% generated by Ott 0.33 from: cbpv.ott
\newcommand{\ottdrule}[4][]{{\displaystyle\frac{\begin{array}{l}#2\end{array}}{#3}\quad\ottdrulename{#4}}}
\newcommand{\ottusedrule}[1]{\[#1\]}
\newcommand{\ottpremise}[1]{ #1 \\}
\newenvironment{ottdefnblock}[3][]{ \framebox{\mbox{#2}} \quad #3 \\[0pt]}{}
\newenvironment{ottfundefnblock}[3][]{ \framebox{\mbox{#2}} \quad #3 \\[0pt]\begin{displaymath}\begin{array}{l}}{\end{array}\end{displaymath}}
\newcommand{\ottfunclause}[2]{ #1 \equiv #2 \\}
\newcommand{\ottnt}[1]{\mathit{#1}}
\newcommand{\ottmv}[1]{\mathit{#1}}
\newcommand{\ottkw}[1]{\mathbf{#1}}
\newcommand{\ottsym}[1]{#1}
\newcommand{\ottcom}[1]{\text{#1}}
\newcommand{\ottdrulename}[1]{\textsc{#1}}
\newcommand{\ottcomplu}[5]{\overline{#1}^{\,#2\in #3 #4 #5}}
\newcommand{\ottcompu}[3]{\overline{#1}^{\,#2<#3}}
\newcommand{\ottcomp}[2]{\overline{#1}^{\,#2}}
\newcommand{\ottgrammartabular}[1]{\begin{supertabular}{llcllllll}#1\end{supertabular}}
\newcommand{\ottmetavartabular}[1]{\begin{supertabular}{ll}#1\end{supertabular}}
\newcommand{\ottrulehead}[3]{$#1$ & & $#2$ & & & \multicolumn{2}{l}{#3}}
\newcommand{\ottprodline}[6]{& & $#1$ & $#2$ & $#3 #4$ & $#5$ & $#6$}
\newcommand{\ottfirstprodline}[6]{\ottprodline{#1}{#2}{#3}{#4}{#5}{#6}}
\newcommand{\ottlongprodline}[2]{& & $#1$ & \multicolumn{4}{l}{$#2$}}
\newcommand{\ottfirstlongprodline}[2]{\ottlongprodline{#1}{#2}}
\newcommand{\ottbindspecprodline}[6]{\ottprodline{#1}{#2}{#3}{#4}{#5}{#6}}
\newcommand{\ottprodnewline}{\\}
\newcommand{\ottinterrule}{\\[5.0mm]}
\newcommand{\ottafterlastrule}{\\}
    \newcommand{\gap}{\:}
    \newcommand{\kw}[1]{ \mathsf{#1} }
  
\newcommand{\ottmetavars}{
\ottmetavartabular{
 $ \ottmv{x} ,\, \ottmv{y} ,\, \ottmv{z} $ & \ottcom{term variables} \\
}}

\newcommand{\ottv}{
\ottrulehead{\ottnt{v}  ,\ \ottnt{w}}{::=}{\ottcom{values}}\ottprodnewline
\ottfirstprodline{|}{\ottmv{x}}{}{}{}{}\ottprodnewline
\ottprodline{|}{ \kw{unit} }{}{}{}{}\ottprodnewline
\ottprodline{|}{ \kw{inl} \gap  \ottnt{v} }{}{}{}{}\ottprodnewline
\ottprodline{|}{ \kw{inr} \gap  \ottnt{v} }{}{}{}{}\ottprodnewline
\ottprodline{|}{ \kw{thunk} \gap  \ottnt{m} }{}{}{}{}\ottprodnewline
\ottprodline{|}{ ( \ottnt{v} ) } {\textsf{S}}{}{}{\ottcom{parentheses}}\ottprodnewline
\ottprodline{|}{ \ottnt{v} [  \sigma  ] } {\textsf{S}}{}{}{}}

\newcommand{\ottm}{
\ottrulehead{\ottnt{m}  ,\ \ottnt{n}}{::=}{\ottcom{computations}}\ottprodnewline
\ottfirstprodline{|}{ \kw{force} \gap  \ottnt{v} }{}{}{}{}\ottprodnewline
\ottprodline{|}{ \lambda  \ottmv{x}  \mathpunct{.}  \ottnt{m} }{}{\textsf{bind}\; \ottmv{x}\; \textsf{in}\; \ottnt{m}}{}{}\ottprodnewline
\ottprodline{|}{ \ottnt{m}  \gap  \ottnt{v} }{}{}{}{}\ottprodnewline
\ottprodline{|}{ \kw{return} \gap  \ottnt{v} }{}{}{}{}\ottprodnewline
\ottprodline{|}{ \kw{let} \gap  \ottmv{x}  \leftarrow  \ottnt{m}  \gap \kw{in} \gap  \ottnt{n} }{}{\textsf{bind}\; \ottmv{x}\; \textsf{in}\; \ottnt{n}}{}{}\ottprodnewline
\ottprodline{|}{ \kw{case} \gap  \ottnt{v}  \gap \kw{of} \gap \lbrace \kw{inl} \gap  \ottmv{y}  \Rightarrow  \ottnt{m}  \mathrel{;} \kw{inr} \gap  \ottmv{z}  \Rightarrow  \ottnt{n}  \rbrace }{}{\textsf{bind}\; \ottmv{y}\; \textsf{in}\; \ottnt{m}}{}{}\ottprodnewline
\ottbindspecprodline{}{}{}{\textsf{bind}\; \ottmv{z}\; \textsf{in}\; \ottnt{n}}{}{}\ottprodnewline
\ottprodline{|}{ ( \ottnt{m} ) } {\textsf{S}}{}{}{\ottcom{parentheses}}\ottprodnewline
\ottprodline{|}{ \ottnt{m} [  \sigma  ] } {\textsf{S}}{}{}{}}

\newcommand{\ottA}{
\ottrulehead{\ottnt{A}}{::=}{\ottcom{value types}}\ottprodnewline
\ottfirstprodline{|}{ \kw{Unit} }{}{}{}{}\ottprodnewline
\ottprodline{|}{ \ottnt{A_{{\mathrm{1}}}}  +  \ottnt{A_{{\mathrm{2}}}} }{}{}{}{}\ottprodnewline
\ottprodline{|}{ \kw{U} \gap  \ottnt{B} }{}{}{}{}}

\newcommand{\ottB}{
\ottrulehead{\ottnt{B}}{::=}{\ottcom{computation types}}\ottprodnewline
\ottfirstprodline{|}{ \kw{F} \gap  \ottnt{A} }{}{}{}{}\ottprodnewline
\ottprodline{|}{ \ottnt{A}  \rightarrow  \ottnt{B} }{}{}{}{}}

\newcommand{\otts}{
\ottrulehead{\sigma}{::=}{\ottcom{substitutions}}\ottprodnewline
\ottfirstprodline{|}{ \cdot }{}{}{}{\ottcom{identity substitution}}\ottprodnewline
\ottprodline{|}{ \sigma ,  \ottmv{x}  \mapsto  \ottnt{v} }{}{}{}{\ottcom{substitution extension}}\ottprodnewline
\ottprodline{|}{ \ottmv{x}  \mapsto  \ottnt{v} } {\textsf{S}}{}{}{\ottcom{single substitution}}\ottprodnewline
\ottprodline{|}{ \mathop{\Uparrow}  \sigma }{}{}{}{\ottcom{lifting substitution}}}

\newcommand{\ottG}{
\ottrulehead{\Gamma  ,\ \Delta}{::=}{\ottcom{contexts}}\ottprodnewline
\ottfirstprodline{|}{ \cdot }{}{}{}{\ottcom{empty context}}\ottprodnewline
\ottprodline{|}{ \Gamma ,  \ottmv{x}  \mathbin{:}  \ottnt{A} }{}{}{}{\ottcom{context extension}}}

\newcommand{\ottP}{
\ottrulehead{\ottnt{P}  ,\ \ottnt{Q}}{::=}{}\ottprodnewline
\ottfirstprodline{|}{ \lbrace  \ottnt{v}  \mid  \ottnt{formula}  \rbrace }{}{}{}{}\ottprodnewline
\ottprodline{|}{ \lbrace  \ottnt{m}  \mid  \ottnt{formula}  \rbrace }{}{}{}{}}

\newcommand{\ottgrammar}{\ottgrammartabular{
\ottv\ottinterrule
\ottm\ottinterrule
\ottA\ottinterrule
\ottB\ottinterrule
\otts\ottinterrule
\ottG\ottinterrule
\ottP\ottafterlastrule
}}

% defnss
% defns SN
%% defn SNeVal
\newcommand{\ottdruleSNeXXVar}[1]{\ottdrule[#1]{%
}{
 \ottmv{x}  \in \kw{SNe} }{%
{\ottdrulename{SNe\_Var}}{}%
}}

\newcommand{\ottdefnSNeVal}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{v}  \in \kw{SNe} $}{}
\ottusedrule{\ottdruleSNeXXVar{}}
\end{ottdefnblock}}

%% defn SNeCom
\newcommand{\ottdruleSNeXXForce}[1]{\ottdrule[#1]{%
}{
  \kw{force} \gap  \ottmv{x}   \in \kw{SNe} }{%
{\ottdrulename{SNe\_Force}}{}%
}}


\newcommand{\ottdruleSNeXXApp}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \in \kw{SNe} }%
\ottpremise{ \ottnt{v}  \in \kw{SN} }%
}{
  \ottnt{m}  \gap  \ottnt{v}   \in \kw{SNe} }{%
{\ottdrulename{SNe\_App}}{}%
}}


\newcommand{\ottdruleSNeXXLet}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \in \kw{SNe} }%
\ottpremise{ \ottnt{n}  \in \kw{SN} }%
}{
  \kw{let} \gap  \ottmv{x}  \leftarrow  \ottnt{m}  \gap \kw{in} \gap  \ottnt{n}   \in \kw{SNe} }{%
{\ottdrulename{SNe\_Let}}{}%
}}


\newcommand{\ottdruleSNeXXCase}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \in \kw{SN} }%
\ottpremise{ \ottnt{n}  \in \kw{SN} }%
}{
  \kw{case} \gap  \ottmv{x}  \gap \kw{of} \gap \lbrace \kw{inl} \gap  \ottmv{y}  \Rightarrow  \ottnt{m}  \mathrel{;} \kw{inr} \gap  \ottmv{z}  \Rightarrow  \ottnt{n}  \rbrace   \in \kw{SNe} }{%
{\ottdrulename{SNe\_Case}}{}%
}}

\newcommand{\ottdefnSNeCom}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{m}  \in \kw{SNe} $}{}
\ottusedrule{\ottdruleSNeXXForce{}}
\ottusedrule{\ottdruleSNeXXApp{}}
\ottusedrule{\ottdruleSNeXXLet{}}
\ottusedrule{\ottdruleSNeXXCase{}}
\end{ottdefnblock}}

%% defn SNVal
\newcommand{\ottdruleSNXXVar}[1]{\ottdrule[#1]{%
}{
 \ottmv{x}  \in \kw{SN} }{%
{\ottdrulename{SN\_Var}}{}%
}}


\newcommand{\ottdruleSNXXUnit}[1]{\ottdrule[#1]{%
}{
  \kw{unit}   \in \kw{SN} }{%
{\ottdrulename{SN\_Unit}}{}%
}}


\newcommand{\ottdruleSNXXInl}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{SN} }%
}{
  \kw{inl} \gap  \ottnt{v}   \in \kw{SN} }{%
{\ottdrulename{SN\_Inl}}{}%
}}


\newcommand{\ottdruleSNXXInr}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{SN} }%
}{
  \kw{inr} \gap  \ottnt{v}   \in \kw{SN} }{%
{\ottdrulename{SN\_Inr}}{}%
}}


\newcommand{\ottdruleSNXXThunk}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \in \kw{SN} }%
}{
  \kw{thunk} \gap  \ottnt{m}   \in \kw{SN} }{%
{\ottdrulename{SN\_Thunk}}{}%
}}


\newcommand{\ottdruleSNXXForceXXinv}[1]{\ottdrule[#1]{%
\ottpremise{  \kw{force} \gap  \ottnt{v}   \in \kw{SN} }%
}{
 \ottnt{v}  \in \kw{SN} }{%
{\ottdrulename{SN\_Force\_inv}}{}%
}}

\newcommand{\ottdefnSNVal}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{v}  \in \kw{SN} $}{}
\ottusedrule{\ottdruleSNXXVar{}}
\ottusedrule{\ottdruleSNXXUnit{}}
\ottusedrule{\ottdruleSNXXInl{}}
\ottusedrule{\ottdruleSNXXInr{}}
\ottusedrule{\ottdruleSNXXThunk{}}
\ottusedrule{\ottdruleSNXXForceXXinv{}}
\end{ottdefnblock}}

%% defn SNCom
\newcommand{\ottdruleSNXXLam}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \in \kw{SN} }%
}{
  \lambda  \ottmv{x}  \mathpunct{.}  \ottnt{m}   \in \kw{SN} }{%
{\ottdrulename{SN\_Lam}}{}%
}}


\newcommand{\ottdruleSNXXRet}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{SN} }%
}{
  \kw{return} \gap  \ottnt{v}   \in \kw{SN} }{%
{\ottdrulename{SN\_Ret}}{}%
}}


\newcommand{\ottdruleSNXXSNe}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \in \kw{SNe} }%
}{
 \ottnt{m}  \in \kw{SN} }{%
{\ottdrulename{SN\_SNe}}{}%
}}


\newcommand{\ottdruleSNXXRed}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \leadsto  \ottnt{n} }%
\ottpremise{ \ottnt{n}  \in \kw{SN} }%
}{
 \ottnt{m}  \in \kw{SN} }{%
{\ottdrulename{SN\_Red}}{}%
}}


\newcommand{\ottdruleSNXXReds}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \leadsto^*  \ottnt{n} }%
\ottpremise{ \ottnt{n}  \in \kw{SN} }%
}{
 \ottnt{m}  \in \kw{SN} }{%
{\ottdrulename{SN\_Reds}}{}%
}}


\newcommand{\ottdruleSNXXExt}[1]{\ottdrule[#1]{%
\ottpremise{  \ottnt{m}  \gap  \ottmv{x}   \in \kw{SN} }%
}{
 \ottnt{m}  \in \kw{SN} }{%
{\ottdrulename{SN\_Ext}}{}%
}}


\newcommand{\ottdruleSNXXLift}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vDash  \sigma }%
\ottpremise{  \Gamma ,  \ottmv{x}  \mathbin{:}  \ottnt{A}   \vDash  \ottnt{m}  :  \ottnt{B} }%
}{
  \ottnt{m} [   \mathop{\Uparrow}  \sigma   ]   \in \kw{SN} }{%
{\ottdrulename{SN\_Lift}}{}%
}}

\newcommand{\ottdefnSNCom}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{m}  \in \kw{SN} $}{}
\ottusedrule{\ottdruleSNXXLam{}}
\ottusedrule{\ottdruleSNXXRet{}}
\ottusedrule{\ottdruleSNXXSNe{}}
\ottusedrule{\ottdruleSNXXRed{}}
\ottusedrule{\ottdruleSNXXReds{}}
\ottusedrule{\ottdruleSNXXExt{}}
\ottusedrule{\ottdruleSNXXLift{}}
\end{ottdefnblock}}

%% defn SR
\newcommand{\ottdruleSRXXThunk}[1]{\ottdrule[#1]{%
}{
  \kw{force} \gap   (  \kw{thunk} \gap  \ottnt{m}  )    \leadsto  \ottnt{m} }{%
{\ottdrulename{SR\_Thunk}}{}%
}}


\newcommand{\ottdruleSRXXLam}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{SN} }%
}{
   (  \lambda  \ottmv{x}  \mathpunct{.}  \ottnt{m}  )   \gap  \ottnt{v}   \leadsto   \ottnt{m} [   \ottmv{x}  \mapsto  \ottnt{v}   ]  }{%
{\ottdrulename{SR\_Lam}}{}%
}}


\newcommand{\ottdruleSRXXRet}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{SN} }%
}{
  \kw{let} \gap  \ottmv{x}  \leftarrow   (  \kw{return} \gap  \ottnt{v}  )   \gap \kw{in} \gap  \ottnt{m}   \leadsto   \ottnt{m} [   \ottmv{x}  \mapsto  \ottnt{v}   ]  }{%
{\ottdrulename{SR\_Ret}}{}%
}}


\newcommand{\ottdruleSRXXInl}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{SN} }%
\ottpremise{ \ottnt{n}  \in \kw{SN} }%
}{
  \kw{case} \gap   (  \kw{inl} \gap  \ottnt{v}  )   \gap \kw{of} \gap \lbrace \kw{inl} \gap  \ottmv{y}  \Rightarrow  \ottnt{m}  \mathrel{;} \kw{inr} \gap  \ottmv{z}  \Rightarrow  \ottnt{n}  \rbrace   \leadsto   \ottnt{m} [   \ottmv{y}  \mapsto  \ottnt{v}   ]  }{%
{\ottdrulename{SR\_Inl}}{}%
}}


\newcommand{\ottdruleSRXXInr}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{SN} }%
\ottpremise{ \ottnt{m}  \in \kw{SN} }%
}{
  \kw{case} \gap   (  \kw{inr} \gap  \ottnt{v}  )   \gap \kw{of} \gap \lbrace \kw{inl} \gap  \ottmv{y}  \Rightarrow  \ottnt{m}  \mathrel{;} \kw{inr} \gap  \ottmv{z}  \Rightarrow  \ottnt{n}  \rbrace   \leadsto   \ottnt{n} [   \ottmv{z}  \mapsto  \ottnt{v}   ]  }{%
{\ottdrulename{SR\_Inr}}{}%
}}


\newcommand{\ottdruleSRXXApp}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \leadsto  \ottnt{n} }%
}{
  \ottnt{m}  \gap  \ottnt{v}   \leadsto   \ottnt{n}  \gap  \ottnt{v}  }{%
{\ottdrulename{SR\_App}}{}%
}}


\newcommand{\ottdruleSRXXLet}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \leadsto  \ottnt{m'} }%
}{
  \kw{let} \gap  \ottmv{x}  \leftarrow  \ottnt{m}  \gap \kw{in} \gap  \ottnt{n}   \leadsto   \kw{let} \gap  \ottmv{x}  \leftarrow  \ottnt{m'}  \gap \kw{in} \gap  \ottnt{n}  }{%
{\ottdrulename{SR\_Let}}{}%
}}

\newcommand{\ottdefnSR}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{m}  \leadsto  \ottnt{n} $}{}
\ottusedrule{\ottdruleSRXXThunk{}}
\ottusedrule{\ottdruleSRXXLam{}}
\ottusedrule{\ottdruleSRXXRet{}}
\ottusedrule{\ottdruleSRXXInl{}}
\ottusedrule{\ottdruleSRXXInr{}}
\ottusedrule{\ottdruleSRXXApp{}}
\ottusedrule{\ottdruleSRXXLet{}}
\end{ottdefnblock}}

%% defn SRs
\newcommand{\ottdruleSRsXXRefl}[1]{\ottdrule[#1]{%
}{
 \ottnt{m}  \leadsto^*  \ottnt{m} }{%
{\ottdrulename{SRs\_Refl}}{}%
}}


\newcommand{\ottdruleSRsXXTrans}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \leadsto  \ottnt{m'} }%
\ottpremise{ \ottnt{m'}  \leadsto^*  \ottnt{n} }%
}{
 \ottnt{m}  \leadsto^*  \ottnt{n} }{%
{\ottdrulename{SRs\_Trans}}{}%
}}


\newcommand{\ottdruleSRsXXOnce}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \leadsto  \ottnt{n} }%
}{
 \ottnt{m}  \leadsto^*  \ottnt{n} }{%
{\ottdrulename{SRs\_Once}}{}%
}}


\newcommand{\ottdruleSRsXXTransPP}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \leadsto^*  \ottnt{m'} }%
\ottpremise{ \ottnt{m'}  \leadsto^*  \ottnt{n} }%
}{
 \ottnt{m}  \leadsto^*  \ottnt{n} }{%
{\ottdrulename{SRs\_Trans'}}{}%
}}


\newcommand{\ottdruleSRsXXApp}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \leadsto^*  \ottnt{n} }%
}{
  \ottnt{m}  \gap  \ottnt{v}   \leadsto^*   \ottnt{n}  \gap  \ottnt{v}  }{%
{\ottdrulename{SRs\_App}}{}%
}}


\newcommand{\ottdruleSRsXXLet}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \leadsto^*  \ottnt{m'} }%
}{
  \kw{let} \gap  \ottmv{x}  \leftarrow  \ottnt{m}  \gap \kw{in} \gap  \ottnt{n}   \leadsto^*   \kw{let} \gap  \ottmv{x}  \leftarrow  \ottnt{m'}  \gap \kw{in} \gap  \ottnt{n}  }{%
{\ottdrulename{SRs\_Let}}{}%
}}

\newcommand{\ottdefnSRs}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{m}  \leadsto^*  \ottnt{n} $}{}
\ottusedrule{\ottdruleSRsXXRefl{}}
\ottusedrule{\ottdruleSRsXXTrans{}}
\ottusedrule{\ottdruleSRsXXOnce{}}
\ottusedrule{\ottdruleSRsXXTransPP{}}
\ottusedrule{\ottdruleSRsXXApp{}}
\ottusedrule{\ottdruleSRsXXLet{}}
\end{ottdefnblock}}


\newcommand{\ottdefnsSN}{
\ottdefnSNeVal{}\ottdefnSNeCom{}\ottdefnSNVal{}\ottdefnSNCom{}\ottdefnSR{}\ottdefnSRs{}}

% defns LR
%% defn ValType
\newcommand{\ottdruleLRXXUnit}[1]{\ottdrule[#1]{%
}{
 \mathopen{\llbracket}   \kw{Unit}   \mathclose{\rrbracket} \searrow   \lbrace  \ottnt{v}  \mid    \ottnt{v}  \in \kw{SNe}   \vee   \ottnt{v}  =   \kw{unit}     \rbrace  }{%
{\ottdrulename{LR\_Unit}}{}%
}}


\newcommand{\ottdruleLRXXSum}[1]{\ottdrule[#1]{%
\ottpremise{ \mathopen{\llbracket}  \ottnt{A_{{\mathrm{1}}}}  \mathclose{\rrbracket} \searrow  \ottnt{P} }%
\ottpremise{ \mathopen{\llbracket}  \ottnt{A_{{\mathrm{2}}}}  \mathclose{\rrbracket} \searrow  \ottnt{Q} }%
}{
 \mathopen{\llbracket}   \ottnt{A_{{\mathrm{1}}}}  +  \ottnt{A_{{\mathrm{2}}}}   \mathclose{\rrbracket} \searrow   \lbrace  \ottnt{v}  \mid    \ottnt{v}  \in \kw{SNe}   \vee     (   \exists  \ottnt{w}  \mathpunct{.}     \ottnt{v}  =   \kw{inl} \gap  \ottnt{w}    \wedge   \ottnt{w}  \in  \ottnt{P}      )   \vee   (   \exists  \ottnt{w}  \mathpunct{.}     \ottnt{v}  =   \kw{inr} \gap  \ottnt{w}    \wedge   \ottnt{w}  \in  \ottnt{Q}      )      \rbrace  }{%
{\ottdrulename{LR\_Sum}}{}%
}}


\newcommand{\ottdruleLRXXU}[1]{\ottdrule[#1]{%
\ottpremise{ \mathopen{\llbracket}  \ottnt{B}  \mathclose{\rrbracket} \searrow  \ottnt{P} }%
}{
 \mathopen{\llbracket}   \kw{U} \gap  \ottnt{B}   \mathclose{\rrbracket} \searrow   \lbrace  \ottnt{v}  \mid    \kw{force} \gap  \ottnt{v}   \in  \ottnt{P}   \rbrace  }{%
{\ottdrulename{LR\_U}}{}%
}}

\newcommand{\ottdefnValType}[1]{\begin{ottdefnblock}[#1]{$ \mathopen{\llbracket}  \ottnt{A}  \mathclose{\rrbracket} \searrow  \ottnt{P} $}{}
\ottusedrule{\ottdruleLRXXUnit{}}
\ottusedrule{\ottdruleLRXXSum{}}
\ottusedrule{\ottdruleLRXXU{}}
\end{ottdefnblock}}

%% defn ComType
\newcommand{\ottdruleLRXXF}[1]{\ottdrule[#1]{%
\ottpremise{ \mathopen{\llbracket}  \ottnt{A}  \mathclose{\rrbracket} \searrow  \ottnt{P} }%
}{
 \mathopen{\llbracket}   \kw{F} \gap  \ottnt{A}   \mathclose{\rrbracket} \searrow   \lbrace  \ottnt{m}  \mid    (   \exists  \ottnt{n}  \mathpunct{.}     \ottnt{m}  \leadsto^*  \ottnt{n}   \wedge   \ottnt{n}  \in \kw{SNe}      )   \vee   (   \exists  \ottnt{v}  \mathpunct{.}     \ottnt{m}  \leadsto^*   \kw{return} \gap  \ottnt{v}    \wedge   \ottnt{v}  \in  \ottnt{P}      )    \rbrace  }{%
{\ottdrulename{LR\_F}}{}%
}}


\newcommand{\ottdruleLRXXArr}[1]{\ottdrule[#1]{%
\ottpremise{ \mathopen{\llbracket}  \ottnt{A}  \mathclose{\rrbracket} \searrow  \ottnt{P} }%
\ottpremise{ \mathopen{\llbracket}  \ottnt{B}  \mathclose{\rrbracket} \searrow  \ottnt{Q} }%
}{
 \mathopen{\llbracket}   \ottnt{A}  \rightarrow  \ottnt{B}   \mathclose{\rrbracket} \searrow   \lbrace  \ottnt{m}  \mid   \forall  \ottnt{v}  \mathpunct{.}     \ottnt{v}  \in  \ottnt{P}   \Rightarrow    \ottnt{m}  \gap  \ottnt{v}   \in  \ottnt{Q}      \rbrace  }{%
{\ottdrulename{LR\_Arr}}{}%
}}

\newcommand{\ottdefnComType}[1]{\begin{ottdefnblock}[#1]{$ \mathopen{\llbracket}  \ottnt{B}  \mathclose{\rrbracket} \searrow  \ottnt{P} $}{}
\ottusedrule{\ottdruleLRXXF{}}
\ottusedrule{\ottdruleLRXXArr{}}
\end{ottdefnblock}}


\newcommand{\ottdefnsLR}{
\ottdefnValType{}\ottdefnComType{}}

% defns LRs
%% defn ValTypes
\newcommand{\ottdruleLRPPXXUnitXXvar}[1]{\ottdrule[#1]{%
}{
 \ottmv{x}  \in \mathopen{\llbracket}   \kw{Unit}   \mathclose{\rrbracket} }{%
{\ottdrulename{LR'\_Unit\_var}}{}%
}}


\newcommand{\ottdruleLRPPXXUnitXXunit}[1]{\ottdrule[#1]{%
}{
  \kw{unit}   \in \mathopen{\llbracket}   \kw{Unit}   \mathclose{\rrbracket} }{%
{\ottdrulename{LR'\_Unit\_unit}}{}%
}}


\newcommand{\ottdruleLRPPXXSumXXvar}[1]{\ottdrule[#1]{%
}{
 \ottmv{x}  \in \mathopen{\llbracket}   \ottnt{A_{{\mathrm{1}}}}  +  \ottnt{A_{{\mathrm{2}}}}   \mathclose{\rrbracket} }{%
{\ottdrulename{LR'\_Sum\_var}}{}%
}}


\newcommand{\ottdruleLRPPXXSumXXinl}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \mathopen{\llbracket}  \ottnt{A_{{\mathrm{1}}}}  \mathclose{\rrbracket} }%
}{
  \kw{inl} \gap  \ottnt{v}   \in \mathopen{\llbracket}   \ottnt{A_{{\mathrm{1}}}}  +  \ottnt{A_{{\mathrm{2}}}}   \mathclose{\rrbracket} }{%
{\ottdrulename{LR'\_Sum\_inl}}{}%
}}


\newcommand{\ottdruleLRPPXXSumXXinr}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \mathopen{\llbracket}  \ottnt{A_{{\mathrm{2}}}}  \mathclose{\rrbracket} }%
}{
  \kw{inr} \gap  \ottnt{v}   \in \mathopen{\llbracket}   \ottnt{A_{{\mathrm{1}}}}  +  \ottnt{A_{{\mathrm{2}}}}   \mathclose{\rrbracket} }{%
{\ottdrulename{LR'\_Sum\_inr}}{}%
}}


\newcommand{\ottdruleLRPPXXForce}[1]{\ottdrule[#1]{%
\ottpremise{  \kw{force} \gap  \ottnt{v}   \in \mathopen{\llbracket}  \ottnt{B}  \mathclose{\rrbracket} }%
}{
 \ottnt{v}  \in \mathopen{\llbracket}   \kw{U} \gap  \ottnt{B}   \mathclose{\rrbracket} }{%
{\ottdrulename{LR'\_Force}}{}%
}}

\newcommand{\ottdefnValTypes}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{v}  \in \mathopen{\llbracket}  \ottnt{A}  \mathclose{\rrbracket} $}{}
\ottusedrule{\ottdruleLRPPXXUnitXXvar{}}
\ottusedrule{\ottdruleLRPPXXUnitXXunit{}}
\ottusedrule{\ottdruleLRPPXXSumXXvar{}}
\ottusedrule{\ottdruleLRPPXXSumXXinl{}}
\ottusedrule{\ottdruleLRPPXXSumXXinr{}}
\ottusedrule{\ottdruleLRPPXXForce{}}
\end{ottdefnblock}}

%% defn ComTypes
\newcommand{\ottdruleLRPPXXFXXvar}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \leadsto^*  \ottnt{n} }%
\ottpremise{ \ottnt{n}  \in \kw{SNe} }%
}{
 \ottnt{m}  \in \mathopen{\llbracket}   \kw{F} \gap  \ottnt{A}   \mathclose{\rrbracket} }{%
{\ottdrulename{LR'\_F\_var}}{}%
}}


\newcommand{\ottdruleLRPPXXFXXret}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \leadsto^*   \kw{return} \gap  \ottnt{v}  }%
\ottpremise{ \ottnt{v}  \in \mathopen{\llbracket}  \ottnt{A}  \mathclose{\rrbracket} }%
}{
 \ottnt{m}  \in \mathopen{\llbracket}   \kw{F} \gap  \ottnt{A}   \mathclose{\rrbracket} }{%
{\ottdrulename{LR'\_F\_ret}}{}%
}}


\newcommand{\ottdruleLRPPXXArr}[1]{\ottdrule[#1]{%
\ottpremise{ \forall  \ottnt{v}  \mathpunct{.}     \ottnt{v}  \in \mathopen{\llbracket}  \ottnt{A}  \mathclose{\rrbracket}   \Rightarrow    \ottnt{m}  \gap  \ottnt{v}   \in \mathopen{\llbracket}  \ottnt{B}  \mathclose{\rrbracket}    }%
}{
 \ottnt{m}  \in \mathopen{\llbracket}   \ottnt{A}  \rightarrow  \ottnt{B}   \mathclose{\rrbracket} }{%
{\ottdrulename{LR'\_Arr}}{}%
}}

\newcommand{\ottdefnComTypes}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{m}  \in \mathopen{\llbracket}  \ottnt{B}  \mathclose{\rrbracket} $}{}
\ottusedrule{\ottdruleLRPPXXFXXvar{}}
\ottusedrule{\ottdruleLRPPXXFXXret{}}
\ottusedrule{\ottdruleLRPPXXArr{}}
\end{ottdefnblock}}


\newcommand{\ottdefnsLRs}{
\ottdefnValTypes{}\ottdefnComTypes{}}

% defns Sem
%% defn SemCtxt
\newcommand{\ottdruleSXXNil}[1]{\ottdrule[#1]{%
}{
 \Gamma  \vDash   \cdot  }{%
{\ottdrulename{S\_Nil}}{}%
}}


\newcommand{\ottdruleSXXCons}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vDash  \sigma }%
\ottpremise{ \mathopen{\llbracket}  \ottnt{A}  \mathclose{\rrbracket} \searrow  \ottnt{P} }%
\ottpremise{ \ottnt{v}  \in  \ottnt{P} }%
}{
  \Gamma ,  \ottmv{x}  \mathbin{:}  \ottnt{A}   \vDash   \sigma ,  \ottmv{x}  \mapsto  \ottnt{v}  }{%
{\ottdrulename{S\_Cons}}{}%
}}

\newcommand{\ottdefnSemCtxt}[1]{\begin{ottdefnblock}[#1]{$ \Gamma  \vDash  \sigma $}{}
\ottusedrule{\ottdruleSXXNil{}}
\ottusedrule{\ottdruleSXXCons{}}
\end{ottdefnblock}}

%% defn SemVal
\newcommand{\ottdruleSXXVar}[1]{\ottdrule[#1]{%
\ottpremise{ \ottmv{x}  :  \ottnt{A}  \in  \Gamma }%
}{
 \Gamma  \vDash  \ottmv{x}  :  \ottnt{A} }{%
{\ottdrulename{S\_Var}}{}%
}}


\newcommand{\ottdruleSXXUnit}[1]{\ottdrule[#1]{%
}{
 \Gamma  \vDash   \kw{unit}   :   \kw{Unit}  }{%
{\ottdrulename{S\_Unit}}{}%
}}


\newcommand{\ottdruleSXXInl}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vDash  \ottnt{v}  :  \ottnt{A_{{\mathrm{1}}}} }%
}{
 \Gamma  \vDash   \kw{inl} \gap  \ottnt{v}   :   \ottnt{A_{{\mathrm{1}}}}  +  \ottnt{A_{{\mathrm{2}}}}  }{%
{\ottdrulename{S\_Inl}}{}%
}}


\newcommand{\ottdruleSXXInr}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vDash  \ottnt{v}  :  \ottnt{A_{{\mathrm{2}}}} }%
}{
 \Gamma  \vDash   \kw{inr} \gap  \ottnt{v}   :   \ottnt{A_{{\mathrm{1}}}}  +  \ottnt{A_{{\mathrm{2}}}}  }{%
{\ottdrulename{S\_Inr}}{}%
}}


\newcommand{\ottdruleSXXThunk}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vDash  \ottnt{m}  :  \ottnt{B} }%
}{
 \Gamma  \vDash   \kw{thunk} \gap  \ottnt{m}   :   \kw{U} \gap  \ottnt{B}  }{%
{\ottdrulename{S\_Thunk}}{}%
}}

\newcommand{\ottdefnSemVal}[1]{\begin{ottdefnblock}[#1]{$ \Gamma  \vDash  \ottnt{v}  :  \ottnt{A} $}{}
\ottusedrule{\ottdruleSXXVar{}}
\ottusedrule{\ottdruleSXXUnit{}}
\ottusedrule{\ottdruleSXXInl{}}
\ottusedrule{\ottdruleSXXInr{}}
\ottusedrule{\ottdruleSXXThunk{}}
\end{ottdefnblock}}

%% defn SemCom
\newcommand{\ottdruleSXXForce}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vDash  \ottnt{v}  :   \kw{U} \gap  \ottnt{B}  }%
}{
 \Gamma  \vDash   \kw{force} \gap  \ottnt{v}   :  \ottnt{B} }{%
{\ottdrulename{S\_Force}}{}%
}}


\newcommand{\ottdruleSXXArr}[1]{\ottdrule[#1]{%
\ottpremise{  \Gamma ,  \ottmv{x}  \mathbin{:}  \ottnt{A}   \vDash  \ottnt{m}  :  \ottnt{B} }%
}{
 \Gamma  \vDash   \lambda  \ottmv{x}  \mathpunct{.}  \ottnt{m}   :   \ottnt{A}  \rightarrow  \ottnt{B}  }{%
{\ottdrulename{S\_Arr}}{}%
}}


\newcommand{\ottdruleSXXApp}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vDash  \ottnt{m}  :   \ottnt{A}  \rightarrow  \ottnt{B}  }%
\ottpremise{ \Gamma  \vDash  \ottnt{v}  :  \ottnt{A} }%
}{
 \Gamma  \vDash   \ottnt{m}  \gap  \ottnt{v}   :  \ottnt{B} }{%
{\ottdrulename{S\_App}}{}%
}}


\newcommand{\ottdruleSXXRet}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vDash  \ottnt{v}  :  \ottnt{A} }%
}{
 \Gamma  \vDash   \kw{return} \gap  \ottnt{v}   :   \kw{F} \gap  \ottnt{A}  }{%
{\ottdrulename{S\_Ret}}{}%
}}


\newcommand{\ottdruleSXXLet}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vDash  \ottnt{m}  :   \kw{F} \gap  \ottnt{A}  }%
\ottpremise{  \Gamma ,  \ottmv{x}  \mathbin{:}  \ottnt{A}   \vDash  \ottnt{n}  :  \ottnt{B} }%
}{
 \Gamma  \vDash   \kw{let} \gap  \ottmv{x}  \leftarrow  \ottnt{m}  \gap \kw{in} \gap  \ottnt{n}   :  \ottnt{B} }{%
{\ottdrulename{S\_Let}}{}%
}}


\newcommand{\ottdruleSXXCase}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vDash  \ottnt{v}  :   \ottnt{A_{{\mathrm{1}}}}  +  \ottnt{A_{{\mathrm{2}}}}  }%
\ottpremise{  \Gamma ,  \ottmv{y}  \mathbin{:}  \ottnt{A_{{\mathrm{1}}}}   \vDash  \ottnt{m}  :  \ottnt{B} }%
\ottpremise{  \Gamma ,  \ottmv{z}  \mathbin{:}  \ottnt{A_{{\mathrm{2}}}}   \vDash  \ottnt{n}  :  \ottnt{B} }%
}{
 \Gamma  \vDash   \kw{case} \gap  \ottnt{v}  \gap \kw{of} \gap \lbrace \kw{inl} \gap  \ottmv{y}  \Rightarrow  \ottnt{m}  \mathrel{;} \kw{inr} \gap  \ottmv{z}  \Rightarrow  \ottnt{n}  \rbrace   :  \ottnt{B} }{%
{\ottdrulename{S\_Case}}{}%
}}

\newcommand{\ottdefnSemCom}[1]{\begin{ottdefnblock}[#1]{$ \Gamma  \vDash  \ottnt{m}  :  \ottnt{B} $}{}
\ottusedrule{\ottdruleSXXForce{}}
\ottusedrule{\ottdruleSXXArr{}}
\ottusedrule{\ottdruleSXXApp{}}
\ottusedrule{\ottdruleSXXRet{}}
\ottusedrule{\ottdruleSXXLet{}}
\ottusedrule{\ottdruleSXXCase{}}
\end{ottdefnblock}}


\newcommand{\ottdefnsSem}{
\ottdefnSemCtxt{}\ottdefnSemVal{}\ottdefnSemCom{}}

% defns Typing
%% defn ValWt
\newcommand{\ottdruleTXXVar}[1]{\ottdrule[#1]{%
\ottpremise{ \ottmv{x}  :  \ottnt{A}  \in  \Gamma }%
}{
 \Gamma  \vdash  \ottmv{x}  :  \ottnt{A} }{%
{\ottdrulename{T\_Var}}{}%
}}


\newcommand{\ottdruleTXXUnit}[1]{\ottdrule[#1]{%
}{
 \Gamma  \vdash   \kw{unit}   :   \kw{Unit}  }{%
{\ottdrulename{T\_Unit}}{}%
}}


\newcommand{\ottdruleTXXInl}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vdash  \ottnt{v}  :  \ottnt{A_{{\mathrm{1}}}} }%
}{
 \Gamma  \vdash   \kw{inl} \gap  \ottnt{v}   :   \ottnt{A_{{\mathrm{1}}}}  +  \ottnt{A_{{\mathrm{2}}}}  }{%
{\ottdrulename{T\_Inl}}{}%
}}


\newcommand{\ottdruleTXXInr}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vdash  \ottnt{v}  :  \ottnt{A_{{\mathrm{2}}}} }%
}{
 \Gamma  \vdash   \kw{inr} \gap  \ottnt{v}   :   \ottnt{A_{{\mathrm{1}}}}  +  \ottnt{A_{{\mathrm{2}}}}  }{%
{\ottdrulename{T\_Inr}}{}%
}}


\newcommand{\ottdruleTXXThunk}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vdash  \ottnt{m}  :  \ottnt{B} }%
}{
 \Gamma  \vdash   \kw{thunk} \gap  \ottnt{m}   :   \kw{U} \gap  \ottnt{B}  }{%
{\ottdrulename{T\_Thunk}}{}%
}}

\newcommand{\ottdefnValWt}[1]{\begin{ottdefnblock}[#1]{$ \Gamma  \vdash  \ottnt{v}  :  \ottnt{A} $}{}
\ottusedrule{\ottdruleTXXVar{}}
\ottusedrule{\ottdruleTXXUnit{}}
\ottusedrule{\ottdruleTXXInl{}}
\ottusedrule{\ottdruleTXXInr{}}
\ottusedrule{\ottdruleTXXThunk{}}
\end{ottdefnblock}}

%% defn ComWt
\newcommand{\ottdruleTXXForce}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vdash  \ottnt{v}  :   \kw{U} \gap  \ottnt{B}  }%
}{
 \Gamma  \vdash   \kw{force} \gap  \ottnt{v}   :  \ottnt{B} }{%
{\ottdrulename{T\_Force}}{}%
}}


\newcommand{\ottdruleTXXLam}[1]{\ottdrule[#1]{%
\ottpremise{  \Gamma ,  \ottmv{x}  \mathbin{:}  \ottnt{A}   \vdash  \ottnt{m}  :  \ottnt{B} }%
}{
 \Gamma  \vdash   \lambda  \ottmv{x}  \mathpunct{.}  \ottnt{m}   :   \ottnt{A}  \rightarrow  \ottnt{B}  }{%
{\ottdrulename{T\_Lam}}{}%
}}


\newcommand{\ottdruleTXXApp}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vdash  \ottnt{m}  :   \ottnt{A}  \rightarrow  \ottnt{B}  }%
\ottpremise{ \Gamma  \vdash  \ottnt{v}  :  \ottnt{A} }%
}{
 \Gamma  \vdash   \ottnt{m}  \gap  \ottnt{v}   :  \ottnt{B} }{%
{\ottdrulename{T\_App}}{}%
}}


\newcommand{\ottdruleTXXRet}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vdash  \ottnt{v}  :  \ottnt{A} }%
}{
 \Gamma  \vdash   \kw{return} \gap  \ottnt{v}   :   \kw{F} \gap  \ottnt{A}  }{%
{\ottdrulename{T\_Ret}}{}%
}}


\newcommand{\ottdruleTXXLet}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vdash  \ottnt{m}  :   \kw{F} \gap  \ottnt{A}  }%
\ottpremise{  \Gamma ,  \ottmv{x}  \mathbin{:}  \ottnt{A}   \vdash  \ottnt{n}  :  \ottnt{B} }%
}{
 \Gamma  \vdash   \kw{let} \gap  \ottmv{x}  \leftarrow  \ottnt{m}  \gap \kw{in} \gap  \ottnt{n}   :  \ottnt{B} }{%
{\ottdrulename{T\_Let}}{}%
}}


\newcommand{\ottdruleTXXCase}[1]{\ottdrule[#1]{%
\ottpremise{ \Gamma  \vdash  \ottnt{v}  :   \ottnt{A_{{\mathrm{1}}}}  +  \ottnt{A_{{\mathrm{2}}}}  }%
\ottpremise{  \Gamma ,  \ottmv{y}  \mathbin{:}  \ottnt{A_{{\mathrm{1}}}}   \vdash  \ottnt{m}  :  \ottnt{B} }%
\ottpremise{  \Gamma ,  \ottmv{z}  \mathbin{:}  \ottnt{A_{{\mathrm{2}}}}   \vdash  \ottnt{n}  :  \ottnt{B} }%
}{
 \Gamma  \vdash   \kw{case} \gap  \ottnt{v}  \gap \kw{of} \gap \lbrace \kw{inl} \gap  \ottmv{y}  \Rightarrow  \ottnt{m}  \mathrel{;} \kw{inr} \gap  \ottmv{z}  \Rightarrow  \ottnt{n}  \rbrace   :  \ottnt{B} }{%
{\ottdrulename{T\_Case}}{}%
}}

\newcommand{\ottdefnComWt}[1]{\begin{ottdefnblock}[#1]{$ \Gamma  \vdash  \ottnt{m}  :  \ottnt{B} $}{}
\ottusedrule{\ottdruleTXXForce{}}
\ottusedrule{\ottdruleTXXLam{}}
\ottusedrule{\ottdruleTXXApp{}}
\ottusedrule{\ottdruleTXXRet{}}
\ottusedrule{\ottdruleTXXLet{}}
\ottusedrule{\ottdruleTXXCase{}}
\end{ottdefnblock}}


\newcommand{\ottdefnsTyping}{
\ottdefnValWt{}\ottdefnComWt{}}

% defns Red
%% defn StepVal

\newcommand{\ottdefnStepVal}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{v}  \rightsquigarrow  \ottnt{w} $}{}
\end{ottdefnblock}}

%% defn StepCom

\newcommand{\ottdefnStepCom}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{m}  \rightsquigarrow  \ottnt{n} $}{}
\end{ottdefnblock}}

%% defn StepVals

\newcommand{\ottdefnStepVals}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{v}  \rightsquigarrow^*  \ottnt{w} $}{}
\end{ottdefnblock}}

%% defn StepComs

\newcommand{\ottdefnStepComs}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{m}  \rightsquigarrow^*  \ottnt{n} $}{}
\end{ottdefnblock}}


\newcommand{\ottdefnsRed}{
\ottdefnStepVal{}\ottdefnStepCom{}\ottdefnStepVals{}\ottdefnStepComs{}}

% defns sn
%% defn snVal
\newcommand{\ottdrulesnXXVal}[1]{\ottdrule[#1]{%
\ottpremise{ \forall  \ottnt{w}  \mathpunct{.}     \ottnt{v}  \rightsquigarrow  \ottnt{w}   \Rightarrow   \ottnt{w}  \in \kw{sn}    }%
}{
 \ottnt{v}  \in \kw{sn} }{%
{\ottdrulename{sn\_Val}}{}%
}}


\newcommand{\ottdrulesnXXForceXXinv}[1]{\ottdrule[#1]{%
\ottpremise{  \kw{force} \gap  \ottnt{v}   \in \kw{sn} }%
}{
 \ottnt{v}  \in \kw{sn} }{%
{\ottdrulename{sn\_Force\_inv}}{}%
}}


\newcommand{\ottdrulesnXXAppXXinvTwo}[1]{\ottdrule[#1]{%
\ottpremise{  \ottnt{m}  \gap  \ottnt{v}   \in \kw{sn} }%
}{
 \ottnt{v}  \in \kw{sn} }{%
{\ottdrulename{sn\_App\_inv2}}{}%
}}


\newcommand{\ottdrulesnXXVar}[1]{\ottdrule[#1]{%
}{
 \ottmv{x}  \in \kw{sn} }{%
{\ottdrulename{sn\_Var}}{}%
}}


\newcommand{\ottdrulesnXXUnit}[1]{\ottdrule[#1]{%
}{
  \kw{unit}   \in \kw{sn} }{%
{\ottdrulename{sn\_Unit}}{}%
}}


\newcommand{\ottdrulesnXXInl}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{sn} }%
}{
  \kw{inl} \gap  \ottnt{v}   \in \kw{sn} }{%
{\ottdrulename{sn\_Inl}}{}%
}}


\newcommand{\ottdrulesnXXInr}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{sn} }%
}{
  \kw{inr} \gap  \ottnt{v}   \in \kw{sn} }{%
{\ottdrulename{sn\_Inr}}{}%
}}


\newcommand{\ottdrulesnXXThunk}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \in \kw{sn} }%
}{
  \kw{thunk} \gap  \ottnt{m}   \in \kw{sn} }{%
{\ottdrulename{sn\_Thunk}}{}%
}}

\newcommand{\ottdefnsnVal}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{v}  \in \kw{sn} $}{}
\ottusedrule{\ottdrulesnXXVal{}}
\ottusedrule{\ottdrulesnXXForceXXinv{}}
\ottusedrule{\ottdrulesnXXAppXXinvTwo{}}
\ottusedrule{\ottdrulesnXXVar{}}
\ottusedrule{\ottdrulesnXXUnit{}}
\ottusedrule{\ottdrulesnXXInl{}}
\ottusedrule{\ottdrulesnXXInr{}}
\ottusedrule{\ottdrulesnXXThunk{}}
\end{ottdefnblock}}

%% defn snCom
\newcommand{\ottdrulesnXXCom}[1]{\ottdrule[#1]{%
\ottpremise{ \forall  \ottnt{n}  \mathpunct{.}     \ottnt{m}  \rightsquigarrow  \ottnt{n}   \Rightarrow   \ottnt{n}  \in \kw{sn}    }%
}{
 \ottnt{m}  \in \kw{sn} }{%
{\ottdrulename{sn\_Com}}{}%
}}


\newcommand{\ottdrulesnXXAppXXinvOne}[1]{\ottdrule[#1]{%
\ottpremise{  \ottnt{m}  \gap  \ottnt{v}   \in \kw{sn} }%
}{
 \ottnt{m}  \in \kw{sn} }{%
{\ottdrulename{sn\_App\_inv1}}{}%
}}


\newcommand{\ottdrulesnXXLetXXinvOne}[1]{\ottdrule[#1]{%
\ottpremise{  \kw{let} \gap  \ottmv{x}  \leftarrow  \ottnt{m}  \gap \kw{in} \gap  \ottnt{n}   \in \kw{sn} }%
}{
 \ottnt{m}  \in \kw{sn} }{%
{\ottdrulename{sn\_Let\_inv1}}{}%
}}


\newcommand{\ottdrulesnXXLetXXinvTwo}[1]{\ottdrule[#1]{%
\ottpremise{  \kw{let} \gap  \ottmv{x}  \leftarrow  \ottnt{m}  \gap \kw{in} \gap  \ottnt{n}   \in \kw{sn} }%
}{
 \ottnt{n}  \in \kw{sn} }{%
{\ottdrulename{sn\_Let\_inv2}}{}%
}}


\newcommand{\ottdrulesnXXantisubst}[1]{\ottdrule[#1]{%
\ottpremise{  \ottnt{m} [   \ottmv{x}  \mapsto  \ottnt{v}   ]   \in \kw{sn} }%
\ottpremise{ \ottnt{v}  \in \kw{sn} }%
}{
 \ottnt{m}  \in \kw{sn} }{%
{\ottdrulename{sn\_antisubst}}{}%
}}


\newcommand{\ottdrulesnXXForceXXThunk}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \in \kw{sn} }%
}{
  \kw{force} \gap   (  \kw{thunk} \gap  \ottnt{m}  )    \in \kw{sn} }{%
{\ottdrulename{sn\_Force\_Thunk}}{}%
}}


\newcommand{\ottdrulesnXXAppXXLam}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{sn} }%
\ottpremise{  \ottnt{m} [   \ottmv{x}  \mapsto  \ottnt{v}   ]   \in \kw{sn} }%
}{
   (  \lambda  \ottmv{x}  \mathpunct{.}  \ottnt{m}  )   \gap  \ottnt{v}   \in \kw{sn} }{%
{\ottdrulename{sn\_App\_Lam}}{}%
}}


\newcommand{\ottdrulesnXXLetXXRet}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{sn} }%
\ottpremise{  \ottnt{m} [   \ottmv{x}  \mapsto  \ottnt{v}   ]   \in \kw{sn} }%
}{
  \kw{let} \gap  \ottmv{x}  \leftarrow   (  \kw{return} \gap  \ottnt{v}  )   \gap \kw{in} \gap  \ottnt{m}   \in \kw{sn} }{%
{\ottdrulename{sn\_Let\_Ret}}{}%
}}


\newcommand{\ottdrulesnXXCaseXXInl}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{sn} }%
\ottpremise{  \ottnt{m} [   \ottmv{y}  \mapsto  \ottnt{v}   ]   \in \kw{sn} }%
\ottpremise{ \ottnt{n}  \in \kw{sn} }%
}{
  \kw{case} \gap   (  \kw{inl} \gap  \ottnt{v}  )   \gap \kw{of} \gap \lbrace \kw{inl} \gap  \ottmv{y}  \Rightarrow  \ottnt{m}  \mathrel{;} \kw{inr} \gap  \ottmv{z}  \Rightarrow  \ottnt{n}  \rbrace   \in \kw{sn} }{%
{\ottdrulename{sn\_Case\_Inl}}{}%
}}


\newcommand{\ottdrulesnXXCaseXXInr}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{sn} }%
\ottpremise{ \ottnt{m}  \in \kw{sn} }%
\ottpremise{  \ottnt{n} [   \ottmv{z}  \mapsto  \ottnt{v}   ]   \in \kw{sn} }%
}{
  \kw{case} \gap   (  \kw{inr} \gap  \ottnt{v}  )   \gap \kw{of} \gap \lbrace \kw{inl} \gap  \ottmv{y}  \Rightarrow  \ottnt{m}  \mathrel{;} \kw{inr} \gap  \ottmv{z}  \Rightarrow  \ottnt{n}  \rbrace   \in \kw{sn} }{%
{\ottdrulename{sn\_Case\_Inr}}{}%
}}


\newcommand{\ottdrulesnXXAppXXbwd}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \leadsto_{ \kw{sn} }  \ottnt{n} }%
\ottpremise{ \ottnt{v}  \in \kw{sn} }%
\ottpremise{  \ottnt{n}  \gap  \ottnt{v}   \in \kw{sn} }%
}{
  \ottnt{m}  \gap  \ottnt{v}   \in \kw{sn} }{%
{\ottdrulename{sn\_App\_bwd}}{}%
}}


\newcommand{\ottdrulesnXXLetXXbwd}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \leadsto_{ \kw{sn} }  \ottnt{m'} }%
\ottpremise{ \ottnt{n}  \in \kw{sn} }%
\ottpremise{  \kw{let} \gap  \ottmv{x}  \leftarrow  \ottnt{m'}  \gap \kw{in} \gap  \ottnt{n}   \in \kw{sn} }%
}{
  \kw{let} \gap  \ottmv{x}  \leftarrow  \ottnt{m}  \gap \kw{in} \gap  \ottnt{n}   \in \kw{sn} }{%
{\ottdrulename{sn\_Let\_bwd}}{}%
}}


\newcommand{\ottdrulesnXXclosure}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \leadsto_{ \kw{sn} }  \ottnt{n} }%
\ottpremise{ \ottnt{n}  \in \kw{sn} }%
}{
 \ottnt{m}  \in \kw{sn} }{%
{\ottdrulename{sn\_closure}}{}%
}}


\newcommand{\ottdrulesnXXForce}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{sn} }%
}{
  \kw{force} \gap  \ottnt{v}   \in \kw{sn} }{%
{\ottdrulename{sn\_Force}}{}%
}}


\newcommand{\ottdrulesnXXLam}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \in \kw{sn} }%
}{
  \lambda  \ottmv{x}  \mathpunct{.}  \ottnt{m}   \in \kw{sn} }{%
{\ottdrulename{sn\_Lam}}{}%
}}


\newcommand{\ottdrulesnXXRet}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{sn} }%
}{
  \kw{return} \gap  \ottnt{v}   \in \kw{sn} }{%
{\ottdrulename{sn\_Ret}}{}%
}}


\newcommand{\ottdrulesnXXApp}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \in \kw{sne} }%
\ottpremise{ \ottnt{v}  \in \kw{sn} }%
}{
  \ottnt{m}  \gap  \ottnt{v}   \in \kw{sn} }{%
{\ottdrulename{sn\_App}}{}%
}}


\newcommand{\ottdrulesnXXLet}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \in \kw{sne} }%
\ottpremise{ \ottnt{n}  \in \kw{sn} }%
}{
  \kw{let} \gap  \ottmv{x}  \leftarrow  \ottnt{m}  \gap \kw{in} \gap  \ottnt{n}   \in \kw{sn} }{%
{\ottdrulename{sn\_Let}}{}%
}}


\newcommand{\ottdrulesnXXCase}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{sne} }%
\ottpremise{ \ottnt{m}  \in \kw{sn} }%
\ottpremise{ \ottnt{n}  \in \kw{sn} }%
}{
  \kw{case} \gap  \ottnt{v}  \gap \kw{of} \gap \lbrace \kw{inl} \gap  \ottmv{y}  \Rightarrow  \ottnt{m}  \mathrel{;} \kw{inr} \gap  \ottmv{z}  \Rightarrow  \ottnt{n}  \rbrace   \in \kw{sn} }{%
{\ottdrulename{sn\_Case}}{}%
}}

\newcommand{\ottdefnsnCom}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{m}  \in \kw{sn} $}{}
\ottusedrule{\ottdrulesnXXCom{}}
\ottusedrule{\ottdrulesnXXAppXXinvOne{}}
\ottusedrule{\ottdrulesnXXLetXXinvOne{}}
\ottusedrule{\ottdrulesnXXLetXXinvTwo{}}
\ottusedrule{\ottdrulesnXXantisubst{}}
\ottusedrule{\ottdrulesnXXForceXXThunk{}}
\ottusedrule{\ottdrulesnXXAppXXLam{}}
\ottusedrule{\ottdrulesnXXLetXXRet{}}
\ottusedrule{\ottdrulesnXXCaseXXInl{}}
\ottusedrule{\ottdrulesnXXCaseXXInr{}}
\ottusedrule{\ottdrulesnXXAppXXbwd{}}
\ottusedrule{\ottdrulesnXXLetXXbwd{}}
\ottusedrule{\ottdrulesnXXclosure{}}
\ottusedrule{\ottdrulesnXXForce{}}
\ottusedrule{\ottdrulesnXXLam{}}
\ottusedrule{\ottdrulesnXXRet{}}
\ottusedrule{\ottdrulesnXXApp{}}
\ottusedrule{\ottdrulesnXXLet{}}
\ottusedrule{\ottdrulesnXXCase{}}
\end{ottdefnblock}}

%% defn sr
\newcommand{\ottdrulesrXXThunk}[1]{\ottdrule[#1]{%
}{
  \kw{force} \gap   (  \kw{thunk} \gap  \ottnt{m}  )    \leadsto_{ \kw{sn} }  \ottnt{m} }{%
{\ottdrulename{sr\_Thunk}}{}%
}}


\newcommand{\ottdrulesrXXLam}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{sn} }%
}{
   (  \lambda  \ottmv{x}  \mathpunct{.}  \ottnt{m}  )   \gap  \ottnt{v}   \leadsto_{ \kw{sn} }   \ottnt{m} [   \ottmv{x}  \mapsto  \ottnt{v}   ]  }{%
{\ottdrulename{sr\_Lam}}{}%
}}


\newcommand{\ottdrulesrXXRet}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{sn} }%
}{
  \kw{let} \gap  \ottmv{x}  \leftarrow   (  \kw{return} \gap  \ottnt{v}  )   \gap \kw{in} \gap  \ottnt{m}   \leadsto_{ \kw{sn} }   \ottnt{m} [   \ottmv{x}  \mapsto  \ottnt{v}   ]  }{%
{\ottdrulename{sr\_Ret}}{}%
}}


\newcommand{\ottdrulesrXXInl}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{sn} }%
\ottpremise{ \ottnt{n}  \in \kw{sn} }%
}{
  \kw{case} \gap   (  \kw{inl} \gap  \ottnt{v}  )   \gap \kw{of} \gap \lbrace \kw{inl} \gap  \ottmv{y}  \Rightarrow  \ottnt{m}  \mathrel{;} \kw{inr} \gap  \ottmv{z}  \Rightarrow  \ottnt{n}  \rbrace   \leadsto_{ \kw{sn} }   \ottnt{m} [   \ottmv{y}  \mapsto  \ottnt{v}   ]  }{%
{\ottdrulename{sr\_Inl}}{}%
}}


\newcommand{\ottdrulesrXXInr}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \in \kw{sn} }%
\ottpremise{ \ottnt{m}  \in \kw{sn} }%
}{
  \kw{case} \gap   (  \kw{inr} \gap  \ottnt{v}  )   \gap \kw{of} \gap \lbrace \kw{inl} \gap  \ottmv{y}  \Rightarrow  \ottnt{m}  \mathrel{;} \kw{inr} \gap  \ottmv{z}  \Rightarrow  \ottnt{n}  \rbrace   \leadsto_{ \kw{sn} }   \ottnt{n} [   \ottmv{z}  \mapsto  \ottnt{v}   ]  }{%
{\ottdrulename{sr\_Inr}}{}%
}}


\newcommand{\ottdrulesrXXApp}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \leadsto_{ \kw{sn} }  \ottnt{n} }%
}{
  \ottnt{m}  \gap  \ottnt{v}   \leadsto_{ \kw{sn} }   \ottnt{n}  \gap  \ottnt{v}  }{%
{\ottdrulename{sr\_App}}{}%
}}


\newcommand{\ottdrulesrXXLet}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \leadsto_{ \kw{sn} }  \ottnt{m'} }%
}{
  \kw{let} \gap  \ottmv{x}  \leftarrow  \ottnt{m}  \gap \kw{in} \gap  \ottnt{n}   \leadsto_{ \kw{sn} }   \kw{let} \gap  \ottmv{x}  \leftarrow  \ottnt{m'}  \gap \kw{in} \gap  \ottnt{n}  }{%
{\ottdrulename{sr\_Let}}{}%
}}

\newcommand{\ottdefnsr}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{m}  \leadsto_{ \kw{sn} }  \ottnt{n} $}{}
\ottusedrule{\ottdrulesrXXThunk{}}
\ottusedrule{\ottdrulesrXXLam{}}
\ottusedrule{\ottdrulesrXXRet{}}
\ottusedrule{\ottdrulesrXXInl{}}
\ottusedrule{\ottdrulesrXXInr{}}
\ottusedrule{\ottdrulesrXXApp{}}
\ottusedrule{\ottdrulesrXXLet{}}
\end{ottdefnblock}}

%% defn neVal
\newcommand{\ottdruleneXXVar}[1]{\ottdrule[#1]{%
}{
 \ottmv{x}  \in \kw{ne} }{%
{\ottdrulename{ne\_Var}}{}%
}}


\newcommand{\ottdruleneXXStepVal}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{v}  \rightsquigarrow  \ottnt{w} }%
\ottpremise{ \ottnt{v}  \in \kw{ne} }%
}{
 \ottnt{w}  \in \kw{ne} }{%
{\ottdrulename{ne\_StepVal}}{}%
}}

\newcommand{\ottdefnneVal}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{v}  \in \kw{ne} $}{}
\ottusedrule{\ottdruleneXXVar{}}
\ottusedrule{\ottdruleneXXStepVal{}}
\end{ottdefnblock}}

%% defn neCom
\newcommand{\ottdruleneXXForce}[1]{\ottdrule[#1]{%
}{
  \kw{force} \gap  \ottmv{x}   \in \kw{ne} }{%
{\ottdrulename{ne\_Force}}{}%
}}


\newcommand{\ottdruleneXXApp}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \in \kw{ne} }%
}{
  \ottnt{m}  \gap  \ottnt{v}   \in \kw{ne} }{%
{\ottdrulename{ne\_App}}{}%
}}


\newcommand{\ottdruleneXXLet}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \in \kw{ne} }%
}{
  \kw{let} \gap  \ottmv{x}  \leftarrow  \ottnt{m}  \gap \kw{in} \gap  \ottnt{n}   \in \kw{ne} }{%
{\ottdrulename{ne\_Let}}{}%
}}


\newcommand{\ottdruleneXXCase}[1]{\ottdrule[#1]{%
}{
  \kw{case} \gap  \ottmv{x}  \gap \kw{of} \gap \lbrace \kw{inl} \gap  \ottmv{y}  \Rightarrow  \ottnt{m}  \mathrel{;} \kw{inr} \gap  \ottmv{z}  \Rightarrow  \ottnt{n}  \rbrace   \in \kw{ne} }{%
{\ottdrulename{ne\_Case}}{}%
}}


\newcommand{\ottdruleneXXStepCom}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \rightsquigarrow  \ottnt{n} }%
\ottpremise{ \ottnt{n}  \in \kw{ne} }%
}{
 \ottnt{m}  \in \kw{ne} }{%
{\ottdrulename{ne\_StepCom}}{}%
}}


\newcommand{\ottdruleneXXSNe}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \in \kw{SNe} }%
}{
 \ottnt{m}  \in \kw{ne} }{%
{\ottdrulename{ne\_SNe}}{}%
}}

\newcommand{\ottdefnneCom}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{m}  \in \kw{ne} $}{}
\ottusedrule{\ottdruleneXXForce{}}
\ottusedrule{\ottdruleneXXApp{}}
\ottusedrule{\ottdruleneXXLet{}}
\ottusedrule{\ottdruleneXXCase{}}
\ottusedrule{\ottdruleneXXStepCom{}}
\ottusedrule{\ottdruleneXXSNe{}}
\end{ottdefnblock}}

%% defn sneVal
\newcommand{\ottdrulesnevalXXsne}[1]{\ottdrule[#1]{%
}{
 \ottmv{x}  \in \kw{sne} }{%
{\ottdrulename{sneval\_sne}}{}%
}}

\newcommand{\ottdefnsneVal}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{v}  \in \kw{sne} $}{}
\ottusedrule{\ottdrulesnevalXXsne{}}
\end{ottdefnblock}}

%% defn sneCom
\newcommand{\ottdrulesnecomXXsne}[1]{\ottdrule[#1]{%
\ottpremise{ \ottnt{m}  \in \kw{ne} }%
\ottpremise{ \ottnt{m}  \in \kw{sn} }%
}{
 \ottnt{m}  \in \kw{sne} }{%
{\ottdrulename{snecom\_sne}}{}%
}}

\newcommand{\ottdefnsneCom}[1]{\begin{ottdefnblock}[#1]{$ \ottnt{m}  \in \kw{sne} $}{}
\ottusedrule{\ottdrulesnecomXXsne{}}
\end{ottdefnblock}}


\newcommand{\ottdefnssn}{
\ottdefnsnVal{}\ottdefnsnCom{}\ottdefnsr{}\ottdefnneVal{}\ottdefnneCom{}\ottdefnsneVal{}\ottdefnsneCom{}}

\newcommand{\ottdefnss}{
\ottdefnsSN
\ottdefnsLR
\ottdefnsLRs
\ottdefnsSem
\ottdefnsTyping
\ottdefnsRed
\ottdefnssn
}

\newcommand{\ottall}{\ottmetavars\\[0pt]
\ottgrammar\\[5.0mm]
\ottdefnss}