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

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.Sigma

type Sing = SSigma :: Sigma s t -> 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 (a1 :: Either a b) where

Constructors

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

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

Instances

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

Defined in Data.Singletons.Base.Instances

Methods

testCoercion :: forall (a0 :: Either a b) (b0 :: Either a b). 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 :: Either a b) (b0 :: Either a b). 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

Eq (SEither z)

Defined in Data.Singletons.Base.Instances

Methods

(==) :: SEither z -> SEither z -> Bool

(/=) :: SEither z -> SEither z -> Bool

Singletons from Data.Either

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

type family Either_ (a1 :: a ~> c) (a2 :: b ~> c) (a3 :: Either a b) :: c where ...

Equations

Either_ (f :: k1 ~> k2) (_1 :: b ~> k2) ('Left x :: Either k1 b) = Apply f x

Either_ (_1 :: a ~> k2) (g :: k1 ~> k2) ('Right y :: Either a k1) = Apply g y

sEither_ :: forall a c b (t1 :: a ~> c) (t2 :: b ~> c) (t3 :: Either a b). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply (Either_Sym0 :: TyFun (a ~> c) ((b ~> c) ~> (Either a b ~> c)) -> Type) t1) t2) t3)

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 (a1 :: [Either a b]) :: [a] where ...

Equations

Lefts ('[] :: [Either a b]) = NilSym0 :: [a]

Lefts (('Left x :: Either a b) ': xs :: [Either a b]) = Apply (Apply ((:@#@$) :: TyFun a ([a] ~> [a]) -> Type) x) (Apply (LeftsSym0 :: TyFun [Either a b] [a] -> Type) xs)

Lefts (('Right _1 :: Either a b) ': xs :: [Either a b]) = Apply (LeftsSym0 :: TyFun [Either a b] [a] -> Type) xs

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

type family Rights (a1 :: [Either a b]) :: [b] where ...

Equations

Rights ('[] :: [Either a b]) = NilSym0 :: [b]

Rights (('Left _1 :: Either a b) ': xs :: [Either a b]) = Apply (RightsSym0 :: TyFun [Either a b] [b] -> Type) xs

Rights (('Right x :: Either a b) ': xs :: [Either a b]) = Apply (Apply ((:@#@$) :: TyFun b ([b] ~> [b]) -> Type) x) (Apply (RightsSym0 :: TyFun [Either a b] [b] -> Type) xs)

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

type family PartitionEithers (a1 :: [Either a b]) :: ([a], [b]) where ...

Equations

PartitionEithers (a_6989586621679337101 :: [Either a b]) = Apply (Apply (Apply (FoldrSym0 :: TyFun (Either a b ~> (([a], [b]) ~> ([a], [b]))) (([a], [b]) ~> ([Either a b] ~> ([a], [b]))) -> Type) (Apply (Apply (Either_Sym0 :: TyFun (a ~> (TyFun ([a], [b]) ([a], [b]) -> Type)) ((b ~> (TyFun ([a], [b]) ([a], [b]) -> Type)) ~> (Either a b ~> (TyFun ([a], [b]) ([a], [b]) -> Type))) -> Type) (Let6989586621679337107LeftSym1 a_6989586621679337101 :: TyFun a (TyFun ([a], [b]) ([a], [b]) -> Type) -> Type)) (Let6989586621679337107RightSym1 a_6989586621679337101 :: TyFun b (TyFun ([a], [b]) ([a], [b]) -> Type) -> Type))) (Apply (Apply (Tuple2Sym0 :: TyFun [a] ([b] ~> ([a], [b])) -> Type) (NilSym0 :: [a])) (NilSym0 :: [b]))) a_6989586621679337101

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

type family IsLeft (a1 :: Either a b) :: Bool where ...

Equations

IsLeft ('Left _1 :: Either a b) = TrueSym0

IsLeft ('Right _1 :: Either a b) = FalseSym0

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

type family IsRight (a1 :: Either a b) :: Bool where ...

Equations

IsRight ('Left _1 :: Either a b) = FalseSym0

IsRight ('Right _1 :: Either a b) = TrueSym0

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

Defunctionalization symbols

data LeftSym0 (a1 :: TyFun a (Either a b))

Instances

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

Defined in Data.Singletons.Base.Instances

Methods

sing :: Sing (LeftSym0 :: TyFun a (Either a b) -> Type)

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) (a6989586621679046286 :: a)

Defined in Data.Singletons.Base.Instances

type Apply (LeftSym0 :: TyFun a (Either a b) -> Type) (a6989586621679046286 :: a) = 'Left a6989586621679046286 :: Either a b

type family LeftSym1 (a6989586621679046286 :: a) :: Either a b where ...

Equations

LeftSym1 (a6989586621679046286 :: a) = 'Left a6989586621679046286 :: Either a b

data RightSym0 (a1 :: TyFun b (Either a b))

Instances

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

Defined in Data.Singletons.Base.Instances

Methods

sing :: Sing (RightSym0 :: TyFun b (Either a b) -> Type)

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) (a6989586621679046288 :: b)

Defined in Data.Singletons.Base.Instances

type Apply (RightSym0 :: TyFun b (Either a b) -> Type) (a6989586621679046288 :: b) = 'Right a6989586621679046288 :: Either a b

type family RightSym1 (a6989586621679046288 :: b) :: Either a b where ...

Equations

RightSym1 (a6989586621679046288 :: b) = 'Right a6989586621679046288 :: Either a b

data Either_Sym0 (a1 :: TyFun (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 :: TyFun (a ~> c) ((b ~> c) ~> (Either a b ~> c)) -> Type)

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) (a6989586621679334944 :: a ~> c)

Defined in Data.Either.Singletons

type Apply (Either_Sym0 :: TyFun (a ~> c) ((b ~> c) ~> (Either a b ~> c)) -> Type) (a6989586621679334944 :: a ~> c) = Either_Sym1 a6989586621679334944 :: TyFun (b ~> c) (Either a b ~> c) -> Type

data Either_Sym1 (a6989586621679334944 :: a ~> c) (b1 :: TyFun (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 :: a ~> c). Sing x -> Sing (Either_Sym1 x :: TyFun (b ~> c) (Either a b ~> c) -> Type)

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

SuppressUnusedWarnings (Either_Sym1 a6989586621679334944 :: TyFun (b ~> c) (Either a b ~> c) -> Type)

Defined in Data.Either.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (Either_Sym1 a6989586621679334944 :: TyFun (b ~> c) (Either a b ~> c) -> Type) (a6989586621679334945 :: b ~> c)

Defined in Data.Either.Singletons

type Apply (Either_Sym1 a6989586621679334944 :: TyFun (b ~> c) (Either a b ~> c) -> Type) (a6989586621679334945 :: b ~> c) = Either_Sym2 a6989586621679334944 a6989586621679334945

data Either_Sym2 (a6989586621679334944 :: a ~> c) (a6989586621679334945 :: b ~> c) (c1 :: TyFun (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 :: a ~> c) (y :: b ~> c). 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 :: b ~> c). 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 a6989586621679334944 a6989586621679334945 :: TyFun (Either a b) c -> Type)

Defined in Data.Either.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (Either_Sym2 a6989586621679334944 a6989586621679334945 :: TyFun (Either a b) c -> Type) (a6989586621679334946 :: Either a b)

Defined in Data.Either.Singletons

type Apply (Either_Sym2 a6989586621679334944 a6989586621679334945 :: TyFun (Either a b) c -> Type) (a6989586621679334946 :: Either a b) = Either_ a6989586621679334944 a6989586621679334945 a6989586621679334946

type family Either_Sym3 (a6989586621679334944 :: a ~> c) (a6989586621679334945 :: b ~> c) (a6989586621679334946 :: Either a b) :: c where ...

Equations

Either_Sym3 (a6989586621679334944 :: a ~> c) (a6989586621679334945 :: b ~> c) (a6989586621679334946 :: Either a b) = Either_ a6989586621679334944 a6989586621679334945 a6989586621679334946

data LeftsSym0 (a1 :: TyFun [Either a b] [a])

Instances

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

Defined in Data.Either.Singletons

Methods

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

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

Defined in Data.Either.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (LeftsSym0 :: TyFun [Either a b] [a] -> Type) (a6989586621679337128 :: [Either a b])

Defined in Data.Either.Singletons

type Apply (LeftsSym0 :: TyFun [Either a b] [a] -> Type) (a6989586621679337128 :: [Either a b]) = Lefts a6989586621679337128

type family LeftsSym1 (a6989586621679337128 :: [Either a b]) :: [a] where ...

Equations

LeftsSym1 (a6989586621679337128 :: [Either a b]) = Lefts a6989586621679337128

data RightsSym0 (a1 :: TyFun [Either a b] [b])

Instances

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

Defined in Data.Either.Singletons

Methods

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

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

Defined in Data.Either.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (RightsSym0 :: TyFun [Either a b] [b] -> Type) (a6989586621679337122 :: [Either a b])

Defined in Data.Either.Singletons

type Apply (RightsSym0 :: TyFun [Either a b] [b] -> Type) (a6989586621679337122 :: [Either a b]) = Rights a6989586621679337122

type family RightsSym1 (a6989586621679337122 :: [Either a b]) :: [b] where ...

Equations

RightsSym1 (a6989586621679337122 :: [Either a b]) = Rights a6989586621679337122

data IsLeftSym0 (a1 :: TyFun (Either a b) Bool)

Instances

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

Defined in Data.Either.Singletons

Methods

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

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

Defined in Data.Either.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (IsLeftSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621679337100 :: Either a b)

Defined in Data.Either.Singletons

type Apply (IsLeftSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621679337100 :: Either a b) = IsLeft a6989586621679337100

type family IsLeftSym1 (a6989586621679337100 :: Either a b) :: Bool where ...

Equations

IsLeftSym1 (a6989586621679337100 :: Either a b) = IsLeft a6989586621679337100

data IsRightSym0 (a1 :: TyFun (Either a b) Bool)

Instances

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

Defined in Data.Either.Singletons

Methods

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

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

Defined in Data.Either.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (IsRightSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621679337097 :: Either a b)

Defined in Data.Either.Singletons

type Apply (IsRightSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621679337097 :: Either a b) = IsRight a6989586621679337097

type family IsRightSym1 (a6989586621679337097 :: Either a b) :: Bool where ...

Equations

IsRightSym1 (a6989586621679337097 :: Either a b) = IsRight a6989586621679337097