Simplifying Polynomial Expressions in a Proof Assistant
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Simplifying Polynomial Expressions in a Proof Assistant Laurent Théry. N° 5614 Juin 2005. N 0249-6399. ISRN INRIA/RR--5614--FR+ENG. THÈME 2. apport de recherche.
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(151) L NH ? Ef^EPRMOETEBV A XvV QTY c LNE£ MRFiNPREF=ELwVXvVMRQTLMOZ X c F=Q c QE AE£¢7MO^NPREv, W!M c Z\V¡ MOV PREX EZkQTi_EL ^Q V A V A EiQ ZZMO^NMRPOMOVMREZ!Q 9i c Q?]MRLaS,V A EfUQ]jNEUQ cc EUVkX LNj&E ¢7V c X U£VMOLNS MOV0VQSTEVx X
(152) UQ]jNEV A XvV UX L ^E%E C=UMREL VPO[UQTFiNMOPREj2 EUQTLajD¡DMOVi c Q?]MRjNEZ XF=Q c E i_Q c VX ^NPOE MRFiNPOEFELwVXvVMRQTL Q WQTY c VX U£VMRU=ZMOLNUE&FQTZ\VQ B A XvVV A E-VX U£VMOU jNQ7EZ-MRZ=jNQTLNEtMRLNZ\MRjNE
(153) V A EPOQTSTMOU
(154) Qvx!% W!MOLX PRP[T¡"i_E c Q c FMRLaS X X M c XvF=QTYaL V=Q UQTFiNYaVXvVMOQTLxMRLNZ\MRjNEV A E POQTSTMRU%Q x+
(155) MRZ¤LNQ V!Xfi c QT^NPOEF
(156) @BA EkZ\iEUVX UYNPRX c i c Q S c EZZ Q nV A EEvX POYXvVMRQTLFEU A X LNMRZ\F MOLNZMOjNEkV A EBPRQTSTMOUQ 9 !X Z%jNEZ\U c MR^_Ej'MRb L < o > ELNZY c EZ c A c A c c X'UQTFiNYaVMOLNSi_Q5 E V XvVMRZBFQ E0V XvLZ\'Y CUMRELwVWQ QTY LNEEjD . e.
(157) q5o.
(158) "!$#$#%&'#. 4B+B+B8 +
(159) . @BA ExUQ]jNExQ +V A E VX U£VMOUMRZXvX MRPRX ^NPOE0XvV [f VE.
(160) . c PRQwXvjNMRLNS,MOV. . ! !"# $ % '& ( ) ! )*+ . , - $ / .0! ) 2 1" 3 ! )* QTLNE,S EVZ0XVX UVMRU 4 5 ! ). V A XvV A X Zf^EELZ\iEUM XvPRM Ej
(161) VQ i_E c Q c F#i_QTP[7LaQTF=MRX P c A c ZMRFiNPOMOUXvVMOQTLNZ¤Q5 E V E EX PRZ X Laj=V A WE MOLwVES E c ZWnQ c E£¢aX FiNPREv¡wMO_V A EWSTQwX PNVQ Z\QTPO E MRZkV A EQTPRPOQ5 MOLNS. /6879 $ : . ;
(162) <, (
(163) <, +=
(164) <, > > > >> > > > >> > > > >> > > > >> > > > >> > > > ;@?A +2B ( BDCEF6 ( ?AHG/?I; BJ7 E [0iNiNP[]MRLNSV A E 4 5 ! ) VXvUVMOUi c Q7jNYaUEZV A. EQTPRPOQ5 MOLNSZ\YN^NSTQwXvP"qxZYN^NS QwX P. /6I ) 5 ! 4K 7F $ : ;
(165) <, (
(166) <, +=
(167) <, > > > >> > > > >> > > > >> > > > >> > > > >> > > > ;@?A +LMC ? ( BDCEF6 ( N. O 0 +76 ;4 '8 0 + . L V A MRZBiXviE c E A XTEIi c EZELwVEjXZMOF=iaPRMONUXvVMRQTL=i c Q]UEjNY c E Q c i_QTP[7LaQTF=MRX P_E£¢
(168) i c EZZMOQTLNZV Y c MOLNMOVM X P_FQ VM XVMRQ L kXvZWVQ=E`]YaMRiV A Ex+ Z[]Z\VEF# MOV A X'ZMRFiNPOM UXvVMRQTL&i c Q]UEjaY c EV A XvVB QTYNPRji_E c Q c F V A EB\\QT^w]MRQTYNZ;^ Z\MRFiNPRMUXVMRQ LNZ X YaVQ F XvVM UX POPO[TO ? EX c EfX? X c EfV A XvV A XvVkMOZ i c EZ\ELwVEj A E c E0MRZDd\YNZVBXI c Z\VZ\VEiDD LNE` YXvPRMOVMREZ D. eegfih,j;k
(169) lnm.
(170) q?p. !%
(171) . E X c E0jaEX POMRLNS MOV A MRL=QTY c X iNiNPOMRUXvVMOQTLX c EfLNQ Vgd\YNZ\ViQTP[]LNQTFM X PNE ¢7i c EZZMOQTLNZk^aYaV X PRZ\QUQTLwVX MOL
(172) YaLNUVMRQTLNZBPOM : EIE ¢7iQTLaELwVMRX PRZ¡X ^NZ\QTPRYaVE XvPRYNEZ`Q c E Z\iEUMU : LaQ5 P EjNSTE A X Z"VQ0^EX jajNEj c ESwX c jNMRLaSfV A EZEBYNLaUVMOQTLNZ+MRLQ c jNE c VQ i_E c Q c F X iNi c QTi c MRXvVE ZMRFiNPOMOUXvVMOQTLNZ VMOPRP ¡N E^_EPRMOE E,V A XVQTY c i c Q]UEjNY c E A X ZZQ F=ELaMRUE,i c QTi_E c VMOEZ D V A X ZX UPREX c ZEF X LwVMRUZ MV A X c XvV A E c jNM c EU£V'MRFiNPREF=ELwVXvVMRQTLDT? E
(173) ^EPRMRE£TE&MV i c Q?]MRjNEZX
(174) STQ7Q]j UQTFi c MOZE^E£V EEL i_E c Q c FMRLNSZ\MRFiNPRMUXvVMRQTLaZ X LNji c EZ\E c 7MOLNS V A ExZ\V c YNU£VY c ExQ +V A E Q c F,YNP X Ev W c QTF V A E=MOF=iNPOEFELwVXVMRQ Lti_QTMRLwVxQ 7MOE x¡9QTY c i c Q7UEjNY c EMRZxMRLwVE c EZ\VMOLNSN ? E VQ]Q : X javX LwVX STEQ WV A E X UV'V A XvV'V A E
(175) E` YXvPRMOV [ Q?TE c iQ PO[]LNQTFM X P E£¢7i c EZ\ZMRQ LNZ=MOZ jNEUMRjX ^aPRE ? A MOPREMRL V A E c %E AEU£VMO EX iNi c QwX U A V A EUQ]jNEtMOZ=i c Q?TEjUQ c\c EU£V-QTLaUE X LNjQ c X PRP ¡ A E c EI E,YaZExV A EIjNEUMRZ\MRQTL
(176) i c Q]UEjNY c EIVQ=U A EU : V A E c EZYNPV0Q +V A EIZMOF' iNPRMOUXvVMRQTLETE c [VMRFE @BA MRZ MRZV A Ei c MRUEVQiX[Q c LNQ Vxi c Q?]MRLNS&V A EUQ c\c EU£VLNEZZ Q "QTY c Z\MRFiNPRMUXvVMRQTL=i c Q]UEjNY c E 1 ? c MOVMRLNSV A E Q c X UPOExMRLNZ\MRjNE V A E POQTSTMRU0Z\VMOPRPDF=X : EZ ZELaZE H D V%POEXTEZ%QTiELV A EBi_QTZ\ZMR^aMRPRMV [ VQxYNZ\EkV A E c E AE ¢aMTEFEV A Q7j'X LajMV"MOLNU c EX Z\EZ iQ c VX ^aMRPRMV [T WQ c E£¢aX FiNPREv¡ X c EMRFiNPOEFELwVXvVMRQTL,Q DV A EfPOQTSTMRUQ "x+ UQTYNPOj=^_ELNE£NV Q !Q Y c i c Q]UEjNY c Ex MV A Q YaV A X]MRLNSVQMOF=iaPREFELwV V A ExFEVX5 P XvLNSTYX S E / _+76 l # (
(177) ( & & & (
(178) f & f ) #' (&f ( - + - f f f
(179) "!#$%!&(' ) *+#-,./0-('12 &# &' (43657 28:9 ) 0 &+ (
(180) lnm%l; lnk &=< (nf )" &$> f & l?77 m < ' ( &@ ' f BA
(181) f e(%C( If ' & )EDGF (nf f )IH ( $ ( )KJ ('
(182) If ) ( ) ' (
(183) f
(184) L ) 0M N.O & # &' (a!l 65%l P8:9 ) 0 & (
(185) j
(186) l j?;
(187) j*7 &=< (&f )" &-> f & l?773 Q SR J '
(188) '& #' (nf ('e *) ( #' &* f )T #' (&f ( - (&f"( &+ - C" ! f U f f ' + (
(189) f V%X$Y&Z\[$/[-[- ) [?'?[]\[^
(190) *`_a(b?c[.d f )
(191) # "& ;f ( ( "'+ f W c[fe"gdhij(kl 8 d%! & f ' + (
(192) l *j f Ha< &+ (
(193) lnk 7h; ?l 5 m &mD ) f +"' &< & f ) & # l m SR f J #
(194) f )on & - ' f "'+ f ( ) ' ( 4p ' f %$ If ( # - rqLsG )ut & 3 Q v \l ;+$l9j & wl 7Ik j (nf f ( ( f )x # ( ( - "& ( ) "& ( (nf ;f
(195) If ( )+' If f f Z\[/y []6[] ) [?'w[]\[&z=,.[]%6[]m_jd(*T*rc[.d & H R < & (
(196) Q ?j ;+9m"k &
(197) +"' & . & A
(198) & * . . k f t {}|=!%M !T~j,.kl & l Q !f
(199) (nf )< &"
(200) ' ( Q l &m<+ f % f
(201) & lw755 3 > ( & R
(202) (
(203) & ( +
(204) "&%$ ! ;fv * ' ) ( # ( ( & ( ( ( ) ) *T*r,L[]s] )ut & l&m 5v j#3w;%j Q 3 ?l 73
(205) l 5 ' (nf ( - < l#& ]
(206) & # f H .p-v ( ( /U ( # ( & " ( f #& e( # m Q j Q e & * . e. & &.
(207) Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France) Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique 615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38330 Montbonnot-St-Martin (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France). Éditeur INRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France).
(208) . ISSN 0249-6399.
(209)
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