Commit 1b2a70f6 authored by Mickael Laurent's avatar Mickael Laurent
Browse files

update refining2

parent e7742460
......@@ -64,7 +64,7 @@ improves these two points.
{e\text{ a variable or constant}}
\hfill
\Infer[Abs]
{\Gamma,y:s\vdash e\triangleright_x\psi}
{\Gamma,(y:s)\vdash e\triangleright_x\psi}
{
\Gamma\vdash\lambda y:s.e\triangleright_x\psi
}
......@@ -120,8 +120,9 @@ improves these two points.
% \vspace{-2.3mm}\\
\Infer[OverLet]
{
\Gamma \vdash e_2\triangleright_x\psi_x\\
\Gamma \vdash e_2\triangleright_y\psi_y\\
\Gamma \vdash e_1: t\\
\Gamma, (y:t) \vdash e_2\triangleright_x\psi_x\\
\Gamma, (y:t) \vdash e_2\triangleright_y\psi_y\\
\forall u\in \psi_y.\ \Gamma\evdash{e_1}{u}\{\Gamma_u^i\}_{i\in I_u}
}
{ \Gamma \vdash\textstyle
......@@ -150,14 +151,26 @@ improves these two points.
}
\end{array}\]
Typing rule for the LET:
\begin{mathpar}
\Infer[Let]
{
\Gamma \vdash e_1: t_1\\
\Gamma,y:t_1\vdash e_2\triangleright_y \psi\\
\psi' = \psi\cup\{t_1\setminus(\bigvee_{u\in\psi}u)\}\\
\forall u\in\psi'.\ \Gamma\evdash{e_1}{u}\{\Gamma_u^i\}_{i\in I_u}\\
\forall u\in\psi'.\ \forall i\in I_u.\ \Gamma_u^i, (y:u)\vdash e_2:t
}
{ \Gamma \vdash\textstyle
\texttt{let }y\texttt{\,=\,}e_1\texttt{\,in\,}e_2:t}
{}
\vspace{-1.4mm}
\end{mathpar}
TODO: $\triangleright$ should return a set of environments (mapping variables only) instead
of a set of types for a given variable?
TODO: typing rule for the let. If we want full control flow, it should compute
$e_2 \triangleright_y \psi$ and, for all $t$ in $\psi$, type $e_2$ under the hypothesis
that $e_1$ has type $t$ (and, finally,
under the hypothesis that $e_1$ has type $\tyof{e_1}{\Gamma}\setminus\bigcup_{t\in\psi}t$).
TODO: The $\evdash e t$ operator is used in the Case, OverApp and OverLet rules,
but what we would actually need is an operator that computes the other direction:
which environments can surely lead to $e$ having the type $t$?
......
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