One other thing I should add. We'd really, really like to have isomorphism evidence: toThenFrom :: pr p -> To (From x :: Rep a p) :~: (x :: a) fromThenTo :: pr1 a -> pr2 (r :: Rep a p) -> From (To r :: a) :~: (r :: Rep a p) I believe these would make the To and From families considerably more useful. Unfortunately, while I'm pretty sure those are completely legit for any Generic-derived types, I don't think there's ever any way to prove them in Haskell! Ugh. On Thursday, August 31, 2017 3:37:15 PM EDT David Feuer wrote:
I've been thinking for several weeks that it might be useful to offer type-level generics. That is, along with
to :: Rep a k -> a from :: a -> Rep a
perhaps we should also derive
type family To (r :: Rep a x) :: a type family From (v :: a) :: Rep a x
This would allow us to use generic programming at the type level For example, we could write a generic ordering family:
class OrdK (k :: Type) where type Compare (x :: k) (y :: k) :: Ordering type Compare (x :: k) (y :: k) = GenComp (Rep k ()) (From x) (From y)
instance OrdK Nat where type Compare x y = CmpNat x y
instance OrdK Symbol where type Compare x y = CmpSymbol x y
instance OrdK [a] -- No implementation needed!
type family GenComp k (x :: k) (y :: k) :: Ordering where GenComp (M1 i c f p) ('M1 x) ('M1 y) = GenComp (f p) x y GenComp (K1 i c p) ('K1 x) ('K1 y) = Compare x y GenComp ((x :+: y) p) ('L1 m) ('L1 n) = GenComp (x p) m n GenComp ((x :+: y) p) ('R1 m) ('R1 n) = GenComp (y p) m n GenComp ((x :+: y) p) ('L1 _) ('R1 _) = 'LT GenComp ((x :+: y) p) ('R1 _) ('L1 _) = 'GT GenComp ((x :*: y) p) (x1 ':*: y1) (x2 ':*: y2) = PComp (GenComp (x p) x1 x2) (y p) y1 y2 GenComp (U1 p) _ _ = 'EQ GenComp (V1 p) _ _ = 'EQ
type family PComp (c :: Ordering) k (x :: k) (y :: k) :: Ordering where PComp 'EQ k x y = GenComp k x y PComp x _ _ _ = x
For people who want to play around with the idea, here are the definitions of To and From for lists:
To ('M1 ('L1 ('M1 'U1))) = '[] To ('M1 ('R1 ('M1 ('M1 ('K1 x) ':*: 'M1 ('K1 xs))))) = x ': xs From '[] = 'M1 ('L1 ('M1 'U1)) From (x ': xs) = 'M1 ('R1 ('M1 ('M1 ('K1 x) ':*: 'M1 ('K1 xs))))
David