[opentheory-users] extending the standard library

[Konrad Slind]

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
>>> >
>>>
>>> _______________________________________________
>>> opentheory-users mailing list
>>> opentheory-users at gilith.com
>>> http://www.gilith.com/opentheory/mailing-list
>>>
>>
>>
>
> _______________________________________________
> opentheory-users mailing list
> opentheory-users at gilith.com
> http://www.gilith.com/opentheory/mailing-list
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://www.gilith.com/opentheory/mailing-list/attachments/20160413/9605c280/attachment.html>