 5E8E R&t+e E0EGâ W0 5 M 5%E :8+78W<.e E)E *vMK+eLS+;C

?de%:8T 5 ¹ñL>7:8+e+ J M'.eR+W ;$ Ç e';ä 5 7G1

V 5 Y%R< 5 ;$>W 5%E ;$+e 5 :87b 5 W 5 x ∈

L(G1)C f[5 7`g$+W<M 5 l eKKW 5E 5 W

SM.K+W 5E ù*"Iú 5 :G+W 5%E

AB:G>W 5%EAB

M.K+W 5%E ù§/%ú 5 $:8+W 5EB:G>W 5%E

BM.K+W 5E ùoú 5 :G+W 5%E

λ ∈ L(G1)

l eKKW 5E 5 WS

M.K+W 5E ù*"Iú 5 :G+W 5%EAB:G>W 5%E

ABM.K+W 5%E ùú 5 $:8+W 5E

aAbB:G>W 5%EaAbB

M'K+W 5%E ùú 5 $:8+W 5EaaAbbB:G>W 5%E

aaAbbBM'K+W 5%E ù§/ú 5 $:8+W 5E

aabbB:G>W 5%EaabbB

M'K+W 5%E ù %ú 5 $:8+W 5EaabbcB:G>W 5%E

aabbcBM'K+W 5%E ù %ú 5 $:8+W 5E

aabbccB:G>W 5%EaabbccB

M''>W 5E ùXoú 5 $:G>W 5Eaabbcc ∈ L(G1)

fZ5 ;p E J¦§'M.W<+e%:8be 5 :U7^Y%R|L(G1)| = ∞

VL 5 E ;$+t+eL;$+e; 5 ; 5 eXHW<+7 5 ;$b1>_+ EY%R E T 5 M.K+; E E 7 5 ;RS È E ùúd<ù ú V$ 5 ;$+W E +7a78K; E M'I17U E ;»:UWie9 5 :8T 57UeL;$(Y%Re%: 5iE ;$ E v*C

4 ;RW<¬; E MKI178 E 'e%:G>7GW<>;'­7GK E +7U; E :G] E U9>7 J MKI178Y%R E ¯ 5 e%:G]+Wÿ:8+78W)'e E ]U9Wi;;$RWi¦ 5 7GWi E +e%:8+e+'MC m äRWi+;+K

β 5 ;$ E >7

5 :GK;ÍiL7G:G'7 ;#¦ 5 78W< E >e:8+e+'MαW<>;$Ke%:80ÍM''>S+T 5 ;$3RW<,HeK+Í7 5 ;$RLS+T 5 V

;$'_+>W 5%E Y%Rα;$+78.1;$'78:8W<+e%:G

βV 5 RY%R

β]Í;$+78'1I;;$'7G+:8W)>e%:G#;$

αV 5 YR

;$>e 5 :UW 5E 5 7α ⇒ β

C m β 5 ;$ E +7 5 $:GK;W<N;$'e%:GÍM''>S+T 5 ;$#RW´eXHW<+7 5

Ç e.: 5 ;(7 5 ;$RS È E V;$._>+W 5E Y%Rα;$+78.1

βb;$+e 5 :8W 5%E

α∗

⇒ βC

465 W 5 iM'.eR+WL(G)

Vt;$ Ç eK;<t+MKi7UWi­:8'>)M.'17Gb;$b 5 e%:G+g: 5G = 〈Ω, Σ, S,

P 〉V(] 5 5 ev*Re%: 5 ;$-: 5 ; E E MKI178 E ¦ 5 78Wi; E L>e E 5 7+M'+W<+e%: 5E ;$

ΣYR

5 ;+W E +7<;$+78.1; E 7:8.7<; 5-EGâ W3 5 M 5 'e'+'MSVk E8E5 >Y%R'1M'z;$'_+>7)Y%R

L(G) =

x ∈ Σ∗ | S∗

⇒ xC

2.3 Forma de Backus-Naur·¬j 5 78W<»;$ n UºR E pr= R7dù n =»jkúy]dRW< 5 R$:878aWie+'78`; E 6;$ Ç e.7ØM.'eRL>e E M'.178 E ;$ 5 e%:Gg: 5 CB?dMK ] E +W<+M'9e:86»RWi»78W<­:GK+`M''1%786;6 5 e%:Gg: 5 VWi E L>7GW<.:GaY%R 5 M'; 5;$'7G>H: 5 ; E 7 5 ;RS È E 5%EGE RM.Re Ek5 L>78; 5 78 E CÌ? E8E Ed5 L>78; 5 78 EkE +7UT 5 7G E >e%:8; 5E E >R'7NC

ÞÌ Á ¢£(α | β)

u½^W ; 5E >M.>W<+e%: 5%E +e%:87Gz7I+e%:G E E ùα5 R

βú 5 ;$ E +70R$:G'M'._N; 5 eL

M''>S+T 5 ;07 5 ;$RS>T 5 C

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">/

fZ5 7`g$>W)M 5 V E J:8.1] E8E >W 5%E 07 5 ;$RS>T 5

S → a(b | c | d)e

5 ;+7 â W 5%E :G+7 E ;$>7G'1S È E

S ⇒ abeS ⇒ aceS ⇒ ade

5 Y%R E 'e Ç >0Y%Rb)M'.eR+W +7U;0]abe, ace, ade

C½^Wi#¹JA 4 >Y%R'1M'+e%:G) E8E n =»j E >7GK

S → abeS → aceS → ade

ök*vW 5%E`5 R:G7 5 +g>W<M 5

S → (c(aSa | bSb)c | λ)

>78)+;$+K E ; 5 :8. 5 S ⇒ caSac ⇒ cacaSacac ⇒ cacacbSbcacac ⇒ cacacbbcacac

=^ EGE b+ E5 Vi¹JA 4 NYR.1M'+e%:8 E +78K

S → λS → caSacS → cbSbc

Ç<6µ t Á[α]

uͤY%R E :8.1+7a+e%:87G 5E 5 M'U9:G E 5 ;$ E +7aR$:G'M'._N; 5)5 RäeT 5 e)M'K+S>T 5 ;7 5 ;$RS>T 5 C

fZ5 7`g$>W)M 5 V E J:8.1] E8E >W 5%E 07 5 ;$RS>T 5

S → a[bcd]e

5 ;+7 â W 5%E :G+7 E ;$>7G'1S È E

S ⇒ aeS ⇒ abcde

5 Y%R E 'e Ç >0Y%Rb)M'.eR+W +7U;0]ae, abcde

Cök*vW 5%E`5 R:G7 5 +g>W<M 5

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S → a[(A | B)c]dA → a[a]B → [b]

>78) E >;$>' E

S ⇒ adS ⇒ aAcd ⇒ aacdS ⇒ aAcd ⇒ aaacdS ⇒ aBcd ⇒ abcdS ⇒ aBcd ⇒ acd

5 R E vVP>78#ÍM.'eR+Wad, aacd, aaacd, abcd, acd

C ½»W<ä¹JA 4 NY%R.1M.>e:80Í E8E n =»j E >7GK

S → adS → aAcdS → aBcdA → aaA → aB → bB → λ

= 5 :G».e;YR^RWiJ7 5 ;RS+T 5 ; 5 :G' 5α → β[γ]δ

] E >W<7G»>Y%R'1IM.>e%:G J 7 5 ;$RS+T 5α → β(γ | λ)δ

C

È %@ µ ¢£ t¡ ¶àµÂ3t=ÉÂ(α)∗

u,¤¨YRÍ E :G'1>7b+e%:87G#L7I+e%:G E i 5 ;$ E +70R E ; 5 RW´eXHW<+7 5 Y%RMKY%R+7);$1+_> E eL`M''>S>T 5 ;a7 5 ;$RS>T 5 d 5 ;$d:UW3t]+WêeT 5^E >7ÌR E ; 5 ù§7G>L+:GK; 5 e>e9RWi1+_Iú C

fZ5 7`g$>W)M 5 V E J:8.1] E8E >W 5%E 07 5 ;$RS>T 5

S → a(b)∗c

:G>7 â W 5%E 5 W 5 7G E RMH:U; 5 )M.'eRL>W ´ VtVPVPVBC'C'C4µ%C465 W 5 Y%RMKY%R+7 5 R$:G7U n = jFV 5 ;$>W 5E >e 5 e:8787aRWi#¹JA 4 5 7878 E 5 e;$+e%:8V$ 5 W 5 V

5 7`g$>W)M 5

S → aZcZ → bZZ → λ

465 W 5<5 R$:87 5 +g>W<M 5 V$ 5 ;$>W 5E :G>7» n =»jF

S → a(b | c)∗d

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Y%Rb+7U): 5 ; E E >;$>' E Y%Rb'eKKW 5 WaV:G>7GW<'eW 5 W

db:I+W«+e%:G78b E :G E^5

λ5 RY%RMKY%R+7^>;$>'3¦ 5 78Wi;) 5 7b

cC

È %@ µ ¢£Ñt¡ ¶àµÂ3t=ÉÂ(α)+

uQ¤æY%R E :G'1>7i+e%:G787I+e%:8 E ä 5 ;$ E +7iR E ; 5 RWi 5 RQWi E 1>_+ E eM''>S+T 5 ;07 5 ;$RS>T 5 CZ· 7 5 ;$RS>T 5

α → β(γ)+δ](NY%R.1M.>e:8b

α → βγ(γ)∗δC

· E >R'7>VR$:8.M''_>78+W 5%E n =»j780;$ Ç e.7^3e 5E8E 3M.'eR+WX++

C m >78­3¦ +:GR;RWi;$ E 78KS+T 5 ;$iYRL E(E T 5 E E :87GR$:8R7U E ;zM.'eRL>Wæ7G>78 E +e%:8; E +W >;zRWi; E 7 5 ;$RLS È E C

2.4 BNF para a linguagem X++

= 5%EGE -M.'eRL>W´] 5 e E :G78R â ; E5 7GäRWiM.¦§t: 5 Y%Rä 5%EGE R EGâ W0 5 M 5%E YRz 5 ;$+WE +7 5 e$¦ Re;$K; 5E 5 W 5%E W<:U E8Eâ W3 5 M 5E R$:G'M.'_>; 5E 5 W 5Í5 t+7U; 5 7G E eie 5 :8S+T 5 n = j6V 5 W 5 V$ 5 7`g$>W)M 5 V

[

]C fZ5 7` E8E5 V$1IW 5E ; 5 :87` E +R'e:8 5 e1+eS>T 5

• 〈symbol〉78+7G E >e:U 5 eT 5 pX:G>7GW<'eM

symbolm

•EGâ W3 5 M 5E :G>7GW<'e E`E T 5 7G>7G E >e%:8; 5E 5 WË E W3 5 MHm

•W<+:8 E8EGâ W0 5 M 5%E ;)e 5 :US+T 5 n = j E T 5 7G>7G E >e%:8; 5E 7U¦§; 5E 5 W

[ ]C

l eKK78+W 5E ; Ç eKS+T 5 L>M 50Eâ W3 5 M 5 .e'+'ML; n =»jFVY%R`7G>78 E +e%:8J E :87GR$:8R7U;$RW¨7 5 7UWib E +7G.: 5 +W

X++C

〈program〉 → [ 〈classlist〉 ]

? E8E <eT 5 pX:G+78W<.eLM[.e;'>zY%R)RW 7 5 78Wi<+WX++

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〈classlist〉 → ( 〈classdecl〉 )+

5 R

〈classlist〉 → 〈classdecl〉 [ 〈classlist〉 ]

¤òeLT 5 pX:G>7GW<'eMclasslist

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`&h=^iXiÊ^¡ËZXZXZXZÌ`&h=^iXig¼ËZXZXZXZÌZXZXZ=Z`&h=^iXi¤`ËZXZXZXZÌ

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〈classdecl〉 → “class′′ “ident′′ [ “extends′′ “ident′′ ] 〈classbody〉

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extends 5 e 5 W)b; E Rt+7UMK E8E (;

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〈classbody〉 → “′′ [ 〈classlist〉 ] ( 〈vardecl〉 “;′′ )∗

( 〈constructdecl〉 )∗ ( 〈methoddecl〉 )∗ “′′

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vardeclVconstructdecl

methoddecl

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vardeclVI] E >W<+M'9e%:G

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〈vardecl〉 → ( “int′′ | “string′′ | “ident′′ ) “ident′′ ( “[′′ “]′′ )∗

( “,′′ “ident′′ ( “[′′ “]′′ )∗ )∗

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intVstring

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classbodyV$L¯ E +;)78KS+T 5 ;$RW

vardeclC

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〈constructdecl〉 → “constructor′′ 〈methodbody〉〈methoddecl〉 → ( “int′′ | “string′′ | “ident′′ ) ( “[′′ “]′′ )∗

“ident′′ 〈methodbody〉

· ;$NMK7US+T 5 ;$iRW 5 e E :G78R$: 5 7J 5 W<>S> 5 WÿäMKI178constructor

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constructorV»'eKKp E 5

5 7G 5 ; 5 5 e E :G78R$: 5 7>V7G>7G E >e%:8; 5 L>M 5 eT 5 pX:G+78W<.eLMmethodbody

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〈methodbody〉 → “(′′ 〈paramlist〉 “)′′ 〈statement〉

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paramlistCZ· E +Re;)7:8 E T 5<5%E 5 Wie; 5E Y%R 5 W< È +W 5 W)]+: 5 ; 5 C

〈paramlist〉 → [ ( “int′′ | “string′′ | “ident′′ ) “ident′′ ( “[′′ “]′′ )∗

( “,′′ ( “int′′ | “string′′ | “ident′′ ) “ident′′

( “[′′ “]′′ )∗ ]

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statementC l EGEG5(E 'e Ç +(Y%Ra E8E »7G:G

]0 5 W< 5E :8Í;0RWÎHe' 5 5 Wie; 5 V 5 Y%R) 5 ;$)78>++7 E :G7Ue9 5 C = Í1+7U;;$Vt 5 W 51>7G>W 5E e<;$ Ç e'S>T 5 ; 5 eT 5 pX:G+78W<.eLM

statement E +R'7>VRWii 5 e E :G78RS+T 5 ; 5 :8. 5

`\f:^[a7\ = `\f:^[a7\ ~Z=ZXZ `\f:^[a7\Ê[ Ì

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〈statement〉 → (〈vardecl〉 “;′′ |〈atribstat〉 “;′′ |〈printstat〉 “;′′ |〈readstat〉 “;′′ |〈returnstat〉 “;′′ |〈superstat〉 “;′′ |〈ifstat〉 |〈forstat〉 |“′′ 〈statlist〉 “′′ |“break′′ “;′′ |“;′′

)

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• 5 WieL; 5 ;$M.>H:8R7Um

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• 5 WieL; 5 ;$ E >M.NS+T 5 m

• 5 WieL; 5 ;$7G>L+:GKS+T 5 m

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• 5 WieL; 5 1I_+ 5 C

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〈atribstat〉 → 〈lvalue〉 “ =′′ ( 〈expression〉 | 〈alocexpression〉 )

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lvalueú V E +R'; 5 7)RW

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〈printstat〉 → “print′′ 〈expression〉

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printV E >RK;<;$JRWi)g$78 E8E T 5 Y%RMKY%R+7NC fZ5 7ag$+W<M 5

T7d:b'[7S ~XT7d:b'[7S^T7d:b'[7S^ªÒ ÓªZ)g `|Z3a«Ò3_&Ó

〈readstat〉 → “read′′ 〈lvalue〉

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C[?dM'@] E >W)>M.9Le%:GF 5print

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lvalueúF78+7G E >e:U)RWii7G+¦ +7I+e+'iiRW<# 5%E KS+T 5

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expressionV 5 E Y%R>7G>W 5%E YRJ EaE >R'e%:G E >;$>' E 5E8E W E +7a>78; E

5 7` E8E 07 5 ;$RS>T 5

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d_X^&a£^ó¤gd_X^&a ~X

〈returnstat〉 → “return′′ [ 〈expression〉 ]

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return] 5 P 5 eLMXVy 5 E Vy+W0 5 78#: 5 ; 5E(5%E

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methoddeclú V@ E8E5 eT 5E äM.K+ 5%E 5 e E :87GR$: 5 78 E ù 1*v

constructdeclú

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= 5%E 5 e E :G78R$: 5 78 E 5 ;$ E >7 R$:8.M''_>; 5 :8W3t]+W 5 5 Wie; 5super

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〈superstat〉 → “super′′ “(′′ 〈arglist〉 “)′′

¤ifstat

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〈ifstat〉 → “if ′′ “(′′ 〈expression〉 “)′′ 〈statement〉[ “else′′ 〈statement〉 ]

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forV E +W<+M'9e:8b 5 +g E :G+e%:8

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〈forstat〉 → “for′′ “(′′ [ 〈atribstat〉 ] “;′′ [ 〈expression〉 ] “;′′

[ 〈atribstat〉 ] “)′′ 〈statement〉

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atribstatsV^>eY%Re%: 5

5E >Re; 5 ]RWiexpression

CQ¤ 5 WieL; 5 :8+78W<.e 5 W RW 8úXä 5 W 5 5 Wie; 5ùstatement

úFYRJ;+1 E +7`+gNR$:U; 5 C m T 5 5 Wie; 5%E 1I­M.K; 5%E

7\&d = 5 R

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7\&d ^¢ Ë ^£õg ^¢£^ó d_X^&a¦`|Ò3^=Ó T7d:b'[7S¦`ËÒ3^=Ó Ì

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statementCaAØ­):8W3t]+W«¦ 5

;$ Ç eK; 5<5 5 Wie; 5 e%RM 5 V$7G>7G E >e%:8; 5 5 7`RW¨ 5 e%: 5 prpr1 â 78RM' E5 _+'e9 5 5 W 5 +W

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statementV

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statlistVJ:G>7GW<'e< 5 WîRW &µ+UC@¤

statlist]

〈statlist〉 → 〈statement〉 [ 〈statlist〉 ]

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δ(s0, 3) = s0

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δ(s0, 5) = s2

δ(s0, 6) = s0

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δ(s2, 3) = s2

δ(s2, 4) = s0

δ(s2, 5) = s1

δ(s2, 6) = s2

δ(s2, 7) = s0

δ(s2, 8) = s1

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A4

VB E NY&kI+e+'z;$ E :8; 5E :G'1 5E L7U0>;)RW E +78K

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2→ 5

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?òe 5 ·»jZ=»ûA5

V E >7GK

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A4

5 W ü ý0 · V:8+7 â W 5%E5 E :8; 5 o:G'1 5 e 5Ç eMF;g$NRS>T 5 ; 5 · j[= ûîVZ 5 7:Ue%: 5 V@ü ý0 · ;$>1>7GK E >7b78> 5 pe9NK; 5 5 W 5 K;$>e:8 Ç +; 5 7NC °%­#e 5äE >Re; 5 + E5 Vt 5#Ç eM[;Í+;$+Kü ýUVP:8+7 â W 5E ; 5 E E :8; 5E 5 7G78+e%:8 E VW3 5E t+7G:G+eL+e%:8 E 5 5 ev*Re%: 5

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a, b ∪ c, d = a, b, c, d

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101, 110 · 00, 11 = 10100, 10111, 11000, 11011

abc∗ = λ, abc, abcabc, abcabcabc, abcabcabcabc, ...

a, b∗ = λ, a, b, aa, ab, ba, bb, aaa, aab, aba, abb, baa, bab, bba, bbb, ...

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A1

V$ 5 ;+7 â W 5%E R$:G'M'._N7^ E >R'e%:GJ?@c

(digito · digito∗) ∪ (i · f) ∪ (letra · (letra ∪ digito)∗)

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E +7 E >RK; 5 e 5 7GN 5 e9>+.W<+e%: 5 ; 5E 7G¯Ig$'W 5E : 5 º>e E C[½»W<b1+_ YR»RW : 5 º>e0¦ 5 LM'K; 5;Í+e%:G7U;<)+ E ; 5 5 W«M.RW Eâ W3 5 M 5 ;$0RWi#7 5 ;$RS>T 5 VLeT 5 9­# 5 W 5 78:G7 5 N;$+7NV+ E5 M'RW : 5 º+eä 5E :G+78 5 7aeT 5 5 W3'e 5 Wî)7 5 ;RS+T 5 E 5 M'9K;C fZ5 7`g$>W)M 5 V$e7 5 ;$RS+T 5

〈classdecl〉 → “class′′ “ident′′ 〈classbody〉 |“class′′ “ident′′ “extends′′ “ident′′ 〈classbody〉

E 3R$:8.M'._N78W 5E 5 : 5 º>e&;$)+e%:G7U;078i¦§_+>7 5 + E W<+e%: 5 5 Wæ#7G'W<+'78Í7 5 p;$RS>T 5 V+e%:UT 5 :G>7G>W 5E E 5 M'9'; 5bE >R'7d E8E J7 5 ;$RLS+T 5 V^>e%:G7U; E YR^ 5%EGE RW 8 üG`eLT 5 5 ;$>78T 5#E >7`7GN 5 e9>+'; E Cd?ñeM 5 W)>e%:GV E E 5 M.9+78W 5%E E >Re;<7 5 p;$RS>T 5 VeT 53E +7UT 5 ++.:8 E >;$>' E@E +W 8& :^üG&cC fZ5 7G:8e%: 5 V78> E W 5E :G+7FRK;; 5 5 Wî E 7 5 ;$RS È E Y%RJR$:G'M.'_>W 5E e< 5 e E :87GRLS+T 5 ;$JRWîeM' E ; 5 7a;$ E >e;$>e:8J7GNR7GpE .1 5 C· E 7UWi­:GK+ E Y%R0 5 ;$>W E >7»R$:8.M''_>; E eÍ 5 e E :G78RS+T 5 ;$3RW eM. E ; 5 7^; E +ep

;$>e:8378>+R7 E '1 5#E T 5 U9Wi; E ;$0AØA@ù"Nú C¤Ë78.W<+'7 5 A E .e Ç +iM'¦ :(: 5 7G'9%:»0.eL;$'>Y%RJbM'+.:GR7U0;b+e%:878;b] ¦ +.:8);0 E YR+7U;7800;$'78+.:8C@¤ E +Re; 5 A E .e Ç +3M.+¦ :M'.eN7J<.eL;$'>YR E +W<78 5EGâ W3 5 M 5 eT 5 :G+78W<.eLMkY%R< E :G'1+7JWi EyJ E YR+7U; E +7U­78> 5 e9NK; 5 78.W<>.7 5 CJ? 5 eXHW<+7 5 "0.e;'>zY%R 5 eXHW<+7 5 ; EGâ W0 5 M 5%E ;0M 55 º9N;eN E8E ­78 5%E ]i"V 5 R E *vVLY%R E b 5 e9>++e; 5 L>e E RW EGâ W0 5 M 5 ;<>e%:G7U;<] 5E8Eâ 1>M;$NK;$.70YR)7 5 ;$RS>T 5 R$:8.M'._N7NC#=»7 5 ;$RS>T 5 .:8; E >7GKW e> EGE ­78 5E :G7I EbEGâ W0 5 M 5%E78 E ;$NK;$'7»Y%RMy7 5 ;$RS>T 5 R$:G'M.'_>7>Cf 7UÍRg'M''7 eä 5 e E :G78RS+T 5 ;$)RW eLM' E ; 5 7 ;$ E ++e;+e%:G)7GNR7 E .1 5 VP 5E :GRW<p E

5 e E :G78R.76RWiJ:8L>M'378>;$.:G'1CZ? E8E J:Ut+MKb 5E8E RRWibM''e9bL7U+;eT 5 p:8+78W<.eM;3¹JA 4 »RWib 5 M'ReL7U+;J:G>7GW<'eMXC m `:G'1>7GW 5%Ed5 eT 5 pX:G>7GW<'eM ú 5 :8+78W)'eMV»e, 5E 'S>T 5

A × a;+1>W 5E 5 M 5 +7zYRLM»]-,7 5 ;RS+T 5 YR-;$>1+W 5%E R$:G'M'._N7 E V

5 :G>e%:878W 5E 78> 5 e9N+7 ú Vy>e 5 e%:G7U78W 5%E eLÍ>e:878; 5EGâ W3 5 M 5 C fZ5 7(+g$+W<M 5 V E :G'1>7GW 5%E

S → aSAb | bAaA → bAb | c

:G>7G>W 5E E >R'e%:G(:8L>M')78>;H:8.1

D +78W<.eL E= T 5 p:8+78W)'eM

a b cS S → aSAb S → bAaA A → S → bAb S → c

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;$78>R7 E T 5¯J E Y%R>78;C l E8E5 5 e%:GNzY%Re; 5 V@78-M'RW eLT 5 pX:G>7GW<'eM û VZ:G+W 5%Eû ∗

⇒ BαV»W<N;$'e%:G-ÑM'K+S>T 5 ;$-RWi 5 RñWi E 7 5 ;$RS È E C l EGEG5¬E .e Ç +àY%R

7:8.7(;$ û 5 ;$>W 5E +7U7 RWii¦ 5 78Wi E +e%:G>eKMØ+W Y%R 5 7G¯78 5 û 7GN3 5 W 578.W<>.7 5bEâ W3 5 M 5 C l e%:GR.:G'1W<+e%:8^]`¦§­+.ML1>7G Ç +7dY%R^ EGEG5 +R E J7 5 M'+Wi E CØ· 5 :8+e%:8778> 5 e9N+7 û V 5 · m ;$ E ++e;+e%:Gi78>+R7 E '1 5 .e1 5 > 5 W<]: 5 ; 5 5 7878 E 5 e;$+e%:8< 5 eT 5 p:G>7GW<'eMXC^¤ M.9e; 5 78 5 : 5 º>e;i+e%:878;V$ EGE W<]: 5 ; 5 5 ;$b E 5 M'9+7`RW«>W<.e9 5Y%R)M.>10 5 L78>'W<+e%: 5 ;$ 5 R$:G7 5 û V E >W Y%R3e>e9RWæ: 5 º>e:G>e9 E K; 5 5 e E RW<K; 5u 5 Y%Ri>7U :8+78._N#ä7GNR7 E T 5,J E Y%R+7U;C l E8E5 ¦§_< 5 W Y%R 5 W< E W 5 +W<'e9 5E vE +R'; 5 V 5 Y%RJ1yM'+17Fe 5 1IW<+e%:GJ 5 R$:87 5 û V$ EGE .Wî 5 7a;'e:8C l E8E5 ¦§_ 5 WY%R 5· m t+78WieNS+0e%RW<<78>+R7 E T 5 'e Ç e.:8V E >Wî 5 e E RW<.7`e>e9RW: 5 º+eBC·Q7GNR7 E T 5¥J E Y%R>78; 5 ;$^L78>>7[;.78:U 5 R).e;.78:UW<+e%:GCØ?@M'J]`;$'7G+:8Y%Re; 5

:G>W 5EB ⇒ Bα

VI.eL;$.78:UVY%ReL; 5B ⇒ Aα

⇒ BβCØ·¬+M'.W<'eS>T 5 ;^7GNR7 E T 5 .e;.78:U

5 ; E >7y E :8e%:Gd 5 W<M.K+;akeT 5^E >78­6:G7U:U;aYRC[·,+M'.W<'eS>T 5 ;a78>+R7 E T 5 ;$'7G+:8V 5 7 5 R:G7 5 MK; 5 V] E 'W<M' E 5 ; E >7`7G E5 M.1K;0; E +R'e:8JW<e+'7U

•;.1K;$+W)p E d E 7 5 ;RS È E ; 5 eT 5 p:8+78W<.eM û +Wê; 5 EBE Rt 5 ev*Re: 5EB º α1, ..., αn

V; E 7 5 ;$RS È E Y%R`eT 5 5%EGE R+WË7GNR7 E T 5¥J E YR+7U;( º Bβ1, ..., Bβm

V; E7 5 ;$RS È E 5 W78>R7 E T 5"J E YR+7U;m

•>M.'W<.eLW)p E E 7 5 ;$RS È E ;$m

•;$K 5 eW0p E b E 7 5 ;$RS È E

B → α1B′ | ... | αnB′

V 5 eL;$ û* ]3RW e 5 1 5#Eâ W3 5 M 5eLT 5 :G>7GW<'eMXVY%RJeT 5 t+7G:G>eK J 78Wi­:GK+m

•;$K 5 eW0p E Z EBE +R.e%:G E 7 5 ;RS È E 7U ûC

B′ → β1 | ... | βm | β1B′ | ... | βmB′

C

465 WË E8E a7 5 >;.W<+e%: 5 V:87 5 +W)p E ` E 78>R7 EGÈ E|J E Y%R+7U; 5 7d7GNR7 EGÈ E|J ;.78+.:8VY%R^eT 5bE T 5 7 5 M'+Wi­:8'> E 78e­M' E ^;$ E ++e;$>e%:G^78>+R7 E '1ICؽ»WË+g>W<M 5 +M'­ EGE K 5;$>M.'W<.eS+T 5 ;$78>+R7 E T 5J E Y%R+7U;0]7U0)78W<­:GK+

expression → expression + term |expression − term |term

term → term ∗ factor |term/factor |

factor → ident | constant | (expression)

·^M'K+eL; 5 )+M'.W<'eS>T 5 ;$ E 78H:UV:8+7 â W 5%E

expression → term | term expression′

expression′ → −term | + term | − term expression′ | + term expression′

term → factor | factor term′

term′ → ∗fator | /factor | ∗ factor term′ | /factor term′

factor → ident | constant | (expression)

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¤ R$:G7 5 W 5 ; 5 ;äW 5 ;$ Ç +7iRWi,¹JA 4 L7U-Y%R 5E8E E +7<R E ;eRW eM' E ; 5 7;$ E ++e;$>e%:GÍ78>+R7 E '1 5 ]z¦§_>+e; 5 &¦§: 5 78S+T 5ÄJ E Y%R+7U;-;Y%R>M' E 7 5 ;$RS È E ;ÍRWW< E W 5 eT 5 p:8+78W)'eM^YR:I>WþRW 78 Ç g 5 +W 5 W3RWC O 5 + E5 ; 5 +g>W<M 5 1 E : 5e%:8+78 5 7GW<+e%:8

〈classdecl〉 → “class′′ “ident′′ 〈classbody〉 |“class′′ “ident′′ “extends′′ “ident′′ 〈classbody〉

m (¦§: 5 7U78W 5%EªJ E Y%R+7U;V:8+78+W 5E )7 5 ;RS+T 5 Y%RJR E W 5E ei¹JA 4 ;0M''eR>WX++

〈classdecl〉 → “class′′ “ident′′ [ “extends′′ “ident′′ ] 〈classbody〉

¤ Rei¹JA 4 ; E +g7G EGEGÈ E V:8+7 â W 5E

expression → term expression′

expression′ → −term [expression′] | + term [expression′] | λterm → factor term′

term′ → ∗factor [term′] | /factor [term′] | λfactor → ident | constant | (expression)

7G'W<+'78»1 E :8V 5 ;$F7GN+7ئ§­+.M$>MKRMK7Z^:Ut+MK(7GN;$.:G'1I(;$FRWi(¹JA 4 C n E :85 M'97JY%R EJE T 5ä5E : 5 º>e E Y%Ri.e'+'W E 7 5 ;$RS È E ; 5 eT 5 p:8+78W)'eM û # 5 M 5 >7(eM'.e9Lz;$ û VyeLÍ 5 M.ReÍ;$ EGE E : 5 º>e E Vy E 7 5 ;$RS È E Y%R0+M' E 'e'+'WC fZ5 7G]>WäVP+g E :G+W;$'1>7 E EaE H:8RS È E YR 5 ;$>W¨ 5 W<M.K+7a E8E 0:87G+¦§CZök*vW 5E M'Re E ;$ E8E E + E5%E

•E `:8+W 5E

B → Aα | CβV+e%:8T 5 ]`7GN E5bE t+76YRL EdE T 55E : 5 º+e E Y%R».eKKW E

7 5 ;$RS È E ; ú 7Ui;$>+';.7JY%RMØ7 5 ;$RLS+T 5 R:G'M.'_>7>C`?ñ EGE E H:8RS>T 5 5 ;$E 7 5 7>V%RWi)1+_Y%R ú \ 5 ;$>W:UW3t]+W E 'eKK7^ 5 WeT 5 pX:G+78W<.eL E m

•E d:8+W 5E

B → A1A2...AnaαV7GN E W 5EBE t+7 E

A1

V.C'C'CAn

5 ;$>W\+7U7Ø»+;$+K1_+KC m ^ EGEG5 5 e%:G>++7NV+e%:UT 55 : 5 º>e:8W3t]+W;$+1 E >7dR$:G'M'._N; 5 78J;$NK;$'7Y%RMB7 5 ;$RS+T 5 ; û R:G'M.'_>7'm

•E k:8+W 5E

A → aBb; B → αα

⇒ λVI+e%:8T 5 3;$+1 E >7Ø 5 e E ';+7U; 5 5 W 5 RWÊ: 5 º+e

Y%R);$+1 E +7»R:G'M.'_>; 5 78#;>K;$'7»t+MKi7 5 ;$RS+T 5B → α

5 :G+e%:U7»78> 5 e9>>7û C

ödW 5E V@>e%:8T 5 V6;$ Ç e'7ig:UW<+e%:8 5 W 5 &:Ut+MK7GN;$.:G'1I;$>1 E >7# 5 e E :87GR â ;Cf 78.W<>.7 5 V%;$K 5 eW 5E RW e 5 1 5bEGâ W3 5 M 5 :G+78W<.eLM J ¹JA 4 C? E8E `:G>7GW<'eM;+e 5 :8; 5 5 7 L78> E +W<78`e 5Ç eM;b+;$+K;$^>e:878;C[· E +R.7NV1W 5%E E8E5 +'7 J ¹JA 4 ;$R E¦ ReS È E V Jç¼·;Ç J »X»@EeIC

m *vαRWiͦ 5 7GWi E +e%:G>eKMd;ä78W<­:GK+C0?de%:UT 5Jç¼·;Ç/¿

αà ]i;$ Ç e'; 5 5 W 5ä5

5 ev*Re%: 5 ;i: 5 ; 5%E5E0Eâ W3 5 M 5E :8+78W)'e E :8M6Y%Rα

⇒ aβV 5 R E vV 5 5 ev*Re%: 5 ;

:G>7GW<'e E Y%RJ.e'+'W¨M'RW<)+;$+K<;$+78'1I;<)7G:G'7`;$αC

f 7U)>MKRMK7 5*Jç¼·;Ç ;$RW E :87G'eLV;$+1+W 5EaE +R.7^ EFE +R'e:8 E 78+78 E

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•L7U 5 :8+78W)'eMeV Jç¼·;åÇ

(a) = am

•L7U 5 eT 5 pX:G>7GW<'eM û V:8MPY%R

B → A1A2...An

V 5 e;$Ai

E T 53Eâ W3 5 M 5E :G+78W<.eL E5 ReT 5 :G>7GW<'e E V¦§_+>W 5E

ì'e'+'M.W<>e:8 Jç¼·;Ç(B) =

ì78+t:G'W 5E*Jç¼·;åÇ(B) =

Jç¼·;Ç(B) ∪

Jç¼·;åÇ(Ai)

VF7Ui = 1, 2, ...

:8]Y%R+eL 5 e%:87G>W 5%E M'RW

i:8MØYR

Ai

eT 5 ;+78.1λm

•L7UaRW E :87G'e

α = A1A2...An

V 5 eL;$Ai

E T 5^Eâ W3 5 M 5E :G+78W<.eL EB5 ReLT 5 :G>7GW<'e E V¦§_+>W 5%E

ì78+t:G'W 5EJ¼·;Ç(α) =

Jç¼·;Ç(α) ∪

Jç¼·;Ç(Ai)

V^78i = 1, 2, ...

:G]&Y%R+eL 5 e%:87G>W 5%E M'RW

i:8MØYR

Ai

eT 5 ;+78.1λC

=»i¹JA 4 ¦§: 5 78;3Y%R(W 5E :G7UW 5E e%:G>7G 5 78W<+e%:GV:8+7 â W 5E65EaE >R'e%:G E 5 ev*Re%: 5E V78 5E :8+78W)'e E eT 5 pX:G>7GW<'e E

Jç¼·;ÇE! º ´b µJç¼·;ÇE º ´ z1µJç¼·;ÇE&¡ º ´ .)µJç¼·;ÇE¢£ º ´ TXµJç¼·;ÇE(¤@ º ´ QKµJç¼·;ÇEE¦¥@6"§sD/ º ´ üG µJç¼·;ÇE%¨4K§B©!D&1K§sD/ º ´ c µJç¼·;ÇE º ´ p µJç¼·;ÇE 1@¨D42ª º ´ üGXV­ cV p µJç¼·;ÇE&D6ª"«­¬ º ´ TGVEQKµJç¼·;Ç

(term) º ´ üGXV³ cV p µJç¼·;Ç

(expression′) º ´ z`V.)µJç¼·;Ç

(expression) º ´ üGXV­ XV p µm *v û RWÙeT 5 p:8+78W)'eM»;à78Wi­:GK+à® 52E >R EGâ W0 5 M 5 'eKKMXC ¤ÿ 5 ev*Re: 5

J »=»@Ee(B)

]a¦ 5 7GWi; 5 t+M 5E :G+78W<.eL E J:UMLY%RS

⇒ αBaβV 5 R E *vVg$ E :8`RWiJ¦ 5 78Wi

E +e%:G>eKM`;$>7G'1­I1+Ma-7G:G'7i; 5EGâ W3 5 M 5 'eKKMa+W Y%R78>+Í'W)N;$K:8W<+e%:G J;$'7G>H:U<;$ û C·'W< 5 7:U®e+'; 5nJ »X»@Ee¬ 5 ;ÍeT 5&E >7b:UT 5 'e%:GR.:G'1& 5 W 5 ; 5nJç¼·;Ç VÌW< E3E

:G'1>7GW 5%E RW EGâ W0 5 M 5 eLT 5 :8+78W)'eM û Y%R- 5%EGE R RWià7 5 ;$RS+T 5 ; 5 :8. 5B → α

V

α∗

⇒ λV`+e%:8T 5 ].W< 5 7G:8e%:8YR E .LW 5E Y%R E#E T 55%E#Eâ W3 5 M 5E ;$ J »=»@Ee

(B)C

ödW 5%E : 5 Wi7NVP 5 7 +g>W<M 5 V 5 :8+78W)'eMVä E R 5 7Y%Ra ∈

J »X»@Ee(B)

C l E8E5äE 'e Ç >

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Y%RÍe 5 eLM' E ; 5 73;$ E ++e;$>e%:G#78>+R7 E '1 5 VZ 5 g$>+R$:87GW 5E35 W<]: 5 ; 5 5 787G E 5 e;+e%:G û V6.78+W 5%E 5 e E RW<'7iRW ++7G: 5 eXHW<+7 5 ;: 5 º+e E V E E8E E : 5 º>e E + E 7G>W 5 W;$ Ç e'S>T 5 ;$ û V@ 5 ;$>W 5%E :G>7iRW e>e:878;C fZ5 78]+W E

B∗

⇒ λV6 E8E5,E .e Ç +

Y%R#eT 5 5 e E RW)'e; 5 e+e9RW : 5 º+e,;+e%:G7U;V« 5 ;$ä7GN+7Je+e%:G7U;ä E +7U­+ E ; 5 +W M.RW 5 e%: 5 VØL¯ EJ5 78> 5 e9>'W<+e%: 5 ù eRM 5 úJ; û C fZ5 7:Ue%: 5 V E ie 5 'e â 5; 5 7GN 5 e9>+.W<+e%: 5 ;$ û :G'1>7GW 5E RW ze#>e:878;Vt;$+1+W 5E E >R'7 Í7 5 ;RS+T 5 Y%R¦§_ä 5 W´Y%R û ;+78.1z&>;$>'1I_+KC m z:G'1+78W 5E35 R$:878&7 5 ;$RLS+T 5 5 W 5

B → Aαa ∈

Jç¼·;Ç(A)

VÌ>e%:8T 5ä5 5 7G78+7U­iRW 7 5 M.>WiÍe¹JA 4 Vy 5 E 5 W 5 W) E W 5 :G>7GW<'eM:G>W 5E ;$R E 7 5 ;RS È E <M.K+7>Cf 7U)>MKRMK7 5%E 5 ev*Re%: 5EGJ »X»@be78 5E eLT 5 pX:G>7GW<'e E ;#¹JA 4 V;$>1>W 5%E

•;$K 5 e7 5 'e;$K+; 5 7);$ Ç W ;$ä>;$>' 5 5 ev*Re%: 5J »X»@be

(S)V 5 e;$ ] 5

EGâ W3 5 M 5 'eKKMÌ;<¹JA 4 m•;;<)7 5 ;RS+T 5

B → αAβV¦§_>+W 5E

J »X»@Ee(A) =

J »X»¯Ee(A) ∪

Jç¼·;åÇ(β)

E β

⇒ λV+e%:UT 5 ¦§_>+W 5EGJ »X»¯Ee

(A) =J »X»@Ee

(A) ∪J »X»@be

(B)C

4 MKRMKeL; 5<5CJ »X»@be78 5 e 5E8EG5 +g>W<M 5 V:G>7 â W 5E J »=»@Ee

(expression) º ´ VúµJ »=»@Ee

(expression′) º ´ VúµJ »=»@Ee

(term) º ´ x0VpUV Vú µJ »=»@Ee

(term′) º ´ x0VpUV VLú µJ »=»@Ee

(factor) º ´ ÷ VLVLx0VpUV Vúµ½^Wi1+_ä+MKRM'; 5E5%E 5 ev*Re%: 5EmJç¼·;Ç J »X»@beVy 5 ;$+W 5E Vk+e%:UT 5 Vk 5 e E :G78R'73

:8L>M'&78>;$.:G'1&;¹JA 4 C f 78 E8E5 VZ1IW 5E +gW<.eL70 E 7 5 ;$RS È E ;M'.eR+Wÿ:G>e%:87^; E 5 7G'7a+W¨Y%RJ 5E 'S È E 5 M 5 >­prM' E e0:Ut+MKCdû +1>W 5E ¦§_>+7N

•;;7 5 ;$RS>T 5

B → αVØ78ä: 5 ; 5 :G>7GW<'eMí

∈Jç¼·;Ç

(α)Vk;$+1+W 5E 5 M 5 +7

EGE )7 5 ;RS+T 5 e) 5E 'S>T 5(B, a)

;0:8L>M'm•;;7 5 ;$RLS+T 5

B → αV 5 e;

α∗

⇒ λV678: 5 ; 5 :G>7GW<'eMn

∈J »X»@Ee

(B)V

;+1>W 5E 5 M 5 >7a E8E 07 5 ;$RS+T 5 eL< 5%E KS+T 5(B, a)

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; 5 · m ;$<¦ 5 78WiW<eRM E T 5 :87G+¦§ E ­78;R E C#·^'e;Wi EbE i E :G'1>7GW 5%E :878M'9e; 5

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(1)expression → term expression′

(2)expression′ → +term expression′

(3)expression′ → λ(4)term → factor term′

(5)term′ → ∗factor term′

(6)term′ → λ(7)factor → ident(8)factor → constant(9)factor → (expression)

5 W RWi78W<­:GK+-e n =»jFV@ 5 E VF 5 W 5 1.W 5E V 5 +­MKRM 5 ; 5%E 5 ev*Re%: 5%E*J¼·;Ç J »=»@Eeò 5 e E K;$+7UW L>e E 7 5 ;$RS È E e 5 78Wi E V E >W 5E<5 L>78; 5 78 E ; n =»jFCd=^ EGE 5 e%: 5 +e%:G7UW 5%E 7 5 7UWi E 5 W 5)5 °%I1 4`4 VY%RV$ E N; 5 e);$ Ç e'S>T 5 ;3M''eR>W+W n = jFV>78»: 5 ; 5%EØ5%E W<]: 5 ; 5%E 5 7G78 E 5 e;$>e:8 E 5%E eLT 5 pX:G>7GW<'e E F1+78 Ç + 5%EGEGâ 1+ E7 5 M'+Wi E V$I1 E eL; 5 5 .W<M'+W<+e%:U; 5 7 5%E 5 e%: 5E ;078Wi­:GK+)Y%R 5Ea5 7G''e7UWC=» E >S>T 5`E +R.e%:Gk 5 78;7G>W 5E a.W<M'+W<>e:US>T 5 ; 5 · m L7UFaM''eR>W

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4.2 O analisador sintático da linguagem X++

ök+78+W 5%E VI E +R.7NVI 5 W 5 'W<M'+W<+e%:87 5 · m V 5 W E @e^78W<­:GK+F1 E :8^e 5 > â :GRM 5 VR$:8.M'._Ne; 5)5 °%I1I 4`4 C l e'+'M.W<>e:8V;$'+ 5 e78+W 5%E RWi)e 5 1 5 PS+T 5 e)78.W<>.7Ub7:8; 5 7UY%R'1 5 C v vC

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E +7U­b>78; 5 t+M 5 °%I1 4`4 C l EGEG5 ¦§_J 5 WY%R 5 · m W 5%E :87G(e E â ;pXL;$7UT 5 Y%R EFE T 505%EeT 5 pX:G+78W<.eL E Y%R» E :UT 53E +e; 5 *+g$>R:8; 5E a(YRL E6E T 5b5%E : 5 º>e E Y%R E T 5 5 e E RW<'; 5%E+W>;0RW;$>M. E Ck·»M.]>Wî;$ EGEG5 VW 5E :G7U:UW3t]+W E :G+e%:U:G'1 E ;$J+ E W)>e%: 5E ¦ +.:8 E 5eLM' E 7"L&'$& C= 5äÇ eM@;$ E :G#> â :GRM 5 VBW 5E :G7U78+W 5E RW g$+W<M 5 +W Y%R< EGE :G' 5 ;$ E â ;) E :U­09L'M..:8;C

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=^>W E +W<78^Y%R+78+W 5E 1+7@Y%R E@E T 5 E S È E : 5 Wi; E L>M 5 · m C?@WË+7UMXV E :8W 5%EWi E 'e%:G+78 E8E ; 5%E +W E L>7 E 3g$ E :G3RW +787 5iE .e%:8­:GK 5 0YRLMÌ]3 E8E >7G7 5 C^¤Ë°I1 4`4t+78W).:G6YR 5 W<>+e E W 5 ;$@;+R7US>T 5 ; 5 · m E *v`;$ E .M'.:8; 5 +W :G+W< 5 ;$d+g$>RLS+T 5 C· E8E .WVPe 5E8EG5 5 W<.MK; 5 7 >H:UÍ 5 W 5 7U®W<+:G7 5 ;$)+e%:G7U;Í 5 PS+T 5 .6&'ü%þ ú LC m E8E 5 tS>T 5 ¦ 5 7Z¦ 5 78e>+';»Y%ReL; 5 5 e 5%EGEG5 5 W<'M'; 5 7[]ag$>+R$:8; 5 V>e%:8T 5 E 'e$¦ 5 78WiS È E;$;$>R7US+T 5&E +7UT 5 W 5%E :878; E C m E8E 5 PS+T 5 eT 5 ]R$:8.M'._N;Vd+e%:UT 55 · m W 5E :G7Ut+eL EZE `+g$ E :Ga`Y%RM$] 5 +787 5JE .e%:8­:GK 5 C f 7U( E8E5 VM.:G>78W 5%E :8W0L]>W 5 W<]: 5 ; 5y>MA; 5 e 5%EGEG5 · m CB?@M.i1+78 Ç > E i 5 PS+T 5 ¦ 5 @;; 5 ReT 5 VÌ+Wÿ+ E5 e+%:8.1 5 VB'e1 5 + 5W<]: 5 ; 5ÄC'A6ÁÂ1ÄH³AB:CDQ¹?ËA o QÁ1¿Ã ; 5 · m 78K; 5 ù§178'­I1+M N@A6˳cDË ; 5 7 5 7UWiaC /úC

9:;%<:=?>=Sª/Bu@F 9ÍQ6ÎU6Ï&ÐÑÒUÓ/yY%= H <Ô\ n6=L j =Q< G n6=Q:^ G :CÕ_ Z >n;&: KcÖ =Qp=B Z ;B Õdeg n JO Y Z LALQYQ=^Q^tYQ= H <QÔM×h a ZbH =YA^ K = KZ LSÎ K : Z?H <tØ G :^ Z ; H `lEÔffSÙ;>n Z Y G : ¨ Ø G :^ Z ; H DBs ¨X© sQsQªlÕi ZbHK L%; HK 9=%:6^ G :Q:;%:c`SsÕ RRtLQ; HK = [ ;%: [GSG ::;^S^ ZbHKàQKZ LQ;^kFrqFuF RRTÞ G a ZbH6G ; > K ; [ ;ml>= Z?H l [ =AL%YQ=^^ G Y%= H <Ô/BFr\ n JO Y Z Lw^ K = K6Z LPp; Z&[ >= ZbH yÎ K : ZbH <c=Q:<^ K&N :;&ß^T9=Q:6^ G v6L G n KZ ; HFr_ ×F|d O ;;QY G = HM[G&OJ <M`Ta=Y^ G ÕFreFrg Î K : ZbH <Aa Z Y G&H =?> G `llÕÜRR H ;?> GS[ ;T=Q: I%JZ p;S=A^ G :A= H =Y Z ^%= [ ;Fh Y%= H <ÔPn=Q:6^ G :Õ RRP= H =Y Z ^%= [ ;%:cY%Qv Z LQ;QR^ ZbHKàQK6Z LQ;Fri Z?HKcZ ÕFrk O ;;Y G = H >^T`ta=Y^ G Õ\uq\F Î&¥6^ KG >áB; JK Bn: ZbHK Y H yØ G :6^ Z ; H Õ\u\ RQRSYQS;^on6=Q:â?> GQK :;^Xn6=^^%= [ ;^Xn6=Q:=A;ALQ;?>n Z YQ= [ ;%:\u_ a;%:ãy Z `PsÕ ZTä =Q:<^åBY G&H < K%N!¨ DÕ Z ff\d ×\ue Z aãy=Q:<^ Z& B GQI%J =Y^çy?l ¨b[G&OJ <Ï&ÍÎl%\ug [G&OJ <S` K : JG Õ\h G Y^ G\ui ×\uk Î%¥6^ KG >ìB; JK B|n: ZbHK Y H y?lîè^%=Q< GZ ^å­ l f_uq l Ö =Qp=AY%= H <Ôê ¨b[G&OJ <Ï%ÍÎ mZbH n JK a Z Y G l%Õ_F Î%¥6^ KG >ìB G v ZUK ysÕ_u\ ë_u_ ë_d_ue Z aãy=Q:<^ Z& B GQI%J =Y^çy?l ¨ l&_ug × RRtYQ [ = G&HK := [ = ¨ n6= [ : ;_h Î%¥6^ KG >ìB; JK B|n: ZbHK Y H y?lE G = [6ZbH <aQ:;?>z^ K = H[ =Q: [ZbH n JK BSBtBl&Õ_ui n6=Q:^ G :A` HG ßcYQ= H <ÔCyÎ%¥^ KG >ìB ZbH ÕÈRRSLU: Z =tÍÎ_uk ëdq G Y^ GdîF × RRtYQ [ ;t=Q: I&JZ p;

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= 5 W)]+: 5 ; 5,>MA V$:G>W 5%E :UW3t]+Wæ#U9LWi;i 5 W<]: 5 ; 5N³A6˳cDËáÄ/N/Ë ÁËA'> C 465 W 51>7G>W 5E E >R'7>V 5 °%I1 4`4 '7U­ä; Ç e'7bRW W<]: 5 ; 5 78>; Eâ W3 5 M 5 eT 5 :8+78W)'eM;78Wi­:GK+CØ·òL7G:G'76; E 7 5 ;RS È E ;$ E 78.:8 E e 5 7UY%R'1 5 C v vV E T 5 +7GK; 5%Ek5E W)]+: 5 ; 5%EY%R0:G+e%:UW ¦§_>+7 5 > E W<+e%: 5 ;#>e%:G7U;z 5 W 5%E 78 E t> :8.1 5E eT 5 p:8+78W<.e E CJ· E8E 'WV3U9LWi;3; 5 W<]+: 5 ; 5N@A6˳cDËìÄ/N/Ë ÁËA'> '7U­:G>e%:87F78> 5 e9N+76eb>e%:G7U;RW<)+;$+K

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Y%R<+ E < 5 W z;$ E 78KS+T 5 ;;z E >R'7(e 5 78Y%R'1 5 C v v(7U 5 eT 5 p:8+78W<.eMM9:ü!0C? E8E i] 5EGâ W0 5 M 5 'eKKMd;78W<­:GK+C)·>e:878;äR$:G'M'._N;ä]#Y%Ri E :8­äe 5 78Y%R'1 5 EGE ; 5 5 W 5 7U®W<+:G7 5 eLà78'S+T 5 ; 5,5 $v*+: 5nN@A6˳cDË V6e 5 .e â 5 ; 5 W)]+: 5 ; 5>MAù M''e9 E /)%oúC½^WiÍ; E 1Ie%:8+e E ; 5 · m >78; 5 t+M 5 °%I1I 4`4 ])Y%R 5 7GN 5 e9>+.W<+e%: 5 eT 5 7G+p

E E >7¦ +.: 5 e> EGE 78KW<+e%:Gi7:8.70;$ÍM'RW eT 5 pX:G>7GW<'eMk E t> âHÇ 5 C½^WiU9pWi;ѬY%RM'Y%R>7ÍW<]: 5 ; 5 Y%R- 5 787G E 5 eL;,àRWÙeLT 5 pX:G>7GW<'eM .7U­:8+e%:87z78> 5 e9+p>7Í EGE &eT 5 pX:G>7GW<'eM^eLà+e%:878;C fZ5 7Íg$>W)M 5 V E :G'1] E8E +W 5E ¦ +.: 5 ÑU9Wi;,N@A6˳cDËìÄD ¹ N/ËD³³ç V 5 e 5%EGEG5 5 W<'M'; 5 7('7GKz 5 e E RW<'7 5%E : 5 º+e E ;Í>e:878;z7 5 +R$p7Ue; 5 78> 5 e9N+7aRWi<+g7G EGE T 5 t+e E V$JeT 5 RWî7 5 78W<C

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〈nao terminal〉 → 〈tipo〉 “nome′′ “(′′ 〈argumentos〉 “)′′ “ :′′

“′′ 〈decl. locais〉 “′′

“′′ 〈BNF 〉 “′′

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5 W 5 eT 5 pX:G>7GW<'eM[YR E 3 E t+7U#78> 5 e9N>7>CJ½^WiÍ:G+e%:U:G'1Í;$ E 3¦§_++7( EGEG5 ]< 5 e$pE RW<.e; 5 : 5 º+e E ;Í+e%:G7U;i:G]3Y%R)7GNS+iM.RW«Y%R3 5%EGE ..M'H:80# 5 e%:G'eRK;;$0;eL­M' E C s E YRL E#E >7GKWþ E8E E : 5 º>e E ½»W<à 5 ,';]+K E >7GKR$:G'M'._N7 5 5 ev*Re: 5J »=»@Ee; ¶ Cy· E8E 'WV 5 W<]: 5 ; 5o¶ ;$>1< 5 e E RW)'7 : 5 º+e E ;z+e%:G7U;#:8])Y%R<7GNS+RW Eâ W3 5 M 5 t+7G:G+eL+e%:8» 5bE +R# 5 ev*Re%: 5J »X»@Ee# E ¯b;+ 5 E 78: 5 7GeL7kg$NRS>T 5 7U; C?@W ; V:GR; 50E » EGE 5 W 50E (bg$NRS>T 5 ;$ ¶ :8.1 E8E E K; 5 t+W)p E R+>;$K;(3e­M' E 5 e%:G'e%RLVZ 5 W´>7:8+_N;$zY%RVØt+M 5 W<+e 5%E V 5 7G¯Ig$'W 5 : 5 º>eà;+e%:878;.7U­> E 7 5 WË7 5 ;$RS>T 5E +e; 5 R:G'M.'_>;C 465 W E8E E W 5 ; Ç >S È E V 5 · m ; E +eL;$+e%:G`78>+R7 E '1 5Ç >78')M' 5 5 W 5<5 ¯$;$' 5 W 5E :G7U; 5 e 5 7 5 78Wi0o$C'"

9:;%<:=?>=®BEDF p; Z&[ ÎåyE\ ×_ Z a-yîL J :Q; j6G&H B K ¥%n G ``¿=@¿Ed ×e = H =Y G vCyEÕg ÍCyEÕh Z aãyL J :; j6G&H B K ¥%n G ``À¿L2¿Ei ×k = H =Y G vCyEÕFrq Z ayîL J :; jG&H B K ¥&n G `Q`À¿ [ ¿éFuF = H =Y G vCyéÕFr\ G Y^ GFr_ Î Z?HK = K6Z LU::;&:Cy?lE H LQ; HK := [ ;l fAL J :Q; j6G&H B K ¥%n G yESfF|d l G ^?n G := [ ;­ [ l%ÕFre ëFrg G Y^ GFh Î ZbHK = K6Z LU:Q:;%:Cy?lé H LQ; HK := [ ;!lífAL J :; jG&H B K ¥&n G yEtfFri l G ^bn G := [ ;­3Ll&ÕFrk ë\uq G Y^ G

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RWi+g$+>S>T 5 ; 5 :8. 5S¶;6¸ ¹:o D&NO? Cä¤îW<]: 5 ; 5 o ³>³D¹?:C 5 e EG5 W<#>e:878;:8]^Y%R`RWË;:G>7GW<'e; 5 : 5 º+e E v(+e 5 e%:G7U; 5 CÌ? 5 W<]: 5 ; 5æ¶ R$:G'M'._NJRWi 5 e E :87GRS>T 5SXd W`^&S`Q7U&:G+e%:U7<7GN 5 e9>++7<7 5 ;$RLS+T 5 5 7G78 E 5 e;$>e:8ä 5E +RÑeT 5 p:8+78W<.eMVP>W > EG5 ;$0+787 5 V'78­#U9LWi7 5 W<]: 5 ; 5 o ³>³D¹?:C Y%R3¦§_0#7G EGE .eL7 5 e'_>S+T 5;$ E v;Cs E 5 ;+W 5E ¦§_+>7z.e;àRW 5 R 5 W<+M'9 5 7ä; 5 Y%R- E8E5 CödW 5%E : 5 Wi7z 5 W 5

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Geração da ÁrvoreSintática

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Capítulo 7

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Capítulo 10Análise Semântica –Segunda Parte

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10.2 Análise da declaração de variáveis e mé-todos

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