spacing

algorithm.tex

@@ -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]
   { }

language.tex

@@ -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.