Commit 53826a2d authored by Giuseppe Castagna's avatar Giuseppe Castagna
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typos

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latexmk -pdf -bibtex main.tex
latexmk -pdf -bibtex main-elsarticle.tex
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......@@ -37,7 +37,7 @@ Occurrence typing was first defined and formally studied by
programs,\footnote{%
According to Sam Tobin-Hochstadt, the terminology \emph{occurrence
typing} was first used in a simplistic form by~\citet{Komon05},
although he was not aware of it the at the moment of
although he and Felleisen were not aware of it the at the moment of
the writing of~\cite{THF08}.}
and later extended by \citet{THF10}
yielding the development of Typed Racket. From its inception,
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......@@ -30,8 +30,9 @@ memoization environment in the code of the $\Refine {e,t}{\Gamma}$
function, which allows the inference to avoid unnecessary traversals
of $e$.
Lastly, while our prototype allows the user to specify a particular
value for the $n_0$ parameter, the default value of $1$ is sufficient
to check all examples we present in the following sections.
value for the $n_o$ parameter we introduced in
Section~\ref{sec:typenv}, a value of $1$ for $n_o$ is sufficient
to check all examples we present in the rest of the section.
}
\subsection{Experiments}
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......@@ -364,28 +364,30 @@ test how much of their analysis we can capture and enhance by
formalizing it in our system.
\nocite{typescript,flow}
\rev{%%%
More generally, we believe that what sets apart our work in the
palimpsest of the research on occurrence typing is that we have a type-theoretic
foundational approach striving as much as possible to explain
occurrence typing by extending prior (unrelated but standard) work
while keeping prior results. In that respect, we think that our
More generally, we believe that what sets our work apart in the
palimpsest of the research on occurrence typing is that we have a
type-theoretic foundational approach striving as much as possible to
explain occurrence typing by extending prior (unrelated but standard)
work while keeping prior results. In that respect, we think that our
approach is not satisfactory, yet, because it uses non standard
type-environments that map expressions rather than variables to
types: but all the rest is standard type-theory. And even on the latter
type-environments that map expressions rather than variables to types:
but all the rest is standard type-theory. And even on the latter
aspect it must be recognized that the necessity of tracking types not
only for variables but also for more structured expressions is
something that shows up, in different forms, in several other
approaches. For instance, in the approach defined for Typed
Racket~\cite{THF10} the type-system associates to an expression a
quadruple formed by its type, two logical propositions, and an object which is
a pointer to the environment for the type hypothesis about the
expression and, as such, it plays the role of our extended type
quadruple formed by its type, two logical propositions, and an object
which is a pointer to the environment for the type hypothesis about
the expression and, as such, it plays the role of our extended type
environments. Likewise, the \emph{selfification} of \cite{OTMW04}
and \cite{KF09}, propagates the precise type constraints learned
during a test. However, in the latter, whole the information can be
kept at the type level, since dependent types contains terms and can
introduce variables, while in our approach the mapping is kept in an environment.
Nevertheless, we are confident that even this last non-standard aspect
introduce variables, while in our approach the mapping is kept in an
environment. The tracking of types for structured expressions thus
seems a common aspect of different approaches to occurrence types,
nevertheless we are confident that even this last non-standard aspect
of our system can be removed and that occurrence typing can be
explained in a pure standard type-theoretic setting.
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