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A Coq Formalization of a Type Checker for Object Initialization in the Java Virtual Machine

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(1)A Coq Formalization of a Type Checker for Object Initialization in the Java Virtual Machine Yves Bertot. To cite this version: Yves Bertot. A Coq Formalization of a Type Checker for Object Initialization in the Java Virtual Machine. [Research Report] RR-4047, INRIA. 2000, pp.53. �inria-00072591�. HAL Id: inria-00072591 https://hal.inria.fr/inria-00072591 Submitted on 24 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. A Coq formalization of a Type Checker for Object Initialization in the Java Virtual Machine Yves Bertot. N° 4047 Novembre 2000. ISSN 0249-6399. ISRN INRIA/RR--4047--FR+ENG. THÈME 2. apport de recherche.

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(91)    

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(107) hSVY qo hxjfgƒš°¨‚sVm‚hihxSnjh=W}b‚‚_`«€gjkh_cbe^noijkvxYjeacobJYv¡¢bevxW;Y¤Fbe^FhSVYvY¤ozh=be¡‡hxSVYoqhxjegƒš%jk^n%hSnY Œjkvx_cjesVa`Y¤o­ RTSn_co5Y"‚VvxYXoxoYXowhxSnjh'_c^V_`h_ljkac_`£¤jh_cbe^%_co5Œr_loq_csVacYihxSVvbfmVdeS%jkacaJvxY¡¢YXvYX^ngY¤o1hxbhxSVYbes‚yzY¤g3h¤­1ªbf^no_coqhYX^ngp be¡0hSV_loTgbf^nozhxvm€g3hbfv™'_`hS8hSVYgbfvvxYXoJbe^n‚_c^Vd gbe^noqhvxmng3hxbev5_`^8hSVY>beJYvƒjhx_`bf^njkaJoqYXWjk^Lh_lgo_coWje‚Y Y¤jeo_`YXvsrpDhSnY8¡ jfg3h;hSnjkh;™5Y8mnoY%hSVY®ojeW}EY -g$5 -!Djk^n -g$P-!'X-g! ›¡¢mn^ng3hx_`bf^no4hb!JYv¡¢bevxW:hSn_co JYvxŒjeo_`ŒfY mnJVjkhYf­ . G[()'. * +-k/10n 2nE/. . )NY/  2 Q 0a/0hN >IM5W7 /0)58. RTSnY oqhxjhx_cgi_`^V¡¢bevxW}jkh_cbe^df_`ŒfY^ _c^ jk^€ _loje^8jksnoqhvƒjegh_cbe^}bk¡0hxSVY>_`^‚¡¢bfvWjkh_cbe^}hS€jh'oqSVbfmVals€Y fd _`ŒfY^F_`^®hxSVY)Œr_`vhm€jkaAWjegƒSn_`^VY)oqhxjkhY¡¢bev jk% ^rp Y"‚Y¤gm‚hx_`bf^®je^n®jk^rp8ac_c^VY)bk¡

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(111) RTSn_co €jkvhTm€oqY¤o'j4^nY™ VvY¤‚_lgjhxYH! C'&+X-g!*'Z hxSnjh=ac_¬¡ hƒo!& C&+X2H*+,$'& hboqhxjegƒš‚o5_c^®j;^njkhmVvƒjka0™T% jQpe­. . G[()''. %k0k/O-F/0)58. N 58>Q#hQ 0a+ N . R‡bFW}je_`^Lhƒjk_c^ŠhSnY4vxYaljhx_`bf^!sJYhz™5YY^ ‚pr^njkW}_lg4je^n!oqhxjkh_lg_c^‚¡¢bfvWjhx_`bf^A¨AobeW}Y#Y "LhxvxjFgbf^no_coqhYX^ngp 4W mnoqh4sJY%ŒfYvx_¬«nY¤0­5Vbev;_c^V_¬hx_cjea`_c£Xjkh_cbe^A¨1omVsnoqh_`hmVh_cbe^no}jkvxY mnoYX be^ sJbkhxS hxSVYFVpL^€jkW}_cg%jk^n hSVY oqhxjkh_lg}oq_l‚Ye¨|sVm‚h ™5Y4^VYXYX!hb®WjkšfY}omVvxYhxSnjhhxSVYa`b‚gXjh_cbe^€o W}b‚‚_`«nYX srp›hSn_co)omVsnoqh_`hm‚hx_`bf^jkvxY hxSVY®ojeW;Y%be^ sJbkhxS o_cVYe­R prJY%gbevxvY¤oqJbe^nVY^ngY _co4^Vbeh;YX^VbemVdfShb Y^nomVvxY hxSV_co;SVYXvYf¨ws€Y¤gjemnoqY oYŒfYvƒjka5bes‚yzY¤g3hgje^ SnjQŒfY hxSVY›ojeW;YFhzprJYe­ RTSnYFnvbf€YXvqhzp  *%     _`^Lhxvb‚‚mngYX _`^ œcžež3Ÿ hƒjkšfYXogXjkvxY8be¡'hSVYFY "rhvƒjŠvxYXtLmV_cvxYW}Y^LhxoX­ ˜ YF_`W}VacYW}YX^fh}_`h;_c^ªb‚t ) ' ™') _¬hx S j!) Vvbf€YXvqhzp hxSnjh}Snjeo hxSVY4oxjkW}Y ^€jkW}Ye¨°sVm‚h>™Y4mnoYj8‚_`¯°YvxY^LhihzprJbedevƒjknSLp8hb _c^n‚_lgjkhYhSnjkh _`h>_lo=njevqh>bk¡1bfmVv=¡¢bfvWjka VYŒeYXa`bfVW}Y^LhX­ RTSVY>VvxbeJYvhzp  *%     Y^€oqmVvxYXo1hSnjkhTjea`a°acb‚gjhx_`bf^nowhxSnjhTSnjQŒfY=hSnY>oxjkW}Yimn^V_`^n_¬hx_cjea`_c£Y¤ hzprJYjkalob gjkvxvxphSVY4ojeW;Y) 'mV^V) _c ^V_¬hx_c)jea`_c£Y¤®ŒjkacmVYe­ &¹^®hSnY‚Y«€^V_¬hx_`bf^›bk¡ H@P,'h)hzprJYXoX¨€mn^V_`^n_¬hx_cjea`_c£Y¤ hzprJYXo SnjQŒeYhxSVY4¡¢bevxW 1    & 

(112)  7 ¨°™'SVYXvY _co>j galjeoxoije^n  _co>jk^ jeV‚vxYXoxoX­=RTSVY4gƒSnjevxjfg3hxYv¸ _c£Xjkh_cbe^!¡¢bevhSnY4hzprJYWjk hSnY;Œjea`mVY}Wjk ¨|jFgaljeoxo ¨‡jk^Djen‚vY¤oo  ¨|je^n je^ mn^V_`^n_¬hx_cjea`_c£Y¤ Œjea`mVY _co=Y "‚VvxYXoxoqY¤ ™'_`hSFhSVY¡¢bfa`acb™'_c^Vd;¡¢bevxWmValj I . . . .  - #.>!0/ + 1 - 7  1 &   &   7. 1 - 7  1 &

(113)  7 . . ªS€jkvƒjeg3hxYvx_`£X_`^nd%hxSVY%oxjkW}Y šr_c^nbe¡Tnvbf€YXvqhzp ¡¢bev;jkaca acbrgXjhx_`bf^no bf^ ozhƒjegƒš‚o)_lo4‚Y¤ogv_csJYXD™'_`hS je^ _c^n‚m€g3h_cŒeY)‚Y«n^V_`h_cbe^›gjea`acYX %!*'Z +V+_%"#"+&'-*C'_.k+Y'-‚­ ˜ Y)™'_ca`a0™'vx_`hY $. 1  4 #  ' ( &'  6 (G)  % 7 hxb%Y#"‚VvY¤ooihS€jh)_¬¡Tj8acb‚gjkh_cbe^!_c^ FSnjeo hzpr€Y 1 &   &  )  7 ¨°hSVYX^!hxSVYgbevxvxYXo€bf^n‚_c^Vd8acb‚gjhx_`bf^ _c^C-gbf^fhƒjk_c^noThxSVYŒjkacmVY 1 &)  7 ­iRTSV_lo=vxYaljh_cbe^ŠjeacobY"‚VvxYXoxoYXoThxSnjh % jk^n  SnjQŒfY)hSVY;ojeW}Y SnY_cdeSLhX­E T"‚VvxYXoxo_`^Vd gbevxvxYXo€bf^n‚Y^€gY}s€Yhz™YXY^hxSVY8mn^V_`^n_¬hx_cjea`_c£Y¤Dhzpr€Y 1 &   &  )  7 jk^€DhSVY mn^V_`^n_¬hx_cjea`_c£Y¤ Œjea`mVY 1  )  *7 ¡¢bev jkaca'W}YW}bevxp acb‚gjhx_`bf^noX¨ Œjkvx_cjesVacYXo}jk^noqhxjfgƒš gYacalo jkac_`šfYe¨_co. . . . . Y#"‚VvY¤ooYX8™'_¬hxS›j4vxYaljhx_`bf^%be¡|hxSVY¡¢bevxW . 1 # ' ( &'  6 ( )  . . %. . 7. RTSn_coTvxYaljhx_`bf^%_lo'‚Y«€^VYX®jeo'je^%_c^n‚m€g3h_cŒeY)nvbf€bLoq_`h_cbe^F™'_¬hxSFhSVY¡¢bfa`acb™'_`^nd¡¢bfvWjkaAoJYXg_`«€gXjh_cbe^I oqp1„osr.

(114) žQŽ. 

(115)    

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