Commit a0b39865 by Mickael Laurent

### add some explanations in the appendix

parent ddb415d7
 ... @@ -876,7 +876,12 @@ ... @@ -876,7 +876,12 @@ \subsection{New algorithmic type system with type schemes} \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} \subsubsection{Type schemes} ... @@ -1735,7 +1740,7 @@ theorem for the algorithmic type system presented in \ref{sec:algorules}. ... @@ -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 $e_+$. 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 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) becomes useless: \begin{itemize} \begin{itemize} \item When typing an application $e_1 e_2$, the negative part of the type of $e_1$ \item When typing an application $e_1 e_2$, the negative part of the type of $e_1$ ... ...
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