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0bae18c1
Commit
0bae18c1
authored
Sep 02, 2012
by
Adam Chlipala
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Clearer version of sentence on CIC extensions
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...
...
@@ -72,7 +72,7 @@ Languages like Haskell and ML have a convenient%\index{principal types}\index{ty
This
is
as
good
a
time
as
any
to
mention
the
preponderance
of
different
languages
associated
with
Coq
.
The
theoretical
foundation
of
Coq
is
a
formal
system
called
the
%
\
index
{
Calculus
of
Inductive
Constructions
}
\
index
{
CIC
|
see
{
Calculus
of
Inductive
Constructions
}}%
_
Calculus
of
Inductive
Constructions_
(
CIC
)
%~
\
cite
{
CIC
}%,
which
is
an
extension
of
the
older
%
\
index
{
Calculus
of
Constructions
}
\
index
{
CoC
|
see
{
Calculus
of
Constructions
}}%
_
Calculus
of
Constructions_
(
CoC
)
%~
\
cite
{
CoC
}%.
CIC
is
quite
a
spartan
foundation
,
which
is
helpful
for
proving
metatheory
but
not
so
helpful
for
real
development
.
Still
,
it
is
nice
to
know
that
it
has
been
proved
that
CIC
enjoys
properties
like
%
\
index
{
strong
normalization
}%
_
strong
normalization_
%
\
cite
{
CIC
}%,
meaning
that
every
program
(
and
,
more
importantly
,
every
proof
term
)
terminates
;
and
%
\
index
{
relative
consistency
}%
_
relative
consistency_
%
\
cite
{
SetsInTypes
}%
with
systems
like
versions
of
%
\
index
{
Zermelo
-
Fraenkel
set
theory
}%
Zermelo
-
Fraenkel
set
theory
,
which
roughly
means
that
you
can
believe
that
Coq
proofs
mean
that
the
corresponding
propositions
are
"really true,"
if
you
believe
in
set
theory
.
Coq
is
actually
based
on
an
extension
of
CIC
called
%
\
index
{
Gallina
}%
_
Gallina_
.
The
text
after
the
[
:=
]
and
before
the
period
in
the
last
code
example
is
a
term
of
Gallina
.
Gallina
adds
many
useful
features
that
are
not
compiled
internally
to
more
primitive
CIC
features
.
The
important
metatheorems
about
CIC
have
not
been
extended
to
the
full
breadth
of
these
features
,
but
most
Coq
users
do
not
seem
to
lose
much
sleep
over
this
omission
.
Coq
is
actually
based
on
an
extension
of
CIC
called
%
\
index
{
Gallina
}%
_
Gallina_
.
The
text
after
the
[
:=
]
and
before
the
period
in
the
last
code
example
is
a
term
of
Gallina
.
Gallina
includes
several
useful
features
that
must
be
considered
as
extensions
to
CIC
.
The
important
metatheorems
about
CIC
have
not
been
extended
to
the
full
breadth
of
these
features
,
but
most
Coq
users
do
not
seem
to
lose
much
sleep
over
this
omission
.
Next
,
there
is
%
\
index
{
Ltac
}%
_L
tac_
,
Coq
'
s
domain
-
specific
language
for
writing
proofs
and
decision
procedures
.
We
will
see
some
basic
examples
of
Ltac
later
in
this
chapter
,
and
much
of
this
book
is
devoted
to
more
involved
Ltac
examples
.
...
...
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