[opentheory-users] extending the standard library

[Ramana Kumar]

Hi,

I wanted to check if there was further interest in continuing this
discussion from last month.

The reason is that I am putting together a lot of OpenTheory packages based
on theories made with the HOL theorem prover, and I would like it if this
work could fit together nicely with other OpenTheory packages rather than
living in its own universe (and perpetuating the problem of fragmentation).

I think the theories I'm looking into (n-bit words, floating point numbers,
real numbers, integers, rings, streams, quotients, ...) should all
ultimately end up within the Standard Library. But to get there would I
imagine require substantial coordination with the designers of the
OpenTheory standard library, and other interested community members. I am
also looking for technical advice on how to interface with the existing
theories in the Gilith repo that seem to cover some of those topics.

Cheers,
Ramana

On 13 April 2016 at 17:15, Ramana Kumar <ramana at member.fsf.org> wrote:

> Data.List.unzip works as a replacement for list.UNZIP. However, I will
> hold back for a bit on making a new version of hol-base in case there are
> further improvements arising from this thread.
>
> On 13 April 2016 at 15:38, Konrad Slind <konrad.slind at gmail.com> wrote:
>
>> Re: MAP2 in HOL4. This is an example of an underspecified function. I
>> recall having
>> to redefine map2 to completely specify it in order to get it through the
>> HOL-->CakeML translator.
>>
>> So, presumably, different systems can and will define common partial
>> functions differently, as
>> either underspecified or completely specified. Is there an OpenTheory
>> policy on this, for
>> its standard library?
>>
>> Konrad.
>>
>>
>> On Tue, Apr 12, 2016 at 11:56 PM, Ramana Kumar <ramana at member.fsf.org>
>> wrote:
>>
>>> It looks like list.ZIP can't be mapped to Data.List.zip because the
>>> latter is curried. But I'm still looking into unzip.
>>>
>>> On 13 April 2016 at 13:56, Ramana Kumar <ramana at member.fsf.org> wrote:
>>>
>>>> The HOL4 base library has its own version of constants like
>>>> Data.List.take and Number.Natural.- because it needs to prove theorems like:
>>>>
>>>> ⊦ length (list.TAKE n xs) = if n ≤ length xs then n else length xs
>>>>
>>>> ⊦ (∀m. arithmetic.- 0 m = 0) ∧
>>>>   ∀m n.
>>>>     arithmetic.- (suc m) n = if m < n then 0 else suc (arithmetic.- m n
>>>> )
>>>> I don't think these theorems are provable using the OpenTheory standard
>>>> library versions of those constants.
>>>>
>>>> However, I don't know whether Data.List.unzip suffers from this
>>>> problem. If not, then the HOL4 base package should be updated to use the
>>>> standard library constant. It would be helpful if you could make a list of
>>>> any other similar updates that should be made.
>>>>
>>>> I don't think the current OpenTheory standard library base contains
>>>> theories that every HOL theorem prover supports. There are constants like
>>>> Data.List.nub, for example, which are not supported by HOL4. I'm not
>>>> entirely sure whether being the intersection of what every HOL theorem
>>>> prover supports is a good goal, but if that is the rule it should at least
>>>> be followed :)
>>>>
>>>> However, my question was not solely about the base package, but about
>>>> the naming scheme for the standard library. If there are useful constants
>>>> from other theorem provers (like, say, HOL4's list.GENLIST or list.MAP2), I
>>>> think their name and characterising theorems should be fit into the
>>>> OpenTheory namespace (Data.List, for example) in a standardised way, even
>>>> if they don't make it into the base package itself. What do you think of
>>>> that?
>>>>
>>>> I envision OpenTheory being used for the twin goals of portability
>>>> (where being an intersection is good) and designing a rich, cleanly
>>>> organised, useful standard library of HOL theorems (where being a union is
>>>> good). These activities can happen simultaneously in different OpenTheory
>>>> standard packages.
>>>>
>>>> On 13 April 2016 at 04:11, Joe Leslie-Hurd <joe at gilith.com> wrote:
>>>>
>>>>> Hi Ramana,
>>>>>
>>>>> The intent is for the standard theory library to always be evolving,
>>>>> but slowly, because it's supposed to contain the base theories that
>>>>> *every* HOL theorem prover supports.
>>>>>
>>>>> Looking through the theory I see a lot of defined constants that also
>>>>> occur in the OpenTheory standard library (e.g., list.UNZIP), and I was
>>>>> wondering why the HOL4 base theory has its own version?
>>>>>
>>>>> Cheers,
>>>>>
>>>>> Joe
>>>>>
>>>>> On Sun, Apr 10, 2016 at 1:54 PM, Ramana Kumar <ramana at member.fsf.org>
>>>>> wrote:
>>>>> > Hi Joe,
>>>>> >
>>>>> > You will have seen that the HOL developers have uploaded a package
>>>>> called
>>>>> > hol-base to the Gilith repo. The purpose of this package is twofold:
>>>>> >
>>>>> > It proves many useful theorems as found in the basic libraries of
>>>>> the HOL
>>>>> > theorem prover.
>>>>> > It serves to satisfy the assumptions of further theories developed
>>>>> in the
>>>>> > HOL theorem prover, by proving those assumptions using only the
>>>>> theorems of
>>>>> > the OpenTheory standard library base package.
>>>>> >
>>>>> > For purpose 1 in particular, it seems to me that many of the
>>>>> constants
>>>>> > defined by hol-base would benefit from residing in an appropriate
>>>>> place in
>>>>> > OpenTheory's namespace hierarchy, and indeed some of the proofs from
>>>>> > hol-base might beneficially be moved into the base package itself.
>>>>> > (Currently, all constants defined by hol-base are in their own
>>>>> namespace.)
>>>>> >
>>>>> > Is the design of the standard library still evolving, and is it open
>>>>> to
>>>>> > extension? Would you be willing to copy over any useful-looking
>>>>> constants?
>>>>> > And/or settle on some namespace decisions?
>>>>> >
>>>>> > Cheers,
>>>>> > Ramana
>>>>> >
>>>>> > _______________________________________________
>>>>> > opentheory-users mailing list
>>>>> > opentheory-users at gilith.com
>>>>> > http://www.gilith.com/opentheory/mailing-list
>>>>> >
>>>>>
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>>>>>
>>>>
>>>>
>>>
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>>
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