decide this relation can be found in~\cite{Cas15}. For the reader's

convenience we succintly recall the definition of the subtyping

relation in the next subsection but it is possible to skip this subsection at first reading andjump directly to Subsection~\ref{sec:syntax}, since to understand

relation in the next subsection but it is possible to skip this

subsection at first reading and jump directly to Subsection~\ref{sec:syntax}, since to understand

the rest of the paper

\else

to which the reader may refer for the formal

...

...

@@ -265,7 +266,18 @@ $(\Int\to t)\setminus(\Int\to\neg\Bool)$, that is, $(\Int\to t)\wedge\neg(\Int\t

}%%%rev

But the sole rule \Rule{Abs+}

above does not allow us to deduce negations of

arrows for $\lambda$-abstractions: the rule \Rule{Abs-} makes this possible. As an aside, note that this kind

arrows for $\lambda$-abstractions: the rule \Rule{Abs-} makes this

possible.

\rev{%%%%

This rule ensures that given a function $\lambda^t x.e$ (where $t$

is an intersection type), for every type $t_1\to t_2$, either

$t_1\to t_2$ can be obtained by subsumption from $t$ or $\neg(t_1\to

t_2)$ can be added to the intersection $t$. In turn this ensures

that, for any function and any type $t$ either the function has type

$t$ or it has type $\neg t$ (see~\citet[Sections 3.3.2 and

3.3.3]{Pet19phd} for a thorough discussion on this rule).

}%%%rev

As an aside, note that this kind

of deduction is already present in the system by~\citet{Frisch2008}

though in that system this presence was motivated by the semantics of types rather than, as in our case,