<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\usepackage{color}
\usepackage{textcomp}
\newcommand\highlight[2]{{\setlength\fboxsep{1pt}\colorbox{#1}{#2}}}


%\def\NV{\highlight{colorNV}}
\definecolor{colorNV}{rgb}{1,0.8,1}

\providecommand{\dbrkts}[1]{[\![#1]\!]}

\newenvironment{grammar}{\csname align*\endcsname}{\csname endalign*\endcsname}
\newcommand\grammardef[2]{\ensuremath{#1\ \text{::}&amp;\text{=} &amp;&amp; \text{\textit{#2}}}\\}
\newcommand\grammardefnoalt[3]{\ensuremath{#1\ \text{::}&amp;\text{=} #2 &amp;&amp; \text{\textit{#3}}}\\}
\newcommand\grammardefbare[2]{\ensuremath{#1\ \ &amp; &amp;&amp; \text{\textit{#2}}}\\}
\newcommand\grammaralt[2]{\ensuremath{&amp;\mid #1 &amp;&amp; \text{#2}}\\}


\newcommand\phide[1]{}
\newcommand\lhide[1]{}
\newcommand\hide[1]{}

\newcommand\rulename[1]{\textsc{#1}\xspace}

\newcommand\hastype[3]{\ensuremath{#1 \vdash #2 : #3}}
\newcommand\eval[2]{\ensuremath{#1 \hookrightarrow #2 }}


%predicate type
\newcommand\predty{\ensuremath{t}}


%basic
\newcommand\vref{\ensuremath{v}}
\newcommand\tyDef[1]{\ensuremath{\mathbb{#1}}}
\newcommand\tyDefArg[2]{\ensuremath{\tyDef{#1}\left(\tyDef{#2}\right)}}
\newcommand\nhaskell[1]{\mathsf{#1}}


%rule names
\newcommand\tfunction{\rulename{T-Fun}}
\newcommand\tapp{\rulename{T-App}}
\newcommand\tsub{\rulename{T-Sub}}
\newcommand\tconst{\rulename{T-Const}}
\newcommand\tinst{\rulename{T-Inst}}
\newcommand\tgen{\rulename{T-Gen}}
\newcommand\tpinst{\rulename{T-Inst}}
\newcommand\tpgen{\rulename{T-Gen}}
\newcommand\tcase{\rulename{T-Case}}
\newcommand\tbase{\rulename{T-Var-Base}}
\newcommand\tvariable{\rulename{T-Var}}


\newcommand\wsEmp{\rulename{WS-Empty}}
\newcommand\wsExt{\rulename{WS-Ext}}
\newcommand\wsGxt{\rulename{WS-Gxt}}

\newcommand\wstEmp{\rulename{WTS-Empty}}
\newcommand\wstExt{\rulename{WTS-Ext}}
\newcommand\wstGxt{\rulename{WTS-Gxt}}

\newcommand\wtTrue{\rulename{WF-True}}
\newcommand\wtRVApp{\rulename{WF-RApp}}
\newcommand\wtVar{\rulename{WF-Var}}
\newcommand\wtBase{\rulename{WF-Base}}
\newcommand\wtFun{\rulename{WF-Fun}}
\newcommand\wtApp{\rulename{WF-App}}
\newcommand\wtPred{\rulename{WF-Abs}}
\newcommand\wtPoly{\rulename{WF-Abs-$\alpha$}}

\newcommand\tdsubBase{$\subt$\rulename{-Dec-Base}}
\newcommand\tsubBase {$\subt$\rulename{-Base}}
\newcommand\tsubFun  {$\subt$\rulename{-Fun}}
\newcommand\tsubVar  {$\subt$\rulename{-Var}}
\newcommand\tsubApp  {$\subt$\rulename{-App}}
\newcommand\tsubClass{$\subt$\rulename{-Class}}
\newcommand\tsubPred {$\subt$\rulename{-Abs}}
\newcommand\tsubPoly {$\subt$\rulename{-Poly}}


\def\subt{\prec}


\newcommand\hasType[4]{\ensuremath{#1 \vdash_{#2} #3 : #4 }}
\newcommand\hasTypeP[4]{\ensuremath{#1 \vdash #2 : #3 \mid #4 }}
\newcommand\penv{\ensuremath{\Gamma}}
\newcommand\isSubType[3]{\ensuremath{#1 \vdash \subtype{#2}{#3}}}
\newcommand\subtype[2]{\ensuremath{#1 \preceq #2}}
\newcommand\isWellFormed[2]{\ensuremath{#1 \vdash #2 }}
\newcommand\isWellFormedP[3]{\ensuremath{#1, #2 \vdash #3 }}
\newcommand\meet[2]{\ensuremath{\text{meet} \left( {#1}, {#2} \right)}}
\newcommand\strengthen[2]{\ensuremath{\text{strengthen} \left( {#1}, {#2} \right)}}
\newcommand\shape[1]{\ensuremath{\text{shape} \left( {#1} \right)}}
\newcommand\shapep[1]{\ensuremath{\text{shapep} \left( {#1} \right)}}

\newcommand\isSub[3]{\ensuremath{{#1}\vdash {#2}&lt;:{#3}}}
%\newcommand\eval[2]{\ensuremath{{#1}\looparrowright {#2}}}
%\newcommand\eval[2]{\ensuremath{{#1}\hookrightarrow {#2}}}

\newcommand\hastypeEmp[2]{\hastype{\emptyset}{#1}{#2}}
\newcommand\isSubEmp[2]{\isSub{\emptyset}{#1}{#2}}


\newcommand\sch[1]{\ensuremath{\texttt{Schema}\left(#1\right)}}
\newcommand\fv[1]{\ensuremath{\texttt{FreeVars}\left(#1\right)}}



%expressions
\newcommand\etabs[2]{\ensuremath{\Lambda #1 . #2}}
\newcommand\epabs[3]{\ensuremath{\Lambda {#1:#2} . #3}}

\newcommand\efunt[3]{\ensuremath{\lambda {#1:#2}. #3}}
\newcommand\efunbar[2]{\ensuremath{\lambda \overline{#1} . #2}}
%\newcommand\efun[2]{\ensuremath{\lambda #1 . #2}}
\newcommand\eapp[2]{\ensuremath{{#1} \ {#2}}}
\newcommand\etapp[2]{\ensuremath{{#1} \left[ {#2}\right]}}
\newcommand\epapp[2]{\ensuremath{{#1} \left[ #2\right]}}


\newcommand\elam[2]{\efun{#1}{#2}}
\newcommand\eplam[2]{\ensuremath{\epabs{#1}{#2}}}
\newcommand\etlam[2]{\ensuremath{\etabs{#1}{#2}}}

\newcommand\elet[3]{\ensuremath{\nhaskell{let} \ #1 = #2 \ \nhaskell{in} \ #3}}
\newcommand\eletrec[3]{\ensuremath{\nhaskell{let rec} \ #1 = #2 \ \nhaskell{in} \ #3}}
\newcommand\ecase[4]{\ensuremath{\nhaskell{case} \ (#1 = #2) \ \nhaskell{of} \ \mid_i  #3 \ \rightarrow \ #4}}

%translation

\newcommand\tx[1]{\ensuremath{\langle\!| #1 |\!\rangle}}
\newcommand\txinv[1]{\ensuremath{\langle| #1 |\rangle^{-1}}}
%%\newcommand\tx[1]{\ensuremath{\text{tx}(#1)}}
%%\newcommand\txinv[1]{\ensuremath{\text{tx}^{-1}(#1)}}
\newcommand\isWellFormedH[2]{\ensuremath{\tx{#1} \vdash_H \tx{#2}}}
\newcommand\isSubTypeH[3]{\ensuremath{\tx{#1} \vdash_H {\tx{#2}} &lt;: {\tx{#3}}}}
\newcommand\hastypeH[3]{\ensuremath{#1 \vdash_H #2 : #3}}




%types
\newcommand\conlan{\ensuremath{\mathrm{F_H}}\xspace}
\newcommand\corelan{$\lambda_{P}$\xspace}
\newcommand\corelanm{$\lambda_{LP}$'\xspace}

\newcommand{\reft}{\ensuremath{e}\xspace}
\newcommand{\areft}{\ensuremath{p}\xspace}
\newcommand\rvapp[2]{\ensuremath{{#1 \ \overline{#2}}}} 
\newcommand\tref[2]{\ensuremath{\left\lbrace \vref : #1\mid #2\right\rbrace}}
\newcommand{\tpp}[2]{{#1 \langle #2 \rangle}}
\newcommand\tpref[3]{\tref{\tpp{#1}{#2}}{#3}}

\newcommand\tbint{\ensuremath{\texttt{int}}\xspace}
\newcommand\tbbool{\ensuremath{\texttt{bool}}\xspace}
\newcommand\tc[1]{\ensuremath{tc\left(#1\right)}}
\newcommand\tfun[3]{\ensuremath{{#1:#2} \rightarrow #3}}
\newcommand\tcfun[2]{\ensuremath{{#1 \rightarrow #2}}}
\newcommand\ptype[1]{\tcfun{#1}{\tbbool}}
\newcommand\rpinst[3]{\ensuremath{{#1}[{#2} \vartriangleright {#3}]}}
\newcommand\rpapply[5]{\ensuremath{\mathsf{Apply}(#1,#2,#3,#4,#5)}}



\newcommand\trfun[4]{\ensuremath{\tref{\tfun{#1}{#2}{#3}}{#4}}}
\newcommand\trfuntop[3]{\ensuremath{#1 : #2 \rightarrow #3}}
\newcommand\tpabs[3]{\ensuremath{\forall #1 : #2 . #3}}
\newcommand\ttabs[2]{\ensuremath{\forall #1 . #2}}


\newcommand\tbool{\tbbool}
\newcommand\tvar[2]{\tref{#1}{#2}}
\newcommand\tcon[4]{\ensuremath{\tref{\nhaskell{#1} \ #3 \ #4}{#2}}}
\newcommand\tclass[2]{\ensuremath{\nhaskell{#1} \ #2}}
\newcommand\tforallPr[2]{\ensuremath{\forall #1 . #2}}
\newcommand\tforallTy[2]{\ttabs{#1}{#2}}


\newcommand\pdVar[3]{\ensuremath{#1}} %it seems that the pred var is just a var...
%\newcommand\pdVar[3]{\ensuremath{#1 : #2 \left\langle #3 \right\rangle }}

\newcommand\unifyTypes[3]{\ensuremath{ \left\langle {#1} , {#2} \right\rangle \models {#3}}}
\newcommand\refa[3]{\ensuremath{ \left\lbrace #1 : #2 \mid #3 \right\rbrace }}
\newcommand\sub[2]{\ensuremath{ \left[ #1 \mapsto #2 \right] }}
\newcommand\subP[2]{\ensuremath{\left[#1\mapsto_\star #2\right]}}
\newcommand\freshP[1]{\ensuremath{\text{fresh}\ \left( #1\right)}}
\newcommand\freshT[1]{\ensuremath{\text{fresh}\ \left( #1\right)}}
\newcommand\subT[2]{\ensuremath{\sub{#1}{#2}}}


\newcommand\pdTy{\ensuremath{{T_P}}}
\newcommand\lTy{\ensuremath{\hat{T}}}
\newcommand\dTy{\ensuremath{T}}

\newcommand\appTy[2]{\ensuremath{\parAny{#1} \left( #2 \right)  }}
\newcommand\parTy[2]{\ensuremath{\parAny{#1} \left( \parAny{#2} \right)  }}
\newcommand\parAny[1]{\ensuremath{\mathbb{#1}}}
\newcommand\listOf[1]{\ensuremath{\left\langle #1 \right\rangle}}


\newcommand\tyConPs[1]{\ensuremath{\text{predicates} \left( #1 \right)}}
\newcommand\valid[2]{\ensuremath{#1 \Rightarrow #2}}
\newcommand\inter[1]{\ensuremath{\dbrkts{#1}}}
</pre></body></html>