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parent f2e04704
 ... ... @@ -253,7 +253,12 @@ cases. \subsubsection{Algorithmic typing rules}\label{sec:algorules} We now have all the notions we need for our typing algorithm, which is defined by the following rules. We now have all the notions we need for our typing algorithm% \iflongversion% , which is defined by the following rules. \else% : \fi \begin{mathpar} \Infer[Efq\Aa] { } ... ...
 ... ... @@ -197,7 +197,7 @@ arrow types, as long as these negated types do not make the type deduced for the \Infer[Abs-] {\Gamma \vdash \lambda^{\wedge_{i\in I}\arrow {s_i} {t_i}}x.e:t} { \Gamma \vdash\lambda^{\wedge_{i\in I}\arrow {s_i} {t_i}}x.e:\neg(t_1\to t_2) } { ((\wedge_{i\in I}\arrow {s_i} {t_i})\wedge\neg(t_1\to t_2))\not\simeq\Empty }\vspace{-1mm} { ((\wedge_{i\in I}\arrow {s_i} {t_i})\wedge\neg(t_1\to t_2))\not\simeq\Empty }\vspace{-1.2mm} \end{mathpar} %\beppe{I have doubt: is this safe or should we play it safer and % deduce $t\wedge\neg(t_1\to t_2)$? In other terms is is possible to ... ... @@ -228,7 +228,7 @@ integer returns its successor and applied to anything else returns %$\lambda^{(\Int\to\Int)\wedge(\neg\Int\to\Bool)} x\,.\,\tcase{x}{\Int}{x+1}{\textsf{true}} %$ \)}\\[1mm] \)}\\[.6mm] Clearly, the expression above is well typed, but the rule \Rule{Abs+} alone is not enough to type it. In particular, according to \Rule{Abs+} we have to prove that under the hypothesis that $x$ is of type $\Int$ the expression ... ... @@ -253,7 +253,7 @@ expression whose type environment contains an empty assumption: \end{mathpar} Once more, this kind of deduction was already present in the system by~\citet{Frisch2008} to type full fledged overloaded functions, though it was embedded in the typing rule for the type-case.\pagebreak though it was embedded in the typing rule for the type-case.~\pagebreak Here we need the rule \Rule{Efq}, which is more general, to ensure the property of subject reduction. ... ...
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