Attribute grammars and automatic complexity analysis
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(222) R b WSA~A~W b R3@BKM@ b WrV LKMR Y]KMTUV LQP+Ku@U_]Y]WrV LQP+KMZz LNZ.V P.
(223) .
(224) . p LKLQV ZuP b LQRSLK]WrO P b AuWSKMi WrZuLA~hMOQ@BA'@BK3V @UiLK V > @p-VoSH1VSVh]WrT zWrRS@S
(225) WrOQOQPr -Z « V > @~YMZ @ b V Pi]@UZ.T b L^]@uWTUOWXZ ZP WrOQRSP b LQV > ACZYMZ LKMRZ @US@ b WrO Z.LA hMON@uh b PSR b WSA~A'LKMRuh b LA'LQV LQS@UZ2FZ @U_]YM@BKMTU@ P h b PSR b WSACZB[V @UZ V~P+K9Y]KMLQP+KMZB-h]W b V LWrO-h b PSR b W3Ai]@UZ TU@BK3VWSKMi YMOQO-TUP+A~hP+KM@BKSV LNV.@ b WrV LQP+K7eh b P3R b WSA {q!t 2U^%
(226) V5W3r@UZWrZ
(227) LK]h]YMV~Wi]@UTUP+A~h]P3Z5WS^MOQ@Z.V b YMTUV5Y b @'V¨\]h]y @ i]@KM@Ui9LKWSKWrTUTUP+A h]WSKS\MLKMRR b WSA~A~W b =-> @'h b PSR b W3A LQZ
(228) OQLQV V @ b @Uio -LQV > TUPMY]KSV @ b ZB => @TUPSZ VP @U+@UTBYMV.LNPMKuP+K¤LK]h]YMV$ LQZV > @BKuTBWrOQTBYMOWrV @UiWXZ-V > @ Z5Y]A P V > @'TUP+Y]K3V @ b Z@BKMTUP+Y]K3V @ b @UiJLK W b Y]K7 =-> @~h b PSR b WSA b @UVY b KMZ 4{ ! %WSKMi WSKJWrZ.\`A~hMV.PSV LQTrWrOYM@ P b 4{ ! % ]V > @
(229) V PSVWrO7TUPSZ VP Àb Y]K]KMLKM9R {q!|ty2j&%P+KuWrOQO[LK]h]YMV ZP Vd\]h]$@ W3KMiZ hL mU@ [ =-> @'WzS@ b WrRS@ TUP+A~hMOQ@UMLQVd\uLQZV > @BKJ 4{ ! % ] Z! %U ]n3 :+ \ . . . . . . . . (+. . . v's wUwBx.¸t wU£ xzy Jyxrv=-> @ b @
(230) LQZWFi]L b @UTUVTUP b b @UZh]P+KMi]@BKMTU@FV P~WrV V b L^]YMV @
(231) R b WSA~A~W b Z8L V > @-h b PSR b WSA'Z W b @f+LQ@U f@Ui~WrZËWXV V b L^]YMV @UZB =-> @fTUP b.b @UZ5h]PMKMi]@BKMTU@LQZZ5Y]A~A~W b LnmU@Ui'LK'V > @ P3ONOQPr -LKMRV > @UP b @BAu 7£M©xz£ 3 R Q g ijb O Bf R)Q_M Nc\K4dJ`QjeaghM+JabcjNjbM-MCKbkM0JcJaOeaghM+O R<BfM
(232) JaJaMAN QRvezM ]D : . $. bMo b O MER-QdJ$QR-Qb O e0fMijbQZlQ b$bMKUbM0J`MEROBRiyBjM$JaQZMZNc GKgnM .OBKbkjeaghM+. xz©7©, #. rW T > h b PSR b W3A~A'LKMRh b LA'LQV LQS@JTBWSK1^]@A~W3h]h]@UiV.PWSK1WrV V b L^]YMV @TUPMKMZ V b YMTUV LQP+K7 eh b P3R b WSA {q!t-24^%LNZ
(233) V b WSKMZ OWrV @UiJLK3V PWSKWXV V b L^]YMV @q{q!^%
(234) WSKMiJV > @'TUP+A~hMOQ@UMLNV¨\ Y]KMTUV LQP+K4{q! %LQZ
(235) @U_`YMLQrWrOQ@BKSV'V P ] ! 4/%( ] 5 S > @ b @-V > @W b LWS^MOQ@ A~W b SZZ LhmU@W3KMi A~W b 3Z8WrV V b L^]YMV @&{' =-> YMZBMWSK'@U_]YMLNrWrOQ@BKSVZ \+Z.V @BA TBWSKo^]@'P+^MV5WrLKM@UiJWSKMi WSK3\MV > LKMRZ P3ONrWS^MOQ@~LK \ p'7 -LQOQOË^@'Z PSOQWS^MOQ@~^3\uV > @Z5W3A'@jA'@UV > P+i]ZB-V b @BA~WrLKMZ V P~T b @BWrV @
(236) V > @A~W3h b PMA h b PSR b WSA A'LKMRh b LA'LQV LQS@UZV PWrV V b L^]YMV @
(237) TUP+KMZ V b YMTUV P b ZB e h b PSR b WSA TUPMKMZ LQZ V ZP W9Z.@U_`YM@BKMTU@9P ZY]^3dh b PSR b W3A'ZB;V.ZV PSVWrOTUPMA~hMOQ@U+LQV¨\LQZV > @Z5Y]AP V > @ TUP+A~hMOQ@UMLQV LQ@UZP V > @ ZY]^3dh b PSR b W3A'ZB =-> YMZBL WXV V b L^]YMV @ {q!|&%LQZJV > @JWrOYM@9P V > @TUP+A~hMOQ@UMLNV¨\ P b h b PSR b WSA A {«WrTUV LKMRP+K Z V b YMTUV5Y b 9@ fTUOQ@BW b OQ\ V > @WrV V b L^]YMV.@LQZ W Z5Y]A P V > @WXV V b L^]YMV @oWrOYM@UZuP V > @ Z5Y]^3dh b P3R b WSA'ZzËV b @BA~WrLKMZ-V P~TUPMKMZ LQi]@ b @BWrT > Z LKMRSOQ@~h b LA'LQV LQS@S =-> @FLK]h]YMVW b @i]@UTUP+A h]PSZ5W3^MON@'Z V b YMTUV5Y b @UZB => @ b @BA~WXLKMLKMRh b LA'LQV LQS@UZ
(238) i]@Bh@BKMi > @BWz+LQOQ\PMKuV > @FLK]h]YMV Z V b YMTUV5Y b @S' V > @~LK]h]YMVLQZjWuY]KMLQP+KJP TUOWrZ Z @UZz WV @UZ V
(239) PMK Y]KMLQP+KMZ'h b LA'LQV LQS@i]LNZ.V LKMR+YMLQZ > @UZ~^]@UV¨ f@U@BKJV > @ h]P3Z Z L^MLQONLQV LQ@UZWSKMiZ5Y]A'ZfV > @WrOYM@WrTUTUP b i]LKMR'V P'V > @TBWrZ @S =-> LQZfLQZfV > @ZWSA'@
(240) WrZ8V > @
(241) WrV V b L^]YMV @ P b Y]KMLQP+KMZB eh]W b V LWrO]TUPMA~h]P+KM@BK3V8i]@UZ.TU@BKSVfLQZ8@BKMTBWShMZYMOWXV @Ui LNV > V > @ ab P+i P+h]@ b WXV P b P b h b PMiYMTUV ZfWSKMiW
(242) Z.@UON@UTUV.LN3@ WrV V b L^]YMV @-LK~V > @PSV > @ b TBWrZ @UZB => @ YMOQO7TUP+A~hP+KM@BK3V8LQV @ b WrV.LNPMK7`A WShMZ8V PW3K~LQV @ b WXV LQS@-P+h@ b WrV P b eZ8LK V > @ TBWrZ @
(243) P WrV.V b L^]YMV @
(244) R b W3A~A~W b ZzSP+KMOQ\Z5Y]^3dh b PSR b WSA'Z-P Z5Y]^MZ V b YMTUVY b @UZ-TBWSKo^]@
(245) TBWrOQOQ@UiJ -LQV > LKW'TUP+A h]P+KM@BK3V i]@UZ TU@BK3VB . . . . ]A G y £7|+£]xB£w y]w© '=->. '@ WSK]WrOQ\+Z.LNZ
(246) P i]LA@ b @BK3V LWrV LQP+KoLQOQOYMZ V b WrV.@UZ
(247) V > @'LKMTUOYMZ LQP+K P \ p LKWrV.V b L^]YMV @
(248) R b W3A~A~W b Zz fP+KMZ.LNi]@ bb @UR+YMOW b WrOQRS@B^ b WrLQT-@U]h b @UZ Z LQP+KMZfTUP+A h]PSZ @Ui P TUP+KMZ.V5WSK3V ZËmFWSKMiunWSKMi ~YMZ LKMRV > @Vd fP
(249) ^MLK]W b \ P+h@ b WrV LQP+KMZ WSKMix,WSKMiuV > @
(250) Y]K]W b \~P+h@ b WrV LQP+K@U]h]PMKM@BKSV LWrV.LNPMK7]V > WrVfLQZB .] =-> @
(251) R b WSA A~W b P V > LQZ.
(252) 4 =U 4
(253)
(254) . Z @UV-P @U]h b @UZ Z LQP+KMZ -LQV > e-V.P+A'Z. 0.LQZ@BWrZ.LNOQ\ui]@UZ T b L^@Ui2. Z/f/. ?. 8. {. 8. m(Qnf( p(u{q( >l(. . l*&* \* . > 8. 8. l* )*. .. . -= > @ PSOQOQP LKMRh b PSR b W3A 4RR ]WrZfLQV- fP+YMOQi^]@
(255) @BK3V @ b @UiuLK3V P \ p']LQZW'h b PSR b W3A i]@UZ.T b L^MLKMRi]L@ b @BKSV.LW V LQP+K7 => @
(256) TUPSZ V-P W Y]KMTUV.LNPMKuLQZ-V > @KMY]A'^]@ b P WrV PMA'ZfRS@BKM@ b WrV @Ui^3\V > @WrOQRSP b LQV > A¤+V > YMZ-V > @
(257) TUP+Y]KSV.@ b Z W b @
(258) PMKM@ P b @BWrT > WXV P+A'LQT
(259) Z V b YMTUV5Y b @S. R H 4RR3J1 != ,7 < != X * 1 1
(260) -= R @ TB .=> S $ 1 $M1 ' 7 @> w B RRJ1 $ B RR3J1 ' X @ TB 1 $ 1 $M1 7 @> w 1 B 4RRP1 Y$E1 Y$ 1 J1 $ B RRJ1 ' YX @ TB P1 != $ 1 . 7 1 B 4RRP1 Y$ 1" YX 7 1DX 1 7 1 T X 1 o 7 1 T X 1B X 1* /L 1 => w $ 1 $ 1 -= $ 1 T $ 1 $ 7M X =-> @-WrV V b L^]YMV @8R b WSA~A~W b S@ b Z LQP+K > WrZ$P+KM@-KMP+K3Z.LnmU@WrV V b L^]YMV @ 0 z > PSZ @fWXOYM@LNZ$V > @KMY]A'^]@ b > @BK¤V > @
(261) @U`h b @UZ Z LQP+KuLQZi]L @ b @BKSV LWrV.@Ui
(262) &! % 8 nf(nf(Qnf(
(263) &!|{%(
(264) ^!B>G%(
(265) G!$%
(266) ^!{% 8
(267) &! % n
(268) &! % > 8
(269) &! % Z LhmU@1! %
(270) &! % Z LhmU@1! % 8 D
(271) &! % Z LhmU@1! % 4N'1 b @ @ b ZV P'V > @
(272) Z V b YMTUVY b @
(273) Z LhmU@S. =-> @ b @UZYMONV.LKMRRS@BKM@ b WXV LKMR Y]KMTUV LQP+Ku@U_]Y]WrV LQP+KZ.@UV-TBWSK^@jA~W3KMLh]YMOWrV.@Ui.
(274) 5 Q * 7
(275) 9-< -= G @ oB N'1 o
(276) 1( => S
(277) 1(. , N1 T $ 1 $ $ @ oB = > S $A< -=?$ < -=L Y$ 1 $ < !=I$ < != $E@ TB P1 $E< -=L . $ "
(278) 1( $ 1!
(279) G 1V $ $ o >
(280) 1( $O1;
(281) 1V H7. 5 -* Q 7
(282) 9 0 #< != K
(283) GL , $ $ $F@ oB $ 0 < -=L Y$ 0 < -=L Y$ @ oB $ 0 < -=L N1 < -=L Y$ 0 #< != 4N'1#< != $ @ oB $ 0 < -=L N1 < -=L H7 5 1!S 7
(284) *-QR'1S Q * $E*!Q$ >* 1>>1 B $ VV $ 0-WW$EN YX. P WXV P+A'Z.
(285) k.
(286) . MR4J2 8 zP+KM@f!4/ % 8 /h!4/ % 8 /A9!4/ %8 / # ]h!4/ %8\mU@ b P!4/nE% -PMKM@f!4/7n% -! 47 / n% h!4/7n% # ]h!4/ % A9!,4/7n% # `h! / % @f!4/7n% # ]h! / %a/ @f! / % 8 ]/ ! 4/ % 8 /jmU@ b PU!/ % 8 .
(287) *-QR L V 1 ! ( > 1P1!S $ / 7 5 T 7 ;
(288) *-QR L V 1 ! ( > 1P1!S $ 7 5 * Q 7 ; @U+VBV >. u@ RS@BKM@ b WrV LKMR Y]KMTUV LQP+KMZ P b V > @u@U`h b @UZ.Z LQP+KWSKMi V > u@ TBY]A'YMOWrV LQS@Z.LnmU@JW b @uLQZ PSOWrV.@Ui-WSKMi1V > @ WrZ \]A~hMV P3V LQT
(289) WrOYM@P V > @
(290) TUPM@6TULQ@BK3V ZLQZ@U+V b WrTUV @Ui2 5 T 1
(291) -= 7
(292) ow . o $E< !=,#N 7 * Q 1
(293) -= 7
(294) /ow b* Q,$ < -= V!W N 7 5 T ( 1(R 7
(295) "1!S *2>1 o 1
(296) -=I$ N,$A 7 * Q ( 1(R 7
(297) "1!S *2>1 b* Q 1
(298) -=I$ N,$A 7 Q B 1 &*Q ( 1(R o2 - 1 R,$
(299) J RJL 6 $ YXO1"*2>(R' YX . . .
(300) . . . . . . DqSmXl+D]n#"-XlSl+m ). =-> @
(301) rW b LWSKMTU@LQZ
(302) WrOQZ P~TUP+A h]YMV5WS^MOQ@ ;! Y]KMOQLr@'LK \ p%a2. 5 -* QR L V 14 !( >'1P1!S R"* LV 7
(303) 21!S "*2>1 1 *2> R3 Q B 13#R"* /LV . $ . /ow * Q . . . . ! . 1pq! % . . 7. $ < -= V $ -W#N Y$.N,$fL 7 H 1(R 4 - 1- 1 R $D#*Q ( 14R 4 o 2 H 1(R &%$U
(304) J"R JL 6 $ ' YX. 4m Dm- Xl rl+m-nSn
(305) !¨n Dm % ] l © yx.¸vU© \ p b @BA~WrLKMZV > @~A'P b @'K]WrV5Y b WXO -WB\V P@U`h b @UZ ZZ.P+A'@jh b PSR b WSA A'LKMR h b LA'LQV LQS@UZ Z5YMT > WrZi]L b @UTUV
(306) Z.V b YMTUV5Y b @Fi]@UZ TU@BK3VWSKMiJi]@UTUOW b WXV LQP+KMZ
(307) -LQV > A'P b @FV > WSK¤P+KM@LK]h]YMVBVLQZKMPSV
(308) WrZZ V b WXLNR > V¨ P b -W b i' -LQV > WrV V b L^]YMV.@R b WSA~A~W b Z$V Pi]@US@UOQP+huW!TUP b b @UZh]P+KMi]LKMR~Z > P b V > WSKMiKMP3V5WrV LQP+K73TUP+KMZ @U_]YM@BKSV OQ\V > @ R b W3A~A~W b Z-A'YMZ V^@jA~W3KMLh]YMOWrV.@Ui ^3\uV > @YMZ @ b =-> @UZ.@jA~WSKMLh]YMOWrV LQP+KMZW b @WrOQ -WB\MZhPSZ Z L^MOQ@S7Z LKMTU@'Z LA'L¡ OW b A~WSKMLh]YMOWrV LQP+KMZ
(309) W b @i]P+KM@LK3V @ b K]WXONOQ\u -LQV > LKV > @LA~hMOQ@BA'@BK3V5WrV LQP+K¤P
(310) \ p'! -Pr f@US@ b P b PSV > @ b V¨\`h@UZ @U]h b @UZ Z LQP+KMZV > @WrV V b L^]YMV @
(311) i]@UZ T b LhMV LQP+KoTBWSKu^@jA'YMT > Z.LA hMON@ b WSKMiuV > @
(312) RS@BKM@ b WXO A'@UV > PMiuZ LA~hMOQ@ b =-> LQZ[LA hMON@BAC@BKSV5WXV LQP+K'P WrV V b L^]YMV.@8R b W3A~A~W b Z TUP+KMZ LQi]@ b Z$@BWrT > WrV.V b L^]YMV @ rZ V b YMTUV5Y b @$TUP+A'^MLK]WrV LQP+K73@US@BK V > P+YMR > LK¤V > @ \ p A'PMi]@UO W'R3LN3@BK Y]KMTUV LQP+KA~Wz\~PMKMON\ > WzS@P+KM@ b @UOQ@UWSK3V-Z V b YMTUV5Y b @
(313) LK]h]YMVV¨\]h]@S => LNZ TBWSK!ON@BWXi~V PA'YMOQV LQW b LWXV @ Y]KMTUV LQP+KMZ > LQT > KM@U@Ui'V P
(314) ^]@-A~WSKMY]WrOQOQ\ b @UiYMTU@Ui'V P
(315) ^]@fZ P3ON3@UijWSKMi~A~WSKMLh]YMOWrV @Ui =-> @Jh b LKMTULhMOQ@S'WSKMiZ.LNRMKMLTBW3KSVB
(316) Wri]rWSK3V5WrRS@oV PV > @YMZ @oP WrV V b L^]YMV.@R b W3A~A~W b Z LNZuV > @ WXi]i]LNV.LNPMK]WrO LK P b A~WrV LQP+K7 8W b LWSKMTU@~WSKMi Y b V > @ b A'P+AC@BKSV ZTBWSKu^]@'@UMV b WrTUV @Ui b P+A V > @@U_]Y]WrV LQP+KMZBY]KMONLr@'V > @ \ p TUP+Y]K3V @ b h]W b V ZB (' &". =. #). +*.
(317) 4 =U 4
(318)
(319) . .
(320)
(321)
(322)
(323) !" # $ %& '%)(*+(,-./
(324) 021
(325) 3 4 5
(326) 6'
(327) 879.:7;<:1
(328) =/6'.
(329) =.:7>@?.BA87/ '
(330) =<:1 81 5
(331) 6'
(332)
(333) 87C.DE
(334) 87F<G
(335)
(336) HID.J
(337) K
(338) 3&L:
(339) % L "MH
(340) :N %&O'MP L L N
(341) 3&?.QA .
(342) HIR<0
(343) K
(344) 3&L:
(345) % L "MH
(346) :N %&SL T K
(347) 3&?.BA. . '%U(V+(V-WX
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