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Giuseppe Castagna
occurrence-typing
Commits
7d2aa75a
Commit
7d2aa75a
authored
Sep 30, 2021
by
Giuseppe Castagna
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parent
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7d2aa75a
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@@ -26,24 +26,24 @@ the argument has type {\tt Number}, and when the output is {\tt false}, the
argument does not. Such information is used selectively
in the ``then'' and ``else'' branches of a test.
\rev
{
%%%%
Since
\citet
{
THF10
}
focus the
y
analysis on a particular set of pure
operations, the
ir
approach works also in the presence of side-effects. Although
the choices made by our and their approach seem
s diametrically opposed
(
the
Boolean output of few pure operations vs.
\
any output of
an
y
Since
\citet
{
THF10
}
focus the
ir
analysis on a particular set of pure
operations, the approach works also in the presence of side-effects. Although
the choices made by our and their approach seem
poles apart
(Boolean output of few pure operations vs.
\
any output of
ever
y
expression), they share some similar techniques. For instance, our
deduction system for
$
\vdashp
$
plays a similar role as
the proof systems and
\textsf
{
update
}
function of
\citet
[Figures 4,
7
\&
9]
{
THF10
}
. In that framework,
when one needs
to type a variable
(judgeme
t
n ``
$
\Gamma
\vdash
x:
\tau
$
'')
,
one
has to be able
to prove
7
\&
9]
{
THF10
}
. In that framework,
in order
to type a variable
(judgemen
t
``
$
\Gamma
\vdash
x:
\tau
$
'') one
needs
to prove
that the logical formula
$
\tau
_
x
$
holds (under the hypotheses of
$
\Gamma
$
). This atomic formula may not be directly available in
$
\Gamma
$
but may
be proven by a combination of logical deduction rules (Figure~4), or
by recursively exploring a path leading to
$
x
$
(Figure~7 and ~9) a
be proven by a combination of logical deduction rules (Figure~4
of~
\cite
{
THF10
}
), or
by recursively exploring a path leading to
$
x
$
(Figure~7 and ~9
of~
\cite
{
THF10
}
) a
path being a sequence of
\textbf
{
cdr
}
or
\textbf
{
car
}
applications,
much like our
$
f
$
and
$
s
$
components of paths. This idea is also
present in our
$
\vdashp
$
with differences pertaining to our type
framework and design choices
: type restrictions can be encoded using
present in our
deduction system for
$
\vdashp
$
with differences pertaining to our type
framework and design choices: type restrictions can be encoded using
set-theoretic intersections and negations (instead of meta-functions working on the
syntax of types) and our richer language of paths components.
}
%%%%rev
...
...
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