more revision

conclusion.tex

@@ -43,13 +43,16 @@ made to converge and, foremost, whether it is of use in practice is among our ob
 \fi%
 
 But the real challenges that lie ahead are the handling of side
-effects and the addition of polymorphic types. Our analysis works in a
-pure system and extending it to cope with side-effects is not
-immediate. We plan to do it by defining effect systems---notably, we will try to graft
-the effect system of~\citet{Cha2017} on ours---and/or by
-performing some information flow analysis typically by enriching the
-one we will develop to overcome the limitations above. But our plan is not
-more defined than that. For polymorphism, instead, we can easily adapt
+effects and the addition of polymorphic types.
+\rev{%%%
+Our analysis works in a
+pure system and we already discussed at length at the end of the
+previous section our plans to extend it to
+cope with side-effects. However the
+ultimate solution of integrating type and effect analysis in a unique tool
+is not more defined than that.
+}%%%
+For polymorphism, instead, we can easily adapt
 the main idea of this work to the polymorphic setting. Indeed, the
 main idea  is to remove from the type of an expression all
 the results of the expression that would make some test fail (or

main-elsarticle.tex

@@ -251,7 +251,8 @@ gradual typing.
 %% Acknowledgments
 \subsubsection*{Acknowledgments}   
 \noindent The authors thank Paul-André Melliès for his help on type
-ranking and Sam Tobin-Hochstadt for his feedback and useful insight.
+ranking and Sam Tobin-Hochstadt and the other reviewers for their
+feedback and useful insight.
   
   This research was partially supported by Labex DigiCosme (project ANR-11-LABEX-0045-
   DIGICOSME) operated by ANR as part of the program «Investissement d'Avenir» Idex
@@ -259,7 +260,6 @@ ranking and Sam Tobin-Hochstadt for his feedback and useful insight.
 
 
 
-\newpage
 %% Bibliography
  \bibliographystyle{ACM-Reference-Format}
  \bibliography{main}

related.tex

@@ -287,14 +287,14 @@ formalizing it in our system.
  
 \rev{%%%
 We end this presentation of related work with a discussion on side
-effects. Even if in our system we did not take into account
+effects. Although in our system we did not take into account
 side-effects---and actually our system works because all the expressions
 of our language are pure---it is interesting to see how the different
-approaches of gradual typing position themselves with respect to the problem of
-handling side-effects, since this helps to better position our work in the taxonomy
-of the current litterature. As Sam Tobin-Hochstadt insightfully
+approaches of occurrence typing position themselves with respect to the problem of
+handling side effects, since this helps to better place our work in the taxonomy
+of the current literature. As Sam Tobin-Hochstadt insightfully
 noticed, one can distinguish the approaches that use types to reason about
-the dynamic behaviour of programs according to the set of expressions
+the dynamic behavior of programs according to the set of expressions
 that are taken into account by the analysis. In the case of occurrence
 typing, this set is often determined by the way impure expressions are
 taken into account. On one end of the spectrum lies our approach: our
@@ -306,22 +306,47 @@ accessors). Somewhere in-between lies the approach of the
 Flow language which, as hinted above, implements a complex effect systems to determine
 pure expressions. While the system presented here does not work for
 impure languages, we argue that its foundational nature predisposes it
-to be adapted to handle impure expression, by adopting existing
-solutions or providing new ones. For instance, it is not hard to
+to be adapted to handle impure expressions as well, by adopting existing
+solutions or proposing new ones. For instance, it is not hard to
 modify our system so that it takes into account only a set of
 predetermined pure expressions, as done by Typed Racket: it suffices
 to modify the definition of $\Gamma \evdash e
 {(\neg)t} \Gamma'$ (cf.\ Section~\ref{sec:static}) so that $\Gamma'$
 extends $\Gamma$ with type hypotheses for all expressions occurring in
 $e$ that are also in the set of predetermined pure expressions
-(instead of for all subexpressions of $e$, tout court).
-However such a solution would be mildly interesting since by excluding
-from the analysis all functions application we would lose most of the
-advantages of our approach with respect to the one of logical
-propositions. 
-
-
-
-
-
+(instead of extending it for all subexpressions of $e$, \emph{tout court}).
+However, such a solution would be marginally interesting since by excluding
+from the analysis all applications we would lose most of the
+advantages of our approach with respect to the one with logical
+propositions. Thus a more interesting solution would be to use some
+external static analysis tools---e.g., to graft
+the effect system of~\citet{Cha2017} on ours---to detect impure
+expressions. The idea would be to mark different occurrences of a same
+impure expression using different marks. These marks would essentially
+be used to verify the presence of type hypotheses for a given
+expression in a type environment $\Gamma$; the idea being that
+expressions with different marks are to be considered as different
+expressions and, therefore, would not share the same type
+hypothesis. For instance, consider the test
+$\ifty{f\,x}\Int{\,...\,}{\,...}$: if $f x$ were flagged as impure
+then the occurrence of $f x$ in the ``then'' branch would not be
+supposed to be of type $\Int$ since it would be typed in an
+environment $\Gamma$ containing a binding for an $f\,x$ expression
+having a mark different from the one in the ``then'' branch: the
+regular typing rules would apply for $f\, x$ in that case. This
+would certainly improve our analysis, but we believe that ultimately
+our system should not resort to external static analysis tools to detect
+impure expressions but, rather, it should integrate this analysis with
+the typing one, so as to mark \emph{only} those impure expression
+whose side-effects may affect the semantics of some type-cases. For
+instance, consider a JavaScript object \code{obj} that we modify as
+follows \code{obj["key"] = 3}. If the field \code{"key"} is already
+present in \code{obj} with type \Int{} and we do not test it more than
+about this type, then it is not necessary to mark different
+occurrences of \code{obj} with different marks, since the result of
+the type-case would not be changed by the assignment; the same holds
+true if the field is absent but type-cases do not discriminate on its
+presence. Otherwise, some occurrences of \code{obj} must use different
+marks: the analysis will determine which ones. We leave this study for
+future work.
 }%%%rev

scp-reviews-2108.tex

@@ -71,7 +71,9 @@ discussion to compare our work with Andrew Kent dissertation, we
 greatly increased the comparison of our work with the \emph{logical
 proposition} approach of Typed Racket to better stress the limitation
 of our approach and discussed at length some technical choices that
-distinguish our approach from current ones.
+distinguish our approach from current ones. We also positioned our
+work in the design space of occurrence typing systems in particular
+w.r.t. the handling of side effects.
 \end{answer}
 
 \section{Reviewer \#1:}
@@ -176,10 +178,10 @@ in light of the topic and of the fact that it heavily relies on semantic
 subtyping. Probably a consequence of the pandemic.
 
 Of course, the new version of the related work section includes now a
-detailed comparaison with the (highly related) chapter 5 of the
+detailed comparaison with the (indeed highly related) chapter 5 of the
 dissertations, see lines (??-??) and, yes, the function application
 inversion of Kent is, in the spirit, the same as our worra operator
-(we do not know whether the reviewer noticed that ``worra'' is an
+(we do not know whether the reviewers noticed that ``worra'' is an
 inversed ``arrow'': read it from right to left).
 About that, we take the opportunity that the reviewer disclosed the fact
 that he is Kent's supervisor to signal a small error that we think we
@@ -194,7 +196,9 @@ inv(((\True\to\False)\land(\False\to\True))\lor((\True\to\True)\land(\False\to\F
 \end{array}
 \]
 
-However, a function with a type $((\True\to\False) land (\False\to\True)) \lor ((\True\to\True)\land(\False\to\False))$ could definitively give a result in $\True$. The correct result should be \Bool.
+However, a function with a type $((\True\to\False) \land
+(\False\to\True)) \lor ((\True\to\True)\land(\False\to\False))$ may
+definitively yield a result in $\True$ or in $\False$. The correct result should be \Bool.
 
 
 The proof in Coq of the soundness of this definition given in the
@@ -314,7 +318,7 @@ potential dynamic behavior of terms in the way done with occurrence
 typing will need to decide \emph{which} terms the type system should
 take note of, and what equations it will use over those terms. For
 example, if we have the expression
-\texttt{(f\ x) $\in$ (1,\ 1)}, should that refine the
+\texttt{(f\ x) $\in$ (1,1)}, should that refine the
 type of \texttt{(g\ x)}? Possible questions to ask here are: is
 \texttt{f} pure? Is \texttt{f} syntactically equal to \texttt{g}? Can we
 prove that \texttt{f} and \texttt{g} are equivalent?
@@ -339,9 +343,10 @@ paper clearer.
 
 
 \begin{answer}
-Beppe: say that our approach in some sense subsumes the two others. Add
-a part of related work discussing about pure expressions. Use (not
-verbatim) the rebuttal of POPL. Thanks for the insight
+This is a very nice insight. We reproduced it (giving credits) in the
+section on related work, which now ends with a long discussion on the
+design space w.r.t. side effects and on our future plans to cope with
+the presence of impure expressions. (lines ??-??)
 \end{answer}
 
 
@@ -495,7 +500,7 @@ type preservation). We rewrote the sentence to be more clear.
         interpretation of) \any. We added an explaination (see lines
         ???-???). In short \texttt{Undef} is a special singleton type
         whose intepretation contains only a the
-        constant \texttt{undef} which is not in D.
+        constant \texttt{undef} which is not in $\Domain$.
    \end{answer}
 
 \item