### fix compilation

 ... ... @@ -444,10 +444,28 @@ require two distinct technical solutions. The first origin is the rule \Rule{Abs-} by which it is possible to deduce for every well-typed lambda abstractions infinitely many types, that is the annotation of the function intersected with as many negations of arrow types as it is possible without making the type empty. To handle this multiplicity we use the technique of \emph{type schemes} defined by~\citet{Frisch2004}. Type schemes are canonical representations of the infinite set of types of $\lambda$-abstraction and they are presented in Section~\ref{sec:type-schemes}. The second origin is due to the presence of structural rules\footnote{In logic, logical rules refer to a particular connective (here, a type constructor, that is, either $\to$, or $\times$, or $b$), while identity rules (e.g., axioms and cuts) and structural rules (e.g., weakening and contraction) do not.} such as \Rule{Subs} and \Rule{Intersect}. We handle it in the classic way: we define an algorithmic system that tracks the miminum type (actually, type scheme) of an expression which is obtained from the original system by eliminating the two structural rules and distrubuting checks of the subtyping relation is possible without making the type empty. To handle this multiplicity we use the technique of \emph{type schemes} defined by~\citet{Frisch2004}. Type schemes are canonical representations of the infinite set of types of $\lambda$-abstraction and they are presented in Section~\ref{sec:type-schemes}. The second origin is due to the presence of structural rules\footnote{In logic, logical rules refer to a particular connective (here, a type constructor, that is, either $\to$, or $\times$, or $b$), while identity rules (e.g., axioms and cuts) and structural rules (e.g., weakening and contraction) do not.} such as \Rule{Subs} and \Rule{Intersect}. We handle it in the classic way: we define an algorithmic system that tracks the miminum type (actually, minimum type scheme) of an expression which is obtained from the original system by eliminating the two structural rules and distrubuting checks of the subtyping relation in the remaining rules. To do that in the presence of set-theoretic types we need to define some operators on types, given in section~\ref{sec:typeops}. For what concerns the use of the auxiliary derivation for the  judgments, we present in Section~\ref{sec:typenv} an algorithm that we prove sound \beppe{and complete?}. All these notions are used in the algorithmic typing system given in Section~\ref{sec:algorules}. \begin{enumerate} \item type of functions -> type schemes ... ... @@ -477,5 +495,5 @@ change the definition of typeof to take into account type-schemes for lambda abs \subsection{Algorithmic typing rules}\label{sec \subsection{Algorithmic typing rules}\label{sec:algorules}