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gradual-typing
sgdt
Commits
7bf363f7
Commit
7bf363f7
authored
6 years ago
by
Dan Licata
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Merge branch 'master' of
https://github.ccs.neu.edu/coqatoos/cbv-gradual-type-theory
parents
cb8d15a0
6ab5c8e8
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paper/gtt.tex
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−
4
View file @
7bf363f7
...
...
@@ -227,7 +227,7 @@
\newcommand
{
\obcast
}
[2]
{
\langle
{
#1
}
\Leftarrow
{
#2
}
\rangle
}
\newcommand
{
\err
}{
\mho
}
\newcommand
{
\diverge
}{
\Omega
}
\newcommand
{
\print
}{
\kw
{
print
}
\,\,
}
\newcommand
{
\print
}{
\kw
{
print
}}
\newcommand
{
\roll
}{
\kw
{
roll
}}
\newcommand
{
\rollty
}
[1]
{
\texttt
{
roll
}_{
#1
}
\,\,
}
\newcommand
{
\unroll
}{
\kw
{
unroll
}}
...
...
@@ -1071,7 +1071,7 @@ computation type of potentially effectful programs that return a value
of type
$
A
$
, while
$
U
\u
B
$
is the value type of thunked computations of
type
$
\u
B
$
. The introduction rule for
$
\u
F A
$
is returning a value of
type
$
A
$
(
\ret
{
V
}
), while the elimination rule is sequencing a
computation
of an
$
\u
F A
$
with a computation
$
x : A
\vdash
M
:
\u
B
$
to
computation
$
M :
\u
F A
$
with a computation
$
x : A
\vdash
N
:
\u
B
$
to
produce a computation of a
$
\u
B
$
(
$
\bindXtoYinZ
{
M
}{
x
}{
N
}$
). While any
closed complex value
$
V
$
is equivalent to an actual value, a computation
of type
$
\u
F A
$
might perform effects (e.g. printing) before returning
...
...
@@ -1273,8 +1273,8 @@ types will arise from type dynamism and casts.
The
\emph
{
type dynamism
}
relation of gradual type
theory~
\cite
{
nl18cbngtt
}
corresponds to the type precision relation of
\cite
{
siek
}
and the na
\"
ive subtyping of
\cite
{
wadler-findler
}
. We
write type dynamism as
$
A
\ltdyn
A'
$
, which is read as ``
$
A
'
$
is
more
dynamic than
$
A
$
''; intuitively, this means that
$
A'
$
supports more
write type dynamism as
$
A
\ltdyn
A'
$
, which is read as ``
$
A
$
is
less
dynamic than
$
A
'
$
''; intuitively, this means that
$
A'
$
supports more
behaviors than
$
A
$
.
\cite
{
nl18cbngtt,icfp
}
analyze this as the
existence of an
\emph
{
upcast
}
from
$
A
$
to
$
A'
$
and a downcast from
$
A'
$
to
$
A
$
which form an embedding-projection pair (
\emph
{
ep pair
}
) for an
...
...
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