Copyright	(C) 2013-2014 Richard Eisenberg Jan Stolarek
License	BSD-style (see LICENSE)
Maintainer	Ryan Scott
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Singletons.Prelude.Either

Contents

The Either singleton
Singletons from Data.Either
Defunctionalization symbols

Description

Defines functions and datatypes relating to the singleton for Either, including a singletons version 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.

Synopsis

data family Sing :: k -> Type
type SEither = (Sing :: Either a b -> Type)
either_ :: (a -> c) -> (b -> c) -> Either a b -> c
type family Either_ (a :: (~>) a c) (a :: (~>) b c) (a :: Either a b) :: c where ...
sEither_ :: forall a c b (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 family Lefts (a :: [Either a b]) :: [a] where ...
sLefts :: forall a b (t :: [Either a b]). Sing t -> Sing (Apply LeftsSym0 t :: [a])
type family Rights (a :: [Either a b]) :: [b] where ...
sRights :: forall a b (t :: [Either a b]). Sing t -> Sing (Apply RightsSym0 t :: [b])
type family PartitionEithers (a :: [Either a b]) :: ([a], [b]) where ...
sPartitionEithers :: forall a b (t :: [Either a b]). Sing t -> Sing (Apply PartitionEithersSym0 t :: ([a], [b]))
type family IsLeft (a :: Either a b) :: Bool where ...
sIsLeft :: forall a b (t :: Either a b). Sing t -> Sing (Apply IsLeftSym0 t :: Bool)
type family IsRight (a :: Either a b) :: Bool where ...
sIsRight :: forall a b (t :: Either a b). Sing t -> Sing (Apply IsRightSym0 t :: Bool)
data LeftSym0 :: forall (a6989586621679089505 :: Type) (b6989586621679089506 :: Type). (~>) a6989586621679089505 (Either (a6989586621679089505 :: Type) (b6989586621679089506 :: Type))
type LeftSym1 (t6989586621679312485 :: a6989586621679089505) = Left t6989586621679312485
data RightSym0 :: forall (a6989586621679089505 :: Type) (b6989586621679089506 :: Type). (~>) b6989586621679089506 (Either (a6989586621679089505 :: Type) (b6989586621679089506 :: Type))
type RightSym1 (t6989586621679312487 :: b6989586621679089506) = Right t6989586621679312487
data Either_Sym0 :: forall a6989586621680465967 b6989586621680465969 c6989586621680465968. (~>) ((~>) a6989586621680465967 c6989586621680465968) ((~>) ((~>) b6989586621680465969 c6989586621680465968) ((~>) (Either a6989586621680465967 b6989586621680465969) c6989586621680465968))
data Either_Sym1 (a6989586621680466003 :: (~>) a6989586621680465967 c6989586621680465968) :: forall b6989586621680465969. (~>) ((~>) b6989586621680465969 c6989586621680465968) ((~>) (Either a6989586621680465967 b6989586621680465969) c6989586621680465968)
data Either_Sym2 (a6989586621680466003 :: (~>) a6989586621680465967 c6989586621680465968) (a6989586621680466004 :: (~>) b6989586621680465969 c6989586621680465968) :: (~>) (Either a6989586621680465967 b6989586621680465969) c6989586621680465968
type Either_Sym3 (a6989586621680466003 :: (~>) a6989586621680465967 c6989586621680465968) (a6989586621680466004 :: (~>) b6989586621680465969 c6989586621680465968) (a6989586621680466005 :: Either a6989586621680465967 b6989586621680465969) = Either_ a6989586621680466003 a6989586621680466004 a6989586621680466005
data LeftsSym0 :: forall a6989586621680467445 b6989586621680467446. (~>) [Either a6989586621680467445 b6989586621680467446] [a6989586621680467445]
type LeftsSym1 (a6989586621680467835 :: [Either a6989586621680467445 b6989586621680467446]) = Lefts a6989586621680467835
data RightsSym0 :: forall a6989586621680467443 b6989586621680467444. (~>) [Either a6989586621680467443 b6989586621680467444] [b6989586621680467444]
type RightsSym1 (a6989586621680467830 :: [Either a6989586621680467443 b6989586621680467444]) = Rights a6989586621680467830
data IsLeftSym0 :: forall a6989586621680467439 b6989586621680467440. (~>) (Either a6989586621680467439 b6989586621680467440) Bool
type IsLeftSym1 (a6989586621680467806 :: Either a6989586621680467439 b6989586621680467440) = IsLeft a6989586621680467806
data IsRightSym0 :: forall a6989586621680467437 b6989586621680467438. (~>) (Either a6989586621680467437 b6989586621680467438) Bool
type IsRightSym1 (a6989586621680467804 :: Either a6989586621680467437 b6989586621680467438) = IsRight a6989586621680467804

The `Either` singleton

data family Sing :: k -> Type #

The singleton kind-indexed data family.

Instances

SDecide k => TestCoercion (Sing :: k -> Type) #
Instance details Defined in Data.Singletons.Decide Methods testCoercion :: Sing a -> Sing b -> Maybe (Coercion a b) #
SDecide k => TestEquality (Sing :: k -> Type) #
Instance details Defined in Data.Singletons.Decide Methods testEquality :: Sing a -> Sing b -> Maybe (a :~: b) #
Show (SSymbol s) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> SSymbol s -> ShowS # show :: SSymbol s -> String # showList :: [SSymbol s] -> ShowS #
Show (SNat n) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> SNat n -> ShowS # show :: SNat n -> String # showList :: [SNat n] -> ShowS #
Eq (Sing a) #
Instance details Defined in Data.Singletons.TypeRepTYPE Methods (==) :: Sing a -> Sing a -> Bool # (/=) :: Sing a -> Sing a -> Bool #
Ord (Sing a) #
Instance details Defined in Data.Singletons.TypeRepTYPE Methods compare :: Sing a -> Sing a -> Ordering # (<) :: Sing a -> Sing a -> Bool # (<=) :: Sing a -> Sing a -> Bool # (>) :: Sing a -> Sing a -> Bool # (>=) :: Sing a -> Sing a -> Bool # max :: Sing a -> Sing a -> Sing a # min :: Sing a -> Sing a -> Sing a #
Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing [a]) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing b) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
Show (Sing a) #
Instance details Defined in Data.Singletons.TypeRepTYPE Methods showsPrec :: Int -> Sing a -> ShowS # show :: Sing a -> String # showList :: [Sing a] -> ShowS #
Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing b) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing b, ShowSing c) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing b, ShowSing c, ShowSing d) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing b, ShowSing c, ShowSing d, ShowSing e) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing b, ShowSing c, ShowSing d, ShowSing e, ShowSing f) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing b, ShowSing c, ShowSing d, ShowSing e, ShowSing f, ShowSing g) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing b) => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing m => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing (Maybe a) => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing (Maybe a) => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Monoid Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing (Maybe a) => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Monoid Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing Bool => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing Bool => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing [a]) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
data Sing (a :: Bool) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (a :: Bool) where SFalse :: forall (a :: Bool). Sing False STrue :: forall (a :: Bool). Sing True
data Sing (a :: Ordering) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (a :: Ordering) where SLT :: forall (a :: Ordering). Sing LT SEQ :: forall (a :: Ordering). Sing EQ SGT :: forall (a :: Ordering). Sing GT
data Sing (n :: Nat) #
Instance details Defined in Data.Singletons.TypeLits.Internal data Sing (n :: Nat) where SNat :: forall (n :: Nat). KnownNat n => Sing n
data Sing (n :: Symbol) #
Instance details Defined in Data.Singletons.TypeLits.Internal data Sing (n :: Symbol) where SSym :: forall (n :: Symbol). KnownSymbol n => Sing n
data Sing (a :: ()) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (a :: ()) where STuple0 :: forall (a :: ()). Sing ()
data Sing (a :: Void) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (a :: Void)
data Sing (a :: All) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (a :: All) where SAll :: forall (a :: All) (n :: Bool). {..} -> Sing (All n)
data Sing (a :: Any) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (a :: Any) where SAny :: forall (a :: Any) (n :: Bool). {..} -> Sing (Any n)
data Sing (a :: PErrorMessage) #
Instance details Defined in Data.Singletons.TypeError data Sing (a :: PErrorMessage) where SText :: forall (a :: PErrorMessage) (t :: Symbol). Sing t -> Sing (Text t) SShowType :: forall (a :: PErrorMessage) t (ty :: t). Sing ty -> Sing (ShowType ty :: ErrorMessage' Symbol) (:%<>:) :: forall (a :: PErrorMessage) (e1 :: ErrorMessage' Symbol) (e2 :: ErrorMessage' Symbol). Sing e1 -> Sing e2 -> Sing (e1 :<>: e2) (:%$$:) :: forall (a :: PErrorMessage) (e1 :: ErrorMessage' Symbol) (e2 :: ErrorMessage' Symbol). Sing e1 -> Sing e2 -> Sing (e1 :$$: e2)
data Sing (b :: [a]) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (b :: [a]) where SNil :: forall k (b :: [k]). Sing ([] :: [k]) SCons :: forall a (b :: [a]) (n :: a) (n :: [a]). Sing n -> Sing n -> Sing (n ': n)
data Sing (b :: Maybe a) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (b :: Maybe a) where SNothing :: forall a (b :: Maybe a). Sing (Nothing :: Maybe a) SJust :: forall a (b :: Maybe a) (n :: a). Sing n -> Sing (Just n)
newtype Sing (a :: TYPE rep) #	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 -> Type` 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 `TypeRep`s (for instance, `TypeRep`s 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.
Instance details Defined in Data.Singletons.TypeRepTYPE newtype Sing (a :: TYPE rep) = STypeRep (TypeRep a)
data Sing (b :: Min a) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (b :: Min a) where SMin :: forall a (b :: Min a) (n :: a). {..} -> Sing (Min n)
data Sing (b :: Max a) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (b :: Max a) where SMax :: forall a (b :: Max a) (n :: a). {..} -> Sing (Max n)
data Sing (b :: First a) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (b :: First a) where SFirst :: forall a (b :: First a) (n :: a). {..} -> Sing (First n)
data Sing (b :: Last a) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (b :: Last a) where SLast :: forall a (b :: Last a) (n :: a). {..} -> Sing (Last n)
data Sing (a :: WrappedMonoid m) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (a :: WrappedMonoid m) where SWrapMonoid :: forall m (a :: WrappedMonoid m) (n :: m). {..} -> Sing (WrapMonoid n)
data Sing (b :: Option a) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (b :: Option a) where SOption :: forall a (b :: Option a) (n :: Maybe a). {..} -> Sing (Option n)
data Sing (b :: Identity a) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (b :: Identity a) where SIdentity :: forall a (b :: Identity a) (n :: a). {..} -> Sing (Identity n)
data Sing (b :: First a) #
Instance details Defined in Data.Singletons.Prelude.Monoid data Sing (b :: First a) where SFirst :: forall a (b :: First a) (n :: Maybe a). {..} -> Sing (First n)
data Sing (b :: Last a) #
Instance details Defined in Data.Singletons.Prelude.Monoid data Sing (b :: Last a) where SLast :: forall a (b :: Last a) (n :: Maybe a). {..} -> Sing (Last n)
data Sing (b :: Dual a) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (b :: Dual a) where SDual :: forall a (b :: Dual a) (n :: a). {..} -> Sing (Dual n)
data Sing (b :: Sum a) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (b :: Sum a) where SSum :: forall a (b :: Sum a) (n :: a). {..} -> Sing (Sum n)
data Sing (b :: Product a) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (b :: Product a) where SProduct :: forall a (b :: Product a) (n :: a). {..} -> Sing (Product n)
data Sing (b :: Down a) #
Instance details Defined in Data.Singletons.Prelude.Ord data Sing (b :: Down a) where SDown :: forall a (b :: Down a) (n :: a). Sing n -> Sing (Down n)
data Sing (b :: NonEmpty a) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (b :: NonEmpty a) where (:%\|) :: forall a (b :: NonEmpty a) (n :: a) (n :: [a]). Sing n -> Sing n -> Sing (n :\| n)
data Sing (c :: Either a b) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (c :: Either a b) where SLeft :: forall a b (c :: Either a b) (n :: a). Sing n -> Sing (Left n :: Either a b) SRight :: forall a b (c :: Either a b) (n :: b). Sing n -> Sing (Right n :: Either a b)
data Sing (c :: (a, b)) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (c :: (a, b)) where STuple2 :: forall a b (c :: (a, b)) (n :: a) (n :: b). Sing n -> Sing n -> Sing ((,) n n)
data Sing (c :: Arg a b) #
Instance details Defined in Data.Singletons.Prelude.Semigroup data Sing (c :: Arg a b) where SArg :: forall a b (c :: Arg a b) (n :: a) (n :: b). Sing n -> Sing n -> Sing (Arg n n)
newtype Sing (f :: k1 ~> k2) #
Instance details Defined in Data.Singletons.Internal newtype Sing (f :: k1 ~> k2) = SLambda { applySing :: forall (t :: k1). Sing t -> Sing (f @@ t) }
data Sing (d :: (a, b, c)) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (d :: (a, b, c)) where STuple3 :: forall a b c (d :: (a, b, c)) (n :: a) (n :: b) (n :: c). Sing n -> Sing n -> Sing n -> Sing ((,,) n n n)
data Sing (c :: Const a b) #
Instance details Defined in Data.Singletons.Prelude.Const data Sing (c :: Const a b) where SConst :: forall k a (b :: k) (c :: Const a b) (a :: a). {..} -> Sing (Const a :: Const a b)
data Sing (e :: (a, b, c, d)) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (e :: (a, b, c, d)) where STuple4 :: forall a b c d (e :: (a, b, c, d)) (n :: a) (n :: b) (n :: c) (n :: d). Sing n -> Sing n -> Sing n -> Sing n -> Sing ((,,,) n n n n)
data Sing (f :: (a, b, c, d, e)) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (f :: (a, b, c, d, e)) where STuple5 :: forall a b c d e (f :: (a, b, c, d, e)) (n :: a) (n :: b) (n :: c) (n :: d) (n :: e). Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing ((,,,,) n n n n n)
data Sing (g :: (a, b, c, d, e, f)) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (g :: (a, b, c, d, e, f)) where STuple6 :: forall a b c d e f (g :: (a, b, c, d, e, f)) (n :: a) (n :: b) (n :: c) (n :: d) (n :: e) (n :: f). Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing ((,,,,,) n n n n n n)
data Sing (h :: (a, b, c, d, e, f, g)) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (h :: (a, b, c, d, e, f, g)) where STuple7 :: forall a b c d e f g (h :: (a, b, c, d, e, f, g)) (n :: a) (n :: b) (n :: c) (n :: d) (n :: e) (n :: f) (n :: g). Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing ((,,,,,,) n n n n n n n)

Though Haddock doesn't show it, the Sing instance above declares constructors

SLeft  :: Sing a -> Sing (Left a)
SRight :: Sing b -> Sing (Right b)

type SEither = (Sing :: Either a b -> Type) #

SEither is a kind-restricted synonym for Sing: type SEither (a :: Either x y) = Sing a

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 a c b (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) #

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 '[] = '[]
Lefts ((:) (Left x) xs) = Apply (Apply (:@#@$) x) (Apply LeftsSym0 xs)
Lefts ((:) (Right _) xs) = Apply LeftsSym0 xs

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

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

Equations

Rights '[] = '[]
Rights ((:) (Left _) xs) = Apply RightsSym0 xs
Rights ((:) (Right x) xs) = Apply (Apply (:@#@$) x) (Apply RightsSym0 xs)

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

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

Equations

PartitionEithers a_6989586621680467808 = Apply (Apply (Apply FoldrSym0 (Apply (Apply Either_Sym0 (Let6989586621680467813LeftSym1 a_6989586621680467808)) (Let6989586621680467813RightSym1 a_6989586621680467808))) (Apply (Apply Tuple2Sym0 '[]) '[])) a_6989586621680467808

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

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

Equations

IsLeft (Left _) = TrueSym0
IsLeft (Right _) = FalseSym0

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

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

Equations

IsRight (Left _) = FalseSym0
IsRight (Right _) = TrueSym0

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

Defunctionalization symbols

data LeftSym0 :: forall (a6989586621679089505 :: Type) (b6989586621679089506 :: Type). (~>) a6989586621679089505 (Either (a6989586621679089505 :: Type) (b6989586621679089506 :: Type)) #

Instances

SingI (LeftSym0 :: TyFun a (Either a b) -> Type) #
Instance details Defined in Data.Singletons.Prelude.Instances Methods sing :: Sing LeftSym0 #
SuppressUnusedWarnings (LeftSym0 :: TyFun a6989586621679089505 (Either a6989586621679089505 b6989586621679089506) -> Type) #
Instance details Defined in Data.Singletons.Prelude.Instances Methods suppressUnusedWarnings :: () #
type Apply (LeftSym0 :: TyFun a (Either a b6989586621679089506) -> Type) (t6989586621679312485 :: a) #
Instance details Defined in Data.Singletons.Prelude.Instances type Apply (LeftSym0 :: TyFun a (Either a b6989586621679089506) -> Type) (t6989586621679312485 :: a) = (Left t6989586621679312485 :: Either a b6989586621679089506)

type LeftSym1 (t6989586621679312485 :: a6989586621679089505) = Left t6989586621679312485 #

data RightSym0 :: forall (a6989586621679089505 :: Type) (b6989586621679089506 :: Type). (~>) b6989586621679089506 (Either (a6989586621679089505 :: Type) (b6989586621679089506 :: Type)) #

Instances

SingI (RightSym0 :: TyFun b (Either a b) -> Type) #
Instance details Defined in Data.Singletons.Prelude.Instances Methods sing :: Sing RightSym0 #
SuppressUnusedWarnings (RightSym0 :: TyFun b6989586621679089506 (Either a6989586621679089505 b6989586621679089506) -> Type) #
Instance details Defined in Data.Singletons.Prelude.Instances Methods suppressUnusedWarnings :: () #
type Apply (RightSym0 :: TyFun b (Either a6989586621679089505 b) -> Type) (t6989586621679312487 :: b) #
Instance details Defined in Data.Singletons.Prelude.Instances type Apply (RightSym0 :: TyFun b (Either a6989586621679089505 b) -> Type) (t6989586621679312487 :: b) = (Right t6989586621679312487 :: Either a6989586621679089505 b)

type RightSym1 (t6989586621679312487 :: b6989586621679089506) = Right t6989586621679312487 #

data Either_Sym0 :: forall a6989586621680465967 b6989586621680465969 c6989586621680465968. (~>) ((~>) a6989586621680465967 c6989586621680465968) ((~>) ((~>) b6989586621680465969 c6989586621680465968) ((~>) (Either a6989586621680465967 b6989586621680465969) c6989586621680465968)) #

Instances

SingI (Either_Sym0 :: TyFun (a ~> c) ((b ~> c) ~> (Either a b ~> c)) -> Type) #
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing Either_Sym0 #
SuppressUnusedWarnings (Either_Sym0 :: TyFun (a6989586621680465967 ~> c6989586621680465968) ((b6989586621680465969 ~> c6989586621680465968) ~> (Either a6989586621680465967 b6989586621680465969 ~> c6989586621680465968)) -> Type) #
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: () #
type Apply (Either_Sym0 :: TyFun (a6989586621680465967 ~> c6989586621680465968) ((b6989586621680465969 ~> c6989586621680465968) ~> (Either a6989586621680465967 b6989586621680465969 ~> c6989586621680465968)) -> Type) (a6989586621680466003 :: a6989586621680465967 ~> c6989586621680465968) #
Instance details Defined in Data.Singletons.Prelude.Either type Apply (Either_Sym0 :: TyFun (a6989586621680465967 ~> c6989586621680465968) ((b6989586621680465969 ~> c6989586621680465968) ~> (Either a6989586621680465967 b6989586621680465969 ~> c6989586621680465968)) -> Type) (a6989586621680466003 :: a6989586621680465967 ~> c6989586621680465968) = (Either_Sym1 a6989586621680466003 b6989586621680465969 :: TyFun (b6989586621680465969 ~> c6989586621680465968) (Either a6989586621680465967 b6989586621680465969 ~> c6989586621680465968) -> Type)

data Either_Sym1 (a6989586621680466003 :: (~>) a6989586621680465967 c6989586621680465968) :: forall b6989586621680465969. (~>) ((~>) b6989586621680465969 c6989586621680465968) ((~>) (Either a6989586621680465967 b6989586621680465969) c6989586621680465968) #

Instances

SingI d => SingI (Either_Sym1 d b :: TyFun (b ~> c) (Either a b ~> c) -> Type) #
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing (Either_Sym1 d b) #
SuppressUnusedWarnings (Either_Sym1 a6989586621680466003 b6989586621680465969 :: TyFun (b6989586621680465969 ~> c6989586621680465968) (Either a6989586621680465967 b6989586621680465969 ~> c6989586621680465968) -> Type) #
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: () #
type Apply (Either_Sym1 a6989586621680466003 b6989586621680465969 :: TyFun (b6989586621680465969 ~> c6989586621680465968) (Either a6989586621680465967 b6989586621680465969 ~> c6989586621680465968) -> Type) (a6989586621680466004 :: b6989586621680465969 ~> c6989586621680465968) #
Instance details Defined in Data.Singletons.Prelude.Either type Apply (Either_Sym1 a6989586621680466003 b6989586621680465969 :: TyFun (b6989586621680465969 ~> c6989586621680465968) (Either a6989586621680465967 b6989586621680465969 ~> c6989586621680465968) -> Type) (a6989586621680466004 :: b6989586621680465969 ~> c6989586621680465968) = Either_Sym2 a6989586621680466003 a6989586621680466004

data Either_Sym2 (a6989586621680466003 :: (~>) a6989586621680465967 c6989586621680465968) (a6989586621680466004 :: (~>) b6989586621680465969 c6989586621680465968) :: (~>) (Either a6989586621680465967 b6989586621680465969) c6989586621680465968 #

Instances

(SingI d1, SingI d2) => SingI (Either_Sym2 d1 d2 :: TyFun (Either a b) c -> Type) #
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing (Either_Sym2 d1 d2) #
SuppressUnusedWarnings (Either_Sym2 a6989586621680466004 a6989586621680466003 :: TyFun (Either a6989586621680465967 b6989586621680465969) c6989586621680465968 -> Type) #
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: () #
type Apply (Either_Sym2 a6989586621680466004 a6989586621680466003 :: TyFun (Either a b) c -> Type) (a6989586621680466005 :: Either a b) #
Instance details Defined in Data.Singletons.Prelude.Either type Apply (Either_Sym2 a6989586621680466004 a6989586621680466003 :: TyFun (Either a b) c -> Type) (a6989586621680466005 :: Either a b) = Either_ a6989586621680466004 a6989586621680466003 a6989586621680466005

type Either_Sym3 (a6989586621680466003 :: (~>) a6989586621680465967 c6989586621680465968) (a6989586621680466004 :: (~>) b6989586621680465969 c6989586621680465968) (a6989586621680466005 :: Either a6989586621680465967 b6989586621680465969) = Either_ a6989586621680466003 a6989586621680466004 a6989586621680466005 #

data LeftsSym0 :: forall a6989586621680467445 b6989586621680467446. (~>) [Either a6989586621680467445 b6989586621680467446] [a6989586621680467445] #

Instances

SingI (LeftsSym0 :: TyFun [Either a b] [a] -> Type) #
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing LeftsSym0 #
SuppressUnusedWarnings (LeftsSym0 :: TyFun [Either a6989586621680467445 b6989586621680467446] [a6989586621680467445] -> Type) #
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: () #
type Apply (LeftsSym0 :: TyFun [Either a b] [a] -> Type) (a6989586621680467835 :: [Either a b]) #
Instance details Defined in Data.Singletons.Prelude.Either type Apply (LeftsSym0 :: TyFun [Either a b] [a] -> Type) (a6989586621680467835 :: [Either a b]) = Lefts a6989586621680467835

type LeftsSym1 (a6989586621680467835 :: [Either a6989586621680467445 b6989586621680467446]) = Lefts a6989586621680467835 #

data RightsSym0 :: forall a6989586621680467443 b6989586621680467444. (~>) [Either a6989586621680467443 b6989586621680467444] [b6989586621680467444] #

Instances

SingI (RightsSym0 :: TyFun [Either a b] [b] -> Type) #
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing RightsSym0 #
SuppressUnusedWarnings (RightsSym0 :: TyFun [Either a6989586621680467443 b6989586621680467444] [b6989586621680467444] -> Type) #
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: () #
type Apply (RightsSym0 :: TyFun [Either a b] [b] -> Type) (a6989586621680467830 :: [Either a b]) #
Instance details Defined in Data.Singletons.Prelude.Either type Apply (RightsSym0 :: TyFun [Either a b] [b] -> Type) (a6989586621680467830 :: [Either a b]) = Rights a6989586621680467830

type RightsSym1 (a6989586621680467830 :: [Either a6989586621680467443 b6989586621680467444]) = Rights a6989586621680467830 #

data IsLeftSym0 :: forall a6989586621680467439 b6989586621680467440. (~>) (Either a6989586621680467439 b6989586621680467440) Bool #

Instances

SingI (IsLeftSym0 :: TyFun (Either a b) Bool -> Type) #
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing IsLeftSym0 #
SuppressUnusedWarnings (IsLeftSym0 :: TyFun (Either a6989586621680467439 b6989586621680467440) Bool -> Type) #
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: () #
type Apply (IsLeftSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621680467806 :: Either a b) #
Instance details Defined in Data.Singletons.Prelude.Either type Apply (IsLeftSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621680467806 :: Either a b) = IsLeft a6989586621680467806

type IsLeftSym1 (a6989586621680467806 :: Either a6989586621680467439 b6989586621680467440) = IsLeft a6989586621680467806 #

data IsRightSym0 :: forall a6989586621680467437 b6989586621680467438. (~>) (Either a6989586621680467437 b6989586621680467438) Bool #

Instances

SingI (IsRightSym0 :: TyFun (Either a b) Bool -> Type) #
Instance details Defined in Data.Singletons.Prelude.Either Methods sing :: Sing IsRightSym0 #
SuppressUnusedWarnings (IsRightSym0 :: TyFun (Either a6989586621680467437 b6989586621680467438) Bool -> Type) #
Instance details Defined in Data.Singletons.Prelude.Either Methods suppressUnusedWarnings :: () #
type Apply (IsRightSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621680467804 :: Either a b) #
Instance details Defined in Data.Singletons.Prelude.Either type Apply (IsRightSym0 :: TyFun (Either a b) Bool -> Type) (a6989586621680467804 :: Either a b) = IsRight a6989586621680467804

type IsRightSym1 (a6989586621680467804 :: Either a6989586621680467437 b6989586621680467438) = IsRight a6989586621680467804 #

The Either singleton

Singletons from Data.Either

Defunctionalization symbols

The `Either` singleton

Singletons from `Data.Either`