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 <co...@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.fe...@gmail.com > <mailto:david.fe...@gmail.com>> wrote: > On Thu, May 24, 2018, 1:03 PM Conal Elliott <co...@conal.net > <mailto:co...@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.fe...@gmail.com > <mailto:david.fe...@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 <co...@conal.net > <mailto:co...@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@haskell.org <mailto:Glasgow-haskell-users@haskell.org> > http://mail.haskell.org/cgi-bin/mailman/listinfo/glasgow-haskell-users > <http://mail.haskell.org/cgi-bin/mailman/listinfo/glasgow-haskell-users> > > > _______________________________________________ > Glasgow-haskell-users mailing list > Glasgow-haskell-users@haskell.org > http://mail.haskell.org/cgi-bin/mailman/listinfo/glasgow-haskell-users
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