\[
   \begin{array}{l l l}
     v     & \coloneq & x \mid \vlam{x}{e} \mid \ints \mid \vectorvn
   \\[8pt]
     e     & \coloneq & v \mid e~e \mid \vectoren \mid \aref{e}{e}
   \\[8pt]
     \tau  & \coloneq & \tint \mid \tarray \mid \tau \rightarrow \tau
   \\[8pt]
     \tenv & \coloneq & \tenvempty \mid x:\tau,\tenv
   \end{array}
\]


\fbox{$\typesto{e}{\tau}$}
\begin{mathpar}
  \inferrule*[left=T-Var]{
    \tenv(x) = \tau
  }{
    \typesto{x}{\tau}
  }

  \inferrule*[left=T-Lam]{
    \typestogen{x:\tau,\tenv}{e}{\tau'}
  }{
    \typesto{\vlam{x}{e}}{\tau \rightarrow \tau'}
  }

  \inferrule*[left=T-App]{
    \typesto{e_1}{\tau \rightarrow \tau'}
    \\
    \typesto{e_2}{\tau}
  }{
    \typesto{e_1~e_2}{\tau'}
  }

  \inferrule*[left=T-Int]{
    i \in \ints
  }{
    \typesto{i}{\tint}
  }

  \inferrule*[left=T-Arr]{
    \typesto{e_0}{\tint}
    \\
    \ldots
    \\
    \typesto{e_{n-1}}{\tint}
  }{
    \typesto{\vectoren}{\tarray}
  }

  \inferrule*[left=T-Ref]{
    \typesto{e_1}{\tarray}
    \\
    \typesto{e_2}{\tint}
  }{
    \typesto{\aref{e_1}{e_2}}{\tint}
  }

\end{mathpar}