-\TODO{FINQUI, il resto \`e copy and paste dal Whelp paper \dots}
-
-Note that given a content level term with more than one sources of ambiguity,
-not all possible disambiguation choices are valid: for example, given the input
-\texttt{1+1} we must choose an interpretation of \texttt{+} which is typable in
-CIC according to the chosen interpretation for \texttt{1}; choosing as
-\texttt{+} the addition over natural numbers and as \texttt{1} the real number
-$1$ will lead to a type error.
-
-A \emph{disambiguation algorithm} takes as input an ambiguous term and return a
-fully determined CIC term. The \emph{naive disambiguation algorithm} takes as
-input an ambiguous term $t$ and proceeds as follows:
+Evaluating it in \MATITA{} will add an operator interpretation function for the
+binary operator \texttt{eq} which expands to the CIC term on the right hand side
+of the statement. That CIC term can be written using only built-in concrete
+syntax, can contain no ambiguity source; still, it can refer to operator
+arguments bound on the left hand side and can contain implicit terms (denoted
+with \texttt{\_}) which will be expanded to fresh metavariables. The latter
+feature is used in the example above for the first argument of Leibniz's
+polymorhpic equality.
+
+\subsubsection{Disambiguation algorithm}
+
+\NOTE{assumo\\
+ che si sia\\
+ gia' parlato\\
+ di refine}
+
+
+A \emph{disambiguation algorithm} takes as input a content level term and return
+a fully determined CIC term. The key observation on which a disambiguation
+algorithm is based is that given a content level term with more than one sources
+of ambiguity, not all possible combination of interpretation lead to a typable
+CIC term. In the term of Ex.~\ref{ex:disambiguation} for instance the
+interpretation of \texttt{ln} as a function from \IR to \IR and the
+interpretation of \texttt{1} as the Peano number $1$ can't coexists. The notion
+of ``can't coexists'' in the disambiguation of \MATITA{} is inherited from the
+refiner described in Sect.~\ref{sec:metavariables}: as long as
+$\mathit{refine}(c)\neq\bot$, the combination of interpretation which led to $c$
+can coexists.
+
+The \emph{naive disambiguation algorithm} takes as input a content level term
+$t$ and proceeds as follows: