more revision

language.tex

@@ -259,7 +259,7 @@ system to satisfy the property of type preservation, the type system
 must be able to deduce negated arrow types for functions---e.g. the
 type $(\Int\to\Int)\wedge\neg(\Bool\to\Bool)$ for $\lambda^{\Int\to\Int}
 x.x$. We demonstrated this with the expression in
-equation \eqref{bistwo}, where type preservation holds only if we are
+equation \eqref{bistwo}, for which type preservation holds only if we are
 able to deduce for this expression the type
 $(\Int\to t)\setminus(\Int\to\neg\Bool)$, that is, $(\Int\to t)\wedge\neg(\Int\to\neg\Bool)$.
 }%%%rev

related.tex

@@ -66,6 +66,53 @@ for recursive types.}
 %one performed by Code 8 for extensible records is not handled by the
 %current typing systems.
 
+
+\rev{%%%
+For what concerns the first work by~\citet{THF08} it is interesting to
+compare this work with ours because the comparison shows two rather
+different approaches to deal with the property of type
+preservation. \citet{THF08} define a first type-system that does not
+satisfy type-preservation. The reason for that is that this first type
+system checks all the branches of a type-case expression,
+independently from whether they are selectable or not, and this may
+result in a well-typed expression to reduces to an expression that it
+is not well-typed because it contains a type-case expression that,
+because of the reduction, has a branch that became non-selectable but
+also ill-typed (see \cite[Section 3.3]{THF08}). To obviate this
+problem they introduce a \emph{second} type system that extends the
+previous one with some auxiliary typing rules that type type-case
+expressions by skipping the typing of non selectable-branches and use
+this second type-system only to prove type-preservation and obtain,
+thus the soundness of their type system. In our work, instead, we
+prefer to start directly with a system that satisfies
+type-preservation. Our system does not have the problem of their first
+system because we included the \Rule{Efq} rule for that very purpose,
+that is skip the typing of non-selectable branches. The choice of one
+or the other approach is a matter of taste and, in this specific case,
+it boils down to deciding
+whether some typing problems must be statically signalled by an error or a
+warning. The approach of~\citet{THF08} ensures that every
+subexpression of a program is well-typed and, if not, it generates a
+type-error. Our approach allows some subexpression of a program to be ill-typed,
+but only if they occurr in dead branches of type-cases. But in that case case any
+reasonable implementation would flag a warning to signal the presence
+of a dead branch. The very same reasons that explain the presence of \Rule{Eqf}
+explain why in our system we included from the beginning the typing
+rule \Rule{Abs-}
+to deduce negated arrow types: we want a system that satisfies type
+preservation (albeit, for a parallel reduction:
+cf: \Appendix\ref{app:parallel}). We then defined an algorithmic
+system that is not \emph{complete} with respect to the type-system but
+from which it inherits its soundness. Of course we could have started
+directly with a type-system corresponding to the algorithm (i.e., not
+include the rule \Rule{Abs-}) and then extend this system with the
+inference of negated arrows, to prove type preservation. ... the
+advantage is that we can explore different subsystems that are
+complete and argue that they are all we need in practice ....
+
+
+}%%%rev
+
 Another direction of research related to ours is the one of semantic
 types. In particular, several attempts have been made recently to map
 types to first order formul\ae. In that setting, subtyping between

scp-reviews-2108.md

@@ -111,9 +111,14 @@ 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. Similarly the need for an explosion
 rule in order to circumvent difficulties in proofs of type soundness
-is discussed in [22]. 
->> Kim: compare the rules added in Figure 6 of THF2008 and justified in section 3.3 with
->> the fact that we use ex-falso quodlibet 
+is discussed in [22].
+
+>> Kim: compare the rules added in Figure 6 of THF2008 and justified
+>> in section 3.3 with the fact that we use ex-falso quodlibet. We can
+>> add that like 
+>> THF2008 we use a different system since we have to use type-schemes
+>> (see Appendix A.3.2), but also a different reduction since we use
+>> parallel reductions 
 
 ## Discussion of pure expressions
 
@@ -160,7 +165,9 @@ seem unneeded:
   schemes. Why not simply present the system that's actually
   implemented, which as the paper says is all that is really needed.
   
->> Beppe; answer on the interest of the fully complete system  
+>> Beppe; answer on the interest of the fully complete system (and
+   stress en passant that type schemes are needed to prove
+   type-preservation   
   
   
 - the treatment of interdependent tests. Is this needed for any real