\section{Introduction}
The characterization of the provable recursive functions of
Peano Arithmetic as the terms of system T is a well known
-result of G\"odel \cite{Godel58,Godel90}. Although many authors acknowledge
+result of G\"odel \cite{Godel58,Godel90}. Although several authors acknowledge
that the functional interpretation of the Dialectica paper
is not among the major achievements of the author (see e.g. \cite{Girard87}),
the result has been extensively investigated and there is a wide
Girard's System $F$ \cite{Girard86}, but the technical complexity and
the didactical value of the two proofs is not comparable: when you
prove that the Induction Principle is realized by the recursor $R$
-of system $T$ you catch a sudden gleam of intelligence in the
+of system $T$ you catch a sudden gleam of understanding in the
students eyes; usually, the same does not happen when you show, say,
that the ``forgetful'' intrepretation of the higher order predicate defining
the natural numbers is the system $F$ encoding