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esop-clj-grammar.sty
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esop-clj-grammar.sty
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% see mmm.sty for implementation of newmeta etc
% macros for Clojure grammars
\usepackage{mathpartir}
\usepackage{amsfonts}
\usepackage{bbm}
\usepackage{xcolor}
\usepackage{xspace}
% newmeta variables are automatically subscripted
% \x0, \x1, \x{}
%% metavariables
% constants
\newmeta\const{c}
% types
\newcommand\esopsigma{\sigma}
\newmeta\s{\esopsigma} % these are automatically wrapped in \ma
\newmeta\sp{\esopsigma{'}}
\newcommand\esoptau{\tau}
\newmeta\t{\esoptau}
\newmeta\tp{\esoptau{'}}
\newmeta\tpp{\esoptau{''}}
\newmeta\T{T}
% expressions
\newmeta\M{M}
\newmeta\N{N}
\newmeta\P{P}
\newcommand\esope{e}
\newmeta\e{\esope}
\newmeta\ep{\esope'}
\newmeta\epp{\esope''}
\newcommand\esopd{d}
\newmeta\expd{\esopd}
\newmeta\ReflectiveExp{R}
\newmeta\NonReflectiveExp{E}
\newmeta\MultimethodExp{M}
\newmeta\HintedExp{H}
\newmeta\HashMapExp{G}
\newcommand\lambdatc{\ma{\lambda_{TC}}}
% we write a macro for every bit of abstract syntax. That way they
% will all look the same!
% types
\newbfop\int{int}
\newbfop\Boolean{B}
\newbfop\Booleanlong{Boolean}
\newbfop\Booleanhint{Boolean}
\newbfop\IFn{Fn}
\newbfop\MultiFn{MultiFn}
\newbfop\PMulti{Multi}
\newbfop\IPersistentMapLiteral{Map}
\newbfop\MapLiteral{Map}
\newbfop\Uliteral{\ma{\bigcup}}
\newbfop\Iliteral{\ma{\bigcap}}
\newbfop\Not{Not}
\newbfop\Allliteral{All}
\newbfop\TFnliteral{TFn}
\newbfop\Valueliteral{Val}
\newbfop\ArrayTwoLiteral{Array2}
\newbfop\ArrayLiteral{Array}
\newbfop\ArrayPLiteral{ArrayP}
\newbfop\Throwable{Throwable}
\newbfop\Class{Class}
\newbfop\Object{Object}
\newbfop\Expr{Expr}
\newbfop\Order{Order}
\newbfop\Breakfast{Bf}
\newbfop\Lunch{Lu}
\newcommand\MultiFntype[2]{(\PMulti #1\ #2)}
\newcommand\proctype[2]{(#1 \to #2)}
\newcommand\EmptyUnion[0]{\ma{(\Uliteral)}}
\newcommand\Unionsplice[1]{(\ma{\Uliteral\ #1})}
\newcommand\Unionsplicenospace[1]{(\ma{\Uliteral #1})}
\newcommand\Union[2]{(\ma{\Uliteral\ #1\ #2})}
\newcommand\UnionNilNum[0]{\ma{\Union{\Nil}{\Number}}}
\newcommand\UnionNilFile[0]{\ma{\Union{\Nil}{\File}}}
\newcommand\In[1]{(\ma{\Iliteral\ #1})}
\newcommand\ArrayTwo[2]{(\ma{\ArrayTwoLiteral\ #1\ #2})}
\newcommand\Array[1]{(\ArrayLiteral #1)}
\newcommand\ArrayP[1]{(\ArrayPLiteral #1)}
% \proctype is a little overkill.
%% Reynolds' package can also abstract things like (\s1 \to \s2 \to \s3).
\newcommand\Arrow[4]{\ma{#1 \xrightarrow[#4]{#3} #2}}
% TODO figure out how to make #1 : #2 closer to the :
\newcommand\ArrowOne[5]{\ma{{\hastypesmall {#1} {#2}} \xrightarrow[#5]{#4} #3}}
\newcommand\ArrowOverright[5]{\ma{{\overrightarrow{\hastypesmall {#1} {#2}}} \xrightarrow[#5]{#4} #3}}
% minus filters and object, implicitly tt | tt; empty
\newcommand\ArrowTwo[3]{\ma{{\hastypesmall {#1} {#2}} \xrightarrow\ {#3}}}
% easy math mode overrightarrow
\newcommand\overr[1]{\ma{\overrightarrow{#1}}}
\newcommand\getparent{\CLJoperatorfont{getParent}}
\newcommand\getx{getX}
\newcommand\coretyped{\texttt{core.typed}\xspace}
\newcommand\All[2]{(\ma{\Allliteral\ [#1]\ #2})}
\newcommand\TFn[2]{(\ma{\TFnliteral\ [#1]\ #2})}
\newcommand\Value[1]{(\ma{\Valueliteral #1})}
\newcommand\ValueFalse[0]{(\ma{\Valueliteral \false})}
\newcommand\ValueNil[0]{(\ma{\Valueliteral \nil})}
\newcommand\ValueTrue[0]{(\ma{\Valueliteral \true})}
\newcommand\ValueBool[0]{(\ma{\Valueliteral \bool{}})}
\newcommand\ValueClass[0]{(\ma{\Valueliteral \class{}})}
\newcommand\ValueKw[0]{(\ma{\Valueliteral \k{}})}
\newcommand\ValueStr[0]{(\ma{\Valueliteral \str{}})}
\newcommand\Valkw[1]{\ma{\Value{\makekw{#1}}}}
\newmeta\singletonmeta{l}
\newbfop\Top{\ma{\top}}
\newbfop\Bottom{\ma{\bot}}
\newbfop\Bot{\ma{\bot}}
\newbfop\Keyword{K}
\newbfop\Keywordlong{Keyword}
\newbfop\Keywordhint{Keyword}
\newbfop\Symbol{Symbol}
\newbfop\NumberFull{Nat}
\newbfop\Number{N}
\newbfop\Nil{nil}
\newbfop\True{true}
\newbfop\False{false}
\newbfop\falsy{(\ma{\cup\ \Nil\ \False})}
\newbfop\falsydiff{\ma{\trdiff{\falsy}}}
\newcommand\IPersistentMap[2]{(\ma{\IPersistentMapLiteral\ #1\ #2})}
\newcommand\Map[2]{(\ma{\MapLiteral #1\ #2})}
\newcommand\HMapInstance[0]{\ma{\IPersistentMapLiteral}}
\newbfop\HMapliteral{HMap}
\newmeta\completenessmeta{\mathcal{E}}
\newmeta\complete{\mathcal{C}}
\newmeta\partial{\mathcal{P}}
\newcommand\HMapcliteral[0]{\HMapliteral^{\complete{}}}
\newcommand\HMappliteral[0]{\HMapliteral^{\partial{}}}
\newcommand\HMapgenericliteral[0]{\HMapliteral^{\completenessmeta{}}}
\newcommand\HMapgeneric[2]{(\ma{\HMapgenericliteral #1\ #2})}
\newcommand\HMapc[1]{(\ma{\HMapcliteral #1})}
\newcommand\HMapcwithabsent[2]{(\ma{\HMapcliteral #1\ #2})}
\newcommand\HMapp[2]{(\ma{\HMappliteral #1\ #2})}
\newcommand\mandatoryentry[2]{\ma{{#1} \mapsto {#2}}}
\newcommand\mandatoryentrykwnoarrow[2]{\ma{\makekw{#1}\ {#2}}}
\newcommand\mandatoryentrynoarrow[2]{\ma{{#1}\ {#2}}}
\newcommand\mandatoryset[1]{\ma{\{#1\}}}
\newcommand\mandatorysetsingleton[2]{\ma{\mandatoryset{\mandatoryentry{#1}{#2}}}}
\newcommand\mandatorysetoverright[2]{\ma{\{\overrightarrow{\mandatoryentry{#1}{#2}}\}}}
\newcommand\notinmandatory[3]{\ma{#1 \not\in dom({#3})}}
\newcommand\inmandatory[3]{\ma{{#3}[{#1}] = {#2}}}
\newcommand\extendmandatoryset[3]{#1[\mandatoryentry{#2}{#3}]}
\newmeta\mandatory{\ma{\mathcal{M}}}
\newmeta\absent{\ma{\mathcal{A}}}
\newmeta\absentp{\ma{{\mathcal{A}}'}}
\newcommand\absentoverright[1]{\ma{\{{\overrightarrow{#1}}\}}}
\newcommand\emptyabsent[0]{\ma{\{\}}}
\newcommand\inabsent[2]{\ma{#1 \in #2}}
\newcommand\notinabsent[2]{\ma{#1 \not\in #2}}
\newcommand\extendabsentset[2]{\ma{({#1} \cup \{#2\})}}
\newbfop\Satisfiesliteral{Satisfies}
\newcommand\Satisfies[1]{(\ma{\Satisfiesliteral\ #1})}
\newbfop\Instanceliteral{InstanceOf}
\newcommand\Instance[1]{(\ma{\Instanceliteral\ #1})}
\newcommand\HVec[1]{[{#1}]}
\newcommand\makekw[1]{\ma{\metafunctionfont{\mathbin{:}#1}}}
\newcommand\makestr[1]{\ma{``{\metafunctionfont{#1}}"}}
\newcommand\makelocal[1]{\ma{#1}}
\newcommand\secref[1]{Section~\ref{#1}}
\newcommand\figref[1]{Figure~\ref{#1}}
\newcommand\chapref[1]{Chapter~\ref{#1}}
\newcommand\partref[1]{Part~\ref{#1}}
\newcommand\egref[1]{Example~\ref{#1}}
\newcommand\lemref[1]{Lemma~\ref{#1}}
\newcommand\theoremref[1]{Theorem~\ref{#1}}
% terms
\newmeta\x{x} % not sure if \x is reserved...
\newmeta\xp{x{'}} % not sure if \x is reserved...
\newmeta\y{y}
\newmeta\z{z}
\newmeta\v{v}
\newmeta\vp{v'}
\newmeta\vpp{v''}
\newmeta\class{C}
\newmeta\classp{C{'}}
\newmeta\protocol{P}
\newmeta\k{k}
\newmeta\str{s}
\newmeta\num{n}
\newmeta\nat{n}
\newmeta\bool{b}
\newcommand\CLJoperatorfont[1]{\ma{{\mathsf{#1}}}}
\newcommand\literalfont[1]{\ma{{\mathsf{#1}}}}
\newcommand\nil[0]{{\literalfont{nil}}}
\newcommand\true[0]{{\literalfont{true}}}
\newcommand\false[0]{{\literalfont{false}}}
\newcommand\assocliteral[0]{\ma{\CLJoperatorfont{assoc}}}
\newcommand\assocexp[3]{(\assocliteral{}\ #1\ #2\ #3)}
\newcommand\dissocliteral[0]{\ma{\CLJoperatorfont{dissoc}}}
\newmeta\getliteral{{\CLJoperatorfont{get}}}
\newcommand\getexp[2]{\ma{(\getliteral{}\ #1\ #2)}}
\newcommand\ifliteral[0]{{\CLJoperatorfont{if}}}
\newcommand\doliteral[0]{{\CLJoperatorfont{do}}}
\newcommand\letliteral[0]{{\CLJoperatorfont{let}}}
\newcommand\throwliteral[0]{{\CLJoperatorfont{throw}}}
\newcommand\newliteral[0]{{\CLJoperatorfont{new}}}
\newcommand\defmultiliteral[0]{{\CLJoperatorfont{defmulti}}}
\newcommand\defmethodliteral[0]{{\CLJoperatorfont{defmethod}}}
\newcommand\fnliteral[0]{{\CLJoperatorfont{fn}}}
\newcommand\abs[3]{\ma{\l #1^{#2} . #3}}
\newcommand\uabs[2]{\ma{\l #1 . #2}}
\newcommand\absoverright[3]{\ma{\l \overrightarrow{#1^{#2}} . #3}}
\newcommand\curlymap[1]{\ma{\{#1\}}}
\newcommand\emptymap[1]{\ma{\{\}}}
\newcommand\roundpair[2]{\ma{(#1, #2)}}
\newcommand\mapvalentry[2]{\ma{{#1} \mapsto {#2}}}
\newcommand\mapvalentrynoarrow[2]{\ma{{#1}\ {#2}}}
\newcommand\mapvalentrykwkey[2]{\ma{\makekw{#1} \mapsto {#2}}}
\newcommand\mapvalentrykwkeynoarrow[2]{\ma{\makekw{#1}\ {#2}}}
\newcommand\curlymapvaloverright[2]{\ma{\{{\overrightarrow{\mapvalentry{#1}{#2}}}\}}}
\newcommand\curlymapvaloverrightnoarrow[2]{\ma{\{{\overrightarrow{\mapvalentrynoarrow{#1}{#2}}}\}}}
\newcommand\extendmap[3]{\ma{#1[#2 \mapsto #3]}}
\newcommand\getmap[2]{\ma{#1[#2]}}
\newcommand\entryinmap[2]{\ma{{#1} \in {#2}}}
\newcommand\keyinmap[2]{\ma{{#1} \in dom({#2})}}
\newcommand\keynotinmap[2]{\ma{{#1} \not\in dom({#2})}}
\newcommand\comb[2]{\ma{(#1\ #2)}}
\newcommand\zeroliteral[0]{0}
\newcommand\ifexp[3]{\ma{(\ifliteral{}\ #1\ #2\ #3)}}
\newcommand\doexp[2]{\ma{(\doliteral{}\ #1\ #2)}}
\newcommand\letexp[3]{\ma{(\letliteral{}\ [\ma{#1\ #2}]\ #3)}}
\newcommand\letexpmany[2]{\ma{(\letliteral{}\ [\ma{#1}]\ #2)}}
\newcommand\fnexp[1]{\ma{(\fnliteral{}\ #1)}}
\newcommand\appexp[2]{\ma{(#1\ #2)}}
\newcommand\appexpone[1]{\ma{(#1)}}
\newcommand\apptwoexp[3]{\ma{(#1\ #2\ #3)}}
\newcommand\throwexp[1]{\ma{(\throwliteral{}\ #1)}}
\newcommand\newexp[2]{\ma{(\newliteral{}\ #1 #2)}}
% deleted 2nd argument which is just the same as #3
\newcommand\newstaticexp[4]{\ma{({\newliteral}_{[#1]}\ #3\ #4)}}
\newcommand\dotliteral[0]{{\CLJoperatorfont{.}}}
\newcommand\fieldexp[2]{\ma{(\dotliteral\ #2\ #1)}}
\newcommand\fieldstaticexp[4]{\ma{(\dotliteral\ #4\ {#3}^{#1}_{#2})}}
\newcommand\methodexp[3]{\ma{(\dotliteral\ #2\ (#1 #3))}}
\newcommand\methodstaticexp[6]{\ma{(\dotliteral\ #5\ ({#4}^{#1}_{[[#2], #3]} #6))}}
\newcommand\createmultiexp[2]{\ma{(\defmultiliteral{}\ #1\ #2)}}
\newcommand\defmultiexp[2]{(\ma{\defmultiliteral{}\ #1\ #2})}
\newcommand\defmethodexp[4]{(\ma{\defmethodliteral{}\ #1\ #2\ [#3]\ #4})}
\newcommand\extendmultiexp[3]{(\ma{\defmethodliteral{}\ #1\ #2\ #3})}
\newmeta\defliteral{\textbf{def}}
\newcommand\defexp[2]{(\ma{\defliteral{}\ #1\ #2})}
\newcommand\wrong[0]{\ma{wrong}}
\newcommand\errorval[1]{\ma{\metafunctionfont{err}}}
\newcommand\errorvalv[0]{\errorval{\v{}}}
\newcommand\reflerror[0]{\errorval{refl}}
\newcommand\mmerror[0]{\errorval{mm}}
\newcommand\rtvector[1]{[{#1}]}
% Java primitives
\newmeta\pint{int}
\newbfop\Integer{java.lang.Integer}
\newbfop\Int{Int}
\newmeta\plong{long}
\newbfop\Long{Long}
\newmeta\pdouble{double}
\newbfop\Double{java.lang.Double}
\newmeta\pchar{char}
\newbfop\Character{java.lang.Character}
\newmeta\pvoid{void}
\newbfop\Void{Void}
\newbfop\File{F}
\newbfop\FileFull{File}
\newbfop\Point{Point}
\newbfop\String{S}
\newbfop\StringFull{String}
\newmeta\mth{mth}
\newmeta\fld{fld}
% Clojure values
\newmeta\symbol{symbol}
% constant calls
\newbfop\ccclass{class}
\newcommand\instanceliteral[0]{\CLJoperatorfont{instance?}}
\newcommand\isaliteral[0]{{\CLJoperatorfont{isa?}}}
\newcommand\instanceapp[2]{{(\instanceliteral\ #1\ #2)}}
\newcommand\isaapp[2]{(\isaliteral\ #1\ #2)}
\newcommand\equivliteral[0]{\ma{=}}
\newcommand\equivapp[2]{(\equivliteral\ #1\ #2)}
% constant typing
\newcommand\constanttypeliteral[0]{\ma{{\delta}_{\t{}}}}
\newcommand\constantopsemliteral[0]{\ma{\delta}}
\newcommand\constanttypetwo[2]{\ma{\constanttypeliteral{}(#2)}}
\newcommand\constanttype[1]{\constanttypetwo{\t{}}{#1}}
\newcommand\constantopsem[2]{\ma{{\constantopsemliteral{}}(#1, #2)}}
\newcommand\classconst[0]{\emph{class}}
\newcommand\throwconst[0]{\emph{throw}}
\newcommand\numberhuh[0]{\emph{n?}}
\newcommand\inc[0]{\emph{inc}}
\newcommand\mapconst[0]{\emph{map}}
\newcommand\filterconst[0]{\emph{filter}}
% differences from TR
%\newcommand\trdiff[1]{\mathbin{\textcolor{blue}{#1}}}
\newcommand\trdiff[1]{#1}
% update function
\newcommand\metafunctionfont[1]{{\mathsf{#1}}}
\newcommand\updateliteral[0]{\ma{\metafunctionfont{update}}}
\newcommand\update[3]{\updateliteral({#1}, {#2}, {#3})}
\newcommand\restrictliteral[0]{\ma{\metafunctionfont{restrict}}}
\newcommand\restrict[2]{\restrictliteral(#1, #2)}
\newcommand\removeliteral[0]{\ma{\metafunctionfont{remove}}}
\newcommand\remove[2]{\removeliteral(#1, #2)}
\newcommand\emptypath[0]{\ma{\epsilon}}
% class table
\newcommand\ct[0]{\ma{\mathcal{CT}}}
\newmeta\ctentrymeta{ce}
\newmeta\ctmethod{m}
\newmeta\ctfield{f}
\newmeta\ctctor{c}
\newcommand\inct[2]{\ma{#1 \in #2}}
\newcommand\ctmethodsliteral[0]{\metafunctionfont{m}}
\newcommand\ctfieldsliteral[0]{\metafunctionfont{f}}
\newcommand\ctconstructorsliteral[0]{\metafunctionfont{c}}
\newcommand\ctmthentry[3]{\ma{#1 \mapsto [[#2], #3]}}
\newcommand\ctfldentry[2]{\ma{#1 \mapsto #2}}
\newcommand\ctctorentry[1]{\ma{[#1]}}
\newcommand\set[1]{\ma{\{#1\}}}
% WARNING specific formatting for figure
\newcommand\ctlookup[2]{\ma{{#1}[#2]}}
\newcommand\ctlookuptwo[3]{\ma{\ctlookup{{\ctlookup{#1}{#2}}}{#3}}}
\newcommand\ctlookupmethods[2]{\ma{\ctlookuptwo{#1}{#2}{\ctmethodsliteral}}}
\newcommand\ctlookupfields[2]{\ma{\ctlookuptwo{#1}{#2}{\ctfieldsliteral}}}
\newcommand\ctlookupctors[2]{\ma{\ctlookuptwo{#1}{#2}{\ctconstructorsliteral}}}
% typing judgements
\newcommand\rewrites[2]{#1 \Rightarrow #2}
\newcommand\hastype[2]{\ma{#1 \mathbin{:} #2}}
\newcommand\hastypesmall[2]{\ma{#1 {:} #2}}
\newcommand\issubtype[2]{\ma{#1 \mathbin{<:} #2}}
\newcommand\issubtypein[3]{\ma{{\inpropenv{#1} {#2 \mathbin{<:} #3}}}}
\newcommand\issubobjin[3]{\ma{{\inpropenv{#1} {#2 \mathbin{<:} #3}}}}
\newcommand\notsubtypein[3]{\ma{{\inpropenv{#1} {#2 \mathbin{\not<:} #3}}}}
% 5 place relation (TR formalism)
\newcommand\judgement[5]{\ma{#1 \vdash {\hastype{#2}{#3}} \ ;\ #4\ ;\ #5}}
% 6 place relation (w/ rewrite)
\newcommand\judgementselfrewrite[5]{\ma{#1 \vdash {\hastype{#2}{#3}}\ ;\ #4\ ;\ #5}}
%DISABLE REWRITING
\newcommand\judgementrewrite[6]{\ma{#1 \vdash {\hastype{#2}{#3}}\ ;\ #4\ ;\ #5}}
%if you really want the => rewrite to show
\newcommand\judgementshowrewrite[6]{\ma{#1 \vdash {\hastype{\rewrites{#2}{#6}}{#3}}\ ;\ #4\ ;\ #5}}
%\newcommand\judgementsev[7]{\ma{#3 \vdash_{\scriptscriptstyle{\trdiff{\ct{}}}} #4\ ;\ #5\ ;\ #6}}
% lookuping props in the env
% 2 place relation (same as tt | tt; empty)
\newcommand\judgementtwo[3]{\ma{#1 \vdash {\hastype{#2}{#3}}}}
\newcommand\judgementtworewrite[4]{\ma{#1 \vdash {\hastype{\rewrites{#2}{#4}}{#3}} }}
\newcommand\inpropenv[2]{\ma{#1 \vdash #2}}
% operational semantics
\newmeta\openv{\rho}
\newmeta\openvp{\rho'}
\newcommand\emptyopenv[0]{\ma{\{\}}}
\newcommand\inopenvnoeq[2]{\ma{#1 (#2)}}
\newcommand\inopenv[3]{\ma{#1 (#2) = #3}}
\newcommand\inopenvalign[3]{\ma{#1 (#2) &=& #3}}
\newcommand\notinopenv[2]{\ma{#2 \not\in dom(#1)}}
\newcommand\extendopenv[3]{\ma{#1[#2 \mapsto #3]}}
\newcommand\opsem[3]{\ma{#1 \vdash #2 \Downarrow #3}}
\newcommand\notopsem[3]{\ma{#1 \not\vdash #2 \Downarrow #3}}
\newcommand\closuresuffixliteral[0]{\metafunctionfont{c}}
\newcommand\closurenosuffix[2]{\ma{[#1, #2]}}
\newcommand\closure[2]{\ma{[#1, #2]_{\closuresuffixliteral}}}
\newcommand\closuresplice[1]{\ma{[#1]_{\closuresuffixliteral}}}
% multimethod semantics
\newcommand\multisuffixliteral[0]{\metafunctionfont{m}}
\newcommand\multi[2]{\ma{[#1, #2]_{\multisuffixliteral}}}
\newcommand\emptydisptable[0]{\{\}}
\newmeta\disptable{t}
\newmeta\disptablep{t'}
\newmeta\mapval{m}
\newcommand\extenddisptable[3]{\ma{#1[#2 \mapsto #3]}}
\newcommand\getmethodliteral[0]{\ma{\metafunctionfont{GM}}}
\newcommand\getmethoderr[3]{\getmethodliteral(#1, #2) = #3}
\newcommand\getmethod[4]{\getmethodliteral(#1, #2) = #4}
% java reflection rewrite
\newcommand\rewrite[3]{\ma{#1\ \vdash^{\ct{}}_{\metafunctionfont{r}} #2 \Rightarrow #3}}
% tools.analyzer judgements
\newcommand\ta[0]{\mathcal{TA}}
\newcommand\intaenv[3]{\ma{#1 (#2) = #3}}
\newcommand\tajudgement[2]{\ma{#1 \vdash_{\metafunctionfont{h}} #2}}
% type hints
\newmeta\tatypeunknown{\ma{\gamma^{?}}}
\newmeta\tatype{\ma{\gamma}}
\newmeta\tatypep{\ma{\gamma'}}
\newmeta\classhint{C}
\newmeta\primitivehint{p}
\newmeta\unknownhint{\mathbbm{?}}
\newcommand\hinted[2]{\ma{\ \widehat{}\ #1\ #2}}
% convert tools.analyzer types to core.typed types
\newcommand\tatotc[2]{\ma{[[#1]]\ =\ #2}}
% environment
\newcommand\propenv{\ma{\Gamma}}
\newcommand\propenvp{\ma{\Gamma'}}
\newcommand\propenvc{\ma{\Gamma_c}}
\newcommand\mmenv{\Delta}
\newcommand\mmenvp{\mmenv'}
\newcommand\mmenvpp{\mmenvp'}
\newcommand\taenv{\ma{\Sigma}}
\newcommand\taenvp{\taenv'}
% multimethod envs
\newcommand\adddispatchfn[2]{\ma{add\_dispatch\_fn(#1,\ #2)}}
\newcommand\getdispatchfn[2]{\ma{get\_dispatch\_fn(#1)_{#2}}}
\newcommand\inmmenv[3]{\ma{#1 (#2) = #3}}
\newcommand\metafnfont[1]{{\metafunctionfont{#1}}}
% isa? special functions
\newcommand\isacompareliteral[0]{\ma{\metafnfont{IsAProps}}}
\newcommand\isacomparetwo[2]{\ma{\isacompareliteral(#1, #2)}}
\newcommand\isacomparethree[3]{\ma{\isacompareliteral(#2, #3)}} % delete 1st argument, unusued outside of vectors
\newcommand\isacompare[4]{\ma{\isacomparethree{#1}{#2}{#3} = {#4}}}
\newcommand\isacomparealign[4]{\ma{\isacomparethree{#1}{#2}{#3} &=& {#4}}}
\newcommand\isaopsemliteral[0]{\ma{\metafnfont{IsA}}}
\newcommand\isaopsem[2]{\ma{\isaopsemliteral(#1, #2)}}
% new special functions
% Type -> [Type]
\newcommand\ctorparamsliteral[0]{\metafnfont{Ctor}}
\newcommand\ctorparamsnoeq[2]{\ma{\ctorparamsliteral(#1, #2)}}
\newcommand\ctorparams[3]{\ma{\ctorparamsnoeq{#1}{#2} = [#3]}}
\newcommand\ctorparamsalign[3]{\ma{\ctorparamsnoeq{#1}{#2} &=& [#3]}}
% field special functions
% Type Field -> Type
\newcommand\fieldtypeliteral[0]{\ma{\metafnfont{Fld}}}
\newcommand\fieldtypenoeq[3]{\ma{\fieldtypeliteral(#1, #2, #3)}}
\newcommand\fieldtype[4]{\ma{\fieldtypenoeq{#1}{#2}{#3} = [#4]}}
\newcommand\fieldtypealign[4]{\ma{\fieldtypenoeq{#1}{#2}{#3} &=& [#4]}}
% method special functions
% Type [Type] Method -> [Type]
\newcommand\methodtypeliteral[0]{\metafnfont{Mth}}
\newcommand\methodtypenoeq[3]{\ma{\methodtypeliteral(#1, #2, #3)}}
\newcommand\methodtype[5]{\ma{\methodtypenoeq{#1}{#2}{#3} = [[#4], #5]}}
\newcommand\methodtypealign[5]{\ma{\methodtypenoeq{#1}{#2}{#3} &=& [[#4], #5]}}
% java subtyping
\newcommand\assignable[2]{\ma{assignable(#1, #2)}}
% evaluation contexts
\newmeta\E{E}
% propositions
\newmeta\prop{\psi}
\newmeta\propp{\psi'}
\newmeta\proppp{\psi''}
\newmeta\propisnotmeta{\nu}
\newcommand\isprop[2]{\ma{{#1}_{#2}}}
\newcommand\impprop[2]{\ma{#1 \supset #2}}
\newcommand\nottype[1]{\ma{\overline{#1}}}
\newcommand\notprop[2]{\ma{{\nottype{#1}}_{#2}}}
\newcommand\andprop[2]{\ma{#1 \wedge #2}}
\newcommand\orprop[2]{\ma{#1 \vee #2}}
\newmeta\topprop{\mathbbm{tt}}
\newmeta\botprop{\mathbbm{ff}}
\newcommand\filterset[2]{\ma{#1 | #2}}
\newcommand\filtersetparen[2]{\ma{(\filterset{#1}{#2})}}
\newcommand\thenprop[1]{\ma{{#1}_+}}
\newcommand\elseprop[1]{\ma{{#1}_-}}
\newcommand\localfilterset[1]{\ma{\filterset{\notprop{\falsy}{#1}}}{\isprop{\falsy}{#1}}}
% polarities
\newmeta\polaritymeta{pol}
\newcommand\withpolarity[2]{\ma{{#1}^{#2}}}
\newcommand\pluspolarityliteral[0]{\metafunctionfont{pos}}
\newcommand\minuspolarityliteral[0]{\metafunctionfont{neg}}
\newcommand\pluspolarity[1]{\withpolarity{#1}{\pluspolarityliteral}}
\newcommand\minuspolarity[1]{\withpolarity{#1}{\minuspolarityliteral}}
\newcommand\notequal[0]{\ma{\not=}}
% objects
\newcommand\pth[2]{\ma{#1(#2)}}
\newmeta\object{o}
\newmeta\objectp{o'}
\newmeta\emptyobject{\emptyset}
\newmeta\pathelem{\pi}
\newmeta\pathelemp{\pi'}
% abstract syntax for pathelem
\newmeta\pesyntax{pe}
\newcommand\pefont[1]{\textbf{#1}}
\newmeta\classpe{\ma{\pefont{class}}}
\newcommand\keype[1]{\ma{\pefont{key}_{\ma{#1}}}}
\newcommand\carpe[0]{\ma{\pefont{car}}}
\newcommand\cdrpe[0]{\ma{\pefont{cdr}}}
\newcommand\destructpath[2]{\ma{#1 :: #2}}
% scope replacements
\newcommand\replacefor[3]{\ma{#1 [#2 / #3]}}
% Java type conversion functions
\newcommand\javatotcliteral[0]{\ma{\metafnfont{JT}}}
\newcommand\javatotcnilliteral[0]{\ma{\javatotcliteral_{\nil{}}}}
\newcommand\javatotcexp[1]{\javatotcliteral\ma{(#1)}}
\newcommand\javatotc[2]{\javatotcexp{#1}\ =\ #2}
\newcommand\javatotcnilexp[1]{\ma{\javatotcnilliteral\ma{(#1)}}}
\newcommand\javatotcnil[2]{\ma{\javatotcnilliteral\ma{(#1)}\ =\ #2}}
\newcommand\javatotcalign[2]{\javatotcliteral\ma{(#1)}\ &=&\ #2}
\newcommand\javatotcalignnil[2]{\javatotcliteral_{\nil{}}\ma{(#1)}\ &=&\ #2}
% TC type conversion functions
\newcommand\tctojavaliteral[0]{\ma{\metafnfont{TJ}}}
\newcommand\tctojava[2]{\tctojavaliteral\ma{(#1)}\ =\ #2}
\newcommand\tctojavaalign[2]{\tctojavaliteral\ma{(#1)}\ &=&\ #2}
% reflection resolution
\newcommand\resolvenewliteral[0]{\ma{\metafnfont{ResolveNew}}}
\newcommand\resolvenew[2]{\ma{\resolvenewliteral{}(#1, #2)}}
\newcommand\resolveneweq[3]{\ma{\resolvenewliteral{}(#1, #2)\ =\ #3}}
\newcommand\resolvefieldliteral[0]{\ma{\metafnfont{ResolveField}}}
\newcommand\resolvefield[2]{\ma{\resolvefieldliteral{}(#1, #2)}}
\newcommand\resolvefieldeq[4]{\ma{\resolvefieldliteral{}(#1, #2)\ =\ [#3, #4]}}
\newcommand\resolvemethodliteral[0]{\ma{\metafnfont{ResolveMethod}}}
\newcommand\resolvemethod[2]{\ma{\resolvemethodliteral{}(#1, #2)}}
\newcommand\resolvemethodeq[5]{\ma{\resolvemethodliteral{}(#1, #2)\ =\ [#3, [#4], #5]}}
% # Runtime semantics
% ## Runtime class syntax
\newmeta\classvaluemeta{I}
\newcommand\classfieldpair[2]{#1 : #2}
\newcommand\classvalue[2]{\ma{#1\ \{#2\}}}
% ## metafunction to invoke java
% Class Target Method ArgTypes Args ReturnType ReturnValue
\newcommand\JVMliteral[0]{\ma{\metafunctionfont{JVM}}}
\newcommand\invokejavamethodliteral[0]{\ma{\JVMliteral_{\metafunctionfont{invokestatic}}}}
\newcommand\invokejavamethodnoeq[6]{\ma{\invokejavamethodliteral[#1, #2, #3, [#4], [#5], #6]}}
\newcommand\invokejavamethod[7]{\ma{\invokejavamethodnoeq{#1}{#2}{#3}{#4}{#5}{#6} = #7}} % Class Args ReturnValue
% Class ArgTypes Args ReturnValue
\newcommand\newjavaliteral[0]{\ma{\JVMliteral_{\metafunctionfont{new}}}}
\newcommand\newjavanoeq[3]{\ma{\newjavaliteral[#1, [#2], [#3]]}}
\newcommand\newjava[4]{\ma{\newjavanoeq{#1}{#2}{#3} = #4}}
% Class Target Field FieldType ReturnValue
\newcommand\getfieldliteral[0]{\ma{\JVMliteral_{\metafunctionfont{getstatic}}}}
\newcommand\getfieldjavanoeq[4]{\ma{\getfieldliteral[#1, #2, #3, #4]}}
\newcommand\getfieldjava[5]{\ma{\getfieldjavanoeq{#1}{#2}{#3}{#4} = #5}}
\newcommand\jvmfieldliteral[0]{\ma{\JVMliteral_{\metafunctionfont{field}}}}
\newcommand\jvmfieldnoeq[2]{\ma{\jvmfieldliteral[#1, #2]}}
\newcommand\jvmfield[3]{\ma{\jvmfieldnoeq{#1}{#2} = #3}}
\newcommand\jvmmethodliteral[0]{\ma{\JVMliteral_{\metafunctionfont{method}}}}
\newcommand\jvmmethodnoeq[3]{\ma{\jvmmethodliteral[#1, #2, #3]}}
\newcommand\jvmmethod[4]{\ma{\jvmmethodnoeq{#1}{#2}{#3} = #4}}
\newcommand\jvmctorliteral[0]{\ma{\JVMliteral_{\metafunctionfont{ctor}}}}
\newcommand\jvmctornoeq[2]{\ma{\jvmctorliteral[#1, #2]}}
\newcommand\jvmctor[3]{\ma{\jvmctornoeq{#1}{#2} = #3}}
% Class Target Bool
\newcommand\instanceofjava[3]{\ma{JVM_{instanceof}[#1, #2] = #3}}
\newcommand\satisfies[2]{\ma{{#1} \models {#2}}}
\newmeta\wrongorerror{\beta}
\newcommand\consistentwith[2]{\ma{{#1}\ \text{is consistent with}\ {#2}}}
\newcommand\isconsistent[1]{\ma{{#1}\ \text{is consistent}}}
\newcommand\fv[1]{\ma{{\metafunctionfont{fv}}(#1)}}
\newcommand\istruevalOp[0]{\ma{\metafunctionfont{TrueVal}}}
\newcommand\istrueval[1]{\ma{\istruevalOp{}(#1)}}
\newcommand\isfalsevalOp[0]{\ma{\metafunctionfont{FalseVal}}}
\newcommand\isfalseval[1]{\ma{\isfalsevalOp{}(#1)}}
\newmeta\definedreduction{\alpha}
% Joshua Dunfield stuff
%
% ``Judgment boxes'' that should precede a mathpar, so the reader
% can instantly see which judgment is being defined by the rules.
%
% The first argument is the judgment form.
% The second argument tells the reader how to interpret the judgment.
% I don't mean *what* the judgment is, but literally how to *say* it:
% If you're defining \Gamma \entails e : \tau, don't write
%
% \judgbox{\Gamma \entails e : \tau}{Typing}
%
% Instead, write
%
% \judgbox{\Gamma \entails e : \tau}
% {Under context $\Gamma$, expression $e$ has type $\tau$}
%
% This tells the reader what the judgment is supposed to mean. It's also
% an opportunity to remind the reader what your metavariables (like $e$)
% stand for. The reader doesn't know your system as well as you do,
% and will lose track of all the kinds of animals you have in your zoo.
%
% For less familiar judgments than typing, this is even more important.
%
\newcommand{\textgraybox}[1]{\boxed{#1}}
\newcommand{\judgboxfontsize}[1]{\large #1}
\newcommand{\judgbox}[2]{%
{\raggedright \textgraybox{\judgboxfontsize{\ensuremath{#1}}}\!\begin{tabular}[c]{l} #2 \end{tabular} %
\\[-2.1ex] %
}}
% Common typing rules
\newcommand\TLocal[0]{
\infer [T-Local]
{ \inpropenv {\propenv{}} {\isprop {\t{}} {\x{}}}
\\\\
\s{} = {\falsydiff}
}
{ \judgementselfrewrite {\propenv{}}
{\x{}} {\t{}}
{\filterset {{\notprop {\s{}} {\x{}}}} {{\isprop {\s{}} {\x{}}}}}
%{\filterset {{\notprop {\falsy{}} {\x{}}}} {{\isprop {\falsy{}} {\x{}}}}}
{\x{}}
}
}
\newcommand\TNum[0]{
\infer [T-Num]
{}
{ \judgementselfrewrite {\propenv{}}
{\num{}} {\Number{}}
{\filterset {\topprop{}} {\botprop{}}}
{\emptyobject{}}
}
}
\newcommand\TTrue[0]{
\infer [T-True]
{}
{ \judgementselfrewrite {\propenv{}}
{\true{}} {\True{}}
{\filterset {\topprop{}} {\botprop{}}}
{\emptyobject{}}
}
}
\newcommand\TFalse[0]{
\infer [T-False]
{}
{ \judgementselfrewrite {\propenv{}}
{\false{}} {\False{}}
{\filterset {\botprop{}} {\topprop{}}}
{\emptyobject{}}
}
}
\newcommand\TNil[0]{
\infer [T-Nil]
{}
{ \judgementselfrewrite {\propenv{}}
{\nil{}} {\Nil{}}
{\filterset {\trdiff{\botprop{}}} {\topprop{}}}
{\emptyobject{}}
}
}
\newcommand\TDo[0]{
\infer [T-Do]
{
\judgementrewrite {\propenv{}}
{\e1} {\t1}
{\filterset {\thenprop {\prop{1}}} {\elseprop {\prop1}}}
{\object{1}}
{\ep1}
\\\\
\judgementrewrite {\propenv{}, {\orprop {\thenprop {\prop{1}}} {\elseprop {\prop{1}}}}}
{\e{}} {\t{}}
{\filterset {\thenprop {\prop{}}} {\elseprop {\prop{}}}}
{\object{}}
{\ep{}}
}
{ \judgementrewrite
{\propenv{}}
{\doexp {\e1} {\e{}}} {\t{}}
{\filterset {\thenprop {\prop{}}} {\elseprop {\prop{}}}} {\object{}}
{\doexp {\ep1} {\ep{}}}
}
}
\newcommand\TIf[0]{
\infer [T-If]
{ \judgementrewrite {\propenv{}} {\e1} {\t{1}} {\filterset {\thenprop {\prop{1}}} {\elseprop {\prop{1}}}}
{\object{1}}
{\ep1}
\\\\
\judgementrewrite {\propenv{}, {\thenprop {\prop{1}}}}
{\e2} {\t{}} {\filterset {\thenprop {\prop{}}} {\elseprop {\prop{}}}}
{\object{}}
{\ep2}
\\\\
\judgementrewrite {\propenv{}, {\elseprop {\prop{1}}}}
{\e3} {\t{}} {\filterset {\thenprop {\prop{}}} {\elseprop {\prop{}}}}
{\object{}}
{\ep3}
%\\\\
%\ep{} = {\ifexp {\ep1} {\ep2} {\ep3}}
}
{ \judgementrewrite {\propenv{}} {\ifexp {\e1} {\e2} {\e3}} {\t{}}
{\filterset {\thenprop {\prop{}}}
{\elseprop {\prop{}}}}
{\object{}}
{\ep{}}}
}
% WARNING: this is copied in formal-model.tex, no idea why this macro won't work there.
\newcommand\TLet[0]{
\infer [T-Let]
{ \judgementrewrite {\propenv{}} {\e{1}} {\s{}} {\filterset {\thenprop {\prop{1}}} {\elseprop {\prop{1}}}}
{\object{1}}
{\ep{1}}
\\\\
\propp{} = {\impprop {\notprop {\falsydiff{}} {\x{}}} {\thenprop {\prop{1}}}}
\\\\
\proppp{} = {\impprop {\isprop {\falsydiff{}} {\x{}}} {\elseprop {\prop{1}}}}
\\\\
\judgementrewrite
{\propenv{}, {\isprop {\s{}} {\x{}}},
{\propp{}},
{\proppp{}}}
{\e{2}} {\t{}} {\filterset {\thenprop {\prop{}}} {\elseprop {\prop{}}}}
{\object{}}
{\ep{2}}
}
{ \judgementrewrite {\propenv{}} {\letexp {\x{}} {\e{1}} {\e{2}}}
{\replacefor {\t{}}
{\object{1}}
{\x{}}}
{\replacefor {\filterset {\thenprop {\prop{}}} {\elseprop {\prop{}}}}
{\object{1}}
{\x{}}}
{\replacefor {\object{}}
{\object{1}}
{\x{}}}
{\letexp {\x{}} {\ep{1}} {\ep{2}}}
}
}
\newcommand\TApp[0]{
\infer [T-App]
{ \judgementrewrite {\propenv{}} {\e{}} {\ArrowOne {\x{}} {\s{}}
{\t{}}
{\filterset {\thenprop {\prop{f}}}
{\elseprop {\prop{f}}}}
{\object{f}}}
{\filterset {\thenprop {\prop{}}}
{\elseprop {\prop{}}}}
{\object{}}
{\e{1}}
\\\\
\judgementrewrite {\propenv{}}
{\ep{}} {\s{}}
{\filterset {\thenprop {\propp{}}}
{\elseprop {\propp{}}}}
{\objectp{}}
{\ep{1}}
}
{ \judgementrewrite {\propenv{}} {\appexp {\e{}} {\ep{}}}
{\replacefor {\t{}}
{\objectp{}}
{\x{}}}
{\replacefor {\filterset {\thenprop {\prop{f}}}
{\elseprop {\prop{f}}}}
{\objectp{}}
{\x{}}}
{\replacefor {\object{f}}
{\objectp{}}
{\x{}}}
{\appexp {\e{1}} {\ep{1}}}
}
}
\newcommand\TAbs[0]{
\infer [T-Abs]
{ \judgementrewrite {\propenv{}, {\isprop {\s{}} {\x{}}}}
{\e{}} {\sp{}}
{\filterset {\thenprop {\prop{}}}
{\elseprop {\prop{}}}}
{\object{}}
{\ep{}}
}
{ \judgementrewrite {\propenv{}} {\abs {\x{}} {\s{}} {\e{}}}
{\ArrowOne {\x{}} {\s{}}
{\sp{}}
{\filterset {\thenprop {\prop{}}}
{\elseprop {\prop{}}}}
{\object{}}}
{\filterset {\topprop{}}
{\botprop{}}}
{\emptyobject{}}
{\abs {\x{}} {\s{}} {\ep{}}}}
}
\newcommand\TSubsume[0]{
\infer [T-Subsume]
{ \judgementrewrite {\propenv{}} {\e{}} {\t{}}
{\filterset {\thenprop {\prop{}}}
{\elseprop {\prop{}}}}
{\object{}}
{\ep{}}
\\\\
\inpropenv {\propenv{}, {\thenprop {\prop{}}}} {\thenprop {\propp{}}}
\\
\inpropenv {\propenv{}, {\elseprop {\prop{}}}} {\elseprop {\propp{}}}
\\\\
\issubtypein {} {\t{}} {\tp{}}
\\
\issubobjin {} {\object{}} {\objectp{}}
}
{ \judgementrewrite {\propenv{}} {\e{}} {\tp{}}
{\filterset {\thenprop {\propp{}}}
{\elseprop {\propp{}}}}
{\objectp{}}
{\ep{}}
}
}
\newcommand\TNew[0]{
\infer [T-New]
{ \inct{\ctctorentry{\overrightarrow{\class{i}}}}{\ctlookupctors{\ct{}}{\classhint{}}}
\\
\overrightarrow{\javatotcnil{\classhint{i}}{\t{i}}}
\\
\overrightarrow{
\judgementtworewrite {\propenv{}}
{\e{i}} {\t{i}}
{\ep{i}}
}
\\
\javatotc {\classhint{}}
{\t{}}
}
{ \judgementrewrite {\propenv{}} {\newexp {\class{}} {\overrightarrow{\e{i}}}} {\t{}}
{\filterset {\topprop{}} {\botprop{}}}
{\emptyobject{}}
{\newstaticexp {\overrightarrow{\classhint{i}}} {\classhint{}}
{\class{}} {\overrightarrow{\ep{i}}}}
}
}
\newcommand\TNewStatic[0]{
\infer [T-NewStatic]
{
\overrightarrow{
\javatotc {\classhint{i}}
{\t{i}}
}
\\
\javatotc {\classhint{}}
{\t{}}
\\
\overrightarrow{
\judgementtworewrite {\propenv{}}
{\e{i}} {\t{i}}
{\ep{i}}
}
}
{ \judgementrewrite {\propenv{}} {\newstaticexp {\overrightarrow{\classhint{i}}} {\classhint{}}
{\class{}} {\overrightarrow{\e{i}}}} {\t{}}
{\filterset {\topprop{}} {\botprop{}}}
{\emptyobject{}}
{\newstaticexp {\overrightarrow{\classhint{i}}} {\classhint{}}
{\class{}} {\overrightarrow{\ep{i}}}}
}
}
\newcommand\TField[0]{
\infer [T-Field]
{ \judgementtworewrite {\propenv{}} {\e{}} {\s{}} {\ep{}}
\ \ \
%\\
\issubtypein{}{\s{}}{\Object{}}
\ \ \
%\\
\tctojava{\s{}}{\classhint{1}}
\ \ \
%\\
\inct{\ctfldentry{\fld{}}{\classhint{2}}}{\ctlookupfields{\ct{}}{\classhint{1}}}
\ \ \
%\\
\javatotcnil{\classhint{2}}{\t{}}
}
{ \judgementrewrite {\propenv{}} {\fieldexp {\fld{}} {\e{}}} {\t{}}
{\filterset {\topprop{}} {\topprop}}
{\emptyobject{}}
{\fieldstaticexp {\classhint{1}} {\classhint{2}} {\fld{}} {\ep{}}}
}
}
\newcommand\TFieldStatic[0]{
\infer [T-FieldStatic]
{ \javatotc {\classhint{1}} {\s{}}
\\
\issubtypein{}{\s{}}{\Object{}}
\\
\javatotcnil {\classhint{2}} {\t{}}
\\
\judgementtworewrite {\propenv{}} {\e{}} {\s{}} {\ep{}}
}
{ \judgementrewrite {\propenv{}} {\fieldstaticexp {\classhint{1}} {\classhint{2}} {\fld{}} {\e{}}} {\t{}}
{\filterset {\topprop{}} {\topprop}}
{\emptyobject{}}
{\fieldstaticexp {\classhint{1}} {\classhint{2}} {\fld{}} {\ep{}}}
}
}
\newcommand\TMethod[0]{
\infer [T-Method]
{
\judgementtworewrite {\propenv{}} {\e{}} {\s{}} {\ep{}}
\\
\tctojava{\s{}}{\classhint{1}}
\\
\inct{\ctmthentry{\mth{}}{\overrightarrow{\classhint{i}}}{\classhint{2}}}{\ctlookupmethods{\ct{}}{\classhint{1}}}
\\
\overrightarrow{\javatotcnil{\classhint{i}}{\t{i}}}
\\
\overrightarrow{
\judgementtworewrite {\propenv{}} {\e{i}} {\t{i}} {\ep{i}}
}
\\
\javatotcnil{\classhint{2}}{\t{}}
\\
\issubtypein{}{\s{}}{\Object{}}
}
{ \judgementrewrite {\propenv{}} {\methodexp {\mth{}} {\e{}} {\overrightarrow{\e{i}}}}
{\t{}}
{\filterset {\topprop{}} {\topprop{}}}
{\emptyobject{}}
{\methodstaticexp {\classhint{1}}
{\overrightarrow {\classhint{i}}}
{\classhint{2}}
{\mth{}} {\ep{}} {\overrightarrow{\ep{i}}}}
}
}
\newcommand\TMethodStatic[0]{
\infer [T-MethodStatic]
{
\overrightarrow{\javatotc {\classhint{i}} {\t{i}}}
\\
\javatotc {\classhint{1}} {\s{}}
\\
\issubtypein{}{\s{}}{\Object{}}
\\
\javatotcnil {\classhint{2}} {\t{}}
\\
\judgementtworewrite {\propenv{}} {\e{}} {\s{}} {\ep{}}
\\
\overrightarrow{
\judgementtworewrite {\propenv{}} {\e{i}} {\t{i}} {\ep{i}}
}
}
{ \judgementrewrite {\propenv{}} {\methodstaticexp {\classhint{1}}
{\overrightarrow {\classhint{i}}}
{\classhint{2}}
{\mth{}} {\e{}} {\overrightarrow{\e{i}}}}
{\t{}}
{\filterset {\topprop{}} {\topprop{}}}
{\emptyobject{}}
{\methodstaticexp {\classhint{1}}
{\overrightarrow {\classhint{i}}}
{\classhint{2}}
{\mth{}} {\ep{}} {\overrightarrow{\ep{i}}}}
}
}
\newcommand\TClass[0]{
\infer [T-Class]
{}
{ \judgementselfrewrite {\propenv{}} {\class{}}{\ValueClass}{\filterset{\topprop{}}{\botprop{}}}{\emptyobject{}}}
}
\newcommand\TDefMulti[0]{
\infer [T-DefMulti]
{ \s{} = {\ArrowOne {\x{}} {\t{}} {\tp{}}
{\filterset {\thenprop {\prop{}}}
{\elseprop {\prop{}}}}
{\object{}}}
\\
\sp{} = {\ArrowOne {\x{}} {\t{}} {\tpp{}}