Data.Functor.Contravariant.Night

Provides Night, a form of the day convolution that is contravariant and splits on Either.

Since: 0.3.0.0

Documentation

data Night :: (Type -> Type) -> (Type -> Type) -> Type -> Type where

A pairing of contravariant functors to create a new contravariant functor that represents the "choice" between the two.

A Night f g a is a contravariant "consumer" of a, and it does this by either feeding the a to f, or feeding the a to g. Which one it gives it to happens at runtime depending what a is actually given.

For example, if we have x :: f a (a consumer of as) and y :: g b (a consumer of bs), then night x y :: Night f g (Either a b). This is a consumer of Either a bs, and it consumes Left branches by feeding it to x, and Right branches by feeding it to y.

Mathematically, this is a contravariant day convolution, except with a different choice of bifunctor (Either) than the typical one we talk about in Haskell (which uses (,)). Therefore, it is an alternative to the typical Day convolution --- hence, the name Night.

Constructors

Night :: f b -> g c -> (a -> Either b c) -> Night f g a

Instances

Associative Night

Since: 0.3.0.0

Defined in Data.HBifunctor.Associative

Associated Types

type NonEmptyBy Night :: (Type -> Type) -> Type -> Type

type FunctorBy Night :: (Type -> Type) -> Constraint

Methods

associating :: forall (f :: Type -> Type) (g :: Type -> Type) (h :: Type -> Type). (FunctorBy Night f, FunctorBy Night g, FunctorBy Night h) => Night f (Night g h) <~> Night (Night f g) h

appendNE :: forall (f :: Type -> Type). Night (NonEmptyBy Night f) (NonEmptyBy Night f) ~> NonEmptyBy Night f

matchNE :: forall (f :: Type -> Type). FunctorBy Night f => NonEmptyBy Night f ~> (f :+: Night f (NonEmptyBy Night f))

consNE :: forall (f :: Type -> Type). Night f (NonEmptyBy Night f) ~> NonEmptyBy Night f

toNonEmptyBy :: forall (f :: Type -> Type). Night f f ~> NonEmptyBy Night f

Decide f => SemigroupIn Night f

Since: 0.3.0.0

Defined in Data.HBifunctor.Associative

Methods

biretract :: Night f f ~> f

binterpret :: forall (g :: Type -> Type) (h :: Type -> Type). (g ~> f) -> (h ~> f) -> Night g h ~> f

Matchable Night Not

Since: 0.3.0.0

Defined in Data.HBifunctor.Tensor

Methods

unsplitNE :: forall (f :: Type -> Type). FunctorBy Night f => Night f (ListBy Night f) ~> NonEmptyBy Night f

matchLB :: forall (f :: Type -> Type). FunctorBy Night f => ListBy Night f ~> (Not :+: NonEmptyBy Night f)

Tensor Night Not

Since: 0.3.0.0

Defined in Data.HBifunctor.Tensor

Associated Types

type ListBy Night :: (Type -> Type) -> Type -> Type

Methods

intro1 :: forall (f :: Type -> Type). f ~> Night f Not

intro2 :: forall (g :: Type -> Type). g ~> Night Not g

elim1 :: forall (f :: Type -> Type). FunctorBy Night f => Night f Not ~> f

elim2 :: forall (g :: Type -> Type). FunctorBy Night g => Night Not g ~> g

appendLB :: forall (f :: Type -> Type). Night (ListBy Night f) (ListBy Night f) ~> ListBy Night f

splitNE :: forall (f :: Type -> Type). NonEmptyBy Night f ~> Night f (ListBy Night f)

splittingLB :: forall (f :: Type -> Type). ListBy Night f <~> (Not :+: Night f (ListBy Night f))

toListBy :: forall (f :: Type -> Type). Night f f ~> ListBy Night f

fromNE :: forall (f :: Type -> Type). NonEmptyBy Night f ~> ListBy Night f

HBifunctor Night

Since: 0.3.0.0

Defined in Data.HFunctor.Internal

Methods

hleft :: forall (f :: k -> Type) (j :: k -> Type) (g :: k -> Type). (f ~> j) -> Night f g ~> Night j g

hright :: forall (g :: k -> Type) (l :: k -> Type) (f :: k -> Type). (g ~> l) -> Night f g ~> Night f l

hbimap :: forall (f :: k -> Type) (j :: k -> Type) (g :: k -> Type) (l :: k -> Type). (f ~> j) -> (g ~> l) -> Night f g ~> Night j l

Conclude f => MonoidIn Night Not f

Instances of Conclude are monoids in the monoidal category on Night.

Defined in Data.HBifunctor.Tensor

Methods

pureT :: Not ~> f

Contravariant (Night f g)

Defined in Data.Functor.Contravariant.Night

Methods

contramap :: (a' -> a) -> Night f g a -> Night f g a'

(>$) :: b -> Night f g b -> Night f g a

Invariant (Night f g)

Defined in Data.Functor.Contravariant.Night

Methods

invmap :: (a -> b) -> (b -> a) -> Night f g a -> Night f g b

Contravariant f => Decide (Chain1 Night f)

Chain1 Night is the free "semigroup in the semigroupoidal category of endofunctors enriched by Night" --- aka, the free Decide.

Since: 0.3.0.0

Defined in Data.HFunctor.Chain

Methods

decide :: (a -> Either b c) -> Chain1 Night f b -> Chain1 Night f c -> Chain1 Night f a

Conclude (Chain Night Not f)

Chain Night Refutec is the free "monoid in the monoidal category of endofunctors enriched by Night" --- aka, the free Conclude.

Since: 0.3.0.0

Defined in Data.HFunctor.Chain

Methods

conclude :: (a -> Void) -> Chain Night Not f a

Decide (Chain Night Not f)

Since: 0.3.0.0

Defined in Data.HFunctor.Chain

Methods

decide :: (a -> Either b c) -> Chain Night Not f b -> Chain Night Not f c -> Chain Night Not f a

type FunctorBy Night

Defined in Data.HBifunctor.Associative

type FunctorBy Night = Contravariant

type NonEmptyBy Night

Defined in Data.HBifunctor.Associative

type NonEmptyBy Night = Dec1

type ListBy Night

Defined in Data.HBifunctor.Tensor

type ListBy Night = Dec

night :: f a -> g b -> Night f g (Either a b)

Inject into a Night.

night x y is a consumer of Either a b; Left will be passed to x, and Right will be passed to y.

runNight :: Decide h => (f ~> h) -> (g ~> h) -> Night f g ~> h

Interpret out of a Night into any instance of Decide by providing two interpreting functions.

necide :: Decide f => Night f f ~> f

Squash the two items in a Night using their natural Decide instances.

Since: 0.4.0.0

assoc :: Night f (Night g h) ~> Night (Night f g) h

Night is associative.

unassoc :: Night (Night f g) h ~> Night f (Night g h)

Night is associative.

swapped :: Night f g ~> Night g f

The two sides of a Night can be swapped.

trans1 :: (f ~> h) -> Night f g ~> Night h g

Hoist a function over the left side of a Night.

trans2 :: (g ~> h) -> Night f g ~> Night f h

Hoist a function over the right side of a Night.

intro1 :: g ~> Night Not g

The left identity of Night is Not; this is one side of that isomorphism.

intro2 :: f ~> Night f Not

The right identity of Night is Not; this is one side of that isomorphism.

elim1 :: Contravariant g => Night Not g ~> g

The left identity of Night is Not; this is one side of that isomorphism.

elim2 :: Contravariant f => Night f Not ~> f

The right identity of Night is Not; this is one side of that isomorphism.

newtype Not a

A value of type Not a is "proof" that a is uninhabited.

Constructors

Not

Fields

• refute :: a -> Void

Instances

Contravariant Not

Defined in Data.Functor.Contravariant.Night

Methods

contramap :: (a' -> a) -> Not a -> Not a'

(>$) :: b -> Not b -> Not a

Invariant Not

Since: 0.3.1.0

Defined in Data.Functor.Contravariant.Night

Methods

invmap :: (a -> b) -> (b -> a) -> Not a -> Not b

Matchable Night Not

Since: 0.3.0.0

Defined in Data.HBifunctor.Tensor

Methods

unsplitNE :: forall (f :: Type -> Type). FunctorBy Night f => Night f (ListBy Night f) ~> NonEmptyBy Night f

matchLB :: forall (f :: Type -> Type). FunctorBy Night f => ListBy Night f ~> (Not :+: NonEmptyBy Night f)

Matchable Night Not

Defined in Data.HBifunctor.Tensor

Methods

unsplitNE :: forall (f :: Type -> Type). FunctorBy Night f => Night f (ListBy Night f) ~> NonEmptyBy Night f

matchLB :: forall (f :: Type -> Type). FunctorBy Night f => ListBy Night f ~> (Not :+: NonEmptyBy Night f)

Tensor Night Not

Since: 0.3.0.0

Defined in Data.HBifunctor.Tensor

Associated Types

type ListBy Night :: (Type -> Type) -> Type -> Type

Methods

intro1 :: forall (f :: Type -> Type). f ~> Night f Not

intro2 :: forall (g :: Type -> Type). g ~> Night Not g

elim1 :: forall (f :: Type -> Type). FunctorBy Night f => Night f Not ~> f

elim2 :: forall (g :: Type -> Type). FunctorBy Night g => Night Not g ~> g

appendLB :: forall (f :: Type -> Type). Night (ListBy Night f) (ListBy Night f) ~> ListBy Night f

splitNE :: forall (f :: Type -> Type). NonEmptyBy Night f ~> Night f (ListBy Night f)

splittingLB :: forall (f :: Type -> Type). ListBy Night f <~> (Not :+: Night f (ListBy Night f))

toListBy :: forall (f :: Type -> Type). Night f f ~> ListBy Night f

fromNE :: forall (f :: Type -> Type). NonEmptyBy Night f ~> ListBy Night f

Tensor Night Not

Defined in Data.HBifunctor.Tensor

Associated Types

type ListBy Night :: (Type -> Type) -> Type -> Type

Methods

intro1 :: forall (f :: Type -> Type). f ~> Night f Not

intro2 :: forall (g :: Type -> Type). g ~> Night Not g

elim1 :: forall (f :: Type -> Type). FunctorBy Night f => Night f Not ~> f

elim2 :: forall (g :: Type -> Type). FunctorBy Night g => Night Not g ~> g

appendLB :: forall (f :: Type -> Type). Night (ListBy Night f) (ListBy Night f) ~> ListBy Night f

splitNE :: forall (f :: Type -> Type). NonEmptyBy Night f ~> Night f (ListBy Night f)

splittingLB :: forall (f :: Type -> Type). ListBy Night f <~> (Not :+: Night f (ListBy Night f))

toListBy :: forall (f :: Type -> Type). Night f f ~> ListBy Night f

fromNE :: forall (f :: Type -> Type). NonEmptyBy Night f ~> ListBy Night f

Conclude f => MonoidIn Night Not f

Instances of Conclude are monoids in the monoidal category on Night.

Defined in Data.HBifunctor.Tensor

Methods

pureT :: Not ~> f

Inplus f => MonoidIn Night Not f

Since: 0.4.0.0

Defined in Data.HBifunctor.Tensor

Methods

pureT :: Not ~> f

Semigroup (Not a)

Defined in Data.Functor.Contravariant.Night

Methods

(<>) :: Not a -> Not a -> Not a

sconcat :: NonEmpty (Not a) -> Not a

stimes :: Integral b => b -> Not a -> Not a

Conclude (Chain Night Not f)

Chain Night Refutec is the free "monoid in the monoidal category of endofunctors enriched by Night" --- aka, the free Conclude.

Since: 0.3.0.0

Defined in Data.HFunctor.Chain

Methods

conclude :: (a -> Void) -> Chain Night Not f a

Decide (Chain Night Not f)

Since: 0.3.0.0

Defined in Data.HFunctor.Chain

Methods

decide :: (a -> Either b c) -> Chain Night Not f b -> Chain Night Not f c -> Chain Night Not f a

Inalt (Chain Night Not f)

Since: 0.4.0.0

Defined in Data.HFunctor.Chain

Methods

swerve :: (b -> a) -> (c -> a) -> (a -> Either b c) -> Chain Night Not f b -> Chain Night Not f c -> Chain Night Not f a

swerved :: Chain Night Not f a -> Chain Night Not f b -> Chain Night Not f (Either a b)

Inplus (Chain Night Not f)

Since: 0.4.0.0

Defined in Data.HFunctor.Chain

Methods

reject :: (a -> Void) -> Chain Night Not f a

refuted :: Not Void

A useful shortcut for a common usage: Void is always not so.

Since: 0.3.1.0