Data.Free.Union

A type class representing a general open union for first-order effects, independent of the internal implementation.

Documentation

class Union (u :: [Instruction] -> Instruction) where

A type class representing a general open union for first-order effects, independent of the internal implementation.

Minimal complete definition

inject, project, absurdUnion, (comp | inject0, weaken, decomp | (|+|:))

Associated Types

type HasMembership u (f :: Instruction) (fs :: [Instruction]) :: Constraint

Methods

inject :: HasMembership u f fs => f ~> u fs

project :: HasMembership u f fs => u fs a -> Maybe (f a)

absurdUnion :: u '[] a -> x

comp :: Either (f a) (u fs a) -> u (f ': fs) a

decomp :: u (f ': fs) a -> Either (f a) (u fs a)

(|+|:) :: (f a -> r) -> (u fs a -> r) -> u (f ': fs) a -> r infixr 5

inject0 :: f ~> u (f ': fs)

injectUnder :: f2 ~> u (f1 ': (f2 ': fs))

injectUnder2 :: f3 ~> u (f1 ': (f2 ': (f3 ': fs)))

injectUnder3 :: f4 ~> u (f1 ': (f2 ': (f3 ': (f4 ': fs))))

weaken :: u fs a -> u (f ': fs) a

weaken2 :: u fs a -> u (f1 ': (f2 ': fs)) a

weaken3 :: u fs a -> u (f1 ': (f2 ': (f3 ': fs))) a

weaken4 :: u fs a -> u (f1 ': (f2 ': (f3 ': (f4 ': fs)))) a

weakenUnder :: u (f1 ': fs) ~> u (f1 ': (f2 ': fs))

weakenUnder2 :: u (f1 ': (f2 ': fs)) ~> u (f1 ': (f2 ': (f3 ': fs)))

weakenUnder3 :: u (f1 ': (f2 ': (f3 ': fs))) ~> u (f1 ': (f2 ': (f3 ': (f4 ': fs))))

weaken2Under :: u (f1 ': fs) ~> u (f1 ': (f2 ': (f3 ': fs)))

weaken2Under2 :: u (f1 ': (f2 ': fs)) ~> u (f1 ': (f2 ': (f3 ': (f4 ': fs))))

weaken3Under :: u (f1 ': fs) ~> u (f1 ': (f2 ': (f3 ': (f4 ': fs))))

flipUnion :: u (f1 ': (f2 ': fs)) ~> u (f2 ': (f1 ': fs))

flipUnion3 :: u (f1 ': (f2 ': (f3 ': fs))) ~> u (f3 ': (f2 ': (f1 ': fs)))

flipUnionUnder :: u (f1 ': (f2 ': (f3 ': fs))) ~> u (f1 ': (f3 ': (f2 ': fs)))

rot3 :: u (f1 ': (f2 ': (f3 ': fs))) ~> u (f2 ': (f3 ': (f1 ': fs)))

rot3' :: u (f1 ': (f2 ': (f3 ': fs))) ~> u (f3 ': (f1 ': (f2 ': fs)))

bundleUnion2 :: Union u' => u (f1 ': (f2 ': fs)) ~> u (u' '[f1, f2] ': fs)

bundleUnion3 :: Union u' => u (f1 ': (f2 ': (f3 ': fs))) ~> u (u' '[f1, f2, f3] ': fs)

bundleUnion4 :: Union u' => u (f1 ': (f2 ': (f3 ': (f4 ': fs)))) ~> u (u' '[f1, f2, f3, f4] ': fs)

unbundleUnion2 :: Union u' => u (u' '[f1, f2] ': fs) ~> u (f1 ': (f2 ': fs))

unbundleUnion3 :: Union u' => u (u' '[f1, f2, f3] ': fs) ~> u (f1 ': (f2 ': (f3 ': fs)))

unbundleUnion4 :: Union u' => u (u' '[f1, f2, f3, f4] ': fs) ~> u (f1 ': (f2 ': (f3 ': (f4 ': fs))))

Instances

Union ExtensibleUnion

Defined in Data.Free.Extensible

Associated Types

type HasMembership ExtensibleUnion f fs

Methods

inject :: forall (f :: Instruction) (fs :: [Instruction]). HasMembership ExtensibleUnion f fs => f ~> ExtensibleUnion fs

project :: forall f (fs :: [Instruction]) a. HasMembership ExtensibleUnion f fs => ExtensibleUnion fs a -> Maybe (f a)

absurdUnion :: ExtensibleUnion '[] a -> x

comp :: forall f a (fs :: [Instruction]). Either (f a) (ExtensibleUnion fs a) -> ExtensibleUnion (f ': fs) a

decomp :: forall f (fs :: [Instruction]) a. ExtensibleUnion (f ': fs) a -> Either (f a) (ExtensibleUnion fs a)

(|+|:) :: forall f a r (fs :: [Instruction]). (f a -> r) -> (ExtensibleUnion fs a -> r) -> ExtensibleUnion (f ': fs) a -> r

inject0 :: forall (f :: Type -> Type) (fs :: [Type -> Type]). f ~> ExtensibleUnion (f ': fs)

injectUnder :: forall (f2 :: Type -> Type) (f1 :: Type -> Type) (fs :: [Type -> Type]). f2 ~> ExtensibleUnion (f1 ': (f2 ': fs))

injectUnder2 :: forall (f3 :: Type -> Type) (f1 :: Type -> Type) (f2 :: Type -> Type) (fs :: [Type -> Type]). f3 ~> ExtensibleUnion (f1 ': (f2 ': (f3 ': fs)))

injectUnder3 :: forall (f4 :: Type -> Type) (f1 :: Type -> Type) (f2 :: Type -> Type) (f3 :: Type -> Type) (fs :: [Type -> Type]). f4 ~> ExtensibleUnion (f1 ': (f2 ': (f3 ': (f4 ': fs))))

weaken :: forall (fs :: [Instruction]) a (f :: Instruction). ExtensibleUnion fs a -> ExtensibleUnion (f ': fs) a

weaken2 :: forall (fs :: [Instruction]) a (f1 :: Instruction) (f2 :: Instruction). ExtensibleUnion fs a -> ExtensibleUnion (f1 ': (f2 ': fs)) a

weaken3 :: forall (fs :: [Instruction]) a (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction). ExtensibleUnion fs a -> ExtensibleUnion (f1 ': (f2 ': (f3 ': fs))) a

weaken4 :: forall (fs :: [Instruction]) a (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (f4 :: Instruction). ExtensibleUnion fs a -> ExtensibleUnion (f1 ': (f2 ': (f3 ': (f4 ': fs)))) a

weakenUnder :: forall (f1 :: Instruction) (fs :: [Instruction]) (f2 :: Instruction). ExtensibleUnion (f1 ': fs) ~> ExtensibleUnion (f1 ': (f2 ': fs))

weakenUnder2 :: forall (f1 :: Instruction) (f2 :: Instruction) (fs :: [Instruction]) (f3 :: Instruction). ExtensibleUnion (f1 ': (f2 ': fs)) ~> ExtensibleUnion (f1 ': (f2 ': (f3 ': fs)))

weakenUnder3 :: forall (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (fs :: [Instruction]) (f4 :: Instruction). ExtensibleUnion (f1 ': (f2 ': (f3 ': fs))) ~> ExtensibleUnion (f1 ': (f2 ': (f3 ': (f4 ': fs))))

weaken2Under :: forall (f1 :: Instruction) (fs :: [Instruction]) (f2 :: Instruction) (f3 :: Instruction). ExtensibleUnion (f1 ': fs) ~> ExtensibleUnion (f1 ': (f2 ': (f3 ': fs)))

weaken2Under2 :: forall (f1 :: Instruction) (f2 :: Instruction) (fs :: [Instruction]) (f3 :: Instruction) (f4 :: Instruction). ExtensibleUnion (f1 ': (f2 ': fs)) ~> ExtensibleUnion (f1 ': (f2 ': (f3 ': (f4 ': fs))))

weaken3Under :: forall (f1 :: Instruction) (fs :: [Instruction]) (f2 :: Instruction) (f3 :: Instruction) (f4 :: Instruction). ExtensibleUnion (f1 ': fs) ~> ExtensibleUnion (f1 ': (f2 ': (f3 ': (f4 ': fs))))

flipUnion :: forall (f1 :: Instruction) (f2 :: Instruction) (fs :: [Instruction]). ExtensibleUnion (f1 ': (f2 ': fs)) ~> ExtensibleUnion (f2 ': (f1 ': fs))

flipUnion3 :: forall (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (fs :: [Instruction]). ExtensibleUnion (f1 ': (f2 ': (f3 ': fs))) ~> ExtensibleUnion (f3 ': (f2 ': (f1 ': fs)))

flipUnionUnder :: forall (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (fs :: [Instruction]). ExtensibleUnion (f1 ': (f2 ': (f3 ': fs))) ~> ExtensibleUnion (f1 ': (f3 ': (f2 ': fs)))

rot3 :: forall (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (fs :: [Instruction]). ExtensibleUnion (f1 ': (f2 ': (f3 ': fs))) ~> ExtensibleUnion (f2 ': (f3 ': (f1 ': fs)))

rot3' :: forall (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (fs :: [Instruction]). ExtensibleUnion (f1 ': (f2 ': (f3 ': fs))) ~> ExtensibleUnion (f3 ': (f1 ': (f2 ': fs)))

bundleUnion2 :: forall (u' :: [Instruction] -> Instruction) (f1 :: Instruction) (f2 :: Instruction) (fs :: [Instruction]). Union u' => ExtensibleUnion (f1 ': (f2 ': fs)) ~> ExtensibleUnion (u' '[f1, f2] ': fs)

bundleUnion3 :: forall (u' :: [Instruction] -> Instruction) (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (fs :: [Instruction]). Union u' => ExtensibleUnion (f1 ': (f2 ': (f3 ': fs))) ~> ExtensibleUnion (u' '[f1, f2, f3] ': fs)

bundleUnion4 :: forall (u' :: [Instruction] -> Instruction) (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (f4 :: Instruction) (fs :: [Instruction]). Union u' => ExtensibleUnion (f1 ': (f2 ': (f3 ': (f4 ': fs)))) ~> ExtensibleUnion (u' '[f1, f2, f3, f4] ': fs)

unbundleUnion2 :: forall (u' :: [Instruction] -> Instruction) (f1 :: Instruction) (f2 :: Instruction) (fs :: [Instruction]). Union u' => ExtensibleUnion (u' '[f1, f2] ': fs) ~> ExtensibleUnion (f1 ': (f2 ': fs))

unbundleUnion3 :: forall (u' :: [Instruction] -> Instruction) (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (fs :: [Instruction]). Union u' => ExtensibleUnion (u' '[f1, f2, f3] ': fs) ~> ExtensibleUnion (f1 ': (f2 ': (f3 ': fs)))

unbundleUnion4 :: forall (u' :: [Instruction] -> Instruction) (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (f4 :: Instruction) (fs :: [Instruction]). Union u' => ExtensibleUnion (u' '[f1, f2, f3, f4] ': fs) ~> ExtensibleUnion (f1 ': (f2 ': (f3 ': (f4 ': fs))))

Union SumUnion

Defined in Data.Free.Sum

Associated Types

type HasMembership SumUnion f fs

Methods

inject :: forall (f :: Instruction) (fs :: [Instruction]). HasMembership SumUnion f fs => f ~> SumUnion fs

project :: forall f (fs :: [Instruction]) a. HasMembership SumUnion f fs => SumUnion fs a -> Maybe (f a)

absurdUnion :: SumUnion '[] a -> x

comp :: forall f a (fs :: [Instruction]). Either (f a) (SumUnion fs a) -> SumUnion (f ': fs) a

decomp :: forall f (fs :: [Instruction]) a. SumUnion (f ': fs) a -> Either (f a) (SumUnion fs a)

(|+|:) :: forall f a r (fs :: [Instruction]). (f a -> r) -> (SumUnion fs a -> r) -> SumUnion (f ': fs) a -> r

inject0 :: forall (f :: Type -> Type) (fs :: [Type -> Type]). f ~> SumUnion (f ': fs)

injectUnder :: forall (f2 :: Type -> Type) (f1 :: Type -> Type) (fs :: [Type -> Type]). f2 ~> SumUnion (f1 ': (f2 ': fs))

injectUnder2 :: forall (f3 :: Type -> Type) (f1 :: Type -> Type) (f2 :: Type -> Type) (fs :: [Type -> Type]). f3 ~> SumUnion (f1 ': (f2 ': (f3 ': fs)))

injectUnder3 :: forall (f4 :: Type -> Type) (f1 :: Type -> Type) (f2 :: Type -> Type) (f3 :: Type -> Type) (fs :: [Type -> Type]). f4 ~> SumUnion (f1 ': (f2 ': (f3 ': (f4 ': fs))))

weaken :: forall (fs :: [Instruction]) a (f :: Instruction). SumUnion fs a -> SumUnion (f ': fs) a

weaken2 :: forall (fs :: [Instruction]) a (f1 :: Instruction) (f2 :: Instruction). SumUnion fs a -> SumUnion (f1 ': (f2 ': fs)) a

weaken3 :: forall (fs :: [Instruction]) a (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction). SumUnion fs a -> SumUnion (f1 ': (f2 ': (f3 ': fs))) a

weaken4 :: forall (fs :: [Instruction]) a (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (f4 :: Instruction). SumUnion fs a -> SumUnion (f1 ': (f2 ': (f3 ': (f4 ': fs)))) a

weakenUnder :: forall (f1 :: Instruction) (fs :: [Instruction]) (f2 :: Instruction). SumUnion (f1 ': fs) ~> SumUnion (f1 ': (f2 ': fs))

weakenUnder2 :: forall (f1 :: Instruction) (f2 :: Instruction) (fs :: [Instruction]) (f3 :: Instruction). SumUnion (f1 ': (f2 ': fs)) ~> SumUnion (f1 ': (f2 ': (f3 ': fs)))

weakenUnder3 :: forall (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (fs :: [Instruction]) (f4 :: Instruction). SumUnion (f1 ': (f2 ': (f3 ': fs))) ~> SumUnion (f1 ': (f2 ': (f3 ': (f4 ': fs))))

weaken2Under :: forall (f1 :: Instruction) (fs :: [Instruction]) (f2 :: Instruction) (f3 :: Instruction). SumUnion (f1 ': fs) ~> SumUnion (f1 ': (f2 ': (f3 ': fs)))

weaken2Under2 :: forall (f1 :: Instruction) (f2 :: Instruction) (fs :: [Instruction]) (f3 :: Instruction) (f4 :: Instruction). SumUnion (f1 ': (f2 ': fs)) ~> SumUnion (f1 ': (f2 ': (f3 ': (f4 ': fs))))

weaken3Under :: forall (f1 :: Instruction) (fs :: [Instruction]) (f2 :: Instruction) (f3 :: Instruction) (f4 :: Instruction). SumUnion (f1 ': fs) ~> SumUnion (f1 ': (f2 ': (f3 ': (f4 ': fs))))

flipUnion :: forall (f1 :: Instruction) (f2 :: Instruction) (fs :: [Instruction]). SumUnion (f1 ': (f2 ': fs)) ~> SumUnion (f2 ': (f1 ': fs))

flipUnion3 :: forall (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (fs :: [Instruction]). SumUnion (f1 ': (f2 ': (f3 ': fs))) ~> SumUnion (f3 ': (f2 ': (f1 ': fs)))

flipUnionUnder :: forall (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (fs :: [Instruction]). SumUnion (f1 ': (f2 ': (f3 ': fs))) ~> SumUnion (f1 ': (f3 ': (f2 ': fs)))

rot3 :: forall (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (fs :: [Instruction]). SumUnion (f1 ': (f2 ': (f3 ': fs))) ~> SumUnion (f2 ': (f3 ': (f1 ': fs)))

rot3' :: forall (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (fs :: [Instruction]). SumUnion (f1 ': (f2 ': (f3 ': fs))) ~> SumUnion (f3 ': (f1 ': (f2 ': fs)))

bundleUnion2 :: forall (u' :: [Instruction] -> Instruction) (f1 :: Instruction) (f2 :: Instruction) (fs :: [Instruction]). Union u' => SumUnion (f1 ': (f2 ': fs)) ~> SumUnion (u' '[f1, f2] ': fs)

bundleUnion3 :: forall (u' :: [Instruction] -> Instruction) (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (fs :: [Instruction]). Union u' => SumUnion (f1 ': (f2 ': (f3 ': fs))) ~> SumUnion (u' '[f1, f2, f3] ': fs)

bundleUnion4 :: forall (u' :: [Instruction] -> Instruction) (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (f4 :: Instruction) (fs :: [Instruction]). Union u' => SumUnion (f1 ': (f2 ': (f3 ': (f4 ': fs)))) ~> SumUnion (u' '[f1, f2, f3, f4] ': fs)

unbundleUnion2 :: forall (u' :: [Instruction] -> Instruction) (f1 :: Instruction) (f2 :: Instruction) (fs :: [Instruction]). Union u' => SumUnion (u' '[f1, f2] ': fs) ~> SumUnion (f1 ': (f2 ': fs))

unbundleUnion3 :: forall (u' :: [Instruction] -> Instruction) (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (fs :: [Instruction]). Union u' => SumUnion (u' '[f1, f2, f3] ': fs) ~> SumUnion (f1 ': (f2 ': (f3 ': fs)))

unbundleUnion4 :: forall (u' :: [Instruction] -> Instruction) (f1 :: Instruction) (f2 :: Instruction) (f3 :: Instruction) (f4 :: Instruction) (fs :: [Instruction]). Union u' => SumUnion (u' '[f1, f2, f3, f4] ': fs) ~> SumUnion (f1 ': (f2 ': (f3 ': (f4 ': fs))))

type family IsMember (f :: Instruction) fs where ...

Equations

IsMember f (f ': fs) = 'True

IsMember f (_ ': fs) = IsMember f fs

IsMember _ '[] = 'False

type Member u f fs = (HasMembership u f fs, IsMember f fs ~ 'True)