Natural number comparisons with evidence

[Joe Hendrix]

To throw out additional related work, I had a need for runtime values that capture type-level naturals.  It’s used primarily for representing the widths in a type-safe bitvector formulas.

The code is a few years old, but publicly available here:

  https://github.com/GaloisInc/parameterized-utils/blob/master/src/Data/Parameterized/NatRepr.hs

I’d be interested in knowing if there are now any comprehensive libraries for doing this sort of runtime reflection of type-level naturals.

Regards,
Joe

> On May 24, 2018, at 1:07 PM, Conal Elliott <conal at conal.net> wrote:
> 
> I'm glad to know. Thanks for the endorsement, Richard.
> 
> On Thu, May 24, 2018 at 1:05 PM, Richard Eisenberg <rae at cs.brynmawr.edu> wrote:
> Just to add my 2 cents: I've played in this playground and used the same structures as David. I second his suggestions.
> 
> Richard
> 
> 
>> On May 24, 2018, at 3:54 PM, Conal Elliott <conal at conal.net> wrote:
>> 
>> Great! Thanks for the suggestion to use type equality and coerced `Refl`.  - Conal
>> 
>> On Thu, May 24, 2018 at 10:43 AM, David Feuer <david.feuer at gmail.com> wrote:
>> On Thu, May 24, 2018, 1:03 PM Conal Elliott <conal at conal.net> wrote:
>> Thanks for this suggestion, David. It seems to work out well, though I haven't tried running yet.
>> 
>> > unsafeDict :: Dict c
>> > unsafeDict = unsafeCoerce (Dict @ ())
>> >
>> > unsafeSatisfy :: forall c a. (c => a) -> a
>> > unsafeSatisfy z | Dict <- unsafeDict @ c = z
>> 
>> This doesn't really smell right to me, no. Dict @() is actually a rather different value than you seek. In general, these look like they do way more than they ever can. I would suggest you look through those comparison *constraints* to the underlying type equalities involving the primitive CmpNat type family.
>> 
>> -- Better, because there's only one Refl
>> unsafeEqual :: forall a b. a :~: b
>> unsafeEqual :: unsafeCoerce Refl
>> 
>> unsafeWithEqual :: forall a b r. (a ~ b => r) -> r
>> unsafeWithEqual r
>>   | Refl <- unsafeEqual @a @b = r
>> 
>> compareEv = case .... of
>>   LT -> unsafeWithEqual @(CmpNat u v) @LT CompareLT
>>   ...
>> 
>> 
>> Now we can define `compareEv`:
>> 
>> > compareEv :: forall u v. KnownNat2 u v => CompareEv u v
>> > compareEv = case natValAt @ u `compare` natValAt @ v of
>> >               LT -> unsafeSatisfy @ (u < v) CompareLT
>> >               EQ -> unsafeSatisfy @ (u ~ v) CompareEQ
>> >               GT -> unsafeSatisfy @ (u > v) CompareGT
>> 
>> If anyone has other techniques to suggest, I'd love to hear.
>> 
>> -- Conal
>> 
>> 
>> On Wed, May 23, 2018 at 5:44 PM, David Feuer <david.feuer at gmail.com> wrote:
>> I think the usual approach for defining these sorts of primitive operations is to use unsafeCoerce.
>> 
>> On Wed, May 23, 2018, 7:39 PM Conal Elliott <conal at conal.net> wrote:
>> When programming with GHC's type-level natural numbers and `KnownNat` constraints, how can one construct *evidence* of the result of comparisons to be used in further computations? For instance, we might define a type for augmenting the results of `compare` with evidence:
>> 
>> > data CompareEv u v
>> >   = (u < v) => CompareLT
>> >   | (u ~ v) => CompareEQ
>> >   | (u > v) => CompareGT
>> 
>> Then I'd like to define a comparison operation (to be used with `AllowAmbiguousTypes` and `TypeApplications`, alternatively taking proxy arguments):
>> 
>> > compareEv :: (KnownNat m, KnownNat n) => CompareEv u v
>> 
>> With `compareEv`, we can bring evidence into scope in `case` expressions.
>> 
>> I don't know how to implement `compareEv`. The following attempt fails to type-check, since `compare` doesn't produce evidence (which is the motivation for `compareEv` over `compare`):
>> 
>> > compareEv = case natVal (Proxy @ u) `compare` natVal (Proxy @ v) of
>> >               LT -> CompareLT
>> >               EQ -> CompareEQ
>> >               GT -> CompareGT
>> 
>> Can `compareEv` be implemented in GHC Haskell? Is there already an implementation of something similar? Any other advice?
>> 
>> Thanks,  -- Conal
>> 
>> _______________________________________________
>> Glasgow-haskell-users mailing list
>> Glasgow-haskell-users at haskell.org
>> http://mail.haskell.org/cgi-bin/mailman/listinfo/glasgow-haskell-users
>> 
>> 
>> _______________________________________________
>> Glasgow-haskell-users mailing list
>> Glasgow-haskell-users at haskell.org
>> http://mail.haskell.org/cgi-bin/mailman/listinfo/glasgow-haskell-users
> 
> 
> _______________________________________________
> Glasgow-haskell-users mailing list
> Glasgow-haskell-users at haskell.org
> http://mail.haskell.org/cgi-bin/mailman/listinfo/glasgow-haskell-users

-------------- next part --------------
A non-text attachment was scrubbed...
Name: signature.asc
Type: application/pgp-signature
Size: 833 bytes
Desc: Message signed with OpenPGP
URL: <http://mail.haskell.org/pipermail/glasgow-haskell-users/attachments/20180524/e0c1404a/attachment.sig>