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Giuseppe Castagna
occurrence-typing
Commits
bae1da77
Commit
bae1da77
authored
Jul 04, 2019
by
Mickael Laurent
Browse files
minor fix
parent
2ff4839b
Changes
2
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Inline
Side-by-side
gradual.tex
View file @
bae1da77
...
@@ -114,12 +114,12 @@ functions as follows:
...
@@ -114,12 +114,12 @@ functions as follows:
\textsc
{
[
AbsInf
+]
}
\textsc
{
[
AbsInf
+]
}
\frac
\frac
{
{
\begin
{
align
*
}
\begin
{
align
ed
}
\Gamma
,x:
&
\sigma\vdash
e
\triangleright\psi
\qquad
\qquad
\Gamma
,x:
\sigma\vdash
e:
\tau\\
\Gamma
,x:
&
\sigma\vdash
e
\triangleright\psi
\qquad
\qquad
\Gamma
,x:
\sigma\vdash
e:
\tau\\
T
=
\{
(
\sigma
,
\tau
)
\}
T
=
\{
(
\sigma
,
\tau
)
\}
&
\cup
\{
(
\sigma
,
\tau
)
~|~
\sigma
\in
\psi
(
x
)
\land
\Gamma
, x:
\sigma
\vdash
e:
\tau
\}\\
&
\cup
\{
(
\sigma
,
\tau
)
~|~
\sigma
\in
\psi
(
x
)
\land
\Gamma
, x:
\sigma
\vdash
e:
\tau
\}\\
&
\cup
\{
(
\sigma
^
*
,
\tau
)
~|~
\sigma
\in
\psi
(
x
)
\land
\Gamma
, x:
\sigma
^
*
\vdash
e:
\tau
\}
&
\cup
\{
(
\sigma
^
*
,
\tau
)
~|~
\sigma
\in
\psi
(
x
)
\land
\Gamma
, x:
\sigma
^
*
\vdash
e:
\tau
\}
\end
{
align
*
}
\end
{
align
ed
}
}
}
{
{
\Gamma\vdash\lambda
x:
\sigma
.e:
\textstyle\bigwedge
_{
(
\sigma
,
\tau
)
\in
T
}
\sigma\to
\tau
\Gamma\vdash\lambda
x:
\sigma
.e:
\textstyle\bigwedge
_{
(
\sigma
,
\tau
)
\in
T
}
\sigma\to
\tau
...
...
proofs.tex
View file @
bae1da77
...
@@ -968,8 +968,8 @@
...
@@ -968,8 +968,8 @@
\begin{theorem}
[Soundness of the algorithm]
\begin{theorem}
[Soundness of the algorithm]
\begin{align*}
\begin{align*}
&
\forall
\Gamma
, e, t.
\ \tyof
e
\Gamma
\leq
t
\Rightarrow
\Gamma
\vdash
e:t
\\
&
\forall
\Gamma
, e, t.
\ \tyof
e
\Gamma
\leq
t
\Rightarrow
\Gamma
\vdash
e:t
\\
&
\forall
\Gamma
, e, t,
\varpi
.
\ \pvdash
\Gamma
e t
\varpi
:
\env
{
\Gamma
,e,t
}
(
\varpi
)
\\
&
\forall
\Gamma
, e, t,
\varpi
.
\
\tyof
e
\Gamma
\neq
\tsempty
\Rightarrow
\pvdash
\Gamma
e t
\varpi
:
\env
{
\Gamma
,e,t
}
(
\varpi
)
\\
&
\forall
\Gamma
, e, t.
\ \Gamma
\evdash
e t
\Refine
{
e,t
}
\Gamma
&
\forall
\Gamma
, e, t.
\
\tyof
e
\Gamma
\neq
\tsempty
\Rightarrow
\Gamma
\evdash
e t
\Refine
{
e,t
}
\Gamma
\end{align*}
\end{align*}
\end{theorem}
\end{theorem}
...
...
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