From ramana at member.fsf.org Wed Feb 3 05:48:38 2016
From: ramana at member.fsf.org (Ramana Kumar)
Date: Wed, 3 Feb 2016 16:48:38 +1100
Subject: [opentheory-users] removing definitions from theories
In-Reply-To:
References:
Message-ID:
Hi Joe,
Do you have any comments on the plan I described?
And/or would you be able to add the definition-removing functionality to
the opentheory tool?
Thanks,
Ramana
On 30 January 2016 at 12:57, Ramana Kumar wrote:
> I am trying to build a compatibility bridge between HOL4's standard
> library and the OpenTheory standard library.
>
> I've thought about (and started trying) various approaches.
>
> The latest idea (due mostly to Michael Norrish) is:
>
> 1. Record a theory containing the HOL4 standard library, entirely in
> the HOL4 namespace, depending only on the axioms of HOL.
> 2. Remove from this theory all definitions of things that are already
> in the OpenTheory standard library. The constants should then become
> ungrounded, and where they were defined the article should instead add the
> definitional axioms as axioms.
> 3. Instantiate all the ungrounded constants with constants from the
> OpenTheory standard library, and then also add the OpenTheory standard
> library.
> 4. Prove any remaining axioms.
>
> The feature I requested is for step 2. I realise now that I need to be
> able to remove definitions selectively, not just remove them all. There may
> be some way to accomplish that even if the primitive functionality is to
> remove them all, though.
>
> On 30 January 2016 at 03:52, Joe Leslie-Hurd wrote:
>
>> Hi Ramana,
>>
>> There's currently no tool support for this, but I don't think it would
>> be too difficult to implement. What is your use-case?
>>
>> Cheers,
>>
>> Joe
>>
>> On Fri, Jan 29, 2016 at 12:36 AM, Ramana Kumar
>> wrote:
>> > Hi,
>> >
>> > Is it possible to take a theory that makes definitions of
>> types/constants,
>> > and then re-present the same theory _without_ making the definitions
>> > (instead taking them as ungrounded constants, and the definitional
>> theorems
>> > as axioms).
>> >
>> > I know there is already this command:
>> >
>> > opentheory info --theorems ...
>> >
>> > which removes all the proofs, but it still keeps the definitions in.
>> >
>> > Can I also remove the definitions?
>> >
>> > In essence, I want a totally axiomatic presentation of a theory.
>> >
>> > Thanks,
>> > Ramana
>> >
>> > _______________________________________________
>> > opentheory-users mailing list
>> > opentheory-users at gilith.com
>> > http://www.gilith.com/mailman/listinfo/opentheory-users
>> >
>>
>> _______________________________________________
>> opentheory-users mailing list
>> opentheory-users at gilith.com
>> http://www.gilith.com/mailman/listinfo/opentheory-users
>>
>
>
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From joe at gilith.com Wed Feb 3 05:54:00 2016
From: joe at gilith.com (Joe Leslie-Hurd)
Date: Tue, 2 Feb 2016 21:54:00 -0800
Subject: [opentheory-users] removing definitions from theories
In-Reply-To:
References:
Message-ID:
Hi Ramana,
Sorry I didn't reply sooner - I'm actually working right now on adding
functionality to the opentheory tool to replace definitions with
theory assumptions.
Your plan seems sensible to me. And it's definitely an argument for
using Rob's new constant definition primitive as much as possible,
since classical definitions of the form |- c = t are often rather
esoteric.
I'll let you know when I have something working.
Cheers,
Joe
On Tue, Feb 2, 2016 at 9:48 PM, Ramana Kumar wrote:
> Hi Joe,
>
> Do you have any comments on the plan I described?
>
> And/or would you be able to add the definition-removing functionality to the
> opentheory tool?
>
> Thanks,
> Ramana
>
> On 30 January 2016 at 12:57, Ramana Kumar wrote:
>>
>> I am trying to build a compatibility bridge between HOL4's standard
>> library and the OpenTheory standard library.
>>
>> I've thought about (and started trying) various approaches.
>>
>> The latest idea (due mostly to Michael Norrish) is:
>>
>> Record a theory containing the HOL4 standard library, entirely in the HOL4
>> namespace, depending only on the axioms of HOL.
>> Remove from this theory all definitions of things that are already in the
>> OpenTheory standard library. The constants should then become ungrounded,
>> and where they were defined the article should instead add the definitional
>> axioms as axioms.
>> Instantiate all the ungrounded constants with constants from the
>> OpenTheory standard library, and then also add the OpenTheory standard
>> library.
>> Prove any remaining axioms.
>>
>> The feature I requested is for step 2. I realise now that I need to be
>> able to remove definitions selectively, not just remove them all. There may
>> be some way to accomplish that even if the primitive functionality is to
>> remove them all, though.
>>
>> On 30 January 2016 at 03:52, Joe Leslie-Hurd wrote:
>>>
>>> Hi Ramana,
>>>
>>> There's currently no tool support for this, but I don't think it would
>>> be too difficult to implement. What is your use-case?
>>>
>>> Cheers,
>>>
>>> Joe
>>>
>>> On Fri, Jan 29, 2016 at 12:36 AM, Ramana Kumar
>>> wrote:
>>> > Hi,
>>> >
>>> > Is it possible to take a theory that makes definitions of
>>> > types/constants,
>>> > and then re-present the same theory _without_ making the definitions
>>> > (instead taking them as ungrounded constants, and the definitional
>>> > theorems
>>> > as axioms).
>>> >
>>> > I know there is already this command:
>>> >
>>> > opentheory info --theorems ...
>>> >
>>> > which removes all the proofs, but it still keeps the definitions in.
>>> >
>>> > Can I also remove the definitions?
>>> >
>>> > In essence, I want a totally axiomatic presentation of a theory.
>>> >
>>> > Thanks,
>>> > Ramana
>>> >
>>> > _______________________________________________
>>> > opentheory-users mailing list
>>> > opentheory-users at gilith.com
>>> > http://www.gilith.com/mailman/listinfo/opentheory-users
>>> >
>>>
>>> _______________________________________________
>>> opentheory-users mailing list
>>> opentheory-users at gilith.com
>>> http://www.gilith.com/mailman/listinfo/opentheory-users
>>
>>
>
>
> _______________________________________________
> opentheory-users mailing list
> opentheory-users at gilith.com
> http://www.gilith.com/mailman/listinfo/opentheory-users
>
From joe at gilith.com Thu Feb 4 08:59:33 2016
From: joe at gilith.com (Joe Leslie-Hurd)
Date: Thu, 4 Feb 2016 00:59:33 -0800
Subject: [opentheory-users] removing definitions from theories
In-Reply-To:
References:
Message-ID:
Hi Ramana,
I've just released a new version of the opentheory tool, namely
$ opentheory -v
opentheory 1.3 (release 20160204)
which includes support for a --skip-definitions flag when generating
article files. This switch replaces defined symbols with external
symbols and definition theorems with theory assumptions.
For example, here is the unit theory with and without definitions:
$ opentheory info --article unit | opentheory info --theory article:-
2 external type operators: -> bool
8 external constants: = select ! /\ ==> ? ?! T
13 assumptions:
|- T
|- !t. t ==> t
|- (?) = \p. p ((select) p)
|- !t. (!x. t) <=> t
|- (!) = \p. p = \x. T
|- !t. (t <=> T) <=> t
|- !t. T /\ t <=> t
|- (==>) = \p q. p /\ q <=> p
|- !x y. x = y <=> y = x
|- (/\) = \p q. (\f. f p q) = \f. f T T
|- (?) = \p. !q. (!x. p x ==> q) ==> q
|- !f g. (!x. f x = g x) <=> f = g
|- !p. (?!x. p x) <=> (?x. p x) /\ !x x'. p x /\ p x' ==> x = x'
1 defined type operator: Data.Unit.unit
1 defined constant: Data.Unit.()
5 theorems:
|- !v. v = Data.Unit.()
|- !f g. f = g
|- !e. ?fn. fn Data.Unit.() = e
|- !e. ?!fn. fn Data.Unit.() = e
|- !p. p Data.Unit.() ==> !x. p x
$ opentheory info --skip-definitions --article unit | opentheory info
--theory article:-
3 external type operators: -> bool Data.Unit.unit
10 external constants: = ! /\ ==> ? ?! T Data.Unit.() HOLLight.one_ABS
HOLLight.one_REP
14 assumptions:
|- T
|- !t. t ==> t
|- !t. (!x. t) <=> t
|- (!) = \p. p = \x. T
|- (\a. HOLLight.one_ABS (HOLLight.one_REP a)) = \a. a
|- !t. (t <=> T) <=> t
|- !t. T /\ t <=> t
|- (==>) = \p q. p /\ q <=> p
|- (\r. HOLLight.one_REP (HOLLight.one_ABS r) <=> r) =
\r. let b <- r in b
|- !x y. x = y <=> y = x
|- (/\) = \p q. (\f. f p q) = \f. f T T
|- (?) = \p. !q. (!x. p x ==> q) ==> q
|- !f g. (!x. f x = g x) <=> f = g
|- !p. (?!x. p x) <=> (?x. p x) /\ !x x'. p x /\ p x' ==> x = x'
5 theorems:
|- !v. v = Data.Unit.()
|- !f g. f = g
|- !e. ?fn. fn Data.Unit.() = e
|- !e. ?!fn. fn Data.Unit.() = e
|- !p. p Data.Unit.() ==> !x. p x
Hopefully this will help with your HOL4 interface project.
Cheers,
Joe
On Tue, Feb 2, 2016 at 9:54 PM, Joe Leslie-Hurd wrote:
> Hi Ramana,
>
> Sorry I didn't reply sooner - I'm actually working right now on adding
> functionality to the opentheory tool to replace definitions with
> theory assumptions.
>
> Your plan seems sensible to me. And it's definitely an argument for
> using Rob's new constant definition primitive as much as possible,
> since classical definitions of the form |- c = t are often rather
> esoteric.
>
> I'll let you know when I have something working.
>
> Cheers,
>
> Joe
>
> On Tue, Feb 2, 2016 at 9:48 PM, Ramana Kumar wrote:
>> Hi Joe,
>>
>> Do you have any comments on the plan I described?
>>
>> And/or would you be able to add the definition-removing functionality to the
>> opentheory tool?
>>
>> Thanks,
>> Ramana
>>
>> On 30 January 2016 at 12:57, Ramana Kumar wrote:
>>>
>>> I am trying to build a compatibility bridge between HOL4's standard
>>> library and the OpenTheory standard library.
>>>
>>> I've thought about (and started trying) various approaches.
>>>
>>> The latest idea (due mostly to Michael Norrish) is:
>>>
>>> Record a theory containing the HOL4 standard library, entirely in the HOL4
>>> namespace, depending only on the axioms of HOL.
>>> Remove from this theory all definitions of things that are already in the
>>> OpenTheory standard library. The constants should then become ungrounded,
>>> and where they were defined the article should instead add the definitional
>>> axioms as axioms.
>>> Instantiate all the ungrounded constants with constants from the
>>> OpenTheory standard library, and then also add the OpenTheory standard
>>> library.
>>> Prove any remaining axioms.
>>>
>>> The feature I requested is for step 2. I realise now that I need to be
>>> able to remove definitions selectively, not just remove them all. There may
>>> be some way to accomplish that even if the primitive functionality is to
>>> remove them all, though.
>>>
>>> On 30 January 2016 at 03:52, Joe Leslie-Hurd wrote:
>>>>
>>>> Hi Ramana,
>>>>
>>>> There's currently no tool support for this, but I don't think it would
>>>> be too difficult to implement. What is your use-case?
>>>>
>>>> Cheers,
>>>>
>>>> Joe
>>>>
>>>> On Fri, Jan 29, 2016 at 12:36 AM, Ramana Kumar
>>>> wrote:
>>>> > Hi,
>>>> >
>>>> > Is it possible to take a theory that makes definitions of
>>>> > types/constants,
>>>> > and then re-present the same theory _without_ making the definitions
>>>> > (instead taking them as ungrounded constants, and the definitional
>>>> > theorems
>>>> > as axioms).
>>>> >
>>>> > I know there is already this command:
>>>> >
>>>> > opentheory info --theorems ...
>>>> >
>>>> > which removes all the proofs, but it still keeps the definitions in.
>>>> >
>>>> > Can I also remove the definitions?
>>>> >
>>>> > In essence, I want a totally axiomatic presentation of a theory.
>>>> >
>>>> > Thanks,
>>>> > Ramana
>>>> >
>>>> > _______________________________________________
>>>> > opentheory-users mailing list
>>>> > opentheory-users at gilith.com
>>>> > http://www.gilith.com/mailman/listinfo/opentheory-users
>>>> >
>>>>
>>>> _______________________________________________
>>>> opentheory-users mailing list
>>>> opentheory-users at gilith.com
>>>> http://www.gilith.com/mailman/listinfo/opentheory-users
>>>
>>>
>>
>>
>> _______________________________________________
>> opentheory-users mailing list
>> opentheory-users at gilith.com
>> http://www.gilith.com/mailman/listinfo/opentheory-users
>>
From ramana at member.fsf.org Thu Feb 4 09:42:56 2016
From: ramana at member.fsf.org (Ramana Kumar)
Date: Thu, 4 Feb 2016 20:42:56 +1100
Subject: [opentheory-users] removing definitions from theories
In-Reply-To:
References:
Message-ID:
Thanks very much, Joe!
Do you know a simple scheme by which one could skip definitions
selectively? I mean skip some but not all of the definitions in an article.
I imagine this is possible through some sequence of package unions or
interpretations (there's no intersection, though, is there?). If it's
possible to do so without re-recording any articles, that would be quite
useful.
Cheers,
Ramana
On 4 February 2016 at 19:59, Joe Leslie-Hurd wrote:
> Hi Ramana,
>
> I've just released a new version of the opentheory tool, namely
>
> $ opentheory -v
> opentheory 1.3 (release 20160204)
>
> which includes support for a --skip-definitions flag when generating
> article files. This switch replaces defined symbols with external
> symbols and definition theorems with theory assumptions.
>
> For example, here is the unit theory with and without definitions:
>
> $ opentheory info --article unit | opentheory info --theory article:-
> 2 external type operators: -> bool
> 8 external constants: = select ! /\ ==> ? ?! T
> 13 assumptions:
> |- T
> |- !t. t ==> t
> |- (?) = \p. p ((select) p)
> |- !t. (!x. t) <=> t
> |- (!) = \p. p = \x. T
> |- !t. (t <=> T) <=> t
> |- !t. T /\ t <=> t
> |- (==>) = \p q. p /\ q <=> p
> |- !x y. x = y <=> y = x
> |- (/\) = \p q. (\f. f p q) = \f. f T T
> |- (?) = \p. !q. (!x. p x ==> q) ==> q
> |- !f g. (!x. f x = g x) <=> f = g
> |- !p. (?!x. p x) <=> (?x. p x) /\ !x x'. p x /\ p x' ==> x = x'
> 1 defined type operator: Data.Unit.unit
> 1 defined constant: Data.Unit.()
> 5 theorems:
> |- !v. v = Data.Unit.()
> |- !f g. f = g
> |- !e. ?fn. fn Data.Unit.() = e
> |- !e. ?!fn. fn Data.Unit.() = e
> |- !p. p Data.Unit.() ==> !x. p x
>
> $ opentheory info --skip-definitions --article unit | opentheory info
> --theory article:-
> 3 external type operators: -> bool Data.Unit.unit
> 10 external constants: = ! /\ ==> ? ?! T Data.Unit.() HOLLight.one_ABS
> HOLLight.one_REP
> 14 assumptions:
> |- T
> |- !t. t ==> t
> |- !t. (!x. t) <=> t
> |- (!) = \p. p = \x. T
> |- (\a. HOLLight.one_ABS (HOLLight.one_REP a)) = \a. a
> |- !t. (t <=> T) <=> t
> |- !t. T /\ t <=> t
> |- (==>) = \p q. p /\ q <=> p
> |- (\r. HOLLight.one_REP (HOLLight.one_ABS r) <=> r) =
> \r. let b <- r in b
> |- !x y. x = y <=> y = x
> |- (/\) = \p q. (\f. f p q) = \f. f T T
> |- (?) = \p. !q. (!x. p x ==> q) ==> q
> |- !f g. (!x. f x = g x) <=> f = g
> |- !p. (?!x. p x) <=> (?x. p x) /\ !x x'. p x /\ p x' ==> x = x'
> 5 theorems:
> |- !v. v = Data.Unit.()
> |- !f g. f = g
> |- !e. ?fn. fn Data.Unit.() = e
> |- !e. ?!fn. fn Data.Unit.() = e
> |- !p. p Data.Unit.() ==> !x. p x
>
> Hopefully this will help with your HOL4 interface project.
>
> Cheers,
>
> Joe
>
> On Tue, Feb 2, 2016 at 9:54 PM, Joe Leslie-Hurd wrote:
> > Hi Ramana,
> >
> > Sorry I didn't reply sooner - I'm actually working right now on adding
> > functionality to the opentheory tool to replace definitions with
> > theory assumptions.
> >
> > Your plan seems sensible to me. And it's definitely an argument for
> > using Rob's new constant definition primitive as much as possible,
> > since classical definitions of the form |- c = t are often rather
> > esoteric.
> >
> > I'll let you know when I have something working.
> >
> > Cheers,
> >
> > Joe
> >
> > On Tue, Feb 2, 2016 at 9:48 PM, Ramana Kumar
> wrote:
> >> Hi Joe,
> >>
> >> Do you have any comments on the plan I described?
> >>
> >> And/or would you be able to add the definition-removing functionality
> to the
> >> opentheory tool?
> >>
> >> Thanks,
> >> Ramana
> >>
> >> On 30 January 2016 at 12:57, Ramana Kumar
> wrote:
> >>>
> >>> I am trying to build a compatibility bridge between HOL4's standard
> >>> library and the OpenTheory standard library.
> >>>
> >>> I've thought about (and started trying) various approaches.
> >>>
> >>> The latest idea (due mostly to Michael Norrish) is:
> >>>
> >>> Record a theory containing the HOL4 standard library, entirely in the
> HOL4
> >>> namespace, depending only on the axioms of HOL.
> >>> Remove from this theory all definitions of things that are already in
> the
> >>> OpenTheory standard library. The constants should then become
> ungrounded,
> >>> and where they were defined the article should instead add the
> definitional
> >>> axioms as axioms.
> >>> Instantiate all the ungrounded constants with constants from the
> >>> OpenTheory standard library, and then also add the OpenTheory standard
> >>> library.
> >>> Prove any remaining axioms.
> >>>
> >>> The feature I requested is for step 2. I realise now that I need to be
> >>> able to remove definitions selectively, not just remove them all.
> There may
> >>> be some way to accomplish that even if the primitive functionality is
> to
> >>> remove them all, though.
> >>>
> >>> On 30 January 2016 at 03:52, Joe Leslie-Hurd wrote:
> >>>>
> >>>> Hi Ramana,
> >>>>
> >>>> There's currently no tool support for this, but I don't think it would
> >>>> be too difficult to implement. What is your use-case?
> >>>>
> >>>> Cheers,
> >>>>
> >>>> Joe
> >>>>
> >>>> On Fri, Jan 29, 2016 at 12:36 AM, Ramana Kumar >
> >>>> wrote:
> >>>> > Hi,
> >>>> >
> >>>> > Is it possible to take a theory that makes definitions of
> >>>> > types/constants,
> >>>> > and then re-present the same theory _without_ making the definitions
> >>>> > (instead taking them as ungrounded constants, and the definitional
> >>>> > theorems
> >>>> > as axioms).
> >>>> >
> >>>> > I know there is already this command:
> >>>> >
> >>>> > opentheory info --theorems ...
> >>>> >
> >>>> > which removes all the proofs, but it still keeps the definitions in.
> >>>> >
> >>>> > Can I also remove the definitions?
> >>>> >
> >>>> > In essence, I want a totally axiomatic presentation of a theory.
> >>>> >
> >>>> > Thanks,
> >>>> > Ramana
> >>>> >
> >>>> > _______________________________________________
> >>>> > opentheory-users mailing list
> >>>> > opentheory-users at gilith.com
> >>>> > http://www.gilith.com/mailman/listinfo/opentheory-users
> >>>> >
> >>>>
> >>>> _______________________________________________
> >>>> opentheory-users mailing list
> >>>> opentheory-users at gilith.com
> >>>> http://www.gilith.com/mailman/listinfo/opentheory-users
> >>>
> >>>
> >>
> >>
> >> _______________________________________________
> >> opentheory-users mailing list
> >> opentheory-users at gilith.com
> >> http://www.gilith.com/mailman/listinfo/opentheory-users
> >>
>
> _______________________________________________
> opentheory-users mailing list
> opentheory-users at gilith.com
> http://www.gilith.com/mailman/listinfo/opentheory-users
>
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From joe at gilith.com Fri Feb 12 08:49:10 2016
From: joe at gilith.com (Joe Leslie-Hurd)
Date: Thu, 11 Feb 2016 22:49:10 -1000
Subject: [opentheory-users] removing definitions from theories
In-Reply-To:
References:
Message-ID:
Hi Ramana,
[Sorry for the delayed responses, I am on vacation right now.]
I'm sorry, I can't think of any way of selectively deleting definitions
from an article. Currently what's implemented in --skip-definitions is an
all-or-nothing hammer.
If you structured your export as a series of articles then you could use
--skip-definitions on the ones that contained the definitions you wanted to
skip, and then concatenate them together again using a suitable theory file.
This is how the OpenTheory standard theory library is structured, with all
definitions (of exported symbols) living in *-def theories, which export
the defining properties of the symbols rather than the exact internal
definition that you see with --skip-definitions. This structure allows you
to replace all the definitions in the standard theory library with theory
assumptions for their defining properties in one ugly command, as I
demonstrate here:
http://www.gilith.com/pipermail/opentheory-users/2014-March/000368.html
Cheers,
Joe
On Thu, Feb 4, 2016 at 1:42 AM, Ramana Kumar > wrote:
> Thanks very much, Joe!
>
> Do you know a simple scheme by which one could skip definitions
selectively?
> I mean skip some but not all of the definitions in an article. I imagine
> this is possible through some sequence of package unions or
interpretations
> (there's no intersection, though, is there?). If it's possible to do so
> without re-recording any articles, that would be quite useful.
>
> Cheers,
> Ramana
>
> On 4 February 2016 at 19:59, Joe Leslie-Hurd > wrote:
>>
>> Hi Ramana,
>>
>> I've just released a new version of the opentheory tool, namely
>>
>> $ opentheory -v
>> opentheory 1.3 (release 20160204)
>>
>> which includes support for a --skip-definitions flag when generating
>> article files. This switch replaces defined symbols with external
>> symbols and definition theorems with theory assumptions.
>>
>> For example, here is the unit theory with and without definitions:
>>
>> $ opentheory info --article unit | opentheory info --theory article:-
>> 2 external type operators: -> bool
>> 8 external constants: = select ! /\ ==> ? ?! T
>> 13 assumptions:
>> |- T
>> |- !t. t ==> t
>> |- (?) = \p. p ((select) p)
>> |- !t. (!x. t) <=> t
>> |- (!) = \p. p = \x. T
>> |- !t. (t <=> T) <=> t
>> |- !t. T /\ t <=> t
>> |- (==>) = \p q. p /\ q <=> p
>> |- !x y. x = y <=> y = x
>> |- (/\) = \p q. (\f. f p q) = \f. f T T
>> |- (?) = \p. !q. (!x. p x ==> q) ==> q
>> |- !f g. (!x. f x = g x) <=> f = g
>> |- !p. (?!x. p x) <=> (?x. p x) /\ !x x'. p x /\ p x' ==> x = x'
>> 1 defined type operator: Data.Unit.unit
>> 1 defined constant: Data.Unit.()
>> 5 theorems:
>> |- !v. v = Data.Unit.()
>> |- !f g. f = g
>> |- !e. ?fn. fn Data.Unit.() = e
>> |- !e. ?!fn. fn Data.Unit.() = e
>> |- !p. p Data.Unit.() ==> !x. p x
>>
>> $ opentheory info --skip-definitions --article unit | opentheory info
>> --theory article:-
>> 3 external type operators: -> bool Data.Unit.unit
>> 10 external constants: = ! /\ ==> ? ?! T Data.Unit.() HOLLight.one_ABS
>> HOLLight.one_REP
>> 14 assumptions:
>> |- T
>> |- !t. t ==> t
>> |- !t. (!x. t) <=> t
>> |- (!) = \p. p = \x. T
>> |- (\a. HOLLight.one_ABS (HOLLight.one_REP a)) = \a. a
>> |- !t. (t <=> T) <=> t
>> |- !t. T /\ t <=> t
>> |- (==>) = \p q. p /\ q <=> p
>> |- (\r. HOLLight.one_REP (HOLLight.one_ABS r) <=> r) =
>> \r. let b <- r in b
>> |- !x y. x = y <=> y = x
>> |- (/\) = \p q. (\f. f p q) = \f. f T T
>> |- (?) = \p. !q. (!x. p x ==> q) ==> q
>> |- !f g. (!x. f x = g x) <=> f = g
>> |- !p. (?!x. p x) <=> (?x. p x) /\ !x x'. p x /\ p x' ==> x = x'
>> 5 theorems:
>> |- !v. v = Data.Unit.()
>> |- !f g. f = g
>> |- !e. ?fn. fn Data.Unit.() = e
>> |- !e. ?!fn. fn Data.Unit.() = e
>> |- !p. p Data.Unit.() ==> !x. p x
>>
>> Hopefully this will help with your HOL4 interface project.
>>
>> Cheers,
>>
>> Joe
>>
>> On Tue, Feb 2, 2016 at 9:54 PM, Joe Leslie-Hurd > wrote:
>> > Hi Ramana,
>> >
>> > Sorry I didn't reply sooner - I'm actually working right now on adding
>> > functionality to the opentheory tool to replace definitions with
>> > theory assumptions.
>> >
>> > Your plan seems sensible to me. And it's definitely an argument for
>> > using Rob's new constant definition primitive as much as possible,
>> > since classical definitions of the form |- c = t are often rather
>> > esoteric.
>> >
>> > I'll let you know when I have something working.
>> >
>> > Cheers,
>> >
>> > Joe
>> >
>> > On Tue, Feb 2, 2016 at 9:48 PM, Ramana Kumar >
>> > wrote:
>> >> Hi Joe,
>> >>
>> >> Do you have any comments on the plan I described?
>> >>
>> >> And/or would you be able to add the definition-removing functionality
>> >> to the
>> >> opentheory tool?
>> >>
>> >> Thanks,
>> >> Ramana
>> >>
>> >> On 30 January 2016 at 12:57, Ramana Kumar >
>> >> wrote:
>> >>>
>> >>> I am trying to build a compatibility bridge between HOL4's standard
>> >>> library and the OpenTheory standard library.
>> >>>
>> >>> I've thought about (and started trying) various approaches.
>> >>>
>> >>> The latest idea (due mostly to Michael Norrish) is:
>> >>>
>> >>> Record a theory containing the HOL4 standard library, entirely in the
>> >>> HOL4
>> >>> namespace, depending only on the axioms of HOL.
>> >>> Remove from this theory all definitions of things that are already in
>> >>> the
>> >>> OpenTheory standard library. The constants should then become
>> >>> ungrounded,
>> >>> and where they were defined the article should instead add the
>> >>> definitional
>> >>> axioms as axioms.
>> >>> Instantiate all the ungrounded constants with constants from the
>> >>> OpenTheory standard library, and then also add the OpenTheory
standard
>> >>> library.
>> >>> Prove any remaining axioms.
>> >>>
>> >>> The feature I requested is for step 2. I realise now that I need to
be
>> >>> able to remove definitions selectively, not just remove them all.
>> >>> There may
>> >>> be some way to accomplish that even if the primitive functionality is
>> >>> to
>> >>> remove them all, though.
>> >>>
>> >>> On 30 January 2016 at 03:52, Joe Leslie-Hurd > wrote:
>> >>>>
>> >>>> Hi Ramana,
>> >>>>
>> >>>> There's currently no tool support for this, but I don't think it
>> >>>> would
>> >>>> be too difficult to implement. What is your use-case?
>> >>>>
>> >>>> Cheers,
>> >>>>
>> >>>> Joe
>> >>>>
>> >>>> On Fri, Jan 29, 2016 at 12:36 AM, Ramana Kumar
>> >>>> >
>> >>>> wrote:
>> >>>> > Hi,
>> >>>> >
>> >>>> > Is it possible to take a theory that makes definitions of
>> >>>> > types/constants,
>> >>>> > and then re-present the same theory _without_ making the
>> >>>> > definitions
>> >>>> > (instead taking them as ungrounded constants, and the definitional
>> >>>> > theorems
>> >>>> > as axioms).
>> >>>> >
>> >>>> > I know there is already this command:
>> >>>> >
>> >>>> > opentheory info --theorems ...
>> >>>> >
>> >>>> > which removes all the proofs, but it still keeps the definitions
>> >>>> > in.
>> >>>> >
>> >>>> > Can I also remove the definitions?
>> >>>> >
>> >>>> > In essence, I want a totally axiomatic presentation of a theory.
>> >>>> >
>> >>>> > Thanks,
>> >>>> > Ramana
>> >>>> >
>> >>>> > _______________________________________________
>> >>>> > opentheory-users mailing list
>> >>>> > opentheory-users at gilith.com
>> >>>> > http://www.gilith.com/mailman/listinfo/opentheory-users
>> >>>> >
>> >>>>
>> >>>> _______________________________________________
>> >>>> opentheory-users mailing list
>> >>>> opentheory-users at gilith.com
>> >>>> http://www.gilith.com/mailman/listinfo/opentheory-users
>> >>>
>> >>>
>> >>
>> >>
>> >> _______________________________________________
>> >> opentheory-users mailing list
>> >> opentheory-users at gilith.com
>> >> http://www.gilith.com/mailman/listinfo/opentheory-users
>> >>
>>
>> _______________________________________________
>> opentheory-users mailing list
>> opentheory-users at gilith.com
>> http://www.gilith.com/mailman/listinfo/opentheory-users
>
>
>
> _______________________________________________
> opentheory-users mailing list
> opentheory-users at gilith.com
> http://www.gilith.com/mailman/listinfo/opentheory-users
>
On Wed, Feb 3, 2016 at 11:42 PM, Ramana Kumar > wrote:
> Thanks very much, Joe!
>
> Do you know a simple scheme by which one could skip definitions
selectively?
> I mean skip some but not all of the definitions in an article. I imagine
> this is possible through some sequence of package unions or
interpretations
> (there's no intersection, though, is there?). If it's possible to do so
> without re-recording any articles, that would be quite useful.
>
> Cheers,
> Ramana
>
> On 4 February 2016 at 19:59, Joe Leslie-Hurd > wrote:
>>
>> Hi Ramana,
>>
>> I've just released a new version of the opentheory tool, namely
>>
>> $ opentheory -v
>> opentheory 1.3 (release 20160204)
>>
>> which includes support for a --skip-definitions flag when generating
>> article files. This switch replaces defined symbols with external
>> symbols and definition theorems with theory assumptions.
>>
>> For example, here is the unit theory with and without definitions:
>>
>> $ opentheory info --article unit | opentheory info --theory article:-
>> 2 external type operators: -> bool
>> 8 external constants: = select ! /\ ==> ? ?! T
>> 13 assumptions:
>> |- T
>> |- !t. t ==> t
>> |- (?) = \p. p ((select) p)
>> |- !t. (!x. t) <=> t
>> |- (!) = \p. p = \x. T
>> |- !t. (t <=> T) <=> t
>> |- !t. T /\ t <=> t
>> |- (==>) = \p q. p /\ q <=> p
>> |- !x y. x = y <=> y = x
>> |- (/\) = \p q. (\f. f p q) = \f. f T T
>> |- (?) = \p. !q. (!x. p x ==> q) ==> q
>> |- !f g. (!x. f x = g x) <=> f = g
>> |- !p. (?!x. p x) <=> (?x. p x) /\ !x x'. p x /\ p x' ==> x = x'
>> 1 defined type operator: Data.Unit.unit
>> 1 defined constant: Data.Unit.()
>> 5 theorems:
>> |- !v. v = Data.Unit.()
>> |- !f g. f = g
>> |- !e. ?fn. fn Data.Unit.() = e
>> |- !e. ?!fn. fn Data.Unit.() = e
>> |- !p. p Data.Unit.() ==> !x. p x
>>
>> $ opentheory info --skip-definitions --article unit | opentheory info
>> --theory article:-
>> 3 external type operators: -> bool Data.Unit.unit
>> 10 external constants: = ! /\ ==> ? ?! T Data.Unit.() HOLLight.one_ABS
>> HOLLight.one_REP
>> 14 assumptions:
>> |- T
>> |- !t. t ==> t
>> |- !t. (!x. t) <=> t
>> |- (!) = \p. p = \x. T
>> |- (\a. HOLLight.one_ABS (HOLLight.one_REP a)) = \a. a
>> |- !t. (t <=> T) <=> t
>> |- !t. T /\ t <=> t
>> |- (==>) = \p q. p /\ q <=> p
>> |- (\r. HOLLight.one_REP (HOLLight.one_ABS r) <=> r) =
>> \r. let b <- r in b
>> |- !x y. x = y <=> y = x
>> |- (/\) = \p q. (\f. f p q) = \f. f T T
>> |- (?) = \p. !q. (!x. p x ==> q) ==> q
>> |- !f g. (!x. f x = g x) <=> f = g
>> |- !p. (?!x. p x) <=> (?x. p x) /\ !x x'. p x /\ p x' ==> x = x'
>> 5 theorems:
>> |- !v. v = Data.Unit.()
>> |- !f g. f = g
>> |- !e. ?fn. fn Data.Unit.() = e
>> |- !e. ?!fn. fn Data.Unit.() = e
>> |- !p. p Data.Unit.() ==> !x. p x
>>
>> Hopefully this will help with your HOL4 interface project.
>>
>> Cheers,
>>
>> Joe
>>
>> On Tue, Feb 2, 2016 at 9:54 PM, Joe Leslie-Hurd > wrote:
>> > Hi Ramana,
>> >
>> > Sorry I didn't reply sooner - I'm actually working right now on adding
>> > functionality to the opentheory tool to replace definitions with
>> > theory assumptions.
>> >
>> > Your plan seems sensible to me. And it's definitely an argument for
>> > using Rob's new constant definition primitive as much as possible,
>> > since classical definitions of the form |- c = t are often rather
>> > esoteric.
>> >
>> > I'll let you know when I have something working.
>> >
>> > Cheers,
>> >
>> > Joe
>> >
>> > On Tue, Feb 2, 2016 at 9:48 PM, Ramana Kumar >
>> > wrote:
>> >> Hi Joe,
>> >>
>> >> Do you have any comments on the plan I described?
>> >>
>> >> And/or would you be able to add the definition-removing functionality
>> >> to the
>> >> opentheory tool?
>> >>
>> >> Thanks,
>> >> Ramana
>> >>
>> >> On 30 January 2016 at 12:57, Ramana Kumar >
>> >> wrote:
>> >>>
>> >>> I am trying to build a compatibility bridge between HOL4's standard
>> >>> library and the OpenTheory standard library.
>> >>>
>> >>> I've thought about (and started trying) various approaches.
>> >>>
>> >>> The latest idea (due mostly to Michael Norrish) is:
>> >>>
>> >>> Record a theory containing the HOL4 standard library, entirely in the
>> >>> HOL4
>> >>> namespace, depending only on the axioms of HOL.
>> >>> Remove from this theory all definitions of things that are already in
>> >>> the
>> >>> OpenTheory standard library. The constants should then become
>> >>> ungrounded,
>> >>> and where they were defined the article should instead add the
>> >>> definitional
>> >>> axioms as axioms.
>> >>> Instantiate all the ungrounded constants with constants from the
>> >>> OpenTheory standard library, and then also add the OpenTheory
standard
>> >>> library.
>> >>> Prove any remaining axioms.
>> >>>
>> >>> The feature I requested is for step 2. I realise now that I need to
be
>> >>> able to remove definitions selectively, not just remove them all.
>> >>> There may
>> >>> be some way to accomplish that even if the primitive functionality is
>> >>> to
>> >>> remove them all, though.
>> >>>
>> >>> On 30 January 2016 at 03:52, Joe Leslie-Hurd > wrote:
>> >>>>
>> >>>> Hi Ramana,
>> >>>>
>> >>>> There's currently no tool support for this, but I don't think it
>> >>>> would
>> >>>> be too difficult to implement. What is your use-case?
>> >>>>
>> >>>> Cheers,
>> >>>>
>> >>>> Joe
>> >>>>
>> >>>> On Fri, Jan 29, 2016 at 12:36 AM, Ramana Kumar
>> >>>> >
>> >>>> wrote:
>> >>>> > Hi,
>> >>>> >
>> >>>> > Is it possible to take a theory that makes definitions of
>> >>>> > types/constants,
>> >>>> > and then re-present the same theory _without_ making the
>> >>>> > definitions
>> >>>> > (instead taking them as ungrounded constants, and the definitional
>> >>>> > theorems
>> >>>> > as axioms).
>> >>>> >
>> >>>> > I know there is already this command:
>> >>>> >
>> >>>> > opentheory info --theorems ...
>> >>>> >
>> >>>> > which removes all the proofs, but it still keeps the definitions
>> >>>> > in.
>> >>>> >
>> >>>> > Can I also remove the definitions?
>> >>>> >
>> >>>> > In essence, I want a totally axiomatic presentation of a theory.
>> >>>> >
>> >>>> > Thanks,
>> >>>> > Ramana
>> >>>> >
>> >>>> > _______________________________________________
>> >>>> > opentheory-users mailing list
>> >>>> > opentheory-users at gilith.com
>> >>>> > http://www.gilith.com/mailman/listinfo/opentheory-users
>> >>>> >
>> >>>>
>> >>>> _______________________________________________
>> >>>> opentheory-users mailing list
>> >>>> opentheory-users at gilith.com
>> >>>> http://www.gilith.com/mailman/listinfo/opentheory-users
>> >>>
>> >>>
>> >>
>> >>
>> >> _______________________________________________
>> >> opentheory-users mailing list
>> >> opentheory-users at gilith.com
>> >> http://www.gilith.com/mailman/listinfo/opentheory-users
>> >>
>>
>> _______________________________________________
>> opentheory-users mailing list
>> opentheory-users at gilith.com
>> http://www.gilith.com/mailman/listinfo/opentheory-users
>
>
>
> _______________________________________________
> opentheory-users mailing list
> opentheory-users at gilith.com
> http://www.gilith.com/mailman/listinfo/opentheory-users
>
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