From brianh at cs.pdx.edu Thu Apr 14 22:40:53 2011
From: brianh at cs.pdx.edu (Brian Huffman)
Date: Thu, 14 Apr 2011 15:40:53 -0700
Subject: [opentheory-users] importer for Isabelle
Message-ID:
Hello,
I now have a working OpenTheory importer for Isabelle (tested with
Isabelle2011). The code is still kind of a mess, with a bunch of extra
debugging code sitting around, so I'll wait until I've cleaned it up a
bit before I share it. There are still a few improvements that need to
be made, but I think I have all the major bugs fixed now: It can
successfully import the parser-1.5 library (reading the article file
generated by "opentheory info --article parser-1.5").
The implementation adds three new tables to Isabelle's Theory_Data:
1) A set of theorems; there must be an entry here that matches each
"axiom" command.
2) A mapping of type names; there must be a matching entry for each
"typeOp" command.
3) A mapping of constant names; there must be a matching entry for
each "const" command.
The set of theorems is extended using the [opentheory] attribute, like this:
lemma [opentheory]: "ALL m::nat. m + 0 = m"
by simp
(I have lots of these kinds of proofs for natural numbers and booleans.)
The importer also adds new theorems to the set whenever it processes a
"thm" command. The complete list of theorems can be accessed using the
name "opentheory", which is one of those new dynamic theorem
references in Isabelle; it can be used in proof scripts or anywhere
just like any other theorem name.
The other tables are extended using "setup" commands with "add_tyop"
and "add_const" ML functions, like this:
setup {*
fold OpenTheory.add_tyop
[("->", @{type_name "fun"}),
("bool", @{type_name "bool"}),
("Number.Natural.natural", @{type_name "nat"}),
("Data.Pair.*", @{type_name "prod"})]
*}
setup {*
fold OpenTheory.add_const
[("=", @{const_name "HOL.eq"}),
("Data.Bool.!", @{const_name "All"}),
("Data.Bool.==>", @{const_name "HOL.implies"}),
("Data.Bool.\\\\/", @{const_name "HOL.disj"}),
("Data.Bool./\\\\", @{const_name "HOL.conj"}),
("Data.Bool.cond", @{const_name "If"}),
("Data.Bool.select", @{const_name "Eps"})]
*}
The importer should also extend these tables whenever it defines a new
constant or type, but I haven't implemented this yet. Another nice
feature would be a way for users to influence how the importer chooses
names for newly-defined constants and types. Right now it takes the
names directly from the strings in the article file, which isn't so
nice for names like "HOLLight._dest_rec" (Isabelle's parser can't
handle names that start with underscores).
Once I clean up the code, I'm not sure what I should do with it... I
suppose I could add it to the Isabelle repo, but I'm not sure if I
want to advertise to Munich crowd that I've been doing all this work
that is unrelated to finishing my thesis :)
- Brian
From joe at gilith.com Fri Apr 15 02:03:26 2011
From: joe at gilith.com (Joe Hurd)
Date: Thu, 14 Apr 2011 19:03:26 -0700
Subject: [opentheory-users] importer for Isabelle
In-Reply-To:
References:
Message-ID:
Hi Brian,
That is really great work! Am I right in thinking you can import the
parser-1.5 article binding all the input symbols and axioms to
existing ones in Isabelle? I would have guessed that Isabelle type
classes would have managed to get in the way at some point, but
perhaps this would only be for converting Isabelle proofs to
OpenTheory format?
> The set of theorems is extended using the [opentheory] attribute, like this:
>
> lemma [opentheory]: "ALL m::nat. m + 0 = m"
> by simp
>
> (I have lots of these kinds of proofs for natural numbers and booleans.)
>
> The importer also adds new theorems to the set whenever it processes a
> "thm" command. The complete list of theorems can be accessed using the
> name "opentheory", which is one of those new dynamic theorem
> references in Isabelle; it can be used in proof scripts or anywhere
> just like any other theorem name.
The [opentheory] attribute looks like a great scheme that could
perhaps be used in the HOL family of theorem provers to import
OpenTheory proofs.
You mentioned that you prove a lot of theorems that the OpenTheory
article relies on, but it seems you could reduce this by processing a
set of OpenTheory packages that don't make any definitions. When I was
designing the standard theory library I tried to isolate packages that
made definitions and have them export just a minimal theorem interface
- most of the theorems are proved in packages that make no definitions
and so can be safely run to populate the [opentheory] set of theorems.
> The importer should also extend these tables whenever it defines a new
> constant or type, but I haven't implemented this yet. Another nice
> feature would be a way for users to influence how the importer chooses
> names for newly-defined constants and types. Right now it takes the
> names directly from the strings in the article file, which isn't so
> nice for names like "HOLLight._dest_rec" (Isabelle's parser can't
> handle names that start with underscores).
You should find that constants and type operators with names like this
are never exported from a theory (i.e., never appear in exported
theorems), so it's perfectly safe to normalize their names to
something more acceptable to Isabelle. They are `local definitions'
that are used only in proofs.
> Once I clean up the code, I'm not sure what I should do with it... I
> suppose I could add it to the Isabelle repo, but I'm not sure if I
> want to advertise to Munich crowd that I've been doing all this work
> that is unrelated to finishing my thesis :)
I would very much like to see it live on in some fashion - my hope is
that more and more theories will be converted to OpenTheory packages,
and your code could be used to import them into Isabelle in a
principled way.
Thanks for having a go at this - I never thought you'd crank it out so quickly.
Cheers,
Joe
From brianh at cs.pdx.edu Fri Apr 15 16:34:39 2011
From: brianh at cs.pdx.edu (Brian Huffman)
Date: Fri, 15 Apr 2011 09:34:39 -0700
Subject: [opentheory-users] importer for Isabelle
In-Reply-To:
References:
Message-ID:
On Thu, Apr 14, 2011 at 7:03 PM, Joe Hurd wrote:
> Hi Brian,
>
> That is really great work! Am I right in thinking you can import the
> parser-1.5 article binding all the input symbols and axioms to
> existing ones in Isabelle? I would have guessed that Isabelle type
> classes would have managed to get in the way at some point, but
> perhaps this would only be for converting Isabelle proofs to
> OpenTheory format?
Yes, each of the input constants of the article is mapped to a
pre-existing Isabelle constant. Some of these existing Isabelle
constants happen to be overloaded, but that doesn't cause any
problems. This mapping of constant names does not even need to be
one-to-one; for example, I imagine that "Number.Natural.+" and
"Number.Integer.+" would map to the same overloaded "plus" constant in
Isabelle.
Of course, exporting proofs from Isabelle is a completely different story.
> You mentioned that you prove a lot of theorems that the OpenTheory
> article relies on, but it seems you could reduce this by processing a
> set of OpenTheory packages that don't make any definitions. When I was
> designing the standard theory library I tried to isolate packages that
> made definitions and have them export just a minimal theorem interface
> - most of the theorems are proved in packages that make no definitions
> and so can be safely run to populate the [opentheory] set of theorems.
Your idea of keeping definitions in separate, minimal modules is a
good design. I'm sure I could have greatly reduced the number of
[opentheory] lemmas that I needed by finding the right additional
article files to import; I was just too lazy to figure out how the
packages were organized.
>> The importer should also extend these tables whenever it defines a new
>> constant or type, but I haven't implemented this yet. Another nice
>> feature would be a way for users to influence how the importer chooses
>> names for newly-defined constants and types. Right now it takes the
>> names directly from the strings in the article file, which isn't so
>> nice for names like "HOLLight._dest_rec" (Isabelle's parser can't
>> handle names that start with underscores).
>
> You should find that constants and type operators with names like this
> are never exported from a theory (i.e., never appear in exported
> theorems), so it's perfectly safe to normalize their names to
> something more acceptable to Isabelle. They are `local definitions'
> that are used only in proofs.
Actually, it seems like it would be safe to rename *any* constant
(whether exported or not) to any name that I want in Isabelle, as long
as the importer keeps track of the name mapping so that later imports
can use the same names.
I suppose I should write an "import_name" function that converts from
OpenTheory names to Isabelle-friendly ones. It would be nice to
parameterize this by a list of user-specified exceptions to the
mapping, so you could say something like, "import this article, but
when you define constant 'foo', call it 'bar' instead."
>> Once I clean up the code, I'm not sure what I should do with it... I
>> suppose I could add it to the Isabelle repo, but I'm not sure if I
>> want to advertise to Munich crowd that I've been doing all this work
>> that is unrelated to finishing my thesis :)
>
> I would very much like to see it live on in some fashion - my hope is
> that more and more theories will be converted to OpenTheory packages,
> and your code could be used to import them into Isabelle in a
> principled way.
I suppose I'll add it to the Isabelle distribution at some point,
maybe after I finish writing my thesis. In the meantime, I guess I can
post the code to the list, so it will be archived and people can try
it out.
- Brian