Data.Either.Singletons

Defines functions and datatypes relating to the singleton for Either, including singled versions of all the definitions in Data.Either.

Because many of these definitions are produced by Template Haskell, it is not possible to create proper Haddock documentation. Please look up the corresponding operation in Data.Either. Also, please excuse the apparent repeated variable names. This is due to an interaction between Template Haskell and Haddock.

The Either singleton

type family Sing :: k -> Type

The singleton kind-indexed type family.

Instances

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SAll

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SAny

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SVoid

type Sing

Defined in GHC.TypeLits.Singletons.Internal

type Sing = SNat

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SOrdering

type Sing

Defined in Data.Singletons.Base.TypeError

type Sing = SErrorMessage

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = STuple0

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SBool

type Sing

Defined in GHC.TypeLits.Singletons.Internal

type Sing = SChar

type Sing

Defined in GHC.TypeLits.Singletons.Internal

type Sing = SSymbol

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SIdentity :: Identity a -> Type

type Sing

Defined in Data.Monoid.Singletons

type Sing = SFirst :: First a -> Type

type Sing

Defined in Data.Monoid.Singletons

type Sing = SLast :: Last a -> Type

type Sing

Defined in Data.Ord.Singletons

type Sing = SDown :: Down a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SFirst :: First a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SLast :: Last a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SMax :: Max a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SMin :: Min a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SWrappedMonoid :: WrappedMonoid m -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SDual :: Dual a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SProduct :: Product a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SSum :: Sum a -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SNonEmpty :: NonEmpty a -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SMaybe :: Maybe a -> Type

type Sing

A choice of singleton for the kind TYPE rep (for some RuntimeRep rep), an instantiation of which is the famous kind Type.

Conceivably, one could generalize this instance to `Sing @k` for any kind k, and remove all other Sing instances. We don't adopt this design, however, since it is far more convenient in practice to work with explicit singleton values than TypeReps (for instance, TypeReps are more difficult to pattern match on, and require extra runtime checks).

We cannot produce explicit singleton values for everything in TYPE rep, however, since it is an open kind, so we reach for TypeRep in this one particular case.

Defined in Data.Singletons.Base.TypeRepTYPE

type Sing = TypeRep :: TYPE rep -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SList :: [a] -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SEither :: Either a b -> Type

type Sing

Defined in Data.Proxy.Singletons

type Sing = SProxy :: Proxy t -> Type

type Sing

Defined in Data.Semigroup.Singletons

type Sing = SArg :: Arg a b -> Type

type Sing

Defined in Data.Singletons

type Sing = SWrappedSing :: WrappedSing a -> Type

type Sing

Defined in Data.Singletons

type Sing = SLambda :: (k1 ~> k2) -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = STuple2 :: (a, b) -> Type

type Sing

Defined in Data.Functor.Const.Singletons

type Sing = SConst :: Const a b -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = STuple3 :: (a, b, c) -> Type

type Sing

Defined in Data.Functor.Product.Singletons

type Sing = SProduct :: Product f g a -> Type

type Sing

Defined in Data.Functor.Sum.Singletons

type Sing = SSum :: Sum f g a -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = STuple4 :: (a, b, c, d) -> Type

type Sing

Defined in Data.Functor.Compose.Singletons

type Sing = SCompose :: Compose f g a -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = STuple5 :: (a, b, c, d, e) -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = STuple6 :: (a, b, c, d, e, f) -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = STuple7 :: (a, b, c, d, e, f, g) -> Type

data SEither :: forall (a :: Type) (b :: Type). Either a b -> Type where

Constructors

SLeft :: forall (a :: Type) (b :: Type) (n :: a). (Sing n) -> SEither ('Left n :: Either (a :: Type) (b :: Type))

SRight :: forall (a :: Type) (b :: Type) (n :: b). (Sing n) -> SEither ('Right n :: Either (a :: Type) (b :: Type))

Instances

(SDecide a, SDecide b) => TestCoercion (SEither :: Either a b -> Type)

Defined in Data.Singletons.Base.Instances

Methods

testCoercion :: forall (a0 :: k) (b0 :: k). SEither a0 -> SEither b0 -> Maybe (Coercion a0 b0)

(SDecide a, SDecide b) => TestEquality (SEither :: Either a b -> Type)

Defined in Data.Singletons.Base.Instances

Methods

testEquality :: forall (a0 :: k) (b0 :: k). SEither a0 -> SEither b0 -> Maybe (a0 :~: b0)

(ShowSing a, ShowSing b) => Show (SEither z)

Defined in Data.Singletons.Base.Instances

Methods

showsPrec :: Int -> SEither z -> ShowS

show :: SEither z -> String

showList :: [SEither z] -> ShowS

Singletons from Data.Either

either_ :: (a -> c) -> (b -> c) -> Either a b -> c

type family Either_ (a :: (~>) a c) (a :: (~>) b c) (a :: Either a b) :: c where ...

Equations

Either_ f _ ('Left x) = Apply f x

Either_ _ g ('Right y) = Apply g y

sEither_ :: forall (t :: (~>) a c) (t :: (~>) b c) (t :: Either a b). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply Either_Sym0 t) t) t :: c) :: Type

The preceding two definitions are derived from the function either in Data.Either. The extra underscore is to avoid name clashes with the type Either.

type family Lefts (a :: [Either a b]) :: [a] where ...

Equations

Lefts '[] = NilSym0

Lefts ('(:) ('Left x) xs) = Apply (Apply (:@#@$) x) (Apply LeftsSym0 xs)

Lefts ('(:) ('Right _) xs) = Apply LeftsSym0 xs

sLefts :: forall (t :: [Either a b]). Sing t -> Sing (Apply LeftsSym0 t :: [a]) :: Type

type family Rights (a :: [Either a b]) :: [b] where ...

Equations

Rights '[] = NilSym0

Rights ('(:) ('Left _) xs) = Apply RightsSym0 xs

Rights ('(:) ('Right x) xs) = Apply (Apply (:@#@$) x) (Apply RightsSym0 xs)

sRights :: forall (t :: [Either a b]). Sing t -> Sing (Apply RightsSym0 t :: [b]) :: Type

type family PartitionEithers (a :: [Either a b]) :: ([a], [b]) where ...

Equations

PartitionEithers a_6989586621679266990 = Apply (Apply (Apply FoldrSym0 (Apply (Apply Either_Sym0 (Let6989586621679266996LeftSym1 a_6989586621679266990)) (Let6989586621679266996RightSym1 a_6989586621679266990))) (Apply (Apply Tuple2Sym0 NilSym0) NilSym0)) a_6989586621679266990

sPartitionEithers :: forall (t :: [Either a b]). Sing t -> Sing (Apply PartitionEithersSym0 t :: ([a], [b])) :: Type

type family IsLeft (a :: Either a b) :: Bool where ...

Equations

IsLeft ('Left _) = TrueSym0

IsLeft ('Right _) = FalseSym0

sIsLeft :: forall (t :: Either a b). Sing t -> Sing (Apply IsLeftSym0 t :: Bool) :: Type

type family IsRight (a :: Either a b) :: Bool where ...

Equations

IsRight ('Left _) = FalseSym0

IsRight ('Right _) = TrueSym0

sIsRight :: forall (t :: Either a b). Sing t -> Sing (Apply IsRightSym0 t :: Bool) :: Type

Defunctionalization symbols

data LeftSym0 :: (~>) a (Either (a :: Type) (b :: Type))

Instances

SingI (LeftSym0 :: TyFun a (Either a b) -> Type)

Defined in Data.Singletons.Base.Instances

Methods

sing :: Sing LeftSym0

SuppressUnusedWarnings (LeftSym0 :: TyFun a (Either a b) -> Type)

Defined in Data.Singletons.Base.Instances

Methods

suppressUnusedWarnings :: ()

type Apply (LeftSym0 :: TyFun a (Either a b) -> Type) (a6989586621679037600 :: a)

Defined in Data.Singletons.Base.Instances

type Apply (LeftSym0 :: TyFun a (Either a b) -> Type) (a6989586621679037600 :: a) = 'Left a6989586621679037600 :: Either a b

type family LeftSym1 (a6989586621679037600 :: a) :: Either (a :: Type) (b :: Type) where ...

Equations

LeftSym1 a6989586621679037600 = 'Left a6989586621679037600

data RightSym0 :: (~>) b (Either (a :: Type) (b :: Type))

Instances

SingI (RightSym0 :: TyFun b (Either a b) -> Type)

Defined in Data.Singletons.Base.Instances

Methods

sing :: Sing RightSym0

SuppressUnusedWarnings (RightSym0 :: TyFun b (Either a b) -> Type)

Defined in Data.Singletons.Base.Instances

Methods

suppressUnusedWarnings :: ()

type Apply (RightSym0 :: TyFun b (Either a b) -> Type) (a6989586621679037602 :: b)

Defined in Data.Singletons.Base.Instances

type Apply (RightSym0 :: TyFun b (Either a b) -> Type) (a6989586621679037602 :: b) = 'Right a6989586621679037602 :: Either a b

type family RightSym1 (a6989586621679037602 :: b) :: Either (a :: Type) (b :: Type) where ...

Equations

RightSym1 a6989586621679037602 = 'Right a6989586621679037602

data Either_Sym0 :: (~>) ((~>) a c) ((~>) ((~>) b c) ((~>) (Either a b) c))

Instances

SingI (Either_Sym0 :: TyFun (a ~> c) ((b ~> c) ~> (Either a b ~> c)) -> Type)

Defined in Data.Either.Singletons

Methods

sing :: Sing Either_Sym0

SuppressUnusedWarnings (Either_Sym0 :: TyFun (a ~> c) ((b ~> c) ~> (Either a b ~> c)) -> Type)

Defined in Data.Either.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (Either_Sym0 :: TyFun (a ~> c) ((b ~> c) ~> (Either a b ~> c)) -> Type) (a6989586621679264752 :: a ~> c)

Defined in Data.Either.Singletons

type Apply (Either_Sym0 :: TyFun (a ~> c) ((b ~> c) ~> (Either a b ~> c)) -> Type) (a6989586621679264752 :: a ~> c) = Either_Sym1 a6989586621679264752 :: TyFun (b ~> c) (Either a b ~> c) -> Type

data Either_Sym1 (a6989586621679264752 :: (~>) a c) :: (~>) ((~>) b c) ((~>) (Either a b) c)

Instances

SingI1 (Either_Sym1 :: (a ~> c) -> TyFun (b ~> c) (Either a b ~> c) -> Type)

Defined in Data.Either.Singletons

Methods

liftSing :: forall (x :: k1). Sing x -> Sing (Either_Sym1 x)

SingI d => SingI (Either_Sym1 d :: TyFun (b ~> c) (Either a b ~> c) -> Type)

Defined in Data.Either.Singletons

Methods

sing :: Sing (Either_Sym1 d)

SuppressUnusedWarnings (Either_Sym1 a6989586621679264752 :: TyFun (b ~> c) (Either a b ~> c) -> Type)

Defined in Data.Either.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (Either_Sym1 a6989586621679264752 :: TyFun (b ~> c) (Either a b ~> c) -> Type) (a6989586621679264753 :: b ~> c)

Defined in Data.Either.Singletons

type Apply (Either_Sym1 a6989586621679264752 :: TyFun (b ~> c) (Either a b ~> c) -> Type) (a6989586621679264753 :: b ~> c) = Either_Sym2 a6989586621679264752 a6989586621679264753

data Either_Sym2 (a6989586621679264752 :: (~>) a c) (a6989586621679264753 :: (~>) b c) :: (~>) (Either a b) c

Instances

SingI2 (Either_Sym2 :: (a ~> c) -> (b ~> c) -> TyFun (Either a b) c -> Type)

Defined in Data.Either.Singletons

Methods

liftSing2 :: forall (x :: k1) (y :: k2). Sing x -> Sing y -> Sing (Either_Sym2 x y)

SingI d => SingI1 (Either_Sym2 d :: (b ~> c) -> TyFun (Either a b) c -> Type)

Defined in Data.Either.Singletons

Methods

liftSing :: forall (x :: k1). Sing x -> Sing (Either_Sym2 d x)

(SingI d1, SingI d2) => SingI (Either_Sym2 d1 d2 :: TyFun (Either a b) c -> Type)

Defined in Data.Either.Singletons

Methods

sing :: Sing (Either_Sym2 d1 d2)

SuppressUnusedWarnings (Either_Sym2 a6989586621679264752 a6989586621679264753 :: TyFun (Either a b) c -> Type)

Defined in Data.Either.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (Either_Sym2 a6989586621679264752 a6989586621679264753 :: TyFun (Either a b) c -> Type) (a6989586621679264754 :: Either a b)

Defined in Data.Either.Singletons

type Apply (Either_Sym2 a6989586621679264752 a6989586621679264753 :: TyFun (Either a b) c -> Type) (a6989586621679264754 :: Either a b) = Either_ a6989586621679264752 a6989586621679264753 a6989586621679264754

type family Either_Sym3 (a6989586621679264752 :: (~>) a c) (a6989586621679264753 :: (~>) b c) (a6989586621679264754 :: Either a b) :: c where ...

Equations

Either_Sym3 a6989586621679264752 a6989586621679264753 a6989586621679264754 = Either_ a6989586621679264752 a6989586621679264753 a6989586621679264754

data LeftsSym0 :: (~>) [Either a b] [a]

Instances

SingI (LeftsSym0 :: TyFun [Either a b] [a] -> Type)

Defined in Data.Either.Singletons

Methods

sing :: Sing LeftsSym0

SuppressUnusedWarnings (LeftsSym0 :: TyFun [Either a b] [a] -> Type)

Defined in Data.Either.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (LeftsSym0 :: TyFun [Either a b] [a] -> Type) (a6989586621679267017 :: [Either a b])

Defined in Data.Either.Singletons

type Apply (LeftsSym0 :: TyFun [Either a b] [a] -> Type) (a6989586621679267017 :: [Either a b]) = Lefts a6989586621679267017

type family LeftsSym1 (a6989586621679267017 :: [Either a b]) :: [a] where ...

Equations

LeftsSym1 a6989586621679267017 = Lefts a6989586621679267017

data RightsSym0 :: (~>) [Either a b] [b]

Instances

SingI (RightsSym0 :: TyFun [Either a b] [b] -> Type)

Defined in Data.Either.Singletons

Methods

sing :: Sing RightsSym0

SuppressUnusedWarnings (RightsSym0 :: TyFun [Either a b] [b] -> Type)

Defined in Data.Either.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (RightsSym0 :: TyFun [Either a b] [b] -> Type) (a6989586621679267011 :: [Either a b])

Defined in Data.Either.Singletons

type Apply (RightsSym0 :: TyFun [Either a b] [b] -> Type) (a6989586621679267011 :: [Either a b]) = Rights a6989586621679267011

type family RightsSym1 (a6989586621679267011 :: [Either a b]) :: [b] where ...

Equations

RightsSym1 a6989586621679267011 = Rights a6989586621679267011

data IsLeftSym0 :: (~>) (Either a b) Bool

Instances

SingI (IsLeftSym0 :: TyFun (Either a b) Bool -> Type)

Defined in Data.Either.Singletons

Methods

sing :: Sing IsLeftSym0

SuppressUnusedWarnings (IsLeftSym0 :: TyFun (Either a b) Bool -> Type)

Defined in Data.Either.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (IsLeftSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621679266989 :: Either a b)

Defined in Data.Either.Singletons

type Apply (IsLeftSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621679266989 :: Either a b) = IsLeft a6989586621679266989

type family IsLeftSym1 (a6989586621679266989 :: Either a b) :: Bool where ...

Equations

IsLeftSym1 a6989586621679266989 = IsLeft a6989586621679266989

data IsRightSym0 :: (~>) (Either a b) Bool

Instances

SingI (IsRightSym0 :: TyFun (Either a b) Bool -> Type)

Defined in Data.Either.Singletons

Methods

sing :: Sing IsRightSym0

SuppressUnusedWarnings (IsRightSym0 :: TyFun (Either a b) Bool -> Type)

Defined in Data.Either.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (IsRightSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621679266986 :: Either a b)

Defined in Data.Either.Singletons

type Apply (IsRightSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621679266986 :: Either a b) = IsRight a6989586621679266986

type family IsRightSym1 (a6989586621679266986 :: Either a b) :: Bool where ...

Equations

IsRightSym1 a6989586621679266986 = IsRight a6989586621679266986