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macros.tex
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macros.tex
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\def\turnstilesymbol{{$\vdash$}}
\setspecialsymbol{!-}{{\turnstilesymbol}}
\def\divosymbol{{$\div^{o}$}}
\setspecialsymbol{/o}{{\it {\divosymbol}}}
\def\cinsymbol{{c$_{\mathrm{in}}$}}
\setspecialsymbol{cin}{{\it {\cinsymbol}}}
\def\coutsymbol{{c$_{\mathrm{out}}$}}
\setspecialsymbol{cout}{{\it {\coutsymbol}}}
\def\mfosymbol{{mf$^{\thinspace o}$}}
\setspecialsymbol{mfo}{{\it {\mfosymbol}}}
\def\fosymbol{{f$^{\thinspace o}$}}
\setspecialsymbol{fo}{{\it {\fosymbol}}}
\def\gosymbol{{g$^{\thinspace o}$}}
\setspecialsymbol{go}{{\it {\gosymbol}}}
\def\pathosymbol{{path$^{\thinspace o}$}}
\setspecialsymbol{patho}{{\it {\pathosymbol}}}
\def\arcosymbol{{arc$^{\thinspace o}$}}
\setspecialsymbol{arco}{{\it {\arcosymbol}}}
\def\varosymbol{{var$^{\thinspace o}$}}
\setspecialsymbol{varo}{{\it {\varosymbol}}}
\def\genosymbol{{gen$^{\thinspace o}$}}
\setspecialsymbol{geno}{{\it {\genosymbol}}}
\def\genuosymbol{{genu$^{\thinspace o}$}}
\setspecialsymbol{genuo}{{\it {\genuosymbol}}}
\def\genbosymbol{{genb$^{\thinspace o}$}}
\setspecialsymbol{genbo}{{\it {\genbosymbol}}}
\def\zeroosymbol{{zero$^{\thinspace o}$}}
\setspecialsymbol{zeroo}{{\it {\zeroosymbol}}}
\def\splitosymbol{{split$^{\thinspace o}$}}
\setspecialsymbol{splito}{{\it {\splitosymbol}}}
\def\pososymbol{{pos$^{\thinspace o}$}}
\setspecialsymbol{poso}{{\it {\pososymbol}}}
\def\semimulosymbol{{semimul$^{\thinspace o}$}}
\setspecialsymbol{semimulo}{{\it {\semimulosymbol}}}
\def\lessosymbol{{less$^{\thinspace o}$}}
\setspecialsymbol{lesso}{{\it {\lessosymbol}}}
\def\lesslosymbol{{lessl$^{\thinspace o}$}}
\setspecialsymbol{lesslo}{{\it {\lesslosymbol}}}
\def\samelosymbol{{samel$^{\thinspace o}$}}
\setspecialsymbol{samelo}{{\it {\samelosymbol}}}
\def\lesslthreeosymbol{{lessl3$^{\thinspace o}$}}
\setspecialsymbol{lessl3o}{{\it {\lesslthreeosymbol}}}
\def\mulosymbol{{mul$^{\thinspace o}$}}
\setspecialsymbol{mulo}{{\it {\mulosymbol}}}
\def\oddmulosymbol{{odd-mul$^{\thinspace o}$}}
\setspecialsymbol{odd-mulo}{{\it {\oddmulosymbol}}}
\def\boundmulosymbol{{bound-mul$^{\thinspace o}$}}
\setspecialsymbol{bound-mulo}{{\it {\boundmulosymbol}}}
\def\onceosymbol{{once$^{\thinspace o}$}}
\setspecialsymbol{onceo}{{\it {\onceosymbol}}}
\def\repeatedmulosymbol{{repeated-mul$^{\thinspace o}$}}
\setspecialsymbol{repeated-mulo}{{\it {\repeatedmulosymbol}}}
\def\muloneosymbol{{mul1$^{\thinspace o}$}}
\setspecialsymbol{mul1o}{{\it {\muloneosymbol}}}
\def\multwoosymbol{{mul2$^{\thinspace o}$}}
\setspecialsymbol{mul2o}{{\it {\multwoosymbol}}}
\def\multhreeosymbol{{mul3$^{\thinspace o}$}}
\setspecialsymbol{mul3o}{{\it {\multhreeosymbol}}}
\def\gtlosymbol{{gtl$^{\thinspace o}$}}
\setspecialsymbol{gtlo}{{\it {\gtlosymbol}}}
\def\addosymbol{{add$^{\thinspace o}$}}
\setspecialsymbol{addo}{{\it {\addosymbol}}}
\def\minusosymbol{{minus$^{\thinspace o}$}}
\setspecialsymbol{minuso}{{\it {\minusosymbol}}}
\def\newgtoneosymbol{{$>\!$1$^{o}$}}
\setspecialsymbol{>1o}{{\bf{\newgtoneosymbol}}}
\def\genadderosymbol{{gen-adder$^{\thinspace o}$}}
\setspecialsymbol{gen-addero}{{\it {\genadderosymbol}}}
\def\fulladderosymbol{{full-adder$^{\thinspace o}$}}
\setspecialsymbol{full-addero}{{\it {\fulladderosymbol}}}
\def\halfadderosymbol{{half-adder$^{\thinspace o}$}}
\setspecialsymbol{half-addero}{{\it {\halfadderosymbol}}}
\def\fulloneadderosymbol{{full1-adder$^{\thinspace o}$}}
\setspecialsymbol{full1-addero}{{\it {\fulloneadderosymbol}}}
\def\fullnadderosymbol{{fulln-adder$^{\thinspace o}$}}
\setspecialsymbol{fulln-addero}{{\it {\fullnadderosymbol}}}
\def\adderosymbol{{adder$^{\thinspace o}$}}
\setspecialsymbol{addero}{{\it {\adderosymbol}}}
\def\subosymbol{{sub$^{\thinspace o}$}}
\setspecialsymbol{subo}{{\it {\subosymbol}}}
\def\divosymbol{{div$^{\thinspace o}$}}
\setspecialsymbol{divo}{{\it {\divosymbol}}}
\def\logosymbol{{log$^{\thinspace o}$}}
\setspecialsymbol{logo}{{\it {\logosymbol}}}
\def\exposymbol{{exp$^{\thinspace o}$}}
\setspecialsymbol{expo}{{\it {\exposymbol}}}
\def\exptwoosymbol{{exp2$^{\thinspace o}$}}
\setspecialsymbol{exp2o}{{\it {\exptwoosymbol}}}
\def\sfusymbol{{\sf u}}
\setspecialsymbol{sfu}{{\sfusymbol}}
\setspecialsymbol{bn0}{{\bf 0}}
\setspecialsymbol{bn1}{{\bf 1}}
\setspecialsymbol{bn2}{{\bf 2}}
\setspecialsymbol{bn3}{{\bf 3}}
\setspecialsymbol{bn4}{{\bf 4}}
\setspecialsymbol{bn5}{{\bf 5}}
\setspecialsymbol{bn6}{{\bf 6}}
\setspecialsymbol{bn7}{{\bf 7}}
\setspecialsymbol{bnminus1}{{\bf -1}}
\def\lambdasymbol{{$\lambda$}}
\setspecialsymbol{lambda}{{\bf {\lambdasymbol}}}
\def\ulambdasymbol{{u$\lambda$}}
\setspecialsymbol{ulambda}{{\bf {\ulambdasymbol}}}
\setspecialsymbol{fake-ulambda}{{\bf {\ulambdasymbol}}}
\setspecialsymbol{ulambda}{{\bf {\ulambdasymbol}}}
\def\umatchsymbol{{umatch}}
\setspecialsymbol{umatch}{{\bf {\umatchsymbol}}}
\setspecialsymbol{fake-umatch}{{\bf {\umatchsymbol}}}
\def\umatchauxsymbol{{umatch-aux}}
\setspecialsymbol{umatch-aux}{{\bf {\umatchauxsymbol}}}
\def\lambdaesymbol{{$\lambda^{e}$}}
\setspecialsymbol{lambda-e}{{\bf {\lambdaesymbol}}}
\setspecialsymbol{lambdae}{{\bf {\lambdaesymbol}}}
%\def\lambdawsymbol{{$\lambda^{w}$}}
%\setspecialsymbol{lambda-w}{{\bf {\lambdawsymbol}}}
%\setspecialsymbol{lambdaw}{{\bf {\lambdawsymbol}}}
\def\lambdaasymbol{{$\lambda^{a}$}}
\setspecialsymbol{lambda-a}{{\bf {\lambdaasymbol}}}
\setspecialsymbol{lambdaa}{{\bf {\lambdaasymbol}}}
\def\lambdausymbol{{$\lambda^{u}$}}
\setspecialsymbol{lambda-u}{{\bf {\lambdausymbol}}}
\setspecialsymbol{lambdau}{{\bf {\lambdausymbol}}}
\def\lpatsymbol{{lpat}}
\setspecialsymbol{lpat}{{\bf {\lpatsymbol}}}
\def\matchesymbol{{match$^{e}$}}
\setspecialsymbol{match-e}{{\bf {\matchesymbol}}}
\setspecialsymbol{matche}{{\bf {\matchesymbol}}}
\def\matchasymbol{{match$^{a}$}}
\setspecialsymbol{match-a}{{\bf {\matchasymbol}}}
\setspecialsymbol{matcha}{{\bf {\matchasymbol}}}
\def\matchusymbol{{match$^{u}$}}
\setspecialsymbol{match-u}{{\bf {\matchusymbol}}}
\setspecialsymbol{matchu}{{\bf {\matchusymbol}}}
\def\mpatsymbol{{mpat}}
\setspecialsymbol{mpat}{{\bf {\mpatsymbol}}}
\def\ssstarsymbol{{ss$^{*}$}}
\setspecialsymbol{ss*}{{\it {\ssstarsymbol}}}
\def\ifstarsymbol{{if$^{\thinspace *}$}}
\setspecialsymbol{if*}{{\it {\ifstarsymbol}}}
\def\plusstarosymbol{{plus$^{\thinspace *o}$}}
\setspecialsymbol{plus*o}{{\it {\plusstarosymbol}}}
\def\foldlosymbol{{foldl$^{\thinspace o}$}}
\setspecialsymbol{foldlo}{{\it {\foldlosymbol}}}
\def\foldrosymbol{{foldr$^{\thinspace o}$}}
\setspecialsymbol{foldro}{{\it {\foldrosymbol}}}
\setspecialsymbol{proveo}{$prove^o$}
\setspecialsymbol{body1}{$body_1$}
\setspecialsymbol{existsbad}{{\textit{exists}}}
\setspecialsymbol{anom}{{\textit{a}}}
\setspecialsymbol{bnom}{{\textit{b}}}
\setspecialsymbol{Nvar}{{\textit{n}}}
\setspecialsymbol{Mvar}{{\textit{m}}}
\setspecialsymbol{Xvar}{{\textit{x}}}
\setspecialsymbol{Yvar}{{\textit{y}}}
\setspecialsymbol{unexp1}{$unexp_1$}
\setspecialsymbol{prf1}{$pr\!f_1$}
\setspecialsymbol{prf2}{$pr\!f_2$}
\setspecialsymbol{lit1}{$lit_1$}
\setspecialsymbol{tm*}{$tm^*$}
\setspecialsymbol{ansv*}{$ansv^*$}
\setspecialsymbol{cache-ansv*}{$cache$-$ansv^*$}
%\setspecialsymbol{cache-ansv*-set!}{$cache$-$ansv^*$-$set!$}
\setspecialsymbol{cache-ansv*-set!}{{\it cache-ansv$^*$\!-set!}}
\setspecialsymbol{ss-ansv*}{$ss$-$ansv^*$}
\def\truesymbol{{\tt \#}{\sf t}}
\def\falsesymbol{{\tt \#}{\sf f}}
\setspecialsymbol{#t}{{\truesymbol}}
\setspecialsymbol{#f}{{\falsesymbol}}
\def\failsymbol{{\tt \#}{\sf u}}
\def\succeedsymbol{{\tt \#}{\sf s}}
\setspecialsymbol{#u}{{\failsymbol}}
\setspecialsymbol{#s}{{\succeedsymbol}}
\setspecialsymbol{...}{{$\ldots$}}
\def\quotelitsymbol{{(\bf{{quote}} $lit$)}}
\setspecialsymbol{quotelit}{{{\quotelitsymbol}}}
\def\walkstarsymbol{walk$^{*}$}
\setspecialsymbol{walk*}{{\it{\walkstarsymbol}}}
\setspecialsymbol{lambdag@}{{\bf{$\lambda$$_{\raisebox{-1pt}{\mbox{\tiny \sffamily \bfseries G}}}$}}}
\setspecialsymbol{lambdaf@}{{\bf{$\lambda$$_{\raisebox{-1pt}{\mbox{\tiny \sffamily \bfseries F}}}$}}}
\setspecialsymbol{lambdap@}{{\bf{$\lambda$$_{\raisebox{-1pt}{\mbox{\tiny \sffamily \bfseries P}}}$}}}
\def\symboltostringsymbol{{\it{symbol$\rightarrow$string}}}
\setspecialsymbol{symbol->string}{{\symboltostringsymbol}}
\def\stringtosymbolsymbol{{\it{string$\rightarrow$symbol}}}
\setspecialsymbol{string->symbol}{{\stringtosymbolsymbol}}
\def\stringtonumbersymbol{{\it{string$\rightarrow$number}}}
\setspecialsymbol{string->number}{{\stringtonumbersymbol}}
\def\stringtolistsymbol{{\it{string$\rightarrow$list}}}
\setspecialsymbol{string->list}{{\stringtolistsymbol}}
\def\listtostringsymbol{{\it{list$\rightarrow$string}}}
\setspecialsymbol{list->string}{{\listtostringsymbol}}
\def\numbertostringsymbol{{\it{number$\rightarrow$string}}}
\setspecialsymbol{number->string}{{\numbertostringsymbol}}
\def\bindstarsymbol{{bind$^{*}$}}
\setspecialsymbol{bind*}{{\bf {\bindstarsymbol}}}
\def\mplusstarsymbol{{mplus$^{*}$}}
\setspecialsymbol{mplus*}{{\bf {\mplusstarsymbol}}}
\def\incsymbol{{inc}}
\setspecialsymbol{inc}{{\bf {\incsymbol}}}
\def\choosesymbol{{choose}}
\setspecialsymbol{choose}{{\bf{\choosesymbol}}}
\def\choicesymbol{{choice}}
\setspecialsymbol{choice}{{\bf{\choicesymbol}}}
\def\ainfsymbol{a{\tiny $^{^{\infty}}$}}
\setspecialsymbol{a-inf}{{\it{\ainfsymbol}}}
\def\pinfsymbol{p{\tiny $^{^{\infty}}$}}
\setspecialsymbol{p-inf}{{\it{\pinfsymbol}}}
\def\caseinfsymbol{case{\tiny $^{^{\infty}}$}}
\setspecialsymbol{case-inf}{{\bf {\caseinfsymbol}}}
\def\sigmasymbol{{$\sigma$}}
\setspecialsymbol{sigma}{{\it {\sigmasymbol}}}
\def\tausymbol{{$\tau$}}
\setspecialsymbol{tau}{{\it {\tausymbol}}}
\def\nablasymbol{{$\nabla$}}
\setspecialsymbol{nabla}{{\it {\nablasymbol}}}
\def\deltasymbol{{$\delta$}}
\setspecialsymbol{delta}{{\it {\deltasymbol}}}
\def\deltahatsymbol{{$\hat{\delta}$}}
\setspecialsymbol{delta^}{{\it {\deltahatsymbol}}}
\def\eqnssymbol{{$\epsilon$}}
\setspecialsymbol{eqns}{{\it {\eqnssymbol}}}
\def\applysigmarulessymbol{{apply-$\sigma$\!-rules}}
\setspecialsymbol{apply-sigma-rules}{{\it {\applysigmarulessymbol}}}
\def\applypisymbol{{apply-$\pi$}}
\setspecialsymbol{apply-pi}{{\it {\applypisymbol}}}
\def\mvletsymbol{{mv-let}}
\setspecialsymbol{mv-let}{{\bf {\mvletsymbol}}}
\def\pmatchsymbol{{pmatch}}
\setspecialsymbol{pmatch}{{\bf {\pmatchsymbol}}}
\def\ppatsymbol{{ppat}}
\setspecialsymbol{ppat}{{\bf {\ppatsymbol}}}
\def\guardsymbol{{guard}}
\setspecialsymbol{guard}{{\bf {\guardsymbol}}}
\def\bfconssymbol{{cons}}
\setspecialsymbol{bf-cons}{{\bf {\bfconssymbol}}}
\def\bfexpandsymbol{{expand}}
\setspecialsymbol{bf-expand}{{\bf {\bfexpandsymbol}}}
\def\unifyhashsymbol{{unify$\#$}}
\setspecialsymbol{unifyhash}{{\it {\unifyhashsymbol}}}
\def\sigmahatsymbol{{$\hat{\sigma}$}}
\setspecialsymbol{sigma^}{{\it {\sigmahatsymbol}}}
\def\deltaunionsymbol{{$\delta$-union}}
\setspecialsymbol{delta-union}{{\it {\deltaunionsymbol}}}
\def\applysubstsymbol{{apply-subst}}
\setspecialsymbol{apply-subst}{{\it {\applysubstsymbol}}}
\def\composesubstsymbol{{compose-subst}}
\setspecialsymbol{compose-subst}{{\it {\composesubstsymbol}}}
\def\applynablarulessymbol{{apply-\!$\nabla$\!-rules}}
\setspecialsymbol{apply-nabla-rules}{{\it {\applynablarulessymbol}}}
\def\sigmarulessymbol{{$\sigma$\!-rules}}
\setspecialsymbol{sigma-rules}{{\it {\sigmarulessymbol}}}
\def\emptysigmasymbol{{empty-$\sigma$}}
\setspecialsymbol{empty-sigma}{{\it {\emptysigmasymbol}}}
\def\emptynablasymbol{{empty-\!$\nabla$}}
\setspecialsymbol{empty-nabla}{{\it {\emptynablasymbol}}}
\def\emptydeltasymbol{{empty-$\delta$}}
\setspecialsymbol{empty-delta}{{\it {\emptydeltasymbol}}}
\def\nablarulessymbol{{$\nabla$\!-rules}}
\setspecialsymbol{nabla-rules}{{\it {\nablarulessymbol}}}
\def\pisymbol{{$\pi$}}
\setspecialsymbol{pi}{{\bf {\pisymbol}}}
\def\pihatsymbol{{$\hat{\pi}$}}
\setspecialsymbol{pi^}{{\bf {\pihatsymbol}}}
\def\cstarhatsymbol{{$\hat{c}^{*}$}}
\setspecialsymbol{c*^}{{\cstarhatsymbol}}
\def\cstarofsymbol{{$c^{*}$-of}}
\setspecialsymbol{c*-of}{{\it \cstarofsymbol}}
\def\emptycstarsymbol{{empty-$c^{*}$}}
\setspecialsymbol{empty-c*}{{\it \emptycstarsymbol}}
\newcommand{\RfiveRS}{$R^{5}\!RS$}
\newcommand{\RfiveRSsp}{$R^{5}\!RS$ }
\newcommand{\RsixRS}{$R^{6}\!RS$}
\newcommand{\RsixRSsp}{$R^{6}\!RS$ }
\newcommand{\one}{$\textcircled{\raisebox{-.8pt}{1}}\;$}
\newcommand{\two}{$\textcircled{\raisebox{-.8pt}{2}}\;$}
\newcommand{\onet}{$\textcircled{\raisebox{-.8pt}{1}}$}
\newcommand{\twot}{$\textcircled{\raisebox{-.8pt}{2}}$}
\setspecialsymbol{one}{\one} \setspecialsymbol{two}{\two}
\setspecialsymbol{backquotefootnote}{\footnotemark}
\newcommand{\copyterm}{{\tt copy\_term/2}}
\newcommand{\copytermo}{$copy\mbox{-}term^o$}
\setspecialsymbol{copy-termo}{$copy\mbox{-}term^o$}
\setspecialsymbol{subst-lito}{$subst\mbox{-}lit^o$}
\setspecialsymbol{subst-termo}{$subst\mbox{-}term^o$}
\setspecialsymbol{subst-term*}{$subst\mbox{-}term^{*o}$}
\newcommand{\conda}{\textbf{cond}$^a$}
\newcommand{\lambdaprolog}{$\lambda$Pro\-log}
\newcommand{\lambdaprologsp}{$\lambda$Pro\-log }
\newcommand{\alphaprolog}{$\alpha$Pro\-log}
\newcommand{\alphaprologsp}{$\alpha$Pro\-log }
\newcommand{\caml}{C$\alpha$ML}
\newcommand{\alphatap}{\mbox{$\alpha${\sf lean}\-$T\!\!A\!P$}}
\newcommand{\alphatapsp}{\mbox{$\alpha${\sf lean}\-$T\!\!A\!P\;$}}
\newcommand{\alphakanren}{$\alpha$Kan\-ren}
\newcommand{\alphakanrensp}{$\alpha$Kan\-ren }
\newcommand{\leantap}{\mbox{{\sf lean}\-$T\!\!A\!P\!$}}
\newcommand{\leantapsp}{\mbox{{\sf lean}\-$T\!\!A\!P\;$}}
\def\mk{miniKanren}
\def\wspace{\vspace{0.2cm}}
\def\tspace{\vspace{0.1cm}}
\def\nspace{\vspace{-0.08cm}}
\setspecialsymbol{run}{{\textbf{run}}}
\def\runonesymbol{run{$^{\bf{1}}$}}
\def\runtwosymbol{run{$^{\bf{2}}$}}
\def\runthreesymbol{run{$^{\bf{3}}$}}
\def\runfoursymbol{run{$^{\bf{4}}$}}
\def\runfivesymbol{run{$^{\bf{5}}$}}
\def\runsixsymbol{run{$^{\bf{6}}$}}
\def\runsevensymbol{run{$^{\bf{7}}$}}
\def\runeightsymbol{run{$^{\bf{8}}$}}
\def\runninesymbol{run{$^{\bf{9}}$}}
\def\runtensymbol{run{$^{\bf{10}}$}}
\def\runelevensymbol{run{$^{\bf{11}}$}}
\def\runtwelvesymbol{run{$^{\bf{12}}$}}
\def\runthirteensymbol{run{$^{\bf{13}}$}}
\def\runfourteensymbol{run{$^{\bf{14}}$}}
\def\runfifteensymbol{run{$^{\bf{15}}$}}
\def\runsixteensymbol{run{$^{\bf{16}}$}}
\def\runseventeensymbol{run{$^{\bf{17}}$}}
\def\runeighteensymbol{run{$^{\bf{18}}$}}
\def\runnineteensymbol{run{$^{\bf{19}}$}}
\def\runtwentysymbol{run{$^{\bf{20}}$}}
\def\runtwentyonesymbol{run{$^{\bf{21}}$}}
\def\runtwentytwosymbol{run{$^{\bf{22}}$}}
\def\runtwentythreesymbol{run{$^{\bf{23}}$}}
\def\runtwentyfoursymbol{run{$^{\bf{24}}$}}
\setspecialsymbol{run1}{{\bf{\runonesymbol}}}
\setspecialsymbol{run2}{{\bf{\runtwosymbol}}}
\setspecialsymbol{run3}{{\bf{\runthreesymbol}}}
\setspecialsymbol{run4}{{\bf{\runfoursymbol}}}
\setspecialsymbol{run5}{{\bf{\runfivesymbol}}}
\setspecialsymbol{run6}{{\bf{\runsixsymbol}}}
\setspecialsymbol{run7}{{\bf{\runsevensymbol}}}
\setspecialsymbol{run8}{{\bf{\runeightsymbol}}}
\setspecialsymbol{run9}{{\bf{\runninesymbol}}}
\setspecialsymbol{run10}{{\bf{\runtensymbol}}}
\setspecialsymbol{run11}{{\bf{\runelevensymbol}}}
\setspecialsymbol{run12}{{\bf{\runtwelvesymbol}}}
\setspecialsymbol{run13}{{\bf{\runthirteensymbol}}}
\setspecialsymbol{run14}{{\bf{\runfourteensymbol}}}
\setspecialsymbol{run15}{{\bf{\runfifteensymbol}}}
\setspecialsymbol{run16}{{\bf{\runsixteensymbol}}}
\setspecialsymbol{run17}{{\bf{\runseventeensymbol}}}
\setspecialsymbol{run18}{{\bf{\runeighteensymbol}}}
\setspecialsymbol{run19}{{\bf{\runnineteensymbol}}}
\setspecialsymbol{run20}{{\bf{\runtwentysymbol}}}
\setspecialsymbol{run21}{{\bf{\runtwentyonesymbol}}}
\setspecialsymbol{run22}{{\bf{\runtwentytwosymbol}}}
\setspecialsymbol{run23}{{\bf{\runtwentythreesymbol}}}
\setspecialsymbol{run24}{{\bf{\runtwentyfoursymbol}}}
\setspecialsymbol{run*}{{\textbf{run}$^{\bf *}$}}
\setspecialsymbol{tie}{$\bowtie$}
\setspecialsymbol{==}{$\equiv$}
\def\equalequalnochecksymbol{{$\equiv$-no-check}}
\setspecialsymbol{==-no-check}{{\it \equalequalnochecksymbol}}
\def\neverequalnochecksymbol{{$\neq$-no-check}}
\setspecialsymbol{=/=-no-check}{{\it \neverequalnochecksymbol}}
\def\equalequalverifysymbol{{$\equiv$-verify}}
\setspecialsymbol{==-verify}{{\it \equalequalverifysymbol}}
\setspecialsymbol{=/=}{$\neq$}
\def\neverequalverifysymbol{{$\neq$-verify}}
\setspecialsymbol{=/=-verify}{{\it \neverequalverifysymbol}}
\def\neverequalcheckosymbol{{$\neq^{\protect\surd}$}}
\setspecialsymbol{=/=-check}{{\neverequalcheckosymbol}}
\setspecialsymbol{hash}{{\textit{\#}}}
\setspecialsymbol{fresh}{{\textbf{fresh}}}
\setspecialsymbol{exist}{{\textbf{exist}}}
\def\verifycstarsymbol{{verify-c$^{*}$}}
\setspecialsymbol{verify-c*}{{\it \verifycstarsymbol}}
\def\unifystarsymbol{{unify$^{*}$}}
\setspecialsymbol{unify*}{{\it \unifystarsymbol}}
\setspecialsymbol{exist*}{{\textbf{exist$^{\bf *}$}}}
\setspecialsymbol{fresh*}{{\textbf{fresh$^{\bf *}$}}}
\setspecialsymbol{ext-s-check}{{\it{\extendschecksymbol}}}
\setspecialsymbol{unify-check}{{\it{\unifychecksymbol}}}
\setspecialsymbol{occurs-check}{{\it{\occurschecksymbol}}}
\setspecialsymbol{==-check}{{\it{\equalequalchecksymbol}}}
\def\extendschecksymbol{{ext-s$^{\protect\surd}$}}
\def\unifychecksymbol{{unify$^{\protect\surd}$}}
\def\occurschecksymbol{{occurs$^{\protect\surd}$}}
\def\equalequalchecksymbol{{$\equiv^{\protect\surd}$}}
\setspecialsymbol{conde}{{\textbf{cond}$^e$}}
\setspecialsymbol{conda}{{\textbf{cond}$^a$}}
\setspecialsymbol{condu}{{\textbf{cond}$^u$}}
\setspecialsymbol{project}{{\textbf{project}}}
\def\substosymbol{{subst$^{\thinspace o}$}}
\setspecialsymbol{substo}{{\it {\substosymbol}}}
\def\valueosymbol{{value$^{\thinspace o}$}}
\setspecialsymbol{valueo}{{\it {\valueosymbol}}}
\def\expressionosymbol{{expression$^{\thinspace o}$}}
\setspecialsymbol{expressiono}{{\it {\expressionosymbol}}}
\def\contextosymbol{{context$^{\thinspace o}$}}
\setspecialsymbol{contexto}{{\it {\contextosymbol}}}
\def\onesteposymbol{{one-step$^{\thinspace o}$}}
\setspecialsymbol{one-stepo}{{\it {\onesteposymbol}}}
\def\fullyreduceosymbol{{fully-reduce$^{\thinspace o}$}}
\setspecialsymbol{fully-reduceo}{{\it {\fullyreduceosymbol}}}
\def\safefullyreduceosymbol{{safe-fully-reduce$^{\thinspace o}$}}
\setspecialsymbol{safe-fully-reduceo}{{\it {\safefullyreduceosymbol}}}
\def\inholeosymbol{{in-hole$^{\thinspace o}$}}
\setspecialsymbol{in-holeo}{{\it {\inholeosymbol}}}
\def\lookuposymbol{{lookup$^{\thinspace o}$}}
\setspecialsymbol{lookupo}{{\it {\lookuposymbol}}}
\def\bitxorosymbol{{bit-xor$^{\thinspace o}$}}
\setspecialsymbol{bit-xoro}{{\it {\bitxorosymbol}}}
\def\bitandosymbol{{bit-and$^{\thinspace o}$}}
\setspecialsymbol{bit-ando}{{\it {\bitandosymbol}}}
\def\plusosymbol{{plus$^{\thinspace o}$}}
\setspecialsymbol{pluso}{{\it {\plusosymbol}}}
\setspecialsymbol{negateo}{$negate^o$}
\setspecialsymbol{membero}{$member^o$}
\def\rembersymbol{{$rember$}}
\setspecialsymbol{rember}{{\rembersymbol}}
\def\remberosymbol{{$rember^o$}}
\setspecialsymbol{rembero}{{\remberosymbol}}
\setspecialsymbol{swappendo}{$swappend^o$}
\setspecialsymbol{appendo}{$append^o$}
\setspecialsymbol{pairo}{$pair^o$}
\def\typosymbol{{typ$^{\thinspace o}$}}
\setspecialsymbol{typo}{{\it {\typosymbol}}}
\def\anyosymbol{{any$^{\thinspace o}$}}
\setspecialsymbol{anyo}{{\it {\anyosymbol}}}
\def\alwaysosymbol{{always$^{\thinspace o}$}}
\setspecialsymbol{alwayso}{{\it {\alwaysosymbol}}}
\def\neverosymbol{{never$^{\thinspace o}$}}
\setspecialsymbol{nevero}{{\it {\neverosymbol}}}
\def\rightarrowsymbol{{$\rightarrow$}}
\setspecialsymbol{rightarrowsymbol}{{\it {\rightarrowsymbol}}}
\setspecialsymbol{-->}{{\it {\rightarrowsymbol}}}
\def\bindertagsymbol{{tie}}
\setspecialsymbol{tie-tag}{{\sf {\bindertagsymbol}}}
\def\susptagsymbol{{susp}}
\setspecialsymbol{susp-tag}{{\sf {\susptagsymbol}}}
\def\nomtagsymbol{{nom}}
\setspecialsymbol{nom-tag}{{\sf {\nomtagsymbol}}}
\def\vartag{{\sf var}}
\setspecialsymbol{vartag}{{\vartag}}
\def\asubnsymbol{{$a_{n}$}}
\setspecialsymbol{a_n}{{\it {\asubnsymbol}}}
\def\bsubnsymbol{{$b_{n}$}}
\setspecialsymbol{b_n}{{\it {\bsubnsymbol}}}
\def\asubzerosymbol{{$a_{0}$}}
\setspecialsymbol{a_0}{{\it {\asubzerosymbol}}}
\def\bsubzerosymbol{{$b_{0}$}}
\setspecialsymbol{b_0}{{\it {\bsubzerosymbol}}}
\def\asubonesymbol{{$a_{1}$}}
\setspecialsymbol{a_1}{{\it {\asubonesymbol}}}
\def\bsubonesymbol{{$b_{1}$}}
\setspecialsymbol{b_1}{{\it {\bsubonesymbol}}}
\def\asubtwosymbol{{$a_{2}$}}
\setspecialsymbol{a_2}{{\it {\asubtwosymbol}}}
\def\bsubtwosymbol{{$b_{2}$}}
\setspecialsymbol{b_2}{{\it {\bsubtwosymbol}}}
\setspecialsymbol{=>}{$\Rightarrow$}
\def\ahatsymbol{{$\hat{a}$}}
\def\bhatsymbol{{$\hat{b}$}}
\def\chatsymbol{{$\hat{c}$}}
\def\dhatsymbol{{$\hat{d}$}}
\def\ehatsymbol{{$\hat{e}$}}
\def\fhatsymbol{{$\hat{f}$}}
\def\ghatsymbol{{$\hat{g}$}}
\def\hhatsymbol{{$\hat{h}$}}
\def\ihatsymbol{{$\hat{i}$}}
\def\jhatsymbol{{$\hat{j}$}}
\def\khatsymbol{{$\hat{k}$}}
\def\lhatsymbol{{$\hat{l}$}}
\def\mhatsymbol{{$\hat{m}$}}
\def\nhatsymbol{{$\hat{n}$}}
\def\ohatsymbol{{$\hat{o}$}}
\def\phatsymbol{{$\hat{p}$}}
\def\qhatsymbol{{$\hat{q}$}}
\def\rhatsymbol{{$\hat{r}$}}
\def\shatsymbol{{$\hat{s}$}}
\def\thatsymbol{{$\hat{t}$}}
\def\uhatsymbol{{$\hat{u}$}}
\def\vhatsymbol{{$\hat{v}$}}
\def\whatsymbol{{$\hat{w}$}}
\def\xhatsymbol{{$\hat{x}$}}
\def\yhatsymbol{{$\hat{y}$}}
\def\zhatsymbol{{$\hat{z}$}}
\def\txhatsymbol{{$t\hat{x}$}}
\def\tehatsymbol{{$t\hat{e}$}}
\setspecialsymbol{a^}{{\ahatsymbol}}
\setspecialsymbol{b^}{{\bhatsymbol}}
\setspecialsymbol{c^}{{\chatsymbol}}
\setspecialsymbol{d^}{{\dhatsymbol}}
\setspecialsymbol{e^}{{\ehatsymbol}}
\setspecialsymbol{f^}{{\fhatsymbol}}
\setspecialsymbol{g^}{{\ghatsymbol}}
\setspecialsymbol{h^}{{\hhatsymbol}}
\setspecialsymbol{i^}{{\ihatsymbol}}
\setspecialsymbol{j^}{{\jhatsymbol}}
\setspecialsymbol{k^}{{\khatsymbol}}
\setspecialsymbol{l^}{{\lhatsymbol}}
\setspecialsymbol{m^}{{\mhatsymbol}}
\setspecialsymbol{n^}{{\nhatsymbol}}
\setspecialsymbol{o^}{{\ohatsymbol}}
\setspecialsymbol{p^}{{\phatsymbol}}
\setspecialsymbol{q^}{{\qhatsymbol}}
\setspecialsymbol{r^}{{\rhatsymbol}}
\setspecialsymbol{s^}{{\shatsymbol}}
\setspecialsymbol{t^}{{\thatsymbol}}
\setspecialsymbol{u^}{{\uhatsymbol}}
\setspecialsymbol{v^}{{\vhatsymbol}}
\setspecialsymbol{w^}{{\whatsymbol}}
\setspecialsymbol{x^}{{\xhatsymbol}}
\setspecialsymbol{y^}{{\yhatsymbol}}
\setspecialsymbol{z^}{{\zhatsymbol}}
\setspecialsymbol{tx^}{{\txhatsymbol}}
\setspecialsymbol{te^}{{\tehatsymbol}}
\def\tonehatsymbol{{$\hat{t}_{1}$}}
\setspecialsymbol{t1^}{{\bf {\tonehatsymbol}}}
\def\ttwohatsymbol{{$\hat{t}_{2}$}}
\setspecialsymbol{t2^}{{\bf {\ttwohatsymbol}}}
\setspecialsymbol{a0}{$a_{0}$}
\setspecialsymbol{b0}{$b_{0}$}
\setspecialsymbol{c0}{$c_{0}$}
\setspecialsymbol{d0}{$d_{0}$}
\setspecialsymbol{e0}{$e_{0}$}
\setspecialsymbol{f0}{$f_{0}$}
\setspecialsymbol{g0}{$g_{0}$}
\setspecialsymbol{h0}{$h_{0}$}
\setspecialsymbol{i0}{$i_{0}$}
\setspecialsymbol{j0}{$j_{0}$}
\setspecialsymbol{k0}{$k_{0}$}
\setspecialsymbol{l0}{$l_{0}$}
\setspecialsymbol{m0}{$m_{0}$}
\setspecialsymbol{n0}{$n_{0}$}
\setspecialsymbol{o0}{$o_{0}$}
\setspecialsymbol{p0}{$p_{0}$}
\setspecialsymbol{q0}{$q_{0}$}
\setspecialsymbol{r0}{$r_{0}$}
\setspecialsymbol{s0}{$s_{0}$}
\setspecialsymbol{t0}{$t_{0}$}
\setspecialsymbol{u0}{$u_{0}$}
\setspecialsymbol{v0}{$v_{0}$}
\setspecialsymbol{w0}{$w_{0}$}
\setspecialsymbol{x0}{$x_{0}$}
\setspecialsymbol{y0}{$y_{0}$}
\setspecialsymbol{z0}{$z_{0}$}
\setspecialsymbol{a1}{$a_{1}$}
\setspecialsymbol{b1}{$b_{1}$}
\setspecialsymbol{c1}{$c_{1}$}
\setspecialsymbol{d1}{$d_{1}$}
\setspecialsymbol{e1}{$e_{1}$}
\setspecialsymbol{f1}{$f_{1}$}
\setspecialsymbol{g1}{$g_{1}$}
\setspecialsymbol{h1}{$h_{1}$}
\setspecialsymbol{i1}{$i_{1}$}
\setspecialsymbol{j1}{$j_{1}$}
\setspecialsymbol{k1}{$k_{1}$}
\setspecialsymbol{l1}{$l_{1}$}
\setspecialsymbol{m1}{$m_{1}$}
\setspecialsymbol{n1}{$n_{1}$}
\setspecialsymbol{o1}{$o_{1}$}
\setspecialsymbol{p1}{$p_{1}$}
\setspecialsymbol{q1}{$q_{1}$}
\setspecialsymbol{r1}{$r_{1}$}
\setspecialsymbol{s1}{$s_{1}$}
\setspecialsymbol{t1}{$t_{1}$}
\setspecialsymbol{u1}{$u_{1}$}
\setspecialsymbol{v1}{$v_{1}$}
\setspecialsymbol{w1}{$w_{1}$}
\setspecialsymbol{x1}{$x_{1}$}
\setspecialsymbol{y1}{$y_{1}$}
\setspecialsymbol{z1}{$z_{1}$}
\setspecialsymbol{a2}{$a_{2}$}
\setspecialsymbol{b2}{$b_{2}$}
\setspecialsymbol{c2}{$c_{2}$}
\setspecialsymbol{d2}{$d_{2}$}
\setspecialsymbol{e2}{$e_{2}$}
\setspecialsymbol{f2}{$f_{2}$}
\setspecialsymbol{g2}{$g_{2}$}
\setspecialsymbol{g3}{$g_{3}$}
\setspecialsymbol{h2}{$h_{2}$}
\setspecialsymbol{i2}{$i_{2}$}
\setspecialsymbol{j2}{$j_{2}$}
\setspecialsymbol{k2}{$k_{2}$}
\setspecialsymbol{l2}{$l_{2}$}
\setspecialsymbol{m2}{$m_{2}$}
\setspecialsymbol{n2}{$n_{2}$}
\setspecialsymbol{o2}{$o_{2}$}
\setspecialsymbol{p2}{$p_{2}$}
\setspecialsymbol{q2}{$q_{2}$}
\setspecialsymbol{r2}{$r_{2}$}
\setspecialsymbol{s2}{$s_{2}$}
\setspecialsymbol{t2}{$t_{2}$}
\setspecialsymbol{u2}{$u_{2}$}
\setspecialsymbol{v2}{$v_{2}$}
\setspecialsymbol{w2}{$w_{2}$}
\setspecialsymbol{x2}{$x_{2}$}
\setspecialsymbol{y2}{$y_{2}$}
\setspecialsymbol{z2}{$z_{2}$}
\setspecialsymbol{a3}{$a_{3}$}
\setspecialsymbol{b3}{$b_{3}$}
\setspecialsymbol{c3}{$c_{3}$}
\setspecialsymbol{d3}{$d_{3}$}
\setspecialsymbol{e3}{$e_{3}$}
\setspecialsymbol{f3}{$f_{3}$}
\setspecialsymbol{g3}{$g_{3}$}
\setspecialsymbol{g3}{$g_{3}$}
\setspecialsymbol{h3}{$h_{2}$}
\setspecialsymbol{i3}{$i_{3}$}
\setspecialsymbol{j3}{$j_{3}$}
\setspecialsymbol{k3}{$k_{3}$}
\setspecialsymbol{l3}{$l_{3}$}
\setspecialsymbol{m3}{$m_{3}$}
\setspecialsymbol{n3}{$n_{3}$}
\setspecialsymbol{o3}{$o_{3}$}
\setspecialsymbol{p3}{$p_{3}$}
\setspecialsymbol{q3}{$q_{3}$}
\setspecialsymbol{r3}{$r_{3}$}
\setspecialsymbol{s3}{$s_{3}$}
\setspecialsymbol{t3}{$t_{3}$}
\setspecialsymbol{u3}{$u_{3}$}
\setspecialsymbol{v3}{$v_{3}$}
\setspecialsymbol{w3}{$w_{3}$}
\setspecialsymbol{x3}{$x_{3}$}
\setspecialsymbol{y3}{$y_{3}$}
\setspecialsymbol{z3}{$z_{3}$}
\setspecialsymbol{g4}{$g_{4}$}
\setspecialsymbol{tn}{$t_{n}$}
\setspecialsymbol{tm}{$t_{m}$}
\setspecialsymbol{xn}{$x_{n}$}
\setspecialsymbol{t11}{$t_{11}$}
\setspecialsymbol{t1n}{$t_{1n}$}
\setspecialsymbol{t21}{$t_{21}$}
\setspecialsymbol{t2n}{$t_{2n}$}
\setspecialsymbol{q2m}{$q_{2m}$}
\setspecialsymbol{q2md}{$q_{2md}$}
\setspecialsymbol{aa}{$a_{a}$}
\setspecialsymbol{ba}{$b_{a}$}
\setspecialsymbol{ca}{$c_{a}$}
\setspecialsymbol{ma}{$m_{a}$}
\setspecialsymbol{na}{$n_{a}$}
\setspecialsymbol{pa}{$p_{a}$}
\setspecialsymbol{ra}{$r_{a}$}
\setspecialsymbol{ad}{$a_{d}$}
\setspecialsymbol{bd}{$b_{d}$}
\setspecialsymbol{cd}{$c_{d}$}
\setspecialsymbol{md}{$m_{d}$}
\setspecialsymbol{nd}{$n_{d}$}
\setspecialsymbol{pd}{$p_{d}$}
\setspecialsymbol{rd}{$r_{d}$}
\setspecialsymbol{p1d}{$p_{1d}$}
\def\gstarsymbol{g$^{*}$}
\def\fstarsymbol{f$^{\thinspace *}$}
\def\cstarsymbol{c$^{*}$}
\def\vstarsymbol{v$^{*}$}
\def\pstarsymbol{p$^{*}$}
\def\tstarsymbol{t$^{*}$}
\def\wstarsymbol{w$^{*}$}
\setspecialsymbol{g*}{{\it{\gstarsymbol}}}
\setspecialsymbol{f*}{{\it{\fstarsymbol}}}
\setspecialsymbol{w*}{{\it{\wstarsymbol}}}
\setspecialsymbol{c*}{{\it{\cstarsymbol}}}
\setspecialsymbol{v*}{{\it{\vstarsymbol}}}
\setspecialsymbol{p*}{{\it{\pstarsymbol}}}
\setspecialsymbol{t*}{{\it{\tstarsymbol}}}
\setspecialsymbol{ratorres}{$rator$-$res$}
\setspecialsymbol{randres}{$rand$-$res$}
\setspecialsymbol{bodyres}{$body$-$res$}
\setspecialsymbol{e1res}{$e{_{1}}$-$res$}
\setspecialsymbol{e2res}{$e{_{2}}$-$res$}
\setspecialsymbol{e3res}{$e{_{3}}$-$res$}
\def\strstarsymbol{str$^{*}$}
\setspecialsymbol{str*}{{\it{\strstarsymbol}}}
\def\ifasymbol{{if$^{\thinspace a}$}}
\setspecialsymbol{ifa}{{\bf {\ifasymbol}}}
\def\ifusymbol{{if$^{\thinspace u}$}}
\setspecialsymbol{ifu}{{\bf {\ifusymbol}}}
\setspecialsymbol{n-const}{{\bf n}}
\setspecialsymbol{m-const}{{\bf m}}
\setspecialsymbol{__}{{\bf \_}}
\setspecialsymbol{_.0}{$\__{_{0}}$}
\setspecialsymbol{_.1}{$\__{_{1}}$}
\setspecialsymbol{_.2}{$\__{_{2}}$}
\setspecialsymbol{_.3}{$\__{_{3}}$}
\setspecialsymbol{_.4}{$\__{_{4}}$}
\hyphenation{mi-ni-Kan-ren}
% arithm
\hyphenation{co-type}
% representation of a binary numeral
\newcommand{\bn}[1]{\ensuremath{\mathbf{#1}}}
\newcommand{\add}[3]{\ensuremath{\mathtt{add}(#1,#2,#3)}}
\newcommand{\mul}[4][]{\ensuremath{\mathtt{mul#1}(#2,#3,#4)}}
\newcommand{\semimul}[3]{\ensuremath{\mathtt{semimul}(#1,#2,#3)}}
\newcommand{\denot}[1]{[\![#1]\!]}
\newcommand{\set}[1]{\{\, #1 \,\}}
\providecommand{\norm}[1]{\lVert#1\rVert}
\providecommand{\floor}[1]{\lfloor#1\rfloor}
\DeclareMathOperator{\dom}{dom}
\DeclareMathOperator{\UU}{\mathtt{u}}
\DeclareMathOperator{\BO}{\mathtt{o}}
\renewcommand{\o}[0]{\BO}
\DeclareMathOperator{\BL}{\mathtt{l}}
\renewcommand{\l}[0]{\BL}
% \DeclareMathOperator{\fv}{fv}
\newtheorem{definition}{Definition}
\newtheorem{proposition}{Proposition}
\newcommand{\cons}[2]{\ensuremath{[{#1}\mathop{\mid}{#2}]}}
%\newtheorem{definition}{Definition} % [section]
%\newtheorem{example}{Example} % [section]
%\newtheorem{proposition}{Proposition} % [section]
%\newtheorem{corollary}{Corollary} % [section]
%\let\from=\leftarrow
%\newcommand{\oleg}[1]{{\it [Oleg says: #1]}}
%\newcommand{\ccshan}[1]{{\it [Ken says: #1]}}
%\newcommand{\will}[1]{{\it [Will says: #1]}}
%\newcommand{\dan}[1]{{\it [Dan says: #1]}}
\newcommand{\omitit}[1]{\ignorespaces}
%\newcommand{\oleg}[1]{\ignorespaces}
%\newcommand{\ccshan}[1]{\ignorespaces}
%\newcommand{\will}[1]{\ignorespaces}
%\newcommand{\dan}[1]{\ignorespaces}
\setspecialsymbol{mzero}{{\textbf{mzero}}}
\setspecialsymbol{unit}{{\textbf{unit}}}
\setspecialsymbol{var}{{\textbf{var}}}
\setspecialsymbol{var?}{{\textbf{var?}}}
\setspecialsymbol{ak-var}{{\it{var}}}
\setspecialsymbol{ak-var?}{{\it{var?}}}
%%%%%%%%%% ferns
\setspecialsymbol{ints-bottom}{{\textit{ints-from}$_\perp$}} % $
\setspecialsymbol{always-five-bottom}{{\textit{always-five$_\perp$}}}
\setspecialsymbol{map-bottom}{{\it{map$_\perp$}}}
\setspecialsymbol{append-bottom}{{\it{append$_\perp$}}}
\setspecialsymbol{unit-bottom}{{\textit{unit}$_\perp$}}
\setspecialsymbol{mzero-bottom}{{\textit{mzero}$_\perp$}}
\setspecialsymbol{bind-bottom}{{\textit{bind}$_\perp$}}
\setspecialsymbol{mplus-bottom}{{\textbf{{mplus$_\perp$}}}}
\setspecialsymbol{mplus-func-bottom}{{\textit{mplus}$_\perp$}}
\setspecialsymbol{mplus-fn-bottom}{{\textit{mplus-aux}$_\perp$}}
\setspecialsymbol{==-bottom}{{$\equiv$$_\perp$}}
\setspecialsymbol{or-bottom}{{\textit{or}$_\perp$}}
\setspecialsymbol{disj-bottom}{{\textbf{{disj$_\perp$}}}}
\setspecialsymbol{conj-bottom}{{\textbf{{conj$_\perp$}}}}
\setspecialsymbol{run-bottom}{{\textit{run}$_\perp$}}
\setspecialsymbol{choose-bottom}{{\textbf{{choose$_\perp$}}}}
\setspecialsymbol{choose-aux-bottom}{{\textit{choose-aux}$_\perp$}}
\def\lessthanequalolsymbol{{$\leqslant${\it{l}}$^{\thinspace o}$}}
\def\lessthanosymbol{{$<^{o}$}}
\def\lessthanequalosymbol{{$\leqslant^{o}$}}
\def\lessthanolsymbol{{$<${\it{l}}$^{\thinspace o}$}}
\def\equalolsymbol{{$=${\it{l}}$^{\thinspace o}$}}
\setspecialsymbol{<=lo}{{\lessthanequalolsymbol}}
\setspecialsymbol{<lo}{{\lessthanolsymbol}}
\setspecialsymbol{=lo}{{\equalolsymbol}}