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Giuseppe Castagna
occurrencetyping
Commits
26fbc9c0
Commit
26fbc9c0
authored
Jul 10, 2019
by
Giuseppe Castagna
Browse files
rewording
parent
082e483e
Changes
5
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conclusion.tex
View file @
26fbc9c0
...
...
@@ 68,6 +68,6 @@ positive branch the types of $x_1$, of $x_2$, and of $x_1x_2$ by applying $\sigm
idea is clear (see Appendix~
\ref
{
app:roadmap
}
for a more detailed explanation),
the technical details are quite involved, especially when considering
functions typed by intersection types and/or when integrating gradual
typing. This
deserve
s a whole
pan
of non trivial research that we plan to
typing. This
need
s a whole
gamut
of non trivial research that we plan to
develop in the near future.
gradual.tex
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26fbc9c0
...
...
@@ 92,7 +92,7 @@ other words, if a function expects an argument of type $\tau$ but can be
typed under the hypothesis that the argument has type
$
\tauUp
$
, then no casts
are needed, since every cast that succeeds will be a subtype of
$
\tauUp
$
. Taking advantage of this property, we modify the rule for
functions as:
functions as:
\vspace
{
2mm
}
%
%\begin{mathpar}
% \Infer[Abs]
...
...
@@ 115,7 +115,7 @@ functions as:
}
{
\Gamma\vdash\lambda
x:
\sigma
'.e:
\textstyle\bigwedge
_{
(
\sigma
,
\tau
)
\in
T
}
\sigma\to
\tau
}
}
\vspace
{

2
mm
}
\]
The main idea behind this rule is the same as before: we first collect all the
information we can into
$
\psi
$
by analyzing the body of the function. We then
...
...
practical.tex
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26fbc9c0
...
...
@@ 17,7 +17,7 @@ function but not whether it has a specific function type (\emph{cf.}, Footnote~\
implementation becomes complete (see Corollary~
\ref
{
app:completeness
}
in the appendix for a formal proof).
Our implementation is written in OCaml and uses CDuce as a library to
provide the semantic sub

typing machinery. Besides a typechecking
provide the semantic subtyping machinery. Besides a typechecking
algorithm defined on the base language, our implementation supports
record types (Section
\ref
{
ssec:struct
}
) and the refinement of function types
(Section
\ref
{
sec:refining
}
with the rule of Appendix~
\ref
{
app:optimize
}
). The implementation is rather crude and
...
...
@@ 25,8 +25,12 @@ consist of 2000 lines of OCaml code, including parsing, typechecking
of programs, and pretty printing of types. We demonstrate the output of
our typechecking implementation in Table~
\ref
{
tab:implem
}
. These
examples and others can be tested in the online toplevel available at
\url
{
https://occtyping.github.io/
}
(the corresponding repository is
\url
{
https://occtyping.github.io/
}
%
\ifsubmission
~(the corresponding repository is
anonymized).
\else
.
\fi
\input
{
code
_
table
}
In this table, the second column gives a code fragment and the third
column the type deduced by our implementation. Code~1 is a
...
...
@@ 70,8 +74,8 @@ parameter by \Bool{} (which in CDuce is syntactic sugar for
\True
$
\vee
$
\False
) yielding the type
$
(
\True
{
\to
}
\False
)
\wedge
(
\False
{
\to
}
\True
)
$
.
The
\texttt
{
or
\_
}
connective (Code~5) is straightforward as far as the
code goes, but we see that the overloaded type precisely capture all
the
possible cases. Again we use a generalized version of the
code goes, but we see that the overloaded type precisely capture
s
all
possible cases. Again we use a generalized version of the
\texttt
{
or
\_
}
connective that accepts and treats any value that is not
\texttt
{
true
}
as
\texttt
{
false
}
and again, we could easily restrict the
domain to
\Bool
{}
if desired.
...
...
related.tex
View file @
26fbc9c0
...
...
@@ 33,7 +33,7 @@ Section~\ref{sec:practical}. Second, in our setting, {\em types\/} play
the role of formulæ. Using settheoretic types, we can express the
complex types of variables without resorting to a metalogic. This
allows us to type all but two of their key examples (the notable
exceptions being Example~8 and 14 which use the propagation of type
exceptions being Example~8 and 14
in their paper,
which use the propagation of type
information outside of the branches of a test). Also, while they
extend their core calculus with pairs, they only provide a simple
{
\tt
cons?
}
predicate that allows them to test whether some value is a
...
...
setup.sty
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26fbc9c0
...
...
@@ 59,7 +59,7 @@
\newcommand
{
\Rule
}
[1]
{
[
\textsc
{
#1
}
]
}
\newcommand
{
\tcase
}
[4]
{
\ensuremath
{
(#1
{
\in
}
#2)
\,\texttt
{
\textup
{
?
}}
\,
#3
\,\texttt
{
\textup
{
:
}}
\,
#4
}}
\newcommand
{
\morecompact
}{
\baselineskip
=
2.8
pt
}
\newcommand
{
\morecompact
}{
\baselineskip
=
9.5
pt
}
\newcommand
{
\tauUp
}{
\tau
^
\Uparrow
}
\newcommand
{
\sigmaUp
}{
\sigma
^
\Uparrow
}
...
...
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