### typos

parent da6baca7
 ... ... @@ -183,7 +183,7 @@ subtyping. Probably a consequence of the pandemic. Of course, the new version of the related work section includes now a detailed comparison with the (indeed highly related) chapter 5 of the dissertations, see lines (??-??) and, yes, the function application dissertations, (see: p30l??-??) and, yes, the function application inversion of Kent is, in the spirit, the same as our worra operator (we do not know whether the reviewers noticed that worra'' is an inverted arrow'': read it from right to left). ... ... @@ -195,8 +195,8 @@ should be an intersection instead. As it is stated the current definition seems unsound as the following example shows: $\begin{array}{l} inv(((\True\to\False)\land(\False\to\True))\lor((\True\to\True)\land(\False\to\False))\;,\;\True)=\\ \qquad\Bool\setminus(\True\lor\False)=\\ \qquad\Empty\\ \qquad=\Bool\setminus(\True\lor\False)=\\ \qquad=\Empty\\ \end{array}$ That is, we have applied the formula $inv(\tau_f,\sigma_{our}) = ... ... @@ -310,7 +310,7 @@ prove a more general set of propositions (here, about arbitrary expressions, there, about expressions with a limited set a pure functions, but see below) is also present in both. \begin{answer} Done. See lines (???-???) Done (see: p32l???-???) \end{answer} Similarly the need for an explosion rule in order to circumvent ... ... @@ -319,7 +319,7 @@ difficulties in proofs of type soundness is discussed in {[}22{]}. \begin{answer} We added a long discussion on this point, namely how to handle the type preservation property, in the related work section when comparing with {[}22{]} (see lines: ??-??) comparing with {[}22{]} (see: p29l??-??) More generally, we also went more in depth in the comparison with the logical approach by THF, to highlight further limitations of our ... ... @@ -363,7 +363,7 @@ paper clearer. 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 ??-??) the presence of impure expressions. (see: p32l??-??) \end{answer} ... ... @@ -382,7 +382,7 @@ unneeded: \begin{answer} We added a long discussion to explain the reasons of our choice. It is in the related work section (lines ??-??) when choice. It is in the related work section (see: p29l ??-??) when comparing with {[}22{]} (i.e. Tobin-Hochstadt\&Felleisen 2008). In a nutshell we prefer starting with a system that satisfies type preservation, define a sound but not-complete ... ... @@ -501,7 +501,7 @@ is to show an example that works both in Typed Racket and in our system but it does not in TypeScript and Flow. In the case that this were the correct interpretation of the remark of the reviewer,we added a comment in lines ???-??? comment in p28l???-??? \end{answer} ... ... @@ -565,8 +565,8 @@ type preservation). We rewrote the sentence to be more clear. Section 2.2$\semantic{\neg\empt} =\Domain\setminus\semantic{\empt}=\Domain$. So$\semantic{\empt}$is empty and undef is not in (the interpretation of) \any. We added an explanation (see lines ???-???). In short \texttt{Undef} is a special singleton type interpretation of) \any. We added an explanation (see: p17l???-???). In short \texttt{Undef} is a special singleton type whose interpretation contains only a the constant \texttt{undef} which is not in$\Domain$. \end{answer} ... ... @@ -659,7 +659,7 @@ the new contributions. of refined types appearing in arbitrary places, which is very similar to the first contribution of this work. \begin{answer} Done (lines ??-??) Done (page 31??) \end{answer} An alternative approach followed by refinement type systems is to ANF-transform the programs. A discussion is missing on how these two ... ... @@ -668,7 +668,7 @@ the new contributions. while the two alternatives used by refinement types preserve decidability. \begin{answer} Done (lines ??-??) Done (page 31??) \end{answer} \item ... ... @@ -679,7 +679,7 @@ the new contributions. also presents a set theoretic interpretation), thus a comparison is missing. \begin{answer} Done (lines ??-??) Done (page 31??) \end{answer} \item In 3.3 it is mentioned that we are not aware of any study in this ... ... @@ -691,15 +691,12 @@ the new contributions. The reviewer forgot to include the reference  in the report but we are pretty sure that  must refer to Gradual Liquid Type Inference'' (OOPSLA 2018). We were aware of this work of course Inference'' (OOPSLA 2018). We were aware of this work, of course, but we would not define it an example of integration of gradual and occurrence typing ... and occurrence typing. The connection between them seems incidental. \end{answer} \end{itemize} \begin{answer} We have further developed the our section of the related work on refinement types, using the given references has a starting point. \end{answer} \item \textbf{Meta-theory Clarifications:} ... ... @@ -735,7 +732,7 @@ refinement types, using the given references has a starting point. requires less or none annotations and/or infers more precise types. We substantially expanded the related work section for a better comparison with related work. We also added at the end of Section 4 a new example the we capture and for which Flow and Section 4 a new example that our system captures and for which Flow and TypeScript fail. For what concern the first question, viz., whether the presented ... ... @@ -749,7 +746,8 @@ refinement types, using the given references has a starting point. Racket, by admission of the authors themselves (reviewer 1 can contradict us if we are wrong) uses some not very well documented typing features and heuristics. In any case our proof-of-concept implementation constitute a very poor yardstick in this respect. implementation constitutes a very poor yardstick in this respect, but it never meant to be one. What we can say is how we expect some characteristics of our system to impact on the complexity of the inference. For instance ... ... @@ -760,7 +758,7 @@ refinement types, using the given references has a starting point. corresponds to one pass on the function for each arrow in the intersection.(shall we add such a sentence somewhere?) Likewise ... TO BE CONTINUED BY KIM. Likewise ... TO BE CONTINUED BY KIM (fixpoint, memoization ...). \end{answer} ... ... @@ -781,7 +779,7 @@ refinement types, using the given references has a starting point. mentions$n_o$which does not appear in the theorem statement. \begin{answer} We changed the notation of the judgments so that it now explicitly mentions the${n_o}$(lines ??-??) mentions the${n_o}$(see p15l??-??) \end{answer} \item Section ... ... @@ -938,7 +936,7 @@ failed and that after a couple of months were fixed and magically worked in one or the other. We significantly extended the part in Section 5 where we explain this, by enriching it with the comments above. See lines (???-???) by enriching it with the comments above. See p32l???-???. \end{answer} ... ... @@ -1059,7 +1057,7 @@ should be sound. In general, if you know that$x \in A$and$(A \land \not= \emptyset$, then you certainly can't conclude that$x \in \neg B\$. \begin{answer} We added an explanation and given a reference for a thorough discussion (lines ??-??) discussion (see p10l??-??) \end{answer} \item ... ...
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