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A Bisimulation for the Blue Calculus

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(1)A Bisimulation for the Blue Calculus Silvano Dal Zilio. To cite this version: Silvano Dal Zilio. A Bisimulation for the Blue Calculus. RR-3664, INRIA. 1999. �inria-00073008�. HAL Id: inria-00073008 https://hal.inria.fr/inria-00073008 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 Bisimulation for the Blue Calculus Silvano Dal-Zilio. N° 3664 Avril 1999 THÈME 1. ISSN 0249-6399. apport de recherche.

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(66) ! " Ž s‚GIFabTRVMe4>wGHGqxK>g<>TfINH>wcBˆ’PBNR9b>ƒ‡2V_tut‚VFsug<x. x_TRIK=?=?IKT‹. . ! !n>a bkc‹e f   t ‹npf   a"! ‹f e  af #! e  v whxEz$!  i}jl n”‘ qs%! &ƒIKtuJ<>GIKTH>™NH9<> QV_ˆ<G^>THpIKˆbtu>ŠNH>TH=›G ?VK‡y35’‹ K >šcM>g<VXNH>$f('›NH9b>?‡'I_e NdNR9<INOf s‚GI0p—IKtuJ<>K‹8:9b> ">IAS0pK>TfGHsuV_g[VX‡†ˆ<IKTHˆ*GOJ<GH>cns‚g NH9<>™cM><gbsuNHs‚VKg VX‡ ˆŠ s‚Gf*)ƒŽ‰G^J*ef9 NH9*INf+) s•‡”NH9b>TH>™>4LMs„GQNfG“I pIKtuJb>,! GHJ<ef9 NH9<IXN;f .-/›! ‹ %. /. k¥. :<;. =: >.

(67)  

(68) 

(69) ! "$#%&

(70) '

(71) ( . v. K suNH9 NH9bs„GcM>4*gbs•NRsuV_g–Ž–IšpIKtuJb>Šs‚GIabTHVMe>GRGFNH9*INdeIXg TH>wcMJ<e4>ŠF9b>gns•Ns„GBIKababt‚su>wc0NHV0Išg*IX=?>KŽ7VKT  ^Fˆ,9< > >s‚ gbg '’x›‹:suN?I?\¤NOs‚p—G?IKs‚GOtuGHJ<>>>t‚I_>BG^e P>NRLr>NHc‰NHV>‹ g*GHc#\>g >NHV›NRa<9<IXe4ITHV_N NHg_s„e4NR>4JbLrt„'IXNRTwG`su=?Žksug[NHab9<t‚I?s‚> >GQGF>NR=™NRTR9<IKabsuIx_NQN P9’N^TH‡2VK>wf TRe4:VK TfIX'c Tf‡2c›VKT“"IXI—s„Gt‚P_tq‹FgbabKnVKTRN?VM>e4In>GRGRI—pGHP›IX>t‚GNRJb9<f?>KI‹ ‹FN "8:>49b'‡2>0VKsuTR‡kcM>d>IKxK<g<s‚gbc#prsusuNHg<VKs‚VKgbx›gt‚PšNH9bVKsu> ‡‡ cb>4<gbsuNHs‚VKg0VK‡ˆ<IKTHˆ,>c#e4V_gbxKTRJb>g*e4>KŽM">dcM>4*gb>NH9b>gbVKNHs‚VKg0VX‡ 'N\D N ‡

(72) TR>t„INHs‚VKgq‹ 5. 5. 5. "5. # | 2¡  ¡ ƒ¡ {  | 2¡  ~   8:9b>OTR>t„INRsuV_g s‚G"e4V_=™a,V_GHsuNHs‚VKg<IKt5Ž_VKT”etuV’G^>wc?Jbg<cM>T”>pK>THP eVKg’NH>LrNŽMsu‡‡2V_T`IXt‚t–e4VKg’NR>4LrN IKg<c eVKJba<tu>,af Gt e i ŽM" >d9<I—pK> Cya  f   t  e i ‹ . . . . 75. . %. 5. . %

(73) 5. :IKTHˆ,>c#e4V_gbxKTRJb>g*e4>Bs‚G"NR9b>dˆbs‚xKxK>wGQN`eVK=?a*V’G^suNHs‚VKg*IXt7ˆbs„G^s‚=Jbt„INRsuV_gNR9<IN`a<TH>wG^>THp_>G"ˆ<IXTRˆ<G‹ #  | 2¡    ~M}z  ¢ Š¡  }       o TH>t‚IXNHs‚VKg s„GI N ‚HGMHGN„  

(74)  s•‡"‡2VKT >pK>THPšeVKJbabt‚>af Nt e i Žb”>9<I—p_>AC a Ge,f "f -‰s‚=?abt‚su>wG t .-,t"-‰IKg<cƒaf"- Gt"-e i a Ge,f 'ds‚=?abtus‚>G\t )†‹ 8:9<>FTH>t‚IXNHs‚VKg s„GƒIB”>wI&Sˆ<IKTHˆ,>c™ˆbs„GHsu=ŠJbt‚IXNHs‚VKg–ŽKs•‡ IKg<c # IKTH>:">I&Sdˆ*IXTRˆ*>wc™GHs‚=Jbt„INRsuV_g<G‹ 8:9<>†abTRVMe4>GRGH>G‹f IKg<cOt IKTH>ƒV_ˆ<GH>TRp—IXNHs‚VKg<IKtut‚PO>w‘’JbsupIKtu>g_NwŽFTHsuN^NR>gOfpˆ Š t›Žwsu‡*IKg<cVKgbt‚Ps•‡}af Gte i ‡2VKT`GHVK=?>">I&Sˆ<IXTRˆ*>wcˆ<s‚GHsu=ŠJbt„INHs‚VKg NH9<IXN:s„G`eVK=?a*V’G^suNHs‚VKg*IXtŒ‹ . . . .

(75) . . %. /. /. %.  .  . . . . %. . . :9;. C+IF"=$C+GHD=@? IM UZC "=

(76). . . . . IKJ7YCERO=

(77) J7A&=. \g NR9bs‚GG^>we NHs‚VKgqŽ">?abTHVp_>™NH9<IXNˆ*>NRI[e4V_grpK>TfGHsuV_g s„GI QpIKtus„c t„I—™VK‡Fˆ<IXTRˆ*>wcneVKgbx_THJ<>g<e>ACNH9<s‚G s„GB‡2VKTR=›IXt‚tuPnGQNfINH>wc s‚g

(78) >=™=›I0jb‹ jb‹›8:9bs„G>4LbIK=™a<tu>?s„Gdsug’NR>TR>G^NHs‚gbx#GHs‚g<e4>?suNG^9bV`G9<V‘’J<IXg’NRs•b£ eINRsuV_g VpK>TBIKgrP e4VKg’NR>4LrNIXaba,>IKTRG“sug cMs‚TR>e NabTRVrVX‡'GBVX‡:e4VKg<xKTRJb>g<e>Ša<THV_a*>T^NRsu>wG‹™”>‡2VKTR>Ša<THVprs‚gbx

(79) >=?=›Ijb‹ jbŽ_”>:*TRG^N†xKs‚pK>“G^V_=™>Fs‚g’NH>TH=?>cbs‚IKTHPŠTH>wG^JbtuNRG‹\g

(80) >=?=›Ij<‹u@_ŽK">OGQNRJ<cMPŠNH9b>“sug’NR>TfIKe NRsuV_g ˆ,>4NQ">>gŠeVKg’NH>L’NfGkIXg<cVKˆ<GH>TRpINHs‚VKg*G‹–\g

(81) >=™=›IBjb‹@?MŽ">”x_sup_>"I“abTRVKa,>THNQPBNH9<IXNkIKtut‚V`G–NRVdG^s‚=?abtusu‡2P NR9b>dTR>IKGHVKg<sugbxŠVKg#NH9<>dTH>wcMJ<e NRsuV_g<G”NH9<IXNOI™TH>wcM>4L eIXg#a*>T^‡2V_TH= Jbg<cM>TOI?e4VKg’NR>4LrN‹ ”. ~ #   ~M}z{›~  ¢ Š¡  |  |{  %RDŽPM'NN  f  L 

(82) ! " u y P&PL \'N2Q    a Ge ’'G&"   'N"  " 

(83) ( "8  ' Q Q a Pe ’'N"  A &  2&

(84) ! " 'N&"  y&Ž„ f O 2&

(85) ! " } ¡–¡ ›"Pšs‚g<cMJ<e4NHs‚VKg0VKg#NH9<>GHs >dVX‡ “‹ K > cM>4<g<>nNR9b> „AŒDE Œrp'N"  A “ŽBcM>gbVXNR>c ‹a ;eHŽIKG NH9b> grJb=ˆ,>T0VK‡™IXˆ*GQNRTRI_e NHs‚VKg*GIXg*c cb>e4t„IXTfINRsuV_g<G“NH9<IXNVKg<>›xKVr>GNR9bTRVKJbx_9 NRV[TH>wIKef9 NH9b>›9<VKt‚>K‹ K >IKt‚GHV[G^Jba<a*V’G^>›NR9<INdNR9b>cM>aMNH9 VK‡ NR9b> e4V_g’NH>4LrN=ai}jl n .qsf eRŽ"s„G Ra ;e K‹ <”t‚>IKTHt‚PKŽ†NH9b>ncM>aMNR9 s‚G›a<TH>wG^>THp_>c ˆrP/GQNRTHJ<e4NHJbTfIXt =›IKgbsua<Jbt‚IXNHs‚VKg0IXg<c suN`>‘’J<IXt„G >THV?su‡kIKg<c VKgbt‚Pšsu‡ s‚GFIKg0>pIXt‚J<INRsuV_g#eVKg’NH>LrN‹ . . '. '4. . .. '4. "!. . . . . $#. &%. 4. 5. 3. 20. 05. . /. 5. 4. ¥}¥ ¯¦"§¨¨N©. ,+. 5. -%. . . 7. 5. (% )%*#. . 5. 10. 5. 5. 43. 5. 5.

(86) 

(87) 2&Ž 

(88) R

(89) !. @0/. . . . ”. ~ #  .   ¢  ~  ¢ Š¡ |  |{    aPagbkcRegf e   t ‹   P G LD NNH

(90) !  QP$ A='N&"   N "'‚& t a Ge  a›a bdcRegf Ee   QP  ,J_HGo “„AQ" J‚ EHN  & g  on &Ž„ QP ,J  ’ ,

(91)  h   .M'N'Q PQŽ'NŒ  7 ‚PN Q E’&

(92)

(93) DEGM'NGQ ‘ 8    ‘   ‘   y&Ž„ Ra ’e ‹a ;e a Ge t  f  2c  } ¡–¡ K >VKgbt‚Pšx_sup_>“NR9b>GPSK>NRef9#VX‡NH9bs„GFabTRVrVX‡k9b>TR>K‹ƒo“GOG^NRINR>c sug4-‚@M/1ŒŽb>pK>THPša<THVMe4>wGHG:s„G`G^NHTRJ<e £ NRJbTfIXt‚tuPš>w‘’JbsupIKtu>g_N:NRV?I?g<VKTR=?IKt,‡2VKTR=oC v w xE( z aikjIl pqs,"a ! #    ! € #   6 “  * ‘ # =   6  ‘ de›e 9 @0: F9<>TR>ŠNR9b> !  GIXTR>?IXˆ<G^NHTfIKe4NHs‚VKg<GBVKTdTR>eVKTfcbGMC’a bkc‹e f V_T  t ‹nf  ŽIKg<cnNH9b>  GIXTR>™IKababt‚s•£ eINRsuV_g<GOV_TdG^>tu>we NHs‚VKg*GQCaf EeHŽIXg<c F9b>TR>’f IXg<cƒt IXTR>ŠIKt‚GHV#sugngbVKTR=›IXt‡2VKTR=#‹OKn>›eIKgnIKtu:I—PMG GHJbaba,V_GH>?NH9*ING^NHTRJ<e NRJbTRIKtU>‘’Jbs‚pIXt‚>g<e>›s‚GdJ*G^>wcnV_gbt‚PnINdNR9b>šˆ,>x_sugbg<sugbx IKg<c INdNR9b>›>g<c VK‡:I0TR>4£ cbJ<e NRsuV_g–‹"8:9*INOs„GŽ<‡2VKT`>pK>THPšTR>cbJ<e NRsuV_g=f "f -5Ž<">eIKg IXt‚"I—PMG:G^J<aba*V’G^>NH9<IXN`NH9b>TH>d>LMs‚G^N`NQ"V a<THVMe4>wGHGH>Gt IXg<c t - GHJ<ef9 NR9<IN0C“f t?Ž”IKg<c t t - Ž"IXg<c t - f - Ž"IKg<c/G^J<ef9 NH9<IXN›NH9b> s‚gM‡2>TH>g<e4>dVK‡%t "t -cMVr>GFg<VXNOJ<GH>TRJbt‚> 9 TR>c0>‘’Jbs‚p—: ‹`Y0V_TH>VpK>TwŽr”>ŠeIXg[GHJbaba,V_GH>NH9<IXN t s„G`s‚g NR9b>dgbV_TH=›IXt,‡2V_TH= cb>4<gb>wc#ˆ’P >‘’J<IXNHs‚VKg 9 @0:4‹ \g VKJbTeIKGH>KŽ‰">›eIXg G^J<aba*V’G^>™NR9<INNH9<>?eVKg’NH>LrN hs‚Gs‚g gbVKTR=›IXt‡2VKTR=0‹™8:9b>?abTRVrVX‡†s„G=›IKcM> ˆrP sug<cbJ<e NRsuV_g[VKg#NH9b>ŠG^s >dVK‡ “‹LK >VKgbt‚P G^NHJ*cMPšNQ"VšeI_G^>wG‹"8:9b><TfGQNOs„GFF9b>g pn bncfe a 0eH‹"\¤‡  a›agbdc‹e f e   t?ŽrNR9b>TR>dIXTR>BNQ”V?a,V_GRG^s‚ˆbs‚tusuNHs‚>GMC K~b{   aPagbFc‹e f e   }  ¢   {K€ ">BJ*G^>NR9b>dsug*cMJ<e NRsuV_g 9rPra,VXNH9<>GHs‚G K~b{  |  }   {›~ –Ÿ }  ¢ X| 2¡     | ~b}    |  € IKg<c NH9b>TH>wcM>4Ls„GFs‚g Š‹”\¤‡kNH9b>d9bV_tu>  Ž‰s‚GBgbVKNs‚g NR9b>?TH>wcM>4L‰Ž7NR9b>g ”>?IXTR>s‚g eIKGH> a GeHŽ–FsuNH9 n ,‹\¤‡  s„G“s‚gnNH9b>?TR>cM>L7Ž G^s‚g<e> s„GOs‚g gbV_TH=›IKtq‡2V_TH=0Ž7”>Š9<I—pK>  a›a bdc‹e f e   a›agb Že  a›abFc‹e f e   eRŽ–IXg<c[NH9b>TH>‡2VKTR> t  a›abFc‹ef e    X‹ƒ8:9bs„GFs„GFeIKGH>a GeH‹ 8:9<>ŠGH>e4V_g<c[s‚g’NH>TR>G^NHs‚gbxeIKGH>s„GOF9<>g Sn bncfe;ai}jl n rq"s    eHŽ–IKg<c[F9b>g NR9b>TR>cMJ*e NHs‚VKg s‚G  a›agbdc‹e f e   ai}jl n  aPagbdcRef e   qs    a›agbdc‹e f e   eR‹k8:9<s‚G†s‚G”eIKGH>8a GeRŽ_F9b>TH> n 7Ž_IXg*c NR9b>TR>GHJbtuNHs‚gbxe4V_g’NH>4LrN`9<I_GFNQ"V›9bVKt‚>G‹6``VXNR>dNH9*INONR9b> 9 TH>wc[cM>4‡G:`THJ<tu>s„GFNR9b>V_gbtuP#TR>cMJ<e4NHs‚VKg0TRJbtu> NR9<INOeIXg0cMJbabt‚s„eINR>BNH9b>d9bV_tu>ds‚g0I›e4VKg’NR>4LrN‹ K suNH9#NR9b>GH>NQ”V?t‚>=?=›IKGŽM”>deIXg#abTHVp_>ONR9b>dabTRsug*e4s‚a<IXt‰TR>GHJbtuN:VK‡NR9bs„G`G^>we NRsuV_g–‹ ”. ~ #   ™ |~ ¡  * }{ 2¡   ‚

(94) 8‚HGQgƒPN„& "'p=&

(95) † 2HP'‚

(96)  ›“&  J2  aPagbkcRegf Eeƒˆ Š f  c } ¡–¡ , ”. ~ #  

(97) >4N ˆ*>NR9b>dTH>t‚IXNHs‚VKg‹C n j "a  agbFc‹ef    f  c  e  ‡2VKT`IXt‚t Pf IXg<c  `OVXNR>[NH9<IXNšNH9<s‚GTH>t‚IXNHs‚VKg s‚Ge4t‚>IXTRt‚P e4V_=?a*V’G^suNHs‚VKg<IKt5‹ K > abTRVpK>#NH9<IXN IXg<c # IXTR>[”>wI&S ˆ*IXTRˆ*>wcnGHsu=ŠJbt„INHs‚VKg*G‹

(98) >4NOf # IXg<crf ˆ*>?NR9b>šabTRVMe4>GRGH>GcM>4*gb>c ˆrP‡Cf # Sn bncfe  abFc‹e f   IXg*c . . . !. . 5. #. /. 

(99)  

(100)  

(101) 

(102)  

(103)  "!. . . 8.  ". . . . 8. #. #. 5. /. . 8. 4. .. '4.  ". #. (% )%.  . #. #. 8. 1. $# (% )%. &. 0. *). 8. 0. +

(104)  

(105) , -./0 

(106) 12+  33!.  . . #. +. 5. 1. %('. % #.  # . 5. %. .

(107) . -4. 5. 6587. :9. <;. 5. %. /. 1. /. 1. /. 5. . 5. 5. 5. 8. /. 8. =. . %. . =. . . 8. . 98. 8. . 1@>.  ". . 5. 5. . /. ?>. 1. . 8. 8. . 8. . /. . . !. .. . CB. A. . .  . %. . . ED

(108) F. HG. 5. % 5. .  . 2I. 57%. . . . 5. k¥. :<;. =: >.

(109)  

(110) 

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(169)      a Pf"-e t /. 0  

(170) >     t"- µ ¨f¸R¤Q° §71 f€Rt  ( v w ( zgaikjl pqs af"- Rt"-e›e . f    

(171)      a Gf"-We ! ikjl $n‘ qsO!f '( ikjl np‘ƒqs vw I( zgai}jl pqs,a‘ | ‹f"-WePe . ²2œ¹"¤Q° §71 . . /. /. . /. . . 79 8. . /. . /. . <>= JSD5G+D0IKJ IMoGHN7=<>=$M SD ?BD[ RSV0UZG+D0IKJ ,). “G^s‚gbx NH9b>?t„IXˆ,>t‚>c NHTfIXg<GHsuNHs‚VKgnGHPMGQNR>= ‡2V_T“NR9b>?ˆbt‚Jb>›eIXt„e4J<tuJ<GŽ‰suNs„GBa*V’GHGHs‚ˆbtu>ŠNHV[cM><gb>›I t‚IKˆ*>tu>wc ˆ<s‚GHsu=ŠJbt„INHs‚VKgqŽrcb>gbVKNH>c " ŽbGRI—PšcM>4‡ £¤ˆbs„G^s‚=Jbt„INRsuV_g–‹U8:9b>VKa,>TfINRVKT | rcM>g<VXNH>wG"NH9b>dGHs > 9 grJb=ˆ,>T VK‡>tu>=™>g’NRGN:"VX‡qNR9b>NHJ<abtu>.<| ‹  . . #  | 2¡  #    2~M}# |    {  ˜bVKT‰>pK>THP“TH>t‚IXNHs‚VKg Ž">ƒcM>g<VXNH>ai}jl pqs."| e aikjIl -Qqs |0e NR9b>‡'IKe4N:NH9<IXNFNH9b>NQ"V™‡2VKt‚tuVFs‚gbx™abTHV_a*>T^NRsu>wG:9bVKt„c‰‹ a Ge | IKg<c “| 9<I—p_>ONR9b>GRIX=?>dG^s >_ŽbGHI—P U‹U8:9<IXN`s‚GMC | In | An a Ge™‡2VKT`IKtut i  A~ ~  ŽrNR9b>dg<IX=?>wG  UIKg<c  kt‚sug—SšNHV›TR>t„INH>wcTR>GHVKJ<TRe>G”s5‹ >K‹‚Ž aikjl pqs  e ai}jl -Mqs  eH‹ . . . . =. . .

(172) .   

(173) . . .  .

(174) . . . . .

(175) . . K >cM><gb>KŽ*sug “>4*gbs•NRsuV_g[m<‹@?MŽMNR9b>dTR>t„INHs‚VKg0VK‡kcM>‡ £Œˆ<s‚GHsu=ŠJbt„INHs‚VKgqŽMNH9<IXNO>‘’J<IXNH>wGFabTRVre>GRG^>wG:VKˆM£ NfIXs‚gb>cˆrP `TR>abt‚s„eINRsuV_gVX‡*NH9b>FcM><gbsuNHs‚VKgŠVKa,>TfINHV_TRG _ŽXt‚sS_>†‡2V_T>LbIX=?abt‚>AC%ai}jl n‘‚qs,af Rt e›e . . . k¥. :<;. =: >.

(176)  

(177) 

(178) ! "$#%&

(179) '

(180) ( . @. . IKg<c aikjIl n”‘ qs a›aikjl n”‘ qsOf e,Rt eŒeH‹†\g“r>we Nw‹ ™IXg<c#lbŽM">abTHVp_>ONR9<INFNR9bs„G:>‘’Jbs‚p—IKtu>g<e4> s„G:s‚g<e4t‚J<cM>wc s‚g0ˆ<IXTRˆ,>c#e4VKg<xKTRJb>g<e>K‹ . . (. # | 2¡#   5Ÿ z  {   2~M| 2¡  8:9b> TH>t‚IXNHs‚VKg s„GI GQNRTHV_gbxX£G^s‚=J<t‚IXNHs‚VKg–Ž:su‡d‡2VKTIKtut af Gt e i NH9b>NR9bTH>>‡2VKt‚tuVFs‚gbx™abTRVKa,>THNHs‚>G:9bV_t‚cuC a Ge?s•‡hf& f"- IKg<c  a  e"ig   _Ž*NH9<>g[NR9b>TR>>Lrs„G^NRGOIšabTHVMe>GRG;t"-G^J<ef90NR9<IN8t  t-qIXg*c f"- ta Ge?s•‡Lf&  

(181)    1  a }f"W- eRŽ7NH9b>g NR9b>TR>>Lrs„G^NRGBIšabTRVMe4>GRG\t-| IKg<c IKg >grprsuTRVKg<=™>g’N -kG^J*ef9 NH9<IXN\t   

(182)    =  ao- Nt"W- eRŽ<IXg*c.f"- t"5- Ž<IXg<c aikjl pqs Me ai}jlQ- qs A2| e a Ge™‡2VKT`IKtutqGHJbˆ<G^NHsuNHJbNHs‚VKg<Gk Ž*VX‡g*IX=?>G"‡2V_TFp—IKTHs„IXˆ<tu>wGŽr">d9<I—pK>f tk ‹ o TR>t„INRsuV_g NR9<INp_>TRs•*>GBabTRVKa,>THNHs‚>Ga GeOIKg<c # a Ge:s„GeIXt‚tu>wc I †AP ‡„o ’

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