[opentheory-users] extending the standard library

[Ramana Kumar]

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
> >
> > _______________________________________________
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> > opentheory-users at gilith.com
> > http://www.gilith.com/opentheory/mailing-list
> >
>
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