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Joshua Yanovski
iriscoq
Commits
be549d5a
Commit
be549d5a
authored
Feb 16, 2016
by
Ralf Jung
Browse files
add a comment about the OFE vs COFE situation
parent
24a71fb3
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algebra/cofe.v
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be549d5a
From
algebra
Require
Export
base
.
(
**
This
files
defines
(
a
shallow
embedding
of
)
the
category
of
COFEs
:
Complete
ordered
families
of
equivalences
.
This
is
a
cartesian
closed
category
,
and
mathematically
speaking
,
the
entire
development
lives
in
this
category
.
However
,
we
will
generally
prefer
to
work
with
raw
Coq
functions
plus
some
registered
Proper
instances
for
non

expansiveness
.
This
makes
writing
such
functions
much
easier
.
It
turns
out
that
it
many
cases
,
we
do
not
even
need
non

expansiveness
.
In
principle
,
it
would
be
possible
to
perform
a
large
part
of
the
development
on
OFEs
,
i
.
e
.,
on
bisected
metric
spaces
that
are
not
necessary
complete
.
This
is
because
the
function
space
A
→
B
has
a
completion
if
B
has
one

for
A
,
the
metric
itself
suffices
.
That
would
result
in
a
simplification
of
some
constructions
,
becuase
no
completion
would
have
to
be
provided
.
However
,
on
the
other
hand
,
we
would
have
to
introduce
the
notion
of
OFEs
into
our
alebraic
hierarchy
,
which
we
'
d
rather
avoid
.
Furthermore
,
on
paper
,
justifying
this
mix
of
OFEs
and
COFEs
is
a
little
fuzzy
.
*
)
(
**
Unbundeled
version
*
)
Class
Dist
A
:=
dist
:
nat
→
relation
A
.
Instance:
Params
(
@
dist
)
3.
...
...
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