Re: [isabelle] Contracting Abbreviations of Locale Definitions

Hi Julian,

First of all, I would be very happy if you could solve this problem of missing contractions. Clemens has never showed me an example where folding of abbreviations would lead to non-termination. And I do not know precisely how abbreviations and locales are implemented, so it is hard for me to decide whether something would lead to a problem. Nevertheless, here is another example:

locale l = fixes f :: "('a â 'a) â 'a â 'a"
definition (in l) foo where "foo â f (%x. x)"
interpretation l "id" where "l.foo id == id (%x. x)" sorry

If the interpretation installs abbreviations which respect the rewrite morphism, then the abbreviation reads as "id (%x. x) == id (%x. x)" which clearly loops. If it does not, then "id (%x. x)" is always printed as "foo". This might not be optimal, as the right-hand sides can be arbitrary general terms that should remain the way they are.

Andreas

On 28/07/15 11:33, Julian Brunner wrote:
Hi Andreas,

Good call on the overlapping abbreviations, I did not consider this case. However, the
conflict already arises with the current implementation. Consider the following:

locale foo =
fixes f :: "'a => 'a => bool"
fixes g :: "'a => 'a => 'a => bool"
begin

definition test where "test = f"
sublocale f!: foo f "% x y z. g y z x" by this

end

This generates the following abbreviations (they end up in the Consts record in this order):

f.test == foo.test f
f.f.test == foo.test f
test == foo.test f

Since 'test' only depends on the parameter f, which is interpreted under the identity
morphism (eta contraction seems to matter here, so this does not happen with your original
example), all of these abbreviations are set up to be contracted before printing. In fact,
'test' is printed as 'f.test' (presumably due to the order of the abbreviations in the
Consts record).

Given that these contraction conflicts are already a problem as it is, I do not think that
it would make things significantly worse to allow contraction of abbreviations introduced
via other morphisms (barring other problems like the one you discussed with Clemens Ballarin).

On Tue, Jul 28, 2015 at 8:53 AM Andreas Lochbihler <andreas.lochbihler at inf.ethz.ch
<mailto:andreas.lochbihler at inf.ethz.ch>> wrote:

Hi Julian,

I also regularly suffer from these pretty-printing nightmares, but I vaguely remember a
discussion with Clemens Ballarin on the subject. IIRC the problem is that it is not clear
whether collapsing the abbreviations terminates in all cases. Clemens has never showed me
an example where it actually happens, though.

Yet, I can still think of difficult situations as as the following:

locale foo =
fixes f :: "'a => 'a => bool"
and g :: "'a => 'a => 'a => bool"

definition (in foo) test where "test = f"

sublocale foo â f: foo "%x y. f y x" "%x y z. g y z x" .

This sublocale declaration makes the locale subgraph cyclic, However, the round-up
algorithm realises that if you go six times through the circle, the composed parameter
instantiations are alpha-beta-eta-equivalent to f and g again, so it stops. That means
that the sublocale command adds five copies of foo to itself. Now consider the situation
for the abbreviations. We have

local.test == foo.test f

from the original definition. From the sublocale command, we would also get

local.f.test == foo.test (%x y. f y x)
local.f.f.test == foo.test f
local.f.f.f.test == foo.test (%x y. f y x)
local.f.f.f.f.test == foo.test f
local.f.f.f.f.f.test == foo.test (%x y. f y x)

Obviously, they overlap. So which one should be used by the pretty-printer?

Andreas

On 27/07/15 21:12, Julian Brunner wrote:
> Dear all,
>
> Isabelle will not contract the abbreviations introduced for locale
> definitions when the locale is interpreted through a morphism other than
> the identity. This behavior is described in the following threads:
>
> https://lists.cam.ac.uk/mailman/htdig/cl-isabelle-users/2011-September/msg00040.html
> https://lists.cam.ac.uk/mailman/htdig/cl-isabelle-users/2012-January/msg00029.html
>
> The workaround that is proposed in these threads is to introduce additional
> abbreviations after having interpreted the locale. In my formalization,
> this would result in so much boilerplate as to make the whole appproach
> using locales unusable. Now I'm wondering why this behavior was introduced
> in the first place. Since there is no problem with expanding these
> abbreviations, why would there be one with contracting them?
>
> It seems like the reason for the abbreviations not being contracted is that
> they use the "internal" print mode. Unfortunately, I was unable to find the
> place where the print mode is set on these abbreviations in order to do
> more experiments on this. So, before spending more time on this, I wanted
> to ask what the original reasons for this behavor were and if it might be
> possible to enable contraction of these abbreviations.
>

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