[opentheory-users] extracting intermediate theorems

[Joe Leslie-Hurd]

Hi Ramana,

What you're proposing is certainly possible, but first I'd like to
understand a bit more about your use-case for accessing intermediate
theorems.

At present the article standard and opentheory tool conspire to create
an illusion that the intermediate theorems of the theory are
irrelevant, and that only the imported assumptions and exported
theorems are important. As a consequence of this abstraction, tools
that process articles may feel free to replace any or all intermediate
theorems so long as the assumption/theorem interface is maintained.

Supporting post-hoc extraction of intermediate theorems and promoting
them to exported theorems goes against this philosophy, because an
article processing tool that changed intermediate theorems could break
something downstream that was relying on them having a particular form
to extract and export.

Given the above, could you please elaborate on your use-case for
accessing intermediate theorems of articles?

Cheers,

Joe

On Sat, Dec 20, 2014 at 9:31 PM, Ramana Kumar <Ramana.Kumar at cl.cam.ac.uk> wrote:
> Hi Joe,
>
> On Sat, Dec 20, 2014 at 9:09 PM, Joe Leslie-Hurd <joe at gilith.com> wrote:
>>
>> > Show me the intermediate (i.e. unexported) theorems that arise when
>> > running
>> > an article.
>>
>> No, unfortunately not. The best it can do is tell you *how many*
>> theorems are generated, by using the --inference option.
>>
>> Did you have any thoughts on a way to present intermediate theorems to the
>> user?
>
>
> What would be useful to me is if I could search for intermediate theorems
> with a pattern. I'd guess you'd rather stay away from specifying parsing of
> such patterns. I wouldn't mind, however, writing my pattern as OpenTheory
> article commands for creating a term. I'd then like to get back all
> intermediate theorems that match.
>
>>
>> > Create an article that exports a previously unexported theorem, taking
>> > an
>> > existing article as input.
>>
>> Also no I'm afraid.
>
>
> That's a pity. Would it be hard to add? Presuming we solve the problem above
> of specifying an intermediate theorem.
>
> I guess for the moment I can get around this by using a custom reader that
> looks for the theorem I want and cuts off the article as soon as it finds it
> (and adds on an export). It would be nice if the opentheory tool had enough
> features to support this itself, but maybe it's a little outside your design
> goals? On the other hand, I think a good suite of powerful manipulations on
> OpenTheory packages for a variety of purposes would help buy-in.
>
>>
>> > Minimise an article for what is required for a particular theorem (I
>> > think
>> > the answer here is yes, by creating a package with the desired theorem
>> > and
>> > then asking for an article for it to be generated...?)
>>
>> Indeed. Suppose article foo.art exports a set of theorems containing a
>> theorem T of interest, then you can create an article bar.art that
>> proves T by axiom, and then run
>>
>> echo 'a { article: "foo.art" } main { import: a article: "bar.art" }'
>> | opentheory info --article -o baz.art theory:-
>>
>> to get a minimal article baz.art proving T.
>
>
> Great, thanks.
>
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