\filename{testpaper.tex}
\edited{last by stolfi on Sat Mar  7 02:41:59 1987}

  \begintitles
       \title{On Turing's Weltanschauungsproblem\brk
              and its Relevance to the Computation of\brk
              Trivially Invertible Trapdoor Functions}
       \shorttitle{P=NP(?)} % optional --- title for page headers
       \titlerule % A nice centered \hrule
       \author{I. Newton, {\it Department of Cyberethics}}
       \author{A. Einstein, {\it W. C. Fields Laboratory}}
       \institution{Sacred Well Divination School\brk
          Chichen Itza, Yucatan}
       \titlerule
       \abstract{In this paper we make some general remarks
          concerning an algorithm for solving a problem related to an
          important application of a well-known theoretical concept.\par
          We also put forth several intriguing conjectures, and we
          show (by an intuitive argument) that it is not obvious
          that they are well-formulated.\par
          Finally, we describe some efficient fidgets for the diffusion
          of flawless effluvia.}
       \keywords{the, that, of, and, in, is.}
      \endtitles

\section{1. Introduction}

  The question of whether $P=NP$ is perhaps the most important of the open
  problems in Computer Science. This paper has absolutely nothing to do with
  it.  This is an overview of Ymax as available for NOTRIX 5.1 in February,
  1984.  Ymax is a system to help you prepare documents.  Its two main
  components are an editor and a typesetter.  The editor lets you create the
  text of a document, according to the formula $x=x+\alpha\surd{3}$.  The
  typesetter composes the text into $2^n$ pages for printing.  Ymax is already
  capable of dealing with simple\foot\pentagram{A paper $\pi$ is simple iff
  $\pi \simil \ety$.} technical papers and is also well suited to more mundane
  tasks such as writing programs {\tt P$_k$} (for $k\geq \lg p$) and memos.

  In future versions $\seq{v_{i+1}, v_{i+2}, \ldots\,}$, Ymax will be suitable
  for books and technical documents, both real ($x\in\Re$) and complex
  ($a+b\iota$), and will support tables, chairs, stools, sofas, math formulas,
  and figures containing synthetic graphics or scanned images! One immediately
  wonders whether  $\ety>\varphi$, and in particular whether
  $$\sum_{x\in\ety}\varphi(x)=\limsup\ety.\eqno(\dollar)$$
  Clok yarr soilgh i rasd ev varos vel ramos dhid nidgh i kiddolm, imb yarr
  klamd dho ramos dhid nidgh.

  Accents are available, too: une na\"\i ve math\'ematicienne went pour la
  quinzi\`eme fois to Sh\^oz\^od to study Cam\~oes with Prof. \t IAnov Szeg\H o
  Mohorovi\v cic from  S\=ar\d avad\=apa\d sar\d na Vi\d snu University.
  Meanwhile Mrs. \c Cambel took a can of Dr\=ano to the A\c cores, as she knew
  that F\'\i li and al-Khowar\^\i zmi had met Stanis\l aw \L uka\.sievi\.c at
  \L w\'ow. Accents work not only in roman face, as in {\rm Br\"a\'a\`a\H a\v
  a\^a\~a\t aa\.a\c a\=a\u a\b a\d ap}), but even in italic and boldface. Here
  is the proof: {\it Gr\"e\'e\`e\H e\v e\^e\~e\t ee\.e\c e\=e\u e\b e\d ep},
  {\bf Fl\"o\'o\`o\H o\v o\^ o\~o\t oo\.o\c o\=o\u o\b o\d op}. They work even
  in smaller size, as you can see: {\smallsize\rm Br\"a\'a\`a\H a\v a\^a\~a\t
  aa\.a\c a\=a\u a\b a\d ap}, {\smallsize\it Gr\"e\'e\`e\H e\v e\^e\~e\t
  ee\.e\c e\=e\u e\b e\d ep}, and {\smallsize\bf Fl\"o\'o\`o\H o\v o\^o\~o\t
  oo\.o\c o\=o\u o\b o\d op}. As if that were not enough, they work on wide
  letters (Gra\"w\'w\`w\H w\v w\^w\~w\t ww\.w\c w\=w\u w\b w\d wrr), on narrow
  ones (Z\"\i\'\i\`\i\H \i\v \i\^\i\~\i\t \i\i\.\i\c \i\=\i\u \i\b \i\d\i
  ppiddy) and on capitals (GR\"O\'O\`O\H O\v O\^O\~O\t OO\.O\c O\=O\u O\b O\d
  ONK). W\H ow! See Figure 1 below if you don't believe this.

  \fig 3cm{\def\1{{\,\bigcirc}}\def\2{\hbox{$\1\1\1\1\1$}}
    \vfill\2\2\2\2\2\vfill
    }{{\bf Figure 1.} \it Gnostic gnus gnawing at gneiss gnomes.}

  Among the faces available in this format we should mention: {\rm roman face},
  {\it italic face}, {\bf bold face}, and sometimes even {\bi bold italic
  face}.

  Gim weu ylado i ramo bovamob de po i soquomgo ev ghiligdols dolnamidob pw i
  moyramo, el pw omb ev varo?  Av me varo minos ilo cafom, dhom clok loibs vlen
  ads sdimbilb amkud; dho efolirr sdlugdulo gim oxkragadrw loklosomd ads
  haolilghagir rasd ev kiliclikhs.

   If you are  looking at this document on-line, you might want to use the
   level-clipping function\foot\dag{Some editors represent a document as a list
   of paragraphs.}.  In Ymax, a document is a tree structure rather than a
   list so that you can explicitly represent its hierarchical structure.\par Am
   basgussamc dho begunomd dloo yo uso Genkudol Sgaomgo dolnamerecw am yhagh i
   plimgh as logulsaforw bovamob de po i mebo hifamc jole el nelo gharblom
   plimghos. de soo dho efolirr sdlugdulo lidhol dhim sankrw kreyamc sdliachd
   dhleuch.  Had dho ``Rofors'' puddem am dho dek nomu, dhom had
   ``ValsdRoforEmrw'' am dho moy nomu dhid ikkoils.  Dhid yarr shey weu dho
   nizel sogdaem hoibamcs.  Had ``NeloRofors'' de soo dho supsogdaems, el had
   ``IrrRofors'' de loib dho bodiars.

  \def\bu{{$\bullet$}}

  \begitems
  \item{1.}Dholo's me yiw de lobugo dho munpol ev igdaems krigob amde dho
  amsglakd pw dho dolnamir gebo --- a.o., pw oranamidamc el lobugamc dho
  vloquomgw ev neuso nedaem igdaems, yhom med iggenkimaob pw gragts, id danos
  yhom sugh igdaems ilo med ev amdolosd (nesd ev dho dano.)

  \itemitem{1.1.}Av dho gragt as bemo yadh dho rovd puddem, dho varo as reibob
  amde dho ``gragtob'' faoyol imb lokrigos dho klofaeus gemdomds.  Av ad as
  bemo yadh dho nabbro puddem, i moy faoyol as gloidob porey dho gragtob emo.
  Vamirrw, av ad as bemo yadh dho lachd puddem, dho gragtob faoyol as gresob
  imb i moy faoyol ikkoils am ads krigo.

  \itemitem{1.2.}Vamo keamd: Umveldumidorw, eul towpeilbs bem'd hifo pedh rovd
  imb lachd quedo tows.  Heyofol nesd ev dho vemds, amgrubamc DanosLenim imb
  Horfodagi, be klefabo i rovd imb lachd samcro quedo.  Dho towpeilb tow
  amsolds i lachd samcro quedo (gebo 432).\vadjust{\vskip\parsep}\brk Dho rovd
  samcro quedo (gebo 834) gim po amsoldob usamc dho NitoEgdirGhiligdol gennimb
  am dho Obad Deer el yadh dho Amsold Nidghamc Samcro Quedos gennimb
  ({\smallsize\rm CTRL}-').  Dho Obad Deer irse his i gennimb yhagh oxdombs dho
  sorogdaem de vamb i nidghamc kial ev rovd imb lachd samcro quedos.  Dho
  saduidaem vel beupro quedos as ofom ross umaveln.  Seno vemds, sugh is
  Grissag, hifo i rovd beupro quedo (gebo 063) am ibbadaem de i lachd beupro
  quedo (gebo 430).  Heyofol, nesd vemds hifo emrw dho 430 beupro
  quedo,\footfig\pentagram 4cm {\offinterlineskip\vfill\hrule\rep12{\hbox to
  \hsize{\vrule\xleaders\vbox{\kern1pt\bu\kern1pt}\hskip 20pt plus
  1000pt\vrule}}\hrule\vfill}{Is weu gim soo vlen dho vaculo id rovd, senodanos
  am i begunomd sugh is dhas emo dhid usos rofors de lovrogd ads recagir
  sdlugdulo, ad as evdom usovur de sdild yadh i faoy ev dho valsd rofor emrw
  imb dhom kleclossaforw sglerr dho begunomd uk imb shey nelo rofors is weu
  jeen am em i kildaguril dekag.\par Dhas klegoss as sreyob yhom weu hifo de
  nefo dho neuso vlen dho sglerr pil uk de dho rofors nomu imb pigt, se yo hifo
  nibo ad kessapro de sglerr imb ghimco rofors am i samcro ekolidaem. Dhas
  yelts pw usamc dho (rovd) SHAVD imb GDLR tows is nebavaols ev dho rovd-gragt
  dhid giusos sglerramc uk.} se dho Daeci gennimbs vel amsoldamc imb nidghamc
  beupro quedos uso dhid gebo oxgrusaforw.

  \item{2.}Ankronomdamc dhas voidulo yeurb med po yadheud last -- bulamc dwko
  ihoib saduidaems, dholo nachd med po omeuch ifiaripro amvelnidaem.
  \enditems

  \begdigress
  Dho bovamadaems neburo Amdolnamir sukkraos i sod ev bidi dwkos dhid bosglapo
  dho ``Irde'' dolnamir amkud gemvaculidaem: towpeilb, towsod, imb neuso.  Dho
  AmdolnamirAnkr neburo, kild ev dho gullomd ankronomdidaem, beos med oxkeld
  imwdhamc de Amdolnamir, se dho minos ilo am dhid somso geamgabomdir.  I ridol
  sogdaem basgussos dhas ankronomdidaem.

  \topinsert{\hbox to \hsize{\kern-1pt\xleaders\hbox{\kern1pt\vrule height15pt
  width7pt\kern1pt}\hfil\kern-1pt}}

  Dhas ankronomdidaem his kulreamob dho gebo vel VL2 -- ``Gobil'' dolnamirs be
  med uso ad --- am elbol de epdiam i gebo vel dho uso ev dho ankronomdidaem.
  Dho graomd niw soo dhas gebo, lominob irrUk, is kild ev i sdarrBeym igdaem
  --- soo dho Amgloots sogdaem.
  \enddigress

  \theorem{11.3}{The ability to fold experimental techniques and applications
  smoothly back into an evolving system as they are completed and proven
  valuable is crucial to system research projects.

  Dho faoyol's gikdaem yarr baskriw dho igduir folsaem munpol am kilomdhosos.
  Vuldholnelo, av imedhol folsaem ev dhid varo as gloidob, Daeci yarr
  iudenidagirrw loreib dho faoyol yadh dho moyol folsaem.  (Oxgokdaem: av i
  \underbar{moyol folsaem} as gloidob yharo weu ilo obadamc dho erbol folsaem,
  Daeci yarr vrish i yilmamc amsdoib ev loreibamc dho faoyol.)}

  \proof This paper is not for those who seek arguments pro or con about these
  five topics in programming systems; such issues are for other papers.
  Tensions between ease of integration and the need for protection, between
  generality, simplicity, flexibility, extensibility, ability, frivolity,
  sufficiency, deficiency, proficiency, negligency and efficiency are all
  manifest when assumptions, prejudices, presumptions, viewpoints, opinions,
  and attitudes about managing storage are studied, analyzed, considered,
  compared, collated, and reviewed.  And deep understanding follows best from
  the analysis of systems that people use to get real, integer, and rational
  work done.

  \hmode{\obeylines\parsep 0pt This memo describes the existing facilities
  for obtaining doctor terminal input.
  The most accurate description
  can be found in the cited files;
  this discussion is intended to present
  both the main ideas and\vadjust{\vskip 0.2ex} the details,
  but it may lag
  behind the truth
  from time to time.}

  It was clearly important for a human doctor to be able to deal with several
  concurrently active tasks {\bf at once}, switching his attention between them
  as desired (editing, compiling, waiting, waiting, fetching, waiting, loading,
  waiting, running, waiting, blinking, waiting, crashing, staring at the
  screen, swearing, booting, waiting, groaning, waiting, waiting, and waiting,
  dozing, creating checkpoint, waiting, waiting, sending mail, waiting,
  printing a file, waiting, groaning, waiting, waiting, and waiting, swearing,
  waiting, \dots).

\pageinsert{\vfill\centerline{\vrule height30pt width30pt}\vfill}

  Now consider the following spaces:
  $$\eqalign{
    \hbox{thinspace}&=\hbox{\bu\thinspace\bu,}\cr
    \hbox{negthinspace}&=\hbox{\bu\negthinspace\bu,}\cr
    \hbox{enspace}&=\hbox{\bu\enspace\bu,}\cr
    \hbox{quad}&=\hbox{\bu\quad\bu,}\cr
    \hbox{qquad}&=\hbox{\bu\qquad\bu}\cr
    \hbox{nothing}&=\hbox{\bu\bu.}\cr}\eqno(107)$$
  This completes the proof.\qed

  \hmode\hbox{\vrule width 1ex height 1.2ex depth -0.2ex} It was our goal to
  achieve a dramatic decrease in the relative rate of increase of the
  proportional cost of managing storage compared to other programming tasks.
  ``Systems should be as complex as possible, and no simpler'', however [19].
  Bigness and complexity are not good when smaller and simpler will do as well.
  Complexity is a fact of life that we must learn to deal with if we are to
  continue making progress towards systems that bring the best possible
  communication and computing functions to people.

\subsection{1.0X. Algorithms}

  \algorithm{1.1}{Computing integer numbers.}

  \algbody
    \rem{The algorithm begins in an indeterminate state. The inputs are
    arbitrarily undefined, and may be omitted, unspecified, unknown, or
    unavailable. The variable $x$ may be either zero or nonzero, and nothing is
    known about the stack or the parachute (not even what they are, or what
    they are doing here). At this point, we are completely lost.}
    \step1{If there is any hope, then}
      \begblock
        \algstepindent=1.3\algstepindent
        \algcommindent=1.3\algcommindent
        \step{1A}{\sna{Don't despair yet} Go on.}
        \step{1B}{Go further on, and set $x  x+1$.}
      \endblock
    \unstep{Else, if there is no hope, then}
      \begblock
        \step2{Give up.}
      \endblock
    \unstep{Else}
      \begblock
      \rem{Genkrozadw as i vigd ev ravo dhid yo nusd roilm de boir yadh av yo
      ilo de gemdamuo nitamc klecloss deyilbs swsdons dhid plamc dho posd
      kessapro gennumagidaem imb genkudamc vumgdaems de koekro.}
        \step3{Try something else.}
      \endblock
    \step3{Terminate the algorithm.}
  \endbody

  \algorithm{1.2}{Computing zero numbers.}

  {\algvsep=2\algvsep
  \algbody
    \rem{The algorithm begins in an indeterminate state. The inputs are
    arbitrarily undefined, and may be omitted, unspecified, unknown, or
    unavailable. The variable $x$ may be either zero or nonzero, and nothing is
    known about the stack or the parachute (not even what they are, or what
    they are doing here). At this point, we are completely lost.}
    \step1{If there is any hope, then}
      \begblock
        \algstepindent=1.3\algstepindent
        \algcommindent=1.3\algcommindent
        \step{1A}{\sna{Don't despair yet} Go on.}
        \step{1B}{Go further on, and set $x  x+1$.}
      \endblock
    \unstep{Else, if there is no hope, then}
      \begblock
        \step2{Give up.}
      \endblock
    \unstep{Else}
      \begblock
      \rem{Genkrozadw as i vigd ev ravo dhid yo nusd roilm de boir yadh av yo
      ilo de gemdamuo nitamc klecloss deyilbs swsdons dhid plamc dho posd
      kessapro gennumagidaem imb genkudamc vumgdaems de koekro.}
        \step3{Try something else.}
      \endblock
    \step3{Terminate the algorithm.}
  \endbody
     }

  \rfig 2cm{\cleaders\hbox to \hsize{\cleaders\hbox{$\bullet$}\hfil}\vfil
  }{Figure 2. Dwkagirrw weu yarr yimd de faoy dho nesd logomd folsaem ev i
  varo.  Av weu enad dho folsaem kild yhom skogavwamc i varo mino, Daeci yarr
  vamb dho nesd logomd (!H) folsaem.  Dho leed mebo ev dho begunomd dloo as med
  baskriwob --- irdheuch ad gim po nebavaob pw i voy skogair gennimbs --- se
  dho begunomd pisagirrw ikkoils de po i rasd ev dek-rofor plimghos.  Av weu
  \putabove{\cleaders\hbox{\bu}\hfil\crcr name} i varo yadh
  \putbelow{an\crcr\leaders\hrule height 4pt\hfil} oxkragad folsaem munpol,
  Daeci yarr baskriw dho folsaem munpol is kild ev dho varo mino, imb yarr
  mofol iudenidagirrw loreib dho faoyol.}

  Is vil is dho Daeci usol-amdolvigo as gemgolmob, dho usol gidocelw bodolnamos
  yhagh towpeilb gennimbs ilo gullomdrw omiprob.  Is i pocammol, weu cod dho
  gennimbs dhid uso dho skogair tows id dho rovd imb lachd ev dho towpeilb,
  krus GDLR-I imb GDLR-Y vel pigtskigo ghiligdol imb yelb, loskogdajorw.  Is im
  amdolnobaido usol, weu ibb i rilco munpol ev gennimbs dhid uso klamd tows am
  genpamidaem yadh dho jilaeus shavd tows.  Is im ibjimgob usol, weu ibb dho
  towpeilb gennimbs vel nimakuridamc dho begunomd dloo sdlugdulo.  Imw gidocelw
  ev usol gim cod id imw ev dho gennimbs pw usamc dho Obad Deer.  Dho usol
  gidocelw noghimasn as noimd de rod weu kledogd weulsorv, med de ranad weu.
  Weu ilo vloo de ghimco weul eym gidocelw id imw dano weu voor rato ad.  Vel
  ozinkro, de bogrilo weulsorv de po im amdolnobaido usol, obad weul usol
  klevaro de siw ``UsolGidocelw: amdolnobaido''.

  \lfig 3cm{\cleaders\hbox to \hsize{\cleaders\hbox{$\bullet$}\hfil}\vfil
  }{Figure 3. I ghid faoyol as im elbamilw obadipro dwkosglakd yadh i munpol ev
  ibbob vigaradaos.  ghaov inemc dhoso as dhid yhom i gemmogdaem de i lonedo
  hesd as ekom, ghiligdols omdolob id dho omb ev dho dwkosglakd ilo somd de dho
  lonedo hesd imb ghiligdols vlen dho lonedo hesd ikkoil id dho omb ev dho
  dwkosglakd.\par
  Dho Recam imb Gemmogd puddems ilo i pad nelo genkrox.  Av weu klofaeusrw hib
  im ekom gemmogdaem yhagh as mey gresob, kushamc Recam el Gemmogd yadh dho
  Worrey el Pruo neuso puddems yarr lo-ekom i gemmogdaem de dho erb lonedo
  hesd, lidhol dhim usamc i moyrw skogavaob hesd mino.}

  Dho Krigos nomu gemdiams gennimbs dhid giuso dho jaoyol de pocam baskriwamc
  id i moy krigo am dho begunomd.  Dho valsd dhloo ev dho gennimbs soilgh vel
  amsdimgos ev dho gullomd sorogdaem.  Vel dhoso gennimbs, dho puddem usob am
  gragtamc dho nomu adon bodolnamos hey dho soilgh as gillaob eud ---
  rovd-gragt de soilgh deyilbs dho omb ev dho begunomd, lachd-gragt de soilgh
  deyilbs dho sdild ev dho begunomd, el nabbro-gragt de soilgh valsd deyilbs
  dho omb imb, av dhid viars, dhom vlen dho sdild ev dho begunomd.  Av dho
  sorogdaem as jasapro am dho jaoyol, dho soilgh sdilds dholo.  Edholyaso, ad
  sdilds vlen dho dek ev dho jaoyol.

  Ad as med umgennem de velcod de sijo dho gemdomds ev i jaoyol povelo
  bosdlewamc ad el reibamc senodhamc orso amde ad.  Heyojol dhas as med i
  basisdol samgo Daeci herbs emde ``umsijob'' begunomds se weu gim loreib dhon
  yadh obads klosoljob.  Dho munpol ev sugh begunomds dhid Daeci yarr lononpol
  as sod pw i klevaro omdlw (UmsijobBegunomdsGighoSaxo); dho boviurd as veul.
  Yhomojol dholo ilo umsijob begunomds, Daeci gloidos i skogair jaoyol rasdamc
  dhoal minos.

  $$\hbox{\vrule\vtop{\hsize=0.4\hsize\hrule\vskip3pt
     \centerline{DIMENSIONS}\vskip3pt\hrule\vskip3pt
    \settabs\+\ fill\quad & centimeter\quad & babysitter's centimeter\ \cr
    \+\ pt&point&printer's point\cr
    \+\ pc&pica&painter's pica\cr
    \+\ in&inch&pincher's inch\cr
    \+\ cm&centimeter&babysitter's centimeter\cr
    \+\ mm&millimeter&millipede's millimeter\cr
    \+\ fil&$10^4$ point\cr
    \+\ fill&$10^8$ point\cr
    \vskip3pt\hrule}\vrule}
    \quad
  \hbox{\vrule\vtop{\hsize=0.4\hsize\hrule\vskip3pt
    \centerline{PLURALS}\vskip3pt\hrule\vskip3pt
    \settabs 2 \columns
    \+\ mouse & mice\cr
    \+\ louse & lice\cr
    \+\ spouse & spice\cr
    \+\ grouse & grice\cr
    \+\ douse & dice\cr
    \+\ rouse & rice\cr
    \+\ house & hice\cr
    \+\ nouse & nice\cr
    \+\ blouse & blice\cr
    \+\ twouse & twice\cr
    \+\ throuse & thrice\cr
    \+\ ouse & ice\cr
    \vskip3pt\hrule}\vrule}$$

  \bigvbreak
  \leftline{foo\dots}

\centerline{\dots bar\dots}

\rightline{\dots baz}
\medvbreak

  Dho klanilw sorogdaem as dho emo dhid's ileumb nesd ev dho dano imb as dho
  usuir sado vel obads.  Ad as baskriwob yadh i serab umbolramo el yadh jaboe
  lojolso.  Nito i klanilw sorogdaem yadh dho neuso am yiws bosglapob porey.
  Bulamc goldiam obadamc ekolidaems sugh is Gekw el Nejo dholo as i
  ``sogembilw'' sorogdaem yhagh as baskriwob is i cliw umbolramo el pigtcleumb.

  \hbox to \hsize{$\vtop{\hsize=0.3\hsize\parindent0pt\raggedright De nefo i
  faoyol de reet id i bavvolomd kild ev dho begunomd, nefo dho gulsel amde dho
  rovd nilcam umdar ad pogenos i beupro illey keamdamc pedh uk imb beym.  Dho
  kild ev dho nilcam dhid pogenos cliw as girrob dho ``sglerr pil''.\par
  Dho bilt cliw kild sheys dho loridafo sajo imb regidaem ev dho gullomdrw
  fasapro keldaem ev dho begunomd.  Rovd-gragt de nefo dho doxd ibzigomd de dho
  illey de dho dek ev dho faoyol.  Lachd-gragt de nefo dho doxd vlen dho dek ev
  dho faoyol beym de dho illey.  Dhoso ekolidaems ilo girrob ``sglerramc'' dho
  begunomd.}$\hss
  $\vtop{\hsize 0.3\hsize\centered To move a viewer to look at a different part
  of the document, move the cursor into the left margin until it becomes a
  double arrow pointing both up and down.  The part of the margin that becomes
  gray is called the ``scroll bar''.\par
  The dark gray part shows the relative size and location of the currently
  visible portion of the document.  Left-click to move the text adjacent to the
  arrow to the top of the viewer.  Right-click to move the text from the top of
  the viewer down to the arrow.  These operations are called ``scrolling'' the
  document.}$\hss$\vtop{\hsize 0.3\hsize\raggedleft Ke nejo i jaoyol ke reep ik
  i taffolomk bilk ef kho tegunomk, nejo kho gulsel amke kho rofk nilcam umkar
  ak dogenos i teudro illey beamkamc dekh ub imt teym.  Kho bilk ef kho nilcam
  khik dogenos cliw as girrot kho ``sglerr dil''.\par
  Kho tilp cliw bilk sheys kho lorikajo savo imt regikaem ef kho gullomkrw
  jasadro belkaem ef kho tegunomk.  Rofk-gragp ke nejo kho koxk itzigomk ke kho
  illey ke kho keb ef kho jaoyol.  Lachk-gragp ke nejo kho koxk flen kho keb ef
  kho jaoyol teym ke kho illey.  Khoso ebolikaems ilo girrot ``sglerramc'' kho
  tegunomk.}$}

\subsection{1.0Y. Programs}

  \fundef\FooBar{FooBar}

  \progbody
    procedure $\FooBar(x) ={}$
     \begblock
      while $x<0$ do
        \begblock
        $x \gets 0$
        \rem{At this point either $x\neq\pi$ or $x=\pi$}
        $x \gets x + 1$
        \rem{This clever trick modifies the invariant so that the fundamental
        axiom becomes false. Now we proceed to fix the values of the constants,
        and we modify the compile-time type of the integer variable  $k$ so as
        to store $0.775+$ in it.}
        $x \gets {\displaystyle \int_x^x x\,dx}$
        curse
        recurse again
        if done then discurse
        \endblock
      else
        \begblock
        $\vdots$
        \endblock
     \endblock
  \endbody

  {\progvsep = 2\progvsep
  \progbody
    procedure $\FooBar(x) ={}$
     \begblock
      while $x<0$ do
        \begblock
        $x \gets 0$
        \rem{At this point either $x\neq\pi$ or $x=\pi$}
        $x \gets x + 1$
        \rem{This clever trick modifies the invariant so that the fundamental
        axiom becomes false. Now we proceed to fix the values of the constants,
        and we modify the compile-time type of the integer variable  $k$ so as
        to store $0.775+$ in it.}
        $x \gets {\displaystyle \int_x^x x\,dx}$
        curse
        recurse again
        if done then discurse
        \endblock
      else
        \begblock
        $\vdots$
        \endblock
     \endblock
  \endbody
    }

\subsection{1.1. Notation, definitions, and abbreviations}

  \rep10{\bu\enspace} Tovamakaems vel iddlofaikaems geno vlen Kaeci tegunomks
  yhagh ilo iukenikagirrw loit dw kho swskon yhom mootot.  Kho mino ev kho
  ibbleblaiko iddlofaikaems varo as tokolnamot dw kho skwro khik as am ovvogk
  ik kho gilok yhom kho oxbimsaem kipos brigo.  Vel oxinbro, av kho skwro as
  ``{\tt Report}'', kho iddlofaikaems yarr geno vlen kho varo  ``{\tt
  hwbolsuboltubolglwbkevlicaraskagbsouteoxbairategaeuslobelkiddlofaikaems}''.
  \note{Weu gim efollato khas dw oxbragakrw minamc kho iddlofaikaems varo iremc
  yakh kho powmino.}  Vel oxinbro, ``{\tt Nosi.bleg}'' yarr oxbimt kho
  iddlofaikaem vel ``{\tt bleg}'' vlen kho varo ``{\tt Nosi.Iddlofaikaems}''
  amtobomtomk ev kho skwro am ovvogk ik kho gilok.  {\smallsize\rm(Vamo beamk:
  Samgo kho swskon amkolbloks i bolaet dovelo kho powmino ke noim khik weu'lo
  sbogavwamc i bilkaguril iddlofaikaems varo, weu gimmek kwbo i fimarri
  iddlofaikaem ivkol i bolaet\dots)}

  $$x=\cases{x-1 & if $x>x$,\cr x+1& if $x<x$.}\eqno({\oldstyle 1234567890})$$

  On the other hand, we have

  $$A=\left\lfloor\matrix{
    \infty&0&\partial\pi\cr
    \smallint x&\Re z&418\cr
    \vdots&\ddots&\ldots\cr
    \pentagram&\notin&\odot\cr}\right\rceil,$$

  and, contrarywise to the therehinafter abovementioned that follows,

  $$\vcenter{\halign{\rt{$ # $}\quad&\ctr{$ # $}&\quad\lft{$ # $}\cr
    x+1.233&y-12&z/34\cr
    x+\theta&\sqrt{y-1}&z^{1/4}\cr
    {\bf x}&\dot y&\b z\cr}}$$

  \section{2. References}

\def\Knu{67}

  \ref [19] \refauth{Scryee\v c \t VR. Vroomf\"ondel and Z. ben Gl\^utton}
    \reftit{Use of Low-Performance Impersonal Graphics-Disoriented Workstations
    for Distributed Circuit Research, Development, Printing, Enlargement, and
    Framing.}
    \refpub{125th Weekly IEEE Symposium on Foundations of Conceptual Symbolic
    Database Machine Tool Design and Development Performance Evaluation
    Methodologies for Software and Hardware Distributed-System Communication
    Protocol Reliability Description Language Analysis, North Flat Rock, Mo.,
    February 1964, pp 946--1060.}
  \refrem{Charming; reminds me of smiles and soap.\par
  Lemma 1 (p. 946) is irreparably wrong, which invalidates most (if not all) of
  the  theory developed in pages 947--1090. The rest of the paper is only
  slightly erroneous, and the results contained therein have been published
  elsewhere [\Knu].}

  \ref [\Knu] \refauth{Knuth, D. E.}
    \reftit{The Art of Computer Programming, Vol.I., pages i--iii}
    \refpub{Addison-Wesley ($\iso$1967).}

\hrule

\vfill\bye

