NASA/CP-2002-211736 Theorem Proving in Higher Order Logics Edited by Victor A. Carre_o Langley Research Center, Hampton, Virginia Cksar A. Mugoz Institute[or Computer- Applications in Science and Engineering Langley Research Center, Hampton, Virginia So/lOne Tahar Concordia UniversiO; Montreal, Canada August 2002 The NASA STI Program Office... in Profile Since its founding, NASA has been dedicated to the CONFERENCE PUBLICATION. advancement of aeronautics and space science. The Collected papers from scientific and NASA Scientific and Technical Information (STI) technical conferences, symposia, Program Office plays a key part in helping NASA seminars, or other meetings sponsored or maintain this important role. co-sponsored by NASA. The NASA STI Prograrn Office is operated by SPECIAL PUBLICATION. Scientific, Langley Research Center, the lead center for NASA's technical, or historical information from scientific and technical information. 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Mu_oz Institute fbr Computer Applications in Science and Engineering Langley Research CenteJ; Hampton, Virginia SofiOne Tahar Concordia UniversiO; Montreal, Canada Track B Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics, TPHOLs 2002, held in Hampton, Virginia August 20-23, 2002 and Proceedings of the workshop on Formalising Continuous Mathematics. FCM 2002, held in Hampton, Virginia, August 19, 2002 National Aeronautics and Space Administration Langley Research Center Hampton, Virginia 23681-2199 August 2002 Available from: NASA Center for AeroSpace Information (CASI) National Technical Information Service (NTIS) 7121 Standard Drive 5285 Port Royal Road Hanover, MD 21076-1320 Springfield, VA 22161-2171 (301) 621-0390 (703) 605-6000 Preface This volmne contain., The. Track I_ (\York in Pro_r,,ss) i_l,OC,,,,dhig._ of lh_, lSlh lnle rlselw,al (*ostf_ re nc¢ o, "Fh_or_ m Prortng in tf_gh_ r Ord_ , L,,qtc.s. TPItOLs 2(1(12, h,,Id from t l,, 2(lib t_, 2:h',l of Aug;usl :200:L and th,, proc_,_,dings o['lhv worksh(,p _m [brm_th,,_l_(l (',l_ht_ u,,u.,, .llath_ m _lh,.,,, l"( '.\l 20(t "_. I,,hl Oll Ill{ _ ]!)| h of A [IgllSt 200;2. 'lhes,' ew.ms w,'r,, c¢_lh,,'at,',l ia Ilampl<m. Virginia. ITSA. A _ollm_,. coataimua _h,' lrack A pap,,rs of lh{' ('oltfiTt'llC_' ]laS ]){,ell Imbli*h_',l as Sl_ri,lg,'r-Vcrla_zs I,cclur,' Notes i,I ('OIII]llltlq' N('i,_ll(', ' fO]lllllO _1 10. 'lhv TPll()l.s ]lll,Wllal iOtlHI ('()llf,'l'Cll(',' S_'I'\'_'S as a '.'elllF: _ fOl' Ill,' I,l','s_qltali_HI of w_}l'k ill | [l('l.)l'{'lll ])l'(}Villg h, high_,r-ord,'r h_g;h's, all{[ l't,];ll_'d al','as il, d,'duclion, formal sp ':'iti 'ark n. softwar,, and har_lwar," v,_riti,'ati<,u. and oilier apl,licali(ms, t:oul't(,,q, pal,,,rs were SUblHhted lo Tra<'k B, which ar_' i,,clu,Dd ill this v,)lu,m'. Auth_)rs o[' Track 13 I;aln't's gay,, sh(,rt illtrotlll('t,_)ry talks thal Wel+,, f,.:,lloxv,,,.[ ])\ ;Ill <)p+'ll [),)>t<'l' S_'SSi,:)II. Tlw F( '._1:2I._02 Worl,:sll,+l> aiaw, I to brin_, l(>g+,th++r R,s+,arch++rs ",vorl,:h_g ,>a the' t;+rmalisal i,m of c(ml iml_m,., Inat h,mmlics in Ih(,or,.ttt i+r(+',iu_ syst_,lnS wilh lhos_, m'e<ling such lil+rari,'s t(+r their al)plications. ()',_'r lh_, last f(,v..+ years thcl'e has I,<,vu V;r<_t inl_'r<'sl ill formalising real aml cottqd,'x analysis..Many of the major higher ord,'r theor,etn I+roviu_ sysl<'tns nov," have a formalisation _)f the real nutnl,,rs aml vari,:ms h,',+,,ls ,t' r,'al analysis SUl+l_ort. Son>' w,.)rk has also I><'<'n dora' on fot'||mlising cC,mld,'x analysis im'ludin,g standard aml l|On-stal_dal'd analysis. This work is of intel',est ill a nun_t',er of apl_lication ar,*as, such as formal m_thods dPw'lol)me_ll for hardware' aml s,_t'twaz'_' al)plicalion and compmer supported lllath,.matics, q'hc F('M :_UII2 consisted of thr,_, i)al)ers, i,r,,sel,t,,d by lheh' aulhors at. the workshop Velltle, ;Hid ()11(' inviled talk hy .h)hn liarrison (Inlel ('orporalion). 'i'lm three papers were ac('cpled for publication in this volume. All 17 papers in this volu_m, w_'re revicw_.d for relevance am] qualily of presenlalion by a! least ore' p_,rson appointed by the' I)rogralll ('_:,lttll_itt,!,_, of _'ach eVellt. Ill Organization "['P][OL._ :201):2 i.,, orgalli×ed by NA,qA Lmlgl_y a,ld ICA%E itJ collaboration with ('om'ordia Ymv_'x'._ily. t"('M 2002 i.-, orgm_,iz_'_l hY the lTuiv_rsily of t_emliu_ m_d I('ASI': iH collahoratiou with IHt_'l ('orl>oraliott aml INRIA. TPHOLs 2002 Organizing Committee ('otll'_'r,'llc_" ('h_fir: Victor A. ('am'rio (NASA 1,anglcy) Program ('hair: (Ysar A, Mufioz (I('ASI:- NASA LaH(') %ofii, Jw Tahar (('(mcordia I_niv,'l'sily) FCM 2002 Organizing Committee Worksh<_l) (!hair: Amlrow A. Adams (lniv_'rsity of R_?adillg) Program ('hair: ttanH_" (_ottli_'l_seJ_ (I('ASI':- NASA LaR(1) .Iohn llarrison (Intel ( 'or'l)oratioH ) Lam'ent 'l'h_;ry ( I N R IA ) iv Table of Contents TPHOLs 2002 Track B Papers A _A<_kly-Typ,'d Iligh,'r ()r(h'r l:,_ic with (huwral l,aml+da T(,rnls and Y ('ombium(_r . ............. .]am(._ H. ..I,(/,_ u'.+ |:ornml I)e,..i,_n I':nvir<)mm'nls ................................................................ 12 Brm. +.1yd_ met+ . ld.m (;ra.i_ :. ,1...,o. tf._, _1 l'h'fh,('ting; lli_hcr-()rd,'r :\hstra<'t Syf_tax in XUl,rl ............................................. 23 l.'/i Ba r=i/0 q. 51, a,l A Ib, I)OVI;: a (;ral+hi<'al "1()ol fl.,r th,' Analysis and Evaluali()n of (+riti('al Nv_t,'ms ...................... :t;:'I J),.q Ca.t, Jim M_('arlbq. t]r+.da. +llah0nq Formalising (;en.ral ( 'orr,'ct n('s_. ............................................................. 3(i .I+ c_.t t; h'. l)a.'._(,. Auto.marie ('otlstraint ('alculati<>n using' Lax Logic . ............................................ -1_ .](r+mq fi'. Dan'.son. Mall ["a_rllougl, Aulotuating Fra,+nkcl-Mostowsl,:i +qyntax ...................................................... 60 Murdoe'b .]. (;abba:] A i:ormal ( 'orrectness Proof of lh," ,"4I>IDER Diagnosis Protocol .................................. 71 A Ifo ,.+ (;+ .__r. I' o, I .s'+ ,11t, _r Using tI()L to Study Sugar 2.0 S+'mantics ..................................................... S7 .llicha_l .1.('. (;ordo. Extending DOVE v,'ith Product Automata .................................................... 101 El._a L. (;u.l_r, Yi .1I+,q A tlighm'-Ord,,r Syst_-m for I{e,l+r,',+.,mting Metabolic Pathways ................................... 112 ._,'aral(alrala ttiglwr-Order I'altet'n [:nili('atiou attd Proof lrreh'vance . ........................................ 121 ]..'+o. R_+I A Vm'ilication of Rijt_daN in II()[............................................................. 12,u ho. rod 51i. d The I( ('omhinator as a Seniant ically Transparent Tagging .'X,lechgmism ............................ 13!) Ko. rad Sit. d. 3li(ha+ I .\,_t'c:,sb FCM 2002 Invited Talk H,'al Ntimh+.rs itl R+'al Alqdicati()t,s ........................................................... 14_'i Job. Hart+so. FCM 2002 Workshop Papers l"ornmlizhl_ li_,M('nJcnills ill ('oq ............................................................ 1._ L. A ('ru:- t"ilq_* TI." I)OVI': Alq,r,_,a'.'h to tip l).si&n ,c:.t('_,ml,h'x l)yrlami(' i'ro,:'_.ss_._,.............................. 1(_7 fll_ ,d_l, :U.ho,_l Author Index ......................................................................... I_!_ vi A Weakly-Typed Higher Order Logic with General Lambda Terms and Y Combinator James H. Andrews 1 Department of Computer Science University of Western Ontario London, Ontario, Canada N6A 5B7 andrews©csd, uwo. ca Abstract. We define a higher order logic which has only a weak notion of type, and which permits all ternls of the untyped lambda cah:ulus and allows the use of the Y combinator in writing recursiv(, predicates.