semigroupoids-6.0.0.1: Semigroupoids: Category sans id

Copyright | (C) 2021 Edward Kmett
License | BSD-style (see the file LICENSE)
Maintainer | Edward Kmett <ekmett@gmail.com>
Stability | provisional
Portability | portable
Safe Haskell | Safe
Language | Haskell2010

Data.Functor.Contravariant.Decide

Description

Synopsis

- class Contravariant f => Decide (f :: Type -> Type) where
  - decide :: (a -> Either b c) -> f b -> f c -> f a
- gdecide :: (Generic1 f, Decide (Rep1 f)) => (a -> Either b c) -> f b -> f c -> f a
- decided :: Decide f => f b -> f c -> f (Either b c)
- gdecided :: (Generic1 f, Decide (Rep1 f)) => f b -> f c -> f (Either b c)

# Documentation

class Contravariant f => Decide (f :: Type -> Type) where #

The contravariant analogue of `Alt`.

If one thinks of `f a` as a consumer of `a`s, then `decide` allows one to handle the consumption of a value by choosing to handle it via exactly one of two independent consumers. It redirects the input completely into one of two consumers.

`decide` takes the "decision" method and the two potential consumers, and returns the wrapped/combined consumer.

Mathematically, a functor being an instance of `Decide` means that it is "semigroupoidal" with respect to the contravariant "either-based" Day convolution (`data EitherDay f g a = forall b c. EitherDay (f b) (g c) (a -> Either b c)`). That is, it is possible to define a function `(f `EitherDay` f) a -> f a` in a way that is associative.

Since: 5.3.6

Methods

decide :: (a -> Either b c) -> f b -> f c -> f a #

Takes the "decision" method and the two potential consumers, and returns the wrapped/combined consumer.

#### Instances

Instances details

Decide Comparison # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> Comparison b -> Comparison c -> Comparison a #
Decide Equivalence # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> Equivalence b -> Equivalence c -> Equivalence a #
Decide Predicate # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> Predicate b -> Predicate c -> Predicate a #
Decide (Op r) # | Unlike `Decidable`, requires no constraint on `r`. Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> Op r b -> Op r c -> Op r a #
Decide (Proxy :: Type -> Type) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> Proxy b -> Proxy c -> Proxy a #
Decide (U1 :: Type -> Type) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> U1 b -> U1 c -> U1 a #
Decide (V1 :: Type -> Type) # | Has no `Decidable` or `Conclude` instance. Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> V1 b -> V1 c -> V1 a #
Decidable f => Decide (WrappedDivisible f) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> WrappedDivisible f b -> WrappedDivisible f c -> WrappedDivisible f a #
Divise m => Decide (MaybeT m) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> MaybeT m b -> MaybeT m c -> MaybeT m a #
Decide f => Decide (Alt f) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> Alt f b -> Alt f c -> Alt f a #
Decide f => Decide (Rec1 f) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> Rec1 f b -> Rec1 f c -> Rec1 f a #
Decide f => Decide (Backwards f) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> Backwards f b -> Backwards f c -> Backwards f a #
Decide f => Decide (IdentityT f) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> IdentityT f b -> IdentityT f c -> IdentityT f a #
Decide m => Decide (ReaderT r m) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> ReaderT r m b -> ReaderT r m c -> ReaderT r m a #
Decide m => Decide (StateT s m) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> StateT s m b -> StateT s m c -> StateT s m a #
Decide m => Decide (StateT s m) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> StateT s m b -> StateT s m c -> StateT s m a #
Decide m => Decide (WriterT w m) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> WriterT w m b -> WriterT w m c -> WriterT w m a #
Decide m => Decide (WriterT w m) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> WriterT w m b -> WriterT w m c -> WriterT w m a #
Decide f => Decide (Reverse f) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> Reverse f b -> Reverse f c -> Reverse f a #
(Decide f, Decide g) => Decide (Product f g) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> Product f g b -> Product f g c -> Product f g a #
(Decide f, Decide g) => Decide (f :*: g) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> (f :*: g) b -> (f :*: g) c -> (f :*: g) a #
(Apply f, Decide g) => Decide (Compose f g) # | Unlike `Decidable`, requires only `Apply` on `f`. Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> Compose f g b -> Compose f g c -> Compose f g a #
(Apply f, Decide g) => Decide (f :.: g) # | Unlike `Decidable`, requires only `Apply` on `f`. Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> (f :.: g) b -> (f :.: g) c -> (f :.: g) a #
Decide f => Decide (M1 i c f) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c0) -> M1 i c f b -> M1 i c f c0 -> M1 i c f a #
Decide m => Decide (RWST r w s m) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> RWST r w s m b -> RWST r w s m c -> RWST r w s m a #
Decide m => Decide (RWST r w s m) # | Since: 5.3.6
Instance details Defined in Data.Functor.Contravariant.Decide Methods decide :: (a -> Either b c) -> RWST r w s m b -> RWST r w s m c -> RWST r w s m a #

gdecide :: (Generic1 f, Decide (Rep1 f)) => (a -> Either b c) -> f b -> f c -> f a #

Generic `decide`. Caveats:

1. Will not compile if `f` is a sum type.
2. Will not compile if `f` contains fields that do not mention its type variable.
3. `-XDeriveGeneric` is not smart enough to make instances where the type variable appears in negative position.

Since: 5.3.8

decided :: Decide f => f b -> f c -> f (Either b c) #

For ``decided` x y`, the resulting `f (`Either` b c)` will direct `Left`s to be consumed by `x`, and `Right`s to be consumed by y.

Since: 5.3.6

gdecided :: (Generic1 f, Decide (Rep1 f)) => f b -> f c -> f (Either b c) #

Generic `decided`. Caveats are the same as for `gdecide`.

Since: 5.3.8