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Giuseppe Castagna
occurrence-typing
Commits
1a5361ee
Commit
1a5361ee
authored
Nov 24, 2020
by
Mickael Laurent
Browse files
fix
parent
10412c32
Changes
1
Hide whitespace changes
Inline
Side-by-side
new_system3.tex
View file @
1a5361ee
...
...
@@ -332,8 +332,8 @@ rules, because one branch is already unreachable and retyping only occurs with s
\\
\Infer
[Pair]
{
\forall
i
\in
I.
\ \Gamma
_
1
^
i =
\
subst
{
x
_
1
}{
t
_
i
}
\\
\forall
i
\in
I.
\ \Gamma
_
2
^
i =
\
subst
{
x
_
2
}{
s
_
i
}
\forall
i
\in
I.
\ \Gamma
_
1
^
i =
\{
x
_
1
:
t
_
i
\
}\\
\forall
i
\in
I.
\ \Gamma
_
2
^
i =
\{
x
_
2
:
s
_
i
\
}
}
{
\Gamma\bvdash
{
(x
_
1,x
_
2)
}
{
\bigcup
_{
i
\in
I
}
(t
_
i,s
_
i)
}
\textstyle\bigcup
_{
i
\in
I
}
\{\Gamma
_
1
^
i
\land\Gamma
_
2
^
i
\}
}
{
}
...
...
@@ -352,8 +352,8 @@ rules, because one branch is already unreachable and retyping only occurs with s
{
\Gamma
(x
_
1)
\equiv\textstyle\bigvee
_{
i
\in
I
}
\textstyle\bigwedge
_{
j
\in
J
_
i
}
\arrow
{
s
_
j
}{
t
_
j
}
\\
\forall
i
\in
I.
\ \worra
{
(
\textstyle\bigwedge
_{
j
\in
J
_
i
}
\arrow
{
s
_
j
}{
t
_
j
}
)
}
t = s
_
i'
\\
\forall
i
\in
I.
\ \Gamma
_
1
^
i =
\
subst
{
x
_
1
}{
\textstyle\bigwedge
_{
j
\in
J
_
i
}
\arrow
{
s
_
j
}{
t
_
j
}}
\\
\forall
i
\in
I.
\ \Gamma
_
2
^
i =
\
subst
{
x
_
2
}{
s
_
i'
}
\forall
i
\in
I.
\ \Gamma
_
1
^
i =
\{
x
_
1
:
\textstyle\bigwedge
_{
j
\in
J
_
i
}
\arrow
{
s
_
j
}{
t
_
j
}
\
}\\
\forall
i
\in
I.
\ \Gamma
_
2
^
i =
\{
x
_
2
:
s
_
i'
}
}
{
\Gamma\bvdash
{
(x
_
1
\
x
_
2)
}
{
t
}
\textstyle\bigcup
_{
i
\in
I
}
\{\Gamma
_{
1
}^
i
\land\Gamma
_{
2
}^
i
\}
...
...
@@ -440,8 +440,8 @@ $x$ is supposed to be included into $t_x$ or $\neg t_x$.
\\
\Infer
[Pair]
{
\forall
i
\in
I.
\ \Gamma
_
1
^
i =
\
subst
{
x
_
1
}{
t
_
i
}
\\
\forall
i
\in
I.
\ \Gamma
_
2
^
i =
\
subst
{
x
_
2
}{
s
_
i
}
\forall
i
\in
I.
\ \Gamma
_
1
^
i =
\{
x
_
1
:
t
_
i
\
}\\
\forall
i
\in
I.
\ \Gamma
_
2
^
i =
\{
x
_
2
:
s
_
i
\
}
}
{
\Gamma\fvdash
{
(x
_
1,x
_
2)
}
{
\bigcup
_{
i
\in
I
}
(t
_
i,s
_
i)
}
\textstyle\bigcup
_{
i
\in
I
}
\{\Gamma
_
1
^
i
\land\Gamma
_
2
^
i
\}
}
{
}
...
...
@@ -458,12 +458,13 @@ $x$ is supposed to be included into $t_x$ or $\neg t_x$.
\\
\Infer
[App]
{
\Gamma
(x
_
1)
\btr
t = s
\\
\Gamma
_
1 =
\subst
{
x
_
1
}{
\Gamma
(x
_
1)
}
\\
\Gamma
_
2 =
\subst
{
x
_
2
}{
s
}
\Gamma
(x
_
1)
\equiv\textstyle\bigvee
_{
i
\in
I
}
\textstyle\bigwedge
_{
j
\in
J
_
i
}
\arrow
{
s
_
j
}{
t
_
j
}
\\
\forall
i
\in
I.
\
(
\textstyle\bigwedge
_{
j
\in
J
_
i
}
\arrow
{
s
_
j
}{
t
_
j
}
)
\btr
t = s
_
i'
\\
\forall
i
\in
I.
\ \Gamma
_
1
^
i =
\{
x
_
1:
\textstyle\bigwedge
_{
j
\in
J
_
i
}
\arrow
{
s
_
j
}{
t
_
j
}
\}\\
\forall
i
\in
I.
\ \Gamma
_
2
^
i =
\{
x
_
2:s
_
i'
\}
}
{
\Gamma\
f
vdash
{
(x
_
1
\
x
_
2)
}
{
t
}
\{\Gamma
_{
1
}
\land\Gamma
_{
2
}
\}
\Gamma\
b
vdash
{
(x
_
1
\
x
_
2)
}
{
t
}
\textstyle\bigcup
_{
i
\in
I
}
\{\Gamma
_{
1
}
^
i
\land\Gamma
_{
2
}
^
i
\}
}
{
}
\\
...
...
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