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Giuseppe Castagna
occurrence-typing
Commits
a0b39865
Commit
a0b39865
authored
Feb 25, 2020
by
Mickael Laurent
Browse files
add some explanations in the appendix
parent
ddb415d7
Changes
1
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proofs.tex
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a0b39865
...
...
@@ -876,7 +876,12 @@
\subsection
{
New algorithmic type system with type schemes
}
TODO: Why do we introduce type schemes?
As explained in TODO, we introduce for the proofs the notion of
\emph
{
types schemes
}
and we define a new (more powerful) algorithmic type system that uses them.
It allows us to have a stronger (but still partial) completeness theorem.
The proofs for the algorithmic type system presented in
\ref
{
sec:algorules
}
can be derived
from the proofs of this section (see section
\ref
{
sec:proofs
_
algorithmic
_
without
_
ts
}
).
\subsubsection
{
Type schemes
}
...
...
@@ -1735,7 +1740,7 @@ theorem for the algorithmic type system presented in \ref{sec:algorules}.
We can prove it by induction over the structure of
$
e
_
+
$
.
The main idea of this proof is that, as
$
e
_
+
$
is a positive expression, the rule
\Rule
{
Abs-
}
is not needed anymore
because the negative part of functional types (i.e. the
$
N
_
i
$
part of their DNF) become useless:
because the negative part of functional types (i.e. the
$
N
_
i
$
part of their DNF) become
s
useless:
\begin{itemize}
\item
When typing an application
$
e
_
1
e
_
2
$
, the negative part of the type of
$
e
_
1
$
...
...
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