can/should Functor have a quantified coercible constraint?
Oleg Grenrus
oleg.grenrus at iki.fi
Sun Jan 3 17:01:48 UTC 2021
Prelude Control.Monad.Trans.State> :i StateT
type role StateT nominal representational nominal
Note, `StateT` is nominal in last argument (a). Thus if (forall c d.
Coercible ...) where a Functor superclass, Functor (and thus Monad)
wouldn't be definable for StateT. That would be... unfortunate.
Until there are "higher roles" Functor cannot be Coercible1. It would
rule very simple code.
(OTOH Mag can be repaired,
https://oleg.fi/gists/posts/2019-07-31-fmap-coerce-coerce.html#functor-should-be-parametric).
- Oleg
On 3.1.2021 18.31, Carter Schonwald wrote:
> Hey David,
> could you exposit what would go wrong? a concrete proof witness or
> explanation would help me a lot. other people might benefit too.
>
>
> for the stateT s Maybe a, perhaps i'm still waking up this AM, so let
> me try
> newtype StateT s m a = StateT {runStateT :: s -> m (a, s)}
>
> so this should expand to
> '(s -> Maybe (a,s)),'
> but the coerce would be on the 'a' here ... so i'm not seeing the issue?
>
>
>
> the latter example seem to boil down to "a free appplicative/functor
> Gadt" with some extra bits, though i've not worked through to seeing
> the unsafety
> for the latter examples, the definitions are the following :
> traverseBia
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#traverseBia>::(Traversablet
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090275>,Biapplicative
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Biapplicative>p
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090274>)=>(a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090273>->p
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090274>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090272>c
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090271>)->t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090275>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090273>->p
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090274>(t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090275>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090272>)(t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090275>c
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090271>)traverseBia
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#traverseBia>=inline(traverseBiaWith
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#traverseBiaWith>traverse)--------
> traverseBiaWith
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#traverseBiaWith>::forallp
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090289>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090288>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090285>c
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090284>s
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090287>t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090286>.Biapplicative
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Biapplicative>p
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090289>=>(forallf
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090291>x
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090290>.Applicativef
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090291>=>(a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090288>->f
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090291>x
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090290>)->s
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090287>->f
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090291>(t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090286>x
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090290>))->(a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090288>->p
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090289>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090285>c
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090284>)->s
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090287>->p
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090289>(t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090286>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090285>)(t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090286>c
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090284>)traverseBiaWith
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#traverseBiaWith>trav
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089877>p
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089876>s
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089875>=smash
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#smash>p
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089876>(trav
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089877>One
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#One>s
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089875>)
> ------- smash
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#smash>::forallp
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090262>t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090258>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090261>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090260>c
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090259>.Biapplicative
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Biapplicative>p
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090262>=>(a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090261>->p
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090262>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090260>c
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090259>)->(forallx
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090264>.Mag
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Mag>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090261>x
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090264>(t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090258>x
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090264>))->p
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090262>(t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090258>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090260>)(t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090258>c
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090259>)smash
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#smash>p
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089872>m
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089871>=go
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089870>m
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089871>m
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089871>wherego
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089870>::forallx
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090249>y
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090248>.Mag
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Mag>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090261>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090260>x
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090249>->Mag
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Mag>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090261>c
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090259>y
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090248>->p
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090262>x
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090249>y
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090248>go
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089870>(Pure
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Pure>t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089868>)(Pure
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Pure>u
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089867>)=bipure
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#bipure>t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089868>u
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089867>go
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089870>(Map
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Map>f
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089865>x
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089864>)(Map
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Map>g
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089863>y
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089862>)=bimapf
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089865>g
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089863>(go
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089870>x
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089864>y
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089862>)go
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089870>(Ap
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Ap>fs
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089860>xs
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> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089870>fs
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089860>gs
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089858><<*>>
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> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089870>xs
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089859>ys
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089857>#if
> MIN_VERSION_base(4,10,0) go
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089870>(LiftA2
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#LiftA2>f
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089855>xs
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089854>ys
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089853>)(LiftA2
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#LiftA2>g
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089852>zs
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089851>ws
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089850>)=biliftA2
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#biliftA2>f
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089855>g
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089852>(go
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089870>xs
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089854>zs
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089851>)(go
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089870>ys
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089853>ws
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089850>)#endif
> go
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089870>(One
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#One>x
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089849>)(One
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#One>_)=p
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089872>x
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089849>go
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089870>__=impossibleError
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#impossibleError>
> ---- and then the magma is -- This is used to reify a traversal for
> 'traverseBia'. It's a somewhat-- bogus 'Functor' and 'Applicative'
> closely related to 'Magma' from the-- @lens@ package. Valid traversals
> don't use (<$), (<*), or (*>), so-- we leave them out. We offer all
> the rest of the Functor and Applicative-- operations to improve
> performance: we generally want to keep the structure-- as small as
> possible. We might even consider using RULES to widen lifts-- when we
> can:---- liftA2 f x y <*> z ==> liftA3 f x y z,---- etc., up to the
> pointer tagging limit. But we do need to be careful. I don't-- *think*
> GHC will ever inline the traversal into the go function (because
> that-- would duplicate work), but if it did, and if different RULES
> fired for the-- two copies, everything would break horribly.---- Note:
> if it's necessary for some reason, we *could* relax GADTs to--
> ExistentialQuantification by changing the type of One to---- One :: (b
> -> c) -> a -> Mag a b c---- where the function will always end up
> being id. But we allocate a *lot*-- of One constructors, so this would
> definitely be bad for performance.dataMag
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Mag>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089846>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089845>t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089844>wherePure
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Pure>::t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090197>->Mag
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Mag>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090196>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090195>t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090197>Map
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Map>::(x
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089843>->t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090218>)->Mag
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Mag>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090217>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090216>x
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089843>->Mag
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Mag>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090217>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090216>t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090218>Ap
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Ap>::Mag
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Mag>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089842>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089841>(t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089840>->u
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089839>)->Mag
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Mag>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089842>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089841>t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089840>->Mag
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Mag>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089842>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089841>u
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089839>#if
> MIN_VERSION_base(4,10,0) LiftA2
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#LiftA2>::(t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089838>->u
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089837>->v
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090187>)->Mag
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Mag>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090186>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090185>t
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089838>->Mag
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Mag>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090186>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090185>u
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089837>->Mag
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Mag>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090186>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090185>v
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090187>#endif
> One
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#One>::a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090256>->Mag
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Mag>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090256>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090255>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679090255>instanceFunctor(Mag
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Mag>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089836>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089835>)wherefmap=Map
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Map>instanceApplicative(Mag
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Mag>a
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089829>b
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#local-6989586621679089828>)wherepure=Pure
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Pure>(<*>)=Ap
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#Ap>#if
> MIN_VERSION_base(4,10,0) liftA2=LiftA2
> <https://hackage.haskell.org/package/bifunctors-5.5.9/docs/src/Data.Biapplicative.html#LiftA2>#endif
>
>
> On Sun, Jan 3, 2021 at 11:09 AM David Feuer <david.feuer at gmail.com
> <mailto:david.feuer at gmail.com>> wrote:
>
> You're not being very imaginative at all. Try out, oh, `StateT s
> Maybe`. Or play around with a nice fake functor like the magma
> used to implement `traverseBia` in `bifunctors`—pretty sure that
> won't work out.
>
> On Sun, Jan 3, 2021, 11:00 AM Carter Schonwald
> <carter.schonwald at gmail.com <mailto:carter.schonwald at gmail.com>>
> wrote:
>
> Hey everyone!
>
> for context, I have some code where I was seeing how far
> coerce lets me go to avoid doing wrappers for certain codes,
>
> i found i had to write the following (mapping an operation
> over to its newtyped sibling)
>
> ```
> -- > :t QRA.wither
> --- forall a b f . Applicative f => (a -> f (Maybe b)) ->
> RAList a -> f (RAList b)
> ---
> wither :: forall a b f . (Applicative f, (forall c d .
> Coercible c d => Coercible (f c) (f d)) ) =>
> (a -> f (Maybe b)) -> RAList a -> f (RAList b)
> wither = \f la -> coerce $ QRA.wither f $ coerce la
> ```
>
> i'd much rather be able to write
> ```
> wither :: forall a b f . (Applicative f) =>
> (a -> f (Maybe b)) -> RAList a -> f (RAList b)
> wither = \f la -> coerce $ QRA.wither f $ coerce la
> ```
>
>
> this seems like it'd be best done via something like changing
> the functor class definition to
>
> ```
> class (forall c d . Coercible c d => Coercible (f c) (f d))
> ) => Functor f where ..
> ```
>
> is there any specific reason why this is not feasible? I cant
> think of a GADT where this wouldn't be totally safe to do
> (because unlike in foldable, f is in both the domain and
> co-domain), but maybe i'm not being imaginative enough?
>
> look forward to learning what our obstacles are to making this
> happen for ghc 9.2 :)
>
> -Carter
>
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