Data.Hefty.Sum

An implementation of an open union for higher-order effects using recursively nested binary sums.

Documentation

absurdLH :: (NopS :+: h) f ~> h f

absurdRH :: (h :+: NopS) f ~> h f

swapSumH :: (h1 :+: h2) f a -> (h2 :+: h1) f a

type family SumH hs where ...

Equations

SumH '[] = NopS

SumH (h ': hs) = h :+: SumH hs

newtype SumUnionH hs f a

An implementation of an open union for higher-order effects using recursively nested binary sums.

Constructors

SumUnionH

Fields

• unSumUnionH :: SumH hs f a

Instances

UnionH SumUnionH

Defined in Data.Hefty.Sum

Associated Types

type HasMembershipH SumUnionH h hs

Methods

injectH :: forall (h :: Signature) (hs :: [Signature]) (f :: Type -> Type). HasMembershipH SumUnionH h hs => h f ~> SumUnionH hs f

projectH :: forall h (hs :: [Signature]) (f :: Type -> Type) a. HasMembershipH SumUnionH h hs => SumUnionH hs f a -> Maybe (h f a)

absurdUnionH :: forall (f :: Type -> Type) a x. SumUnionH '[] f a -> x

compH :: forall h (f :: Type -> Type) a (hs :: [Signature]). Either (h f a) (SumUnionH hs f a) -> SumUnionH (h ': hs) f a

decompH :: forall h (hs :: [Signature]) (f :: Type -> Type) a. SumUnionH (h ': hs) f a -> Either (h f a) (SumUnionH hs f a)

(|+:) :: forall h (f :: Type -> Type) a r (hs :: [Signature]). (h f a -> r) -> (SumUnionH hs f a -> r) -> SumUnionH (h ': hs) f a -> r

inject0H :: forall (h :: (Type -> Type) -> Type -> Type) (f :: Type -> Type) (hs :: [(Type -> Type) -> Type -> Type]). h f ~> SumUnionH (h ': hs) f

injectUnderH :: forall (h2 :: (Type -> Type) -> Type -> Type) (f :: Type -> Type) (h1 :: (Type -> Type) -> Type -> Type) (hs :: [(Type -> Type) -> Type -> Type]). h2 f ~> SumUnionH (h1 ': (h2 ': hs)) f

injectUnder2H :: forall (h3 :: (Type -> Type) -> Type -> Type) (f :: Type -> Type) (h1 :: (Type -> Type) -> Type -> Type) (h2 :: (Type -> Type) -> Type -> Type) (hs :: [(Type -> Type) -> Type -> Type]). h3 f ~> SumUnionH (h1 ': (h2 ': (h3 ': hs))) f

injectUnder3H :: forall (h4 :: (Type -> Type) -> Type -> Type) (f :: Type -> Type) (h1 :: (Type -> Type) -> Type -> Type) (h2 :: (Type -> Type) -> Type -> Type) (h3 :: (Type -> Type) -> Type -> Type) (hs :: [(Type -> Type) -> Type -> Type]). h4 f ~> SumUnionH (h1 ': (h2 ': (h3 ': (h4 ': hs)))) f

weakenH :: forall (hs :: [Signature]) (f :: Type -> Type) (h :: Signature). SumUnionH hs f ~> SumUnionH (h ': hs) f

weaken2H :: forall (hs :: [Signature]) (f :: Type -> Type) (h1 :: Signature) (h2 :: Signature). SumUnionH hs f ~> SumUnionH (h1 ': (h2 ': hs)) f

weaken3H :: forall (hs :: [Signature]) (f :: Type -> Type) (h1 :: Signature) (h2 :: Signature) (h3 :: Signature). SumUnionH hs f ~> SumUnionH (h1 ': (h2 ': (h3 ': hs))) f

weaken4H :: forall (hs :: [Signature]) (f :: Type -> Type) (h1 :: Signature) (h2 :: Signature) (h3 :: Signature) (h4 :: Signature). SumUnionH hs f ~> SumUnionH (h1 ': (h2 ': (h3 ': (h4 ': hs)))) f

weakenUnderH :: forall (h1 :: Signature) (hs :: [Signature]) (f :: Type -> Type) (h2 :: Signature). SumUnionH (h1 ': hs) f ~> SumUnionH (h1 ': (h2 ': hs)) f

weakenUnder2H :: forall (h1 :: Signature) (h2 :: Signature) (hs :: [Signature]) (f :: Type -> Type) (h3 :: Signature). SumUnionH (h1 ': (h2 ': hs)) f ~> SumUnionH (h1 ': (h2 ': (h3 ': hs))) f

weakenUnder3H :: forall (h1 :: Signature) (h2 :: Signature) (h3 :: Signature) (hs :: [Signature]) (f :: Type -> Type) (h4 :: Signature). SumUnionH (h1 ': (h2 ': (h3 ': hs))) f ~> SumUnionH (h1 ': (h2 ': (h3 ': (h4 ': hs)))) f

weaken2UnderH :: forall (h1 :: Signature) (hs :: [Signature]) (f :: Type -> Type) (h2 :: Signature) (h3 :: Signature). SumUnionH (h1 ': hs) f ~> SumUnionH (h1 ': (h2 ': (h3 ': hs))) f

weaken2Under2H :: forall (h1 :: Signature) (h2 :: Signature) (hs :: [Signature]) (f :: Type -> Type) (h3 :: Signature) (h4 :: Signature). SumUnionH (h1 ': (h2 ': hs)) f ~> SumUnionH (h1 ': (h2 ': (h3 ': (h4 ': hs)))) f

weaken3UnderH :: forall (h1 :: Signature) (hs :: [Signature]) (f :: Type -> Type) (h2 :: Signature) (h3 :: Signature) (h4 :: Signature). SumUnionH (h1 ': hs) f ~> SumUnionH (h1 ': (h2 ': (h3 ': (h4 ': hs)))) f

flipUnionH :: forall (h1 :: Signature) (h2 :: Signature) (hs :: [Signature]) (f :: Type -> Type). SumUnionH (h1 ': (h2 ': hs)) f ~> SumUnionH (h2 ': (h1 ': hs)) f

flipUnion3H :: forall (h1 :: Signature) (h2 :: Signature) (h3 :: Signature) (hs :: [Signature]) (f :: Type -> Type). SumUnionH (h1 ': (h2 ': (h3 ': hs))) f ~> SumUnionH (h3 ': (h2 ': (h1 ': hs))) f

flipUnionUnderH :: forall (h1 :: Signature) (h2 :: Signature) (h3 :: Signature) (hs :: [Signature]) (f :: Type -> Type). SumUnionH (h1 ': (h2 ': (h3 ': hs))) f ~> SumUnionH (h1 ': (h3 ': (h2 ': hs))) f

rot3H :: forall (h1 :: Signature) (h2 :: Signature) (h3 :: Signature) (hs :: [Signature]) (f :: Type -> Type). SumUnionH (h1 ': (h2 ': (h3 ': hs))) f ~> SumUnionH (h2 ': (h3 ': (h1 ': hs))) f

rot3H' :: forall (h1 :: Signature) (h2 :: Signature) (h3 :: Signature) (hs :: [Signature]) (f :: Type -> Type). SumUnionH (h1 ': (h2 ': (h3 ': hs))) f ~> SumUnionH (h3 ': (h1 ': (h2 ': hs))) f

bundleUnion2H :: forall (u' :: [Signature] -> Signature) (h1 :: Signature) (h2 :: Signature) (hs :: [Signature]) (f :: Type -> Type). UnionH u' => SumUnionH (h1 ': (h2 ': hs)) f ~> SumUnionH (u' '[h1, h2] ': hs) f

bundleUnion3H :: forall (u' :: [Signature] -> Signature) (h1 :: Signature) (h2 :: Signature) (h3 :: Signature) (hs :: [Signature]) (f :: Type -> Type). UnionH u' => SumUnionH (h1 ': (h2 ': (h3 ': hs))) f ~> SumUnionH (u' '[h1, h2, h3] ': hs) f

bundleUnion4H :: forall (u' :: [Signature] -> Signature) (h1 :: Signature) (h2 :: Signature) (h3 :: Signature) (h4 :: Signature) (hs :: [Signature]) (f :: Type -> Type). UnionH u' => SumUnionH (h1 ': (h2 ': (h3 ': (h4 ': hs)))) f ~> SumUnionH (u' '[h1, h2, h3, h4] ': hs) f

unbundleUnion2H :: forall (u' :: [Signature] -> Signature) (h1 :: Signature) (h2 :: Signature) (hs :: [Signature]) (f :: Type -> Type). UnionH u' => SumUnionH (u' '[h1, h2] ': hs) f ~> SumUnionH (h1 ': (h2 ': hs)) f

unbundleUnion3H :: forall (u' :: [Signature] -> Signature) (h1 :: Signature) (h2 :: Signature) (h3 :: Signature) (hs :: [Signature]) (f :: Type -> Type). UnionH u' => SumUnionH (u' '[h1, h2, h3] ': hs) f ~> SumUnionH (h1 ': (h2 ': (h3 ': hs))) f

unbundleUnion4H :: forall (u' :: [Signature] -> Signature) (h1 :: Signature) (h2 :: Signature) (h3 :: Signature) (h4 :: Signature) (hs :: [Signature]) (f :: Type -> Type). UnionH u' => SumUnionH (u' '[h1, h2, h3, h4] ': hs) f ~> SumUnionH (h1 ': (h2 ': (h3 ': (h4 ': hs)))) f

HFunctor (SumH hs) => HFunctor (SumUnionH hs)

Defined in Data.Hefty.Sum

Methods

hfmap :: forall (f :: Type -> Type) (g :: Type -> Type). (f :-> g) -> SumUnionH hs f :-> SumUnionH hs g

Foldable (SumUnionH ('[] :: [(Type -> Type) -> Type -> Type]) f)

Defined in Data.Hefty.Sum

Methods

fold :: Monoid m => SumUnionH '[] f m -> m

foldMap :: Monoid m => (a -> m) -> SumUnionH '[] f a -> m

foldMap' :: Monoid m => (a -> m) -> SumUnionH '[] f a -> m

foldr :: (a -> b -> b) -> b -> SumUnionH '[] f a -> b

foldr' :: (a -> b -> b) -> b -> SumUnionH '[] f a -> b

foldl :: (b -> a -> b) -> b -> SumUnionH '[] f a -> b

foldl' :: (b -> a -> b) -> b -> SumUnionH '[] f a -> b

foldr1 :: (a -> a -> a) -> SumUnionH '[] f a -> a

foldl1 :: (a -> a -> a) -> SumUnionH '[] f a -> a

toList :: SumUnionH '[] f a -> [a]

null :: SumUnionH '[] f a -> Bool

length :: SumUnionH '[] f a -> Int

elem :: Eq a => a -> SumUnionH '[] f a -> Bool

maximum :: Ord a => SumUnionH '[] f a -> a

minimum :: Ord a => SumUnionH '[] f a -> a

sum :: Num a => SumUnionH '[] f a -> a

product :: Num a => SumUnionH '[] f a -> a

Traversable (SumUnionH ('[] :: [(Type -> Type) -> Type -> Type]) f)

Defined in Data.Hefty.Sum

Methods

traverse :: Applicative f0 => (a -> f0 b) -> SumUnionH '[] f a -> f0 (SumUnionH '[] f b)

sequenceA :: Applicative f0 => SumUnionH '[] f (f0 a) -> f0 (SumUnionH '[] f a)

mapM :: Monad m => (a -> m b) -> SumUnionH '[] f a -> m (SumUnionH '[] f b)

sequence :: Monad m => SumUnionH '[] f (m a) -> m (SumUnionH '[] f a)

Functor (SumUnionH ('[] :: [(Type -> Type) -> Type -> Type]) f)

Defined in Data.Hefty.Sum

Methods

fmap :: (a -> b) -> SumUnionH '[] f a -> SumUnionH '[] f b

(<$) :: a -> SumUnionH '[] f b -> SumUnionH '[] f a

type HasMembershipH SumUnionH h hs

Defined in Data.Hefty.Sum

type HasMembershipH SumUnionH h hs = h << SumH hs

class isHead ~ (h1 `IsHeadSigOf` h2) => SumMemberH isHead (h1 :: Signature) h2 where

Methods

injSumH :: h1 f a -> h2 f a

projSumH :: h2 f a -> Maybe (h1 f a)

Instances

(IsHeadSigOf f (g :+: h) ~ 'False, f << h) => SumMemberH 'False f (g :+: h)

Defined in Data.Hefty.Sum

Methods

injSumH :: forall (f0 :: Type -> Type) a. f f0 a -> (g :+: h) f0 a

projSumH :: forall (f0 :: Type -> Type) a. (g :+: h) f0 a -> Maybe (f f0 a)

SumMemberH 'True f (f :+: g)

Defined in Data.Hefty.Sum

Methods

injSumH :: forall (f0 :: Type -> Type) a. f f0 a -> (f :+: g) f0 a

projSumH :: forall (f0 :: Type -> Type) a. (f :+: g) f0 a -> Maybe (f f0 a)

type family IsHeadSigOf (h1 :: Signature) h2 where ...

Equations

IsHeadSigOf f (f :+: g) = 'True

IsHeadSigOf _ _ = 'False

type (<<) h1 h2 = SumMemberH (IsHeadSigOf h1 h2) h1 h2

injH :: forall h1 h2 f. h1 << h2 => h1 f ~> h2 f

projH :: forall h1 h2 f a. h1 << h2 => h2 f a -> Maybe (h1 f a)