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Unification via Explicit Substitutions: The Case of Higher-Order Patterns

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(1)Unification via Explicit Substitutions: The Case of Higher-Order Patterns Gilles Dowek, Thérèse Hardin, Claude Kirchner, Frank Pfenning. To cite this version: Gilles Dowek, Thérèse Hardin, Claude Kirchner, Frank Pfenning. Unification via Explicit Substitutions: The Case of Higher-Order Patterns. [Research Report] RR-3591, INRIA. 1998, pp.33. �inria00077203�. HAL Id: inria-00077203 https://hal.inria.fr/inria-00077203 Submitted on 29 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Unification via Explicit Substitutions: The Case of Higher-Order Patterns Gilles Dowek , Th´er`ese Hardin , Claude Kirchner , Frank Pfenning. No 3591 D´ecembre 1998 ` THEME 2. N 0249-6399. apport de recherche.

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(78) . Švk ˆq‰ Àq‘‰ –‘vh„‡†L€€_ sqv%ˆq‰ˆ6†L€Q}qƒ ~ƒ}ʁLÂ4 6†L  vk‘}¸~}¸ sqv‰~uf #€‹X â‹c :vh¡ E ¾¿„‡†L€„kˆ#€ˆq‰ÄÅ ÏÖ

(79)  A± Ú  šW)>65.)%+8791 7R=P+87*$  C+8786˜Lƒ‘ E 9 $  C+878Â遃‘_‰sqƒ‘ ‡˜E~‰_†–‰~uf #€‹` ¿‹Z $vh¡%€Í†LuxŒ:¡q† vk‘u ¼–sqI‰vÂa‘vhv½ƒ†L‘~͆LŒ#€vh‰T †L‘vƒ}#€‹†L # #€~vh¡0 Ï†O‰vhŽˆqvk}q„hvL ¡¨~‰ ~}q„k Œ$ƒˆ#}q¡0½I†L‘~Á¾ †LŒ#€vh‰Ä˜¨~nřvIÅ 0 T 23=-=-= O5M8VÅ šJ‰ ˆq‰ˆ6†L€n˜I¼Æv–†ƒ‰‰ˆ#u?vÆ s#‘ƒˆ#‚Isqƒˆ# œ sqvÆ 6†L $vk‘‡˜¬ s6†L †-½I†L‘~͆LŒ#€vÆ~‰’¡#vk}qƒ vh¡Œ‹!~ ‰4}6†Lu?v Évk½¬vk}¸~ÁÂ4~ ‰-†ƒ„k ˆ6†L€QÂ遃‘u ~}ʆ vk‘uÌuxˆq‰ Œ$ v c¾¿vVè 6†L}q¡#vh¡QÅ ÏÖ 

(80)  A±  Ú "! š E$¾n vk‘u ~‰Š† E9 $  C+878-~ÁÂq†L€€I~ ‰_‰ˆ#Œ# vk‘u?‰ÜLÂZ sqv Â遃‘u 0 TZ !!'72 =-=-=/'"!-8 †L‘v‰ˆq„s¸ s6†L 

(81)  2 =-=-= 5 =CMNO¼–sqvk‘(v  2 <-=-=-=7<

(82)  5 <5' 2 <-=-=-=7<5' ! †L‘v%¡¨~‰ ~}q„k ¡#(v Ƒˆ#~ “}Ï~}¨¾ ¡¨~„hvh‰Ÿ€‡¼Ævk‘ s6†L}Oƒ‘ÆvhŽˆ6†L€

(83)  GœÅ š E$¾n 6†L  vk‘}X~‰Ÿ„‡†L€€vh¡  X  ~ÁÂ܆L€€6~ ‰Ÿu?vk †E¾n½ƒ†L‘~͆LŒ#€vh‰ s6†‡½¬v†L ƒuf~„! ¿‹Z :vIÅ ¶ }ɉˆq„s†f vk‘u†L€€Š sqv‰ˆ#Œ# vk‘u?‰L’ sqv%h Â遃‘& u 0 T$ -! '72 =-=-= '"!D8-†L‘v ‰ˆq„s¸ s6†L$ #

(84) $# Å ¶ } ƒˆ#‘X†L # #‘¬†ƒ„s Çˆ#}#~ÁÀ6„‡†L ~ƒ}_˜–¼ŸvÏ ‘†L}q‰€Í†L v vhŽcˆ6†L ~ƒ}q‰?~} sqv¸‰~uf #€‹¾n â‹c :vh¡ E#¾ „‡†L€„kˆ#€ˆq‰ ÉvhŽcˆ6†L ~ƒ}q‰ sqv E$¾¿„‡†L€„kˆ#€ˆq‰Ï·º¹L»¿ÅǔŸ‘ˆq„k~͆L€–~}Ñ sqv¯ ‘†L}q‰€Í†L ~ƒ})~‰x sqvO #‘ƒ :vk‘ ‘v‡†L u?vk}c ?LÂÂa‘vhv¯½I†L‘~͆LŒ#€vh‰‡˜œ‰~}q„hv¯s#~‚Isqvk‘¾¿ƒ‘¡#vk‘f½I†L‘~͆LŒ#€vh‰?†L}q¡ „‡†L # ˆ#‘vV¾â†h½¬ƒ~¡¨~}#‚щˆ#Œ¨¾ ‰ ~ ˆ# ~ƒ}q‰†L‘vO‘vk #€Í†ƒ„hvh¡ÑŒ‹Ýu?vk †E¾n½ƒ†L‘~͆LŒ#€vh‰e†L}q¡ 57R10

(85)  >5¬˜’~nřvIō˜ Àq‘‰ ¾¿ƒ‘¡#vk‘‘vk #€Í†ƒ„hvku?vk} ¡#vk}qƒ vh¡?Œ+‹ 0 T&%  8VÅ4r s#~‰œ‚†L e~‰’Œ#‘~¡¨‚¬vh¡f s#‘ƒˆ#‚Ise sqv-‰L¾¿„‡†L€€vh/¡  7 +89Q;  6N#>5`LІ` vk‘u ¼–s#~„sݑ†L~‰vh‰! sqvÂa‘vhv?½I†L‘~͆LŒ#€vh‰%  sqvk~‘x #‘ƒ :vk‘!„hƒ} vVè ‡˜ ¼–s#~„s_˜ ~}ҁƒˆ#‘! #‘vh‰vk} †L ~ƒ}_˜ ~‰~}#~ ~͆L€€‹Ò sqvOƒˆ# vk‘u?I‰ ?„hƒ} vVè ‡ÅÝr s#~‰ #‘vV¾¿„hcƒÐZ~}#‚ǁLÂ`† E#¾n vk‘u $˜’¼–‘~  vk'} ('Ÿ˜œ~‰ ¡#vVÀq}qvh¡Ê†ƒ‰  '

(86) *) 01< # 8–¼–sqvk‘*v F §IÅ ) 0S0XE+*  8<SG 8

(87) ES* 0 ) 01 <SG I :78S8V˜ w¨Å ) 0S01 'D8<SG 8

(88) *) 201 <SG 8 ) 0 ' <SG 8V˜ ¤¨Å ) 0,+<SG 8

(89) :M C-/. ! TqÅ ) 0 TH<SG 8

(90) TZ CMNO!¿Å š`‰–‰sqÄ¼–} ~}Ç·º¹E»¿˜# #‘vV¾¿„hZƒÐc~}#‚e~‰-†sqƒu?ƒu?ƒ‘ #s#~‰uÌÂa‘ƒu E#¾¿„‡†L€„kˆ#€ˆq‰ - E$¾¿„‡†L€„kˆ#€ˆq‰‡Å 0 ² Ú  Ú ° A±  Ú  Z_vk xŒ:v-S † E#¾n vk‘u¸Q˜ ~‰ S† E#¾n 6†L  vk‘}e~ÁІL}q¡?ƒ}#€‹~ÁÂ:~ ‰œ #‘vV¾¿„hZƒÐ¬vh¡fÂ遃‘u  ' ~‰-† E$¾n 6†L  vk‘}_Å 1325464/78(Ƌ0¡#vVÀq}#~ ~ƒ}ҁL† E¨¾n 6†L  vk‘}_˜4†OÂa‘vhv½ƒ†L‘~͆LŒ#€v ) Z„h„kˆ#‘‰xƒ}#€‹Éˆ#}q¡#vk‘x sqvÂ遃‘u 0 )  2 =-=-=  5 8VÅOr sqv? #‘vV¾¿„hZƒÐ¬vh¡Â遃‘u L‰ˆq„s҆¸‰ˆ#Œ# vk‘u ~‰%Œ‹Ç¡#vVÀq}#~ ~ƒ}сL– sqv Âaƒ‘& u 0 )  C N ! 2 =-=-=65M8Ƽ–sqvk‘v% sqv 9’†L‘vx†L€€Š¡¨~‰ ~}q„k `¡#(v Ƒˆ#~ “ö}¸~}q¡¨~„hvh‰-¼–s#~„s0†L‘v †L€€_€‡¼Ævk‘- s6†L} ƒ‘vhŽcˆ6†L€_ a GŒ:vh„‡†Lˆq‰:v 323=-=-=;O5?†L‘vŒ:ƒˆ#}q¡X~}¸ sqv vk‘u¸= Å < Z. îÜî,õ^ ‡þ n.

(91) «. <## +" +4(*) 87

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(93)  A± Ú  š $  C+878 "!"8

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(97)   ~‰Ê† E$¾¿‰ˆ#Œq‰ ~ ˆ# ~ƒ}<¼–sqI‰v EQ¾n}qƒ‘ue†L€xÂ遃‘u 2 =-=-=65_= C N ~‰e‰ˆq„s s6†L e†L€€-~ ‰?¡#v?Ƒˆ#~ “ö})~}q¡¨~„hvh‰e9†L‘vÏ¡¨~‰ ~}q„k ¯†L}q¡ €vh‰‰? s6†L} ƒ‘ vhŽcˆ6†L€Q WGœÅ ,.    . r sqv/E$¾n 6†L  vk‘}q‰`†L‘v%‰ †LŒ#€vˆ#}q¡#vk‘J‰ˆ#Œq‰ ~ ˆ# ~ƒ} „hƒuf :I‰~ ~ƒ}ʆL}q¡Ïˆ#}q¡#vk‘‚I‘†EÂa ~}#‚qÅ 0 ² Ú  Ú ° A±  Ú "! ¶  †L}qM ¡ 8 †L‘v% ¿¼Ÿe 6†L  vk‘} ‰ˆ#Œq‰ ~ ˆ# ~ƒ}q‰Ä˜# sqvk}¸ sqv;$¾n}qƒ‘ue†L€ŠÂaƒ‘úL :=\0]W^ C_8–†L}qE ¡  ^ 8–†L‘v 6†L  vk‘}ʉˆ#Œq‰ ~ ˆ# ~ƒ}q‰‡Å 1325464/784Z_vk 

(98) 2 =-=-=465 =*C N †L}q¡ 8

(99) '723=-=-=J'"! =C

(100) !Å :=\0]L^C_8

(101) : =\0S01 2 =-=-=4 5 =CMN8 ^C_2 8

(102) :=\012  C*!M=-=-=D65 C*!`=*C N 8 2

(103) :=\012 I :78 =-=-=60165 I :78=*CMN. ¼–s#~„sÊ~‰„k€v‡†L‘€‹X†f 6†L  vk‘} ‰ˆ#Œq‰ ~ ˆ# ~ƒ}_Å  ¶  G?k #¨˜¨ sqvk}.  ^i8

(104) 10 23=-=-=465 =CMN8 ^(0 '723=-=-=J'"!7=C 8

(105)  2  8Y!M=-=-= 5  8/!`=\0 CMN ^ 0 ' 2 =-=-=Z' ! =C 8S8

(106) 27 8Y!M=-=-=65 8/!`= ' N 2 =-=-= '"!7=C

(107) ‰~}q„hv;69G?k"#¨˜ 9S 8Y!

(108) ' ’ sqvk}Ɇƒ‰ 9 'œG ˜+'  D<-=-=-= <5' O<5' N 23=-=-=J'"!`†L‘v%¡¨~‰ ~}q„k ¡#v?Æ ‘ˆ#~ “ö} ~}q¡¨~„hvh‰e†L}q¡Ñ sqvk‹)†L‘v¯€Ä¼Ÿvk‘? s6†L} ƒ‘?vhŽcˆ6†L€ ÇÅÝr sˆq‰e9^ 8!~‰?†.  6†L  vk‘} ‰ ˆ#Œq‰ ~ ˆ# ~ƒ}_Å  ¶ ÂG #¨˜¨ sqvk}.  ^i8

(109) 10 23=-=-=465 =CMN8 ^(0 '723=-=-=J'"!7=C 8

(110) 27 8Y!M=-=-=65 8/!`=\0 C N !!^ 0 '723=-=-=Z'"! =C

(111) 8S8

(112)  2  8Y!M=-=-= 5  8/!`=C  N. 9S 8Y!

(113) 'Q~Á 69"" # †L}q¡ 9 # # $ I 1¼–sqvk}e9 l ` # sˆq‰Æ†L€€q sqv 69  8Y!$†L‘v-†L€€q¡¨~&%Qvk‘vk} ¡#vƑˆ#~ “}Ê~}q¡¨~„hvh‰‡Å-r sqvk‹Ê†L‘v!†L}q¡Ê€‡¼Ævk‘` s6†L}Ɂƒ‘`vhŽcˆ6†L€Š  0 'G # #*8 (I ԆL}q¡¸ sˆq‰  ^LŸ8 ~‰-† 6†L  vk‘}ʉˆ#Œq‰ ~ ˆ# ~ƒ}_Å ¶ Šue†h‹Œ$vœ sqvœ„‡†ƒ‰v’ s6†L Ü sqv’}qƒ‘ue†L€¬Â遃‘u L 5  8Y! ~‰Š sqvœ¡#v Æ ‘ˆ#~ “ö}x~}q¡#vVÃe0 )G # #M8

(114) *I  ~} s#~‰Š„‡†ƒ‰v4 sqv ‰ˆ#Œq‰ ~ ˆ# ~ƒ}A^2$8 „‡†L}!‰ ~€€IŒ$v4‘vh¡¨ˆq„hvh¡%  27 8Y!M=-=-=65 . 27 8/!`=MC  N6. ! . 2 ~}Ê s#~‰„‡†ƒ‰v! sqv!~}q¡¨~„hvh‰ 2  8Y!¿˜65 . 2 8/!œ†L‘v‰ ~€€4¡¨~‰ ~}q„k †L}q¡Ê sqvk‹Ê†L‘v!€‡¼Ævk‘ s6†L}. ìBí îŠìaï. ˜.

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(124) Å ¶ 3Â 

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(126) 0XES'-8D !

(127) E 0 '[:=\0]6^C_8/! 8VÅ Ÿ‹f sqv- #‘vk½c~ƒˆq‰Ÿ€vkufue†¨˜c sqv }qƒ‘ue†L€ŠÂ遃‘u Lœ sqv!‰ˆ#Œq‰ ~ ˆ# ~ƒZ} :=\0] ^ C_8~‰`†? 6†L  vk‘}‰ˆ#Œq‰ ~ ˆ# ~ƒ}†L}q¡ sˆq‰ Œc‹¯ sqv`~}q¡¨ˆq„k ~ƒ}Ïs‹Z :ƒ sqvh‰~‰ sqv`}qƒ‘ue†L€:Âaƒ‘u LÂÜ sqv` vk‘m u '[:=\0]#^ C_8/! ~‰-†L}ʆL ƒuf~„ 6†L  vk‘}_Å r sˆq‰ sqv%}qƒ‘ue†L€QÂaƒ‘u L   -!_~‰J†L}ʆL ƒuf~„ 6†L  vk‘}_Å ¶ # 

(128) 0 e'72 =-=-= ' 5*8e sqvkL}   -!

(129) 0  -! '727 -!B=-=-=)' 5 -! 8VÅ Ƌ ~}q¡¨ˆq„k ~ƒ} s‹Z $ƒ sqvh‰~‰ sqv}qƒ‘ue†L€4Âaƒ‘uL '72  !`<-=-=-=<5' 5 -!Ÿ†L‘vf†L ƒuf~„ 6†L  vk‘}q‰‡År sˆq‰ sqv}qƒ‘ue†L€QÂ遃‘u,L   !Š~‰-†L} †L ƒuf~„% 6†L  vk‘}_Å ¶  

(130) T$ 8/!Q sqvk?}   -!

(131) TZ 8 ^ !¿Å Ƌ? sqv` #‘vk½c~ƒˆq‰ €vkufue†¨˜¨ sqv`}qƒ‘ue†L€:Â遃‘u L 86^ -~‰œ†` 6†L  vk‘}?‰ˆ#Œq‰ ~ ˆ# ~ƒ}_Œr sˆq‰œ sqvŸ}qƒ‘ue†L€qÂaƒ‘u L  !#~‰œ†L}e†L ƒuf~„  6†L  vk‘}_Å . . . . . <. 0. ² Ú  Ú ° A±  Ú  š ƒuf~„Ò 6†L  vk‘}q‰0†L‘v҉ †LŒ#€vLj#}q¡#vk‘É 6†L  vk‘} ‚I‘†EÂB ~}#‚q˜x~nřvIÅ Âaƒ‘ɆL}‹ †L ƒuf~„% 6†L  vk‘}q‰ X†L}q¡ 'L˜¨ sqv}qƒ‘ue†L€QÂ遃‘u,LÂ@0 T % '-8 O~‰-†L} †L ƒuf~„ 6†L  vk‘}_Å 1325464/78(ƋO~}q¡¨ˆq„k ~ƒ} ƒ}¸ sqv%‰ ‘ˆq„k ˆ#‘vxLÂ$Å ¶  

(132) E R sqvk}L0 T % '-8 

(133) E 0 T % '-8  R ˜ Œ‹Ç~}q¡¨ˆq„k ~ƒ} sc‹c :ƒ sqvh‰~‰! sqv }qƒ‘ue†L€$Âaƒ‘u L 0 T % '-8  R ~‰ †L}φL ƒuf~„` 6†L  vk‘}_Ŝr sˆq‰ sqv`}qƒ‘ue†L€$Â遃‘uL 0 T&% 'D8 O~‰-†L} †L ƒuf~„x 6†L  vk‘}_Å ¶  

(134) 0 H R2 =-=-=  5R 8Ÿ sqvkZ} 0 T&% '-8 

(135) 0 0 T&% 'D8  R2 =-=-=A0 T % '-8  5R 8VÅ Ƌ ~}q¡¨ˆq„k ~ƒ}esc‹c :ƒ sqvh‰~‰œ sqv}qƒ‘ue†L€qÂ遃‘u?‰ LÂ: sqv– vk‘u?‰ 0 T % '-8  R9 †L‘vJ†L ƒuf~„  6†L  vk‘}q‰J†L}q¡Ï scˆq‰ sqv}qƒ‘ue†L€ŠÂaƒ‘úL 0 T&% 'D8 O~‰-†L} †L ƒuf~„x 6†L  vk‘}_Å ¶  

(136) V  -! G1V

(137) T I! sqvkL} 0 T % '-8 

(138) V  -!-†L}q¡Ñ sˆq‰~ ~‰f†L} †L ƒuf~„  6†L  vk‘}_Å ¶  

(139) T$ -!¨ sqvk+} 0 T&% '-8 

(140) ' !#†L}q¡!~ ‰Š}qƒ‘ue†L€ZÂ遃‘u<~‰’†L}f†L ƒuf~„Æ 6†L  vk‘} Œ‹X sqv #‘vk½Z~ƒˆq‰€vkufue†¨Å . . . . . . . . îÜî,õ^ ‡þ n.

(141) §. <## +" +4(*) 87

(142) "'+@2  71=# 3,  %=P+ #7R8)P+87 71S? 0'+8  V5. <. J𠉯u?vk} ~ƒ}qvh¡É†LŒ$Ä½¬v sqv` #‘ƒ $vk‘ ~vh‰L  6†L  vk‘}¸ˆ#}#~ÁÀ6„‡†L ~ƒ}¸‘vk€‹Oƒ}φL€‚¬vkŒ#‘†L~„% #‘ƒ ¨¾ vk‘ ~vh‰–LÂÜ 6†L  vk‘}X‰ˆ#Œq‰ ~ ˆ# ~ƒ}q‰‰ˆq„sφƒ‰Æ~}ƒ“vh„k ~½c~ ⋬ŒËÇvJÂaZ„kˆq‰Æ}q‡¼ ƒ}X sqv` #‘ƒ $vk‘ ~vh‰–L sqvh‰v‰ˆ#Œq‰ ~ ˆ# ~ƒ}q‰‡Å .      ( . . ² Ú  Ú °A± Ú  Z_vk 2-<-=-=-=7<

(143) 65xŒ:v`}ˆ#uxŒ:vk‘‰-†L}q¡? 5

(144) 2 =-=-=  5_=*C N Œ:v†x 6†L  vk‘}¸‰ˆ#Œq‰ ~Á¾ ˆ# ~ƒ}_ÅÆ”Ɓƒ}q‰~¡#vk‘ sqv%‰ˆ#Œq‰ ~ ˆ# ~ƒ} 

(145)

(146) 23=-=-=

(147) N =C ¼–sqvk‘vŒc‹Ï¡#vVÀq}#~ ~ƒ}3F Âaƒ‘-†L€€ , ‰ˆq„s s6†L :*',) >ܘ

(148)  

(149) ,˜ ƒ sqvk‘¼–~‰v

(150) 9

(151)  Â遃‘‰ƒu?v}qvk¼ ½I†L‘~͆LŒ#€v  Å r sqvk} ¼Ÿvs6†‡½¬v  ^ 

(152)  ,/.6Å 1325464/784[ ~‘‰ }qƒ ~„hvf s6†L  sqv

(153)  †L‘v¼Ÿvk€€ ¡#vVÀq}qvh¡Ý‰~}q„hv?†L€€’ sqW v 9 †L‘v?†ƒ‰‰ˆ#u?vh¡0 XŒ:v ¡¨~‰ ~}q„k ‡Å  ^ 

(154) 0123=-=-=4 5_=*C N 8 ^0

(155) 23=-=-=

(156) N =C 5 8 5 012  !M=-=-=65  !`=*C N ^ 68VÅ ƈ# ‰~}q„hv > 'Gœ˜ 9S !

(157) 

(158)  

(159) ,˜q sˆq‰  ^ 

(160) 0 :=-=-=`> =C 8

(161) ,/.6= Å < [6ƒ‘ÉvVÃq†Luf #€v҆ ‘~‚Is É~}½¬vk‘‰vсLÂ? sqvÇ 6†L  vk‘} ‰ˆ#Œq‰ ~ ˆ# ~ƒ} 

(162) 0 :=_= =WC78Ï~‰ 

(163) 0 := =_=_=  =OC  8Ɖ~}q„h v  ^ 

(164) 0 :=_= =OC  8 ^ 0 := =_=_=  =_C  8

(165)  0 :=_=_=QC  8

(166)  ,/.

(167) Å. ƒ ~„hvf s6†L ‡˜ †ƒ‰~} s#~‰%vVÃq†Luf #€vI˜ †O‘~‚Isc %~}½¬vk‘‰veL†O 6†L  vk‘}݉ˆ#Œq‰ ~ ˆ# ~ƒ}Ç~‰%}qƒ ~ ‰vk€Á’† 6†L  vk‘}ɉˆ#Œq‰ ~ ˆ# ~ƒ}¸~}ς¬vk}qvk‘†L€nÅ šJ‰–„hƒuf :I‰~ ~ƒ} ~‰ Œ$v‘v‡†ƒ¡XÂa‘ƒu €vVÂa  ‘~‚Is ‡˜6¼Ÿvs6†‡½¬v sqvÂ遃€€‡¼–~}#‚¯„hƒ‘ƒ€€Í†L‘‹¬Å  Ú ² Ú  A³#² ×  šJ}‹O 6†L  vk‘} ‰ˆ#Œq‰ ~ ˆ# ~ƒ}Ê~‰–~}ƒ“vh„k ~½¬vIÅ 0.  . . !. #". 4†L  vk‘}ljˆ#Œq‰ ~ ˆ# ~ƒ}q‰†L‘v~}ƒ“vh„k ~½¬vI˜

(168) scˆq‰%†L}ÉvhŽcˆ6†L ~ƒ}Lœ sqv!Âaƒ‘u9TZ !

(169) %$ 's6†ƒ‰†L u?I‰ Ÿƒ}qv`‰ƒ€ˆ# ~ƒ}_Å ƈ# sqvk‹?}qvhvh¡¯}qƒ ƌ$vJ‰ˆ#‘a“vh„k ~½¬vI˜Z scˆq‰Æ‰ˆq„sφL}OvhŽcˆ6†L ~ƒ}X&  ue†h‹?s6†‡½¬v }qe‰ƒ€ˆ# ~ƒ}_Å ¶ }¸ s#~‰J‰vh„k ~ƒ} ¼Ævx‰sqÄ¼ s6†L -‚I~½¬vk}0† 6†L  vk‘}0‰ˆ#Œq‰ ~ ˆ# ~ƒ} †L}q¡Ê†f vk‘u e¼Ÿv„‡†L}Ï¡#vh„k~¡#v~Á e~‰ ~}X sqv~ue†L‚¬vL x†L}q¡X~ÁÂ܉!¼Æv„‡†L}¸„hƒuf #ˆ# v sqv` #‘vk~ue†L‚¬v%L  ˆ#}q¡#vk‘ Å ÏÖ 

(170)  A±  Ú  <š ¡# v Ƒˆ#~ “}e~}q¡#vV(à 'e~‰Æ‰†L~¡?   V7Æ~}O†x}qƒ‘ue†L€

(171) vk‘u GB‘vh‰ _Ŝ†x}qƒ‘ue†L€ ‰ˆ#Œq‰ ~ ˆ# ~ƒ} I F . ìBí îŠìaï.

(172)   

(173)  

(174) 

(175)  !"

(176) #

(177) $

(178) 

(179) %"'&(*)$+-,."'+/ 1032465)$+8789;:<71=>+87@?AB  C+87". $˜¨~ÁÂ. I :Z„h„kˆ#‘‰–~}H$˜ 0 ?2 =-=-= 65Q8V˜#~Á '

(180) Gǁƒ‘ 'ρZ„h„kˆ#‘‰–~}¸‰ƒu?v;69ö˜ 0 TZ !  2 =-=-=  5 8V˜q~Á 'ρZ„h„kˆ#‘‰–~}Exƒ‘~}¸‰ƒu?v; 9 ˜ 23=-=-= 5 =CMN:˜¨~Á 'XZ„h„kˆ#‘‰–~} ‰ƒu?v(9’ƒ‘–~Á ' l GœÅ E.    . §I§. '. [qƒ‘`vVÃq†Luf #€vI˜

(181) sqvx~}q¡#vVà :!c„h„kˆ#‘‰J~}É sqvx vk‘u E¨˜$Œ#ˆ# - sqv!~}q¡#vVà e¡#cvh‰J}qƒ ‡Å-šJ}‹ ~}q¡#vVÃρZ„h„kˆ#‘‰~} 0 T 2 =-=-= 65Q8@GB fŒ:v‘v‡†ƒ¡ †ƒ‰0 T$ CQPD! 2 =-=-= 5Q8RIVÅ •J}#€‹ †ÊÀq}#~ vÏ}cˆ#uxŒ:vk‘eLÂ~}q¡¨~„hvh‰?¡#0}qƒ ?c„h„kˆ#‘e~} †Ê‰ˆ#Œq‰ ~ ˆ# ~ƒ} ɆL}q¡)ƒ}qvτ‡†L} „hƒuf #ˆ# vx s#~‰–Àq}#~ v!‰vk ‡Å r sqvk} Âaƒ‘-v‡†ƒ„s ~}q¡#vVÃQ˜qƒ}qvx„‡†L}ʄsqvh„ÐÏ~Á’~ -Z„h„kˆ#‘‰~}Ɇ vk‘u $Å r scˆq‰-ƒ}qv„‡†L} ¡#vh„k~¡#v%~Á’†L€€_ sqv%~}q¡¨~„hvh‰c„h„kˆ#‘‘~}#‚¯~+} ¯Z„h„kˆ#‘~H} cÅ 0 ² Ú  Ú ° A±  Ú   

(182) Ö ²E°  Ú   Ö  dz Z_vk Œ:v-† 6†L  vk‘}O‰ˆ#Œq‰ ~ ˆ# ~ƒ}__˜ Œ$v-†}qƒ‘ue†L€ vk‘u GB‘vh‰ _Å 8’Œ:v†x}qƒ‘ue†L€Q‰ˆ#Œq‰ ~ ˆ# ~ƒ} IVŜr sqvk‘vvVÃZ~‰ ‰ †x vk‘u  R GB‘vh‰ _Ŝ†x‰ˆ#Œq‰ ~ ˆ# ~ƒ} 8 R I4‰ˆq„s¯ s6†L 

(183)  R  ! GB‘vh‰ _/Å 8

(184) 8 R ^ .I ~ÁІL}q¡¯ƒ}#€‹~ÁÂ_vk½¬vk‘‹f~}q¡#vVÃeZ„h„kˆ#‘‘~}#‚x~}  GB‘vh‰ _Å 8 IƁZ„h„kˆ#‘‰–~E } cÅ 1325464/78(ƋO~}q¡¨ˆq„k ~ƒ} ‡½¬vk‘J sqv‰ ‘ˆq„k ˆ#‘vxL GB‘vh‰ _Œ IVÅ ¶  

(185) ES'J sqvk} sqvk‘v%vVè~‰ ‰  R ˜ 

(186)  R  ! ~ÁÂÆ†L}q¡0ƒ}#€‹ ~Á sqvk‘vfvVè~‰ ‰ ' R ˜ 

(187) 0XE' R 8D -!LGBŒ:vh„‡†Lˆq‰v sqv!€ƒ}#‚X}qƒ‘ue†L€4Â遃‘u L  R ~‰–L sqvÂaƒ‘u E' R IV˜ ~Á’†L}q¡ ƒ}#€‹¯~ÁÂ4 sqvk‘v%vVè~‰ ]‰ ' R +˜ '

(188) ' R [:=\0]W^C_8/!¿˜ ~Á’†L}q¡ ƒ}#€‹¯~Á’vk½¬vk‘‹X~}q¡#vVÃXZ„h„kˆ#‘‘~}#‚?~s} '`Z„h„kˆ#‘‰–~} :=\0]W^ C_8V˜ ~ÁŸ†L}q¡Êƒ}#€‹Ï~Á’Â遃‘vk½¬vk‘‹Ï~}q¡#vVà '¸‰ˆq„sÊ s6†L% 'AI :!Z„h„kˆ#‘‰J~K} 'L˜ 'AIL:Z„h„kˆ#‘‰ ~} :=\0]a^C_8V˜ ~Á’†L}q¡ ƒ}#€‹¯~Á Âaƒ‘vk½¬vk‘‹ 'X‰ˆq„s¸ s6†L ';I :xc„h„kˆ#‘‰–~} 'L˜ 'XZ„h„kˆ#‘‰–~E} c˜ ~Á’†L}q¡ ƒ}#€‹¯~Á’vk½¬vk‘‹X~}q¡#vVÃXZ„h„kˆ#‘‘~}#‚?~H} Oc„h„kˆ#‘‰~E} Å ¶  

(189) 0  '72 =-=-=^'"!D8Æ sqvk} sqvk‘v%vVè~‰ ‰  R <

(190) 

(191)  R  ! ~Á’†L}q¡ ƒ}#€‹¯~ÁÂ4 sqvk‘v%vVè~‰ ‰  R <5' R2 <-=-=-=7<5' R! ˜ 

(192) 0  R ' R2 =-=-=^' R! 8D !¿˜ ~Á’†L}q¡ ƒ}#€‹¯~ÁÂ4 sqvk‘v%vVè~‰ ‰  R <5' R2 <-=-=-=7<5' R! ˜ 

(193)  R  !܆L}q¡ ' 9

(194) ' R9  !¿˜ ~Á’†L}q¡ ƒ}#€‹¯~Á  c„h„kˆ#‘‰~E} x†L}q¡¸vk½¬vk‘‹X~}q¡#vVÃρc„h„kˆ#‘‘~}#‚¯~} ' 9 Z„h„kˆ#‘‰~H} c˜ ~Á’†L}q¡ ƒ}#€‹¯~Á’vk½¬vk‘‹X~}q¡#vVÃXZ„h„kˆ#‘‘~}#‚?~H} Oc„h„kˆ#‘‰~E} Å ¶  

(195) 01V  8Y!p'72J=-=-='"!-8Ÿ sqvk} sqvk‘v%vVè~‰ ‰  R ‰ˆq„s¸ s6†L 

(196)  R  ! . . . îÜî,õ^ ‡þ n.

(197) §‡w. <## +" +4(*) 87

(198) "'+@2  71=# 3,  %=P+ #7R8)P+87 71S? 0'+8  V5. . ~Á’†L}q¡ ƒ}#€‹¯~ÁÂ4 sqvk‘v%vVè~‰ ‰ 8 R <5' R2 <-=-=-=<5' R! ‰ˆq„s s6†L 

(199) 01V  8 R !/' R2 =-=-=' R! 8D !¿˜ ~Á’†L}q¡ ƒ}#€‹¯~ÁÂ4 sqvk‘v%vVè~‰ ‰ 8 R <5' R2 <-=-=-=<5' R! ‰ˆq„s s6†L _8

(200) 8 R ^@x†L}q¡s';9

(201) ' R9  -!¿˜ ~Á’†L}q¡ ƒ}#€‹eÂ遃‘vk½¬vk‘‹X~}q¡#vVÃXZ„h„kˆ#‘‘~}#‚e~} 8k˜+'72 =-=-=^'"!E˜qZ„h„kˆ#‘‰–~}Hc˜ ~Á’†L}q¡ ƒ}#€‹¯~Á’vk½¬vk‘‹X~}q¡#vVÃXZ„h„kˆ#‘‘~}#‚?~}HOc„h„kˆ#‘‰~}EÅ ¶ p 8

(202) ' 2 =-=-=Z' ! =*C sqvk}¸€vk Œ:v

(203) 2 =-=-=

(204) 5 =*CMN$Å r sqvk‘v%vVè~‰ ‰ 8 R ‰ˆq„s¸ s6†L _8

(205) 8 R ^@ ~ÁÂÆ†L}q¡0ƒ}#€‹¸~Á sqvk‘vfvVè~‰ ‰^8 R L sqv!Âaƒ‘u 23=-=-= ! N  = C 5 4‰ˆq„s0 s6†L 8

(206) 8 R ^@c˜ GB~nřvIŒvVÃZ 6†L}q¡¨~}#‚f sqv‰ˆ#Œq‰ ~ ˆ# ~ƒ( } 8 R vk}qƒˆ#‚Is_˜¨¼Æv`„‡†L}¸†ƒ‰‰ˆ#u?vJ¼–~ sqƒˆ# €I‰‰ L ‚¬vk}qvk‘†L€~ ¿‹¯ s6†L Æ~ Æs6†ƒ‰Ÿu?ƒ‘vJ s6†L # I G vk‘u?‰–†L}q¡O s6†L Æ sqvJvVè $ƒ}qvk}c –LÂ_ sqv ‰s#~ÁÂa –~‰–Œ#~‚I‚¬vk‘ s6†LW} > I ~ÁÂx†L}q¡ ƒ}#€‹ ~ÁÂ% sqvk‘v vVè~‰ ‰ 2 ˜ÅhÅhÅh˜ ! N  ˜ %‰ˆq„s s6†L 2  !

(207) ' 2 ˜ÅhÅhÅh˜ !6 !

(208) '"!L ˜ "! 2  !

(209)  I :I˜_ÅhÅhÅh ˜ ! N   !

(210)  I GeI

(211) #_˜ C  N

(212) C

(213) N  ˜ ~ÁІL}q¡eƒ}#€‹f~ÁÂ_vk½¬vk‘‹f~}q¡#vVÃec„h„kˆ#‘‘~}#‚!~(} ' 9_Z„h„kˆ#‘‰œ~} c

(214) ˜  I :I˜6ÅhÅhÅh˜ LIHG;I c„h„kˆ#‘-~H} ˜ ~Á’†L}q¡ ƒ}#€‹¯~Á’vk½¬vk‘‹X~}q¡#vVÃXZ„h„kˆ#‘‘~}#‚?~)} 8 c„h„kˆ#‘‰~E} Å. <. [qƒ‘J~}q‰ †L}q„hvI˜6 sqv! vk‘& u 0 (M8–~‰-~}Ê sqvx~ue†L‚¬v!L COŒ$vh„‡†Lˆq‰v :¡#cvh‰-}qƒ `Z„h„kˆ#‘-~}Ê~ ‡Å r scˆq‰ sqvvhŽcˆ6†L ~ƒ}HT$ C*!

(215) %&$  0  M8Æs6†ƒ‰-†f‰ƒ€ˆ# ~ƒ} G T

(216) 0 : M8RIVÅ ƈ# – sqv vk‘u 0 : M8 ~‰ }qƒ J~} sqvx~ue†L‚¬v!LÂC¯Œ:vh„‡†Lˆq‰ve:xZ„h„kˆ#‘‰-~}Ê~ ‡ÅÆr scˆq‰` sqvxvhŽcˆ6†L ~ƒ}ET$ C*!

(217) &$  0 : M8s6†ƒ‰ }qf‰ƒ€ˆ# ~ƒ}_Å 0 ² Ú  Ú ° A±  Ú  Z_vkA ?Œ$v?†O 6†L  vk‘}҉ˆ#Œq‰ ~ ˆ# ~ƒ}_˜  Œ$v?†O}qƒ‘ue†L€ vk‘u GB‘vh‰ _Å 8-Œ:v?† }qƒ‘ue†L€Ÿ‰ˆ#Œq‰ ~ ˆ# ~ƒ} I`‰ˆq„sÇ s6†L  sqv}qƒ‘ue†L€’Â遃‘u L   -!œ~‰%†L}݆L ƒuf~„f 6†L  vk‘} GB‘vh‰ _Å sqv`}qƒ‘ue†L€:Â遃‘u L 8 ^X~‰ †! 6†L  vk‘}¸‰ˆ#Œq‰ ~ ˆ# ~ƒ} IŸ sqvk+} f~‰†L}¸†L ƒuf~„J 6†L  vk‘} GB‘vh‰ _Å 8Æ~‰-† 6†L  vk‘} ‰ˆ#Œq‰ ~ ˆ# ~ƒ} IVÅ 1325464/78(ƋO~}q¡¨ˆq„k ~ƒ} ‡½¬vk‘J sqv‰ ‘ˆq„k ˆ#‘vxL GB‘vh‰ _Œ IVÅ ¶  

(218) ES'f sqvkZ}   -!

(219) E'[:=\0]H^?C_8/!¿Å š`A‰   -!Æ~‰†L} †L ƒuf~„O 6†L  vk‘}_˜4 sqvk} '[:=\0] ^C_8/!4~‰†L}ɆL ƒuf~„! 6†L  vk‘}_˜6 scˆq‰ '~‰J†L}†L ƒuf~„x 6†L  vk‘}†L}qH ¡ X~‰`†L} †L ƒuf~„ 6†L  vk‘}_Å ¶ ( 

(220) 0  '2 =-=-=M'"!D8! sqvk}   !

(221) 0   -!^'72  ! =-=-=('"! -! 8VÅ š`‰   -!~‰¯†L} †L ƒuf~„% 6†L  vk‘}_˜

(222) sqvkG} '727 -!¿˜ÜÅhÅhÅh˜ '"! -! †L‘v†L ƒuf~„% 6†L  vk‘}q‰‡˜

(223) sˆq‰ '72‡˜ŠÅhÅhÅh˜ '"! †L‘vx†L ƒuf~„ 6†L  vk‘}q‰`†L}q+¡ e~‰J†L}ʆL ƒuf~„ 6†L  vk‘}_Å . . ìBí îŠìaï.

(224)   

(225)  

(226) 

(227)  !"

(228) #

(229) $

(230) 

(231) %"'&(*)$+-,."'+/ 1032465)$+8789;:<71=>+87@?AB  C+87" . . §‡¤. ¶  

(232) T$ 8/!_ sqvk}?  -!

(233) TZ 8^ !¿Å’šJ‰   -!Q~‰–†L}¸†L ƒuf~„ 6†L  vk‘}_˜# sqvk}M8^X~‰ †% 6†L  vk‘}X‰ˆ#Œq‰ ~ ˆ# ~ƒ}_˜¨ scˆq‰8’~‰Æ†x 6†L  vk‘}ωˆ#Œq‰ ~ ˆ# ~ƒ}φL}q¡ef~‰ †L}φL ƒuf~„  6†L  vk‘}_Å ¶ p 8

(234) '23=-=-=Z' ! =*C sqvk}¸€vk 2D= = = 65 =CMNOŒ$v sqv‰ˆ#Œq‰ ~ ˆ# ~ƒ} cÅ ËÇvs6†h½¬v 83^@

(235) '27 !M=-=-=Z'"! -!`= . . 23=-=-=465 =C N. ~ÁÂ" k >ܘq†L}q¡ 83^@

(236) '2  !M=-=-=J'"! -!`=*C  . 5 N ~Á"   >ÜÅ ¶ }Œ:ƒ sf„‡†ƒ‰vh‰‡˜I‰~}q„hv86^  ~‰œ†J 6†L  vk‘}?‰ˆ#Œq‰ ~ ˆ# ~ƒ}_˜!'27 !_ÅhÅhÅ ' !* !6†L‘vÆ¡¨~‰ ~}q„k ~}q¡#vVèvh‰%€‡¼Ÿvk‘x s6†L}ǁƒ‘vhŽcˆ6†L€’  GœÅxr scˆq‰ '72‡˜œÅhÅhÅh˜ '"!!†L‘vf¡#vWƑˆ#~ “}É~}q¡¨~„hvh‰ †L}q¡Ï sqvk‹Ï†L‘v%¡¨~‰ ~}q„k ‡Å ¶ Љƒu?v ' 9_~‰Æ‚I‘v‡†L vk‘ s6†L} ǘ¨‰†‡‹ ' 9

(237)  I % sqvk}O¼Ÿv`¼Ÿƒˆ#€¡X‚¬vk , 8Y!

(238) ' 9

(239) 0 # I Q8D 8Y!¿Å r scˆqX‰ ,  8M^3-!

(240) 0 # I Q8D 8Q^ -!:†L}q¡f s#~‰’¼Ÿƒˆ#€¡O„hƒ} ‘†ƒ¡¨~„k Ÿ~}ƒ“vh„k ~½Z~ ¿‹¬Å <. 0 ² Ú  Ú ° A±  Ú  Z_vkA ?Œ$v?†O 6†L  vk‘}҉ˆ#Œq‰ ~ ˆ# ~ƒ}_˜  Œ$v?†O}qƒ‘ue†L€ vk‘u GB‘vh‰ _Å 8-Œ:v?† }qƒ‘ue†L€–‰ˆ#Œq‰ ~ ˆ# ~ƒ} IVÅ ¶  sqvk‘vXvVè~‰ ‰† vk‘u  R GB‘vh‰ _ņ ‰ˆ#Œq‰ ~ ˆ# ~ƒ}78 R I%‰ˆq„s s6†L 

(241)  R  ! GB‘vh‰ _Å 8

(242) 8 R ^ .IŸ sqvk}H RS

(243)   -!GB‘vh‰ _Å 8 R+

(244) 83^  IVÅ 1325464/78 ¶ Â 

(245)  R  !_ sqvkH }   -!

(246)  R  !Y -!

(247)  R   ^ !

(248)  R  ,/.*!

(249)  R Å ¶ p 8

(250) 8 R ^ x sqvk)} 8 ^ 

(251) 8 R ^@ ^@ R+

(252) 8 R ^ ,/.

(253) 8 R Å < . . .  . š`‰:¼Ÿv ‰s6†L€€‰vhv4Œ:vk€‡¼%˜E¼–sqvk}%¼Ÿvœs6†h½¬vŸ†L}%vhŽcˆ6†L ~ƒ}xL¨ sqv4Â遃‘uLT

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