Data.Singletons.Prelude.Either

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.

The Either singleton

data family Sing (a :: k)

The singleton kind-indexed data family.

Instances

SDecide k => TestCoercion (Sing :: k -> *)

Defined in Data.Singletons.Decide

Methods

testCoercion :: Sing a -> Sing b -> Maybe (Coercion a b)

SDecide k => TestEquality (Sing :: k -> *)

Defined in Data.Singletons.Decide

Methods

testEquality :: Sing a -> Sing b -> Maybe (a :~: b)

Show (SSymbol s)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> SSymbol s -> ShowS

show :: SSymbol s -> String

showList :: [SSymbol s] -> ShowS

Show (SNat n)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> SNat n -> ShowS

show :: SNat n -> String

showList :: [SNat n] -> ShowS

Eq (Sing a)

Defined in Data.Singletons.TypeRepStar

Methods

(==) :: Sing a -> Sing a -> Bool

(/=) :: Sing a -> Sing a -> Bool

Ord (Sing a)

Defined in Data.Singletons.TypeRepStar

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)

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)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

ShowSing a => Show (Sing z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

Show (Sing z)

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)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

Show (Sing a)

Defined in Data.Singletons.TypeRepStar

Methods

showsPrec :: Int -> Sing a -> ShowS

show :: Sing a -> String

showList :: [Sing a] -> ShowS

Show (Sing z)

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)

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)

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)

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)

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)

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)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

Show (Sing z)

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)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> Sing z -> ShowS

show :: Sing z -> String

showList :: [Sing z] -> ShowS

data Sing (z :: Bool)

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: Bool) where

• SFalse :: Sing False
• STrue :: Sing True

data Sing (z :: Ordering)

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: Ordering) where

• SLT :: Sing LT
• SEQ :: Sing EQ
• SGT :: Sing GT

data Sing (a :: Type)

Defined in Data.Singletons.TypeRepStar

data Sing (a :: Type) = STypeRep (TypeRep a)

data Sing (n :: Nat)

Defined in Data.Singletons.TypeLits.Internal

data Sing (n :: Nat) where

• SNat :: Sing n

data Sing (n :: Symbol)

Defined in Data.Singletons.TypeLits.Internal

data Sing (n :: Symbol) where

• SSym :: Sing n

data Sing (z :: ())

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: ()) where

• STuple0 :: Sing ()

data Sing (z :: Void)

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: Void)

data Sing (z :: [a])

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: [a]) where

• SNil :: Sing ([] :: [k])
• SCons :: Sing (n ': n)

data Sing (z :: Maybe a)

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: Maybe a) where

• SNothing :: Sing (Nothing :: Maybe a)
• SJust :: Sing (Just n)

data Sing (z :: NonEmpty a)

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: NonEmpty a) where

• (:%|) :: Sing (n :| n)

data Sing (z :: Either a b)

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: Either a b) where

• SLeft :: Sing (Left n :: Either a b)
• SRight :: Sing (Right n :: Either a b)

data Sing (z :: (a, b))

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: (a, b)) where

• STuple2 :: Sing ((,) n n)

data Sing (f :: k1 ~> k2)

Defined in Data.Singletons.Internal

data Sing (f :: k1 ~> k2) = SLambda {

• applySing :: forall (t :: k1). Sing t -> Sing (f @@ t)

}

data Sing (z :: (a, b, c))

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: (a, b, c)) where

• STuple3 :: Sing ((,,) n n n)

data Sing (z :: (a, b, c, d))

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: (a, b, c, d)) where

• STuple4 :: Sing ((,,,) n n n n)

data Sing (z :: (a, b, c, d, e))

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: (a, b, c, d, e)) where

• STuple5 :: Sing ((,,,,) n n n n n)

data Sing (z :: (a, b, c, d, e, f))

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: (a, b, c, d, e, f)) where

• STuple6 :: Sing ((,,,,,) n n n n n n)

data Sing (z :: (a, b, c, d, e, f, g))

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: (a, b, c, d, e, f, g)) where

• STuple7 :: 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 :: TyFun a c -> Type) (a :: TyFun b c -> Type) (a :: Either a b) :: c where ...

Equations

Either_ f _ (Left x) = Apply f x

Either_ _ g (Right y) = Apply g y

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

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

Equations

PartitionEithers a_6989586621679993720 = Apply (Apply (Apply FoldrSym0 (Apply (Apply Either_Sym0 (Let6989586621679993727LeftSym1 a_6989586621679993720)) (Let6989586621679993727RightSym1 a_6989586621679993720))) (Apply (Apply Tuple2Sym0 '[]) '[])) a_6989586621679993720

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

Defunctionalization symbols

data LeftSym0 (l :: TyFun a6989586621679084181 (Either a6989586621679084181 b6989586621679084182))

Instances

SuppressUnusedWarnings (LeftSym0 :: TyFun a6989586621679084181 (Either a6989586621679084181 b6989586621679084182) -> *)

Defined in Data.Singletons.Prelude.Instances

Methods

suppressUnusedWarnings :: ()

type Apply (LeftSym0 :: TyFun a (Either a b6989586621679084182) -> *) (l :: a)

Defined in Data.Singletons.Prelude.Instances

type Apply (LeftSym0 :: TyFun a (Either a b6989586621679084182) -> *) (l :: a) = (Left l :: Either a b6989586621679084182)

type LeftSym1 (t :: a6989586621679084181) = Left t

data RightSym0 (l :: TyFun b6989586621679084182 (Either a6989586621679084181 b6989586621679084182))

Instances

SuppressUnusedWarnings (RightSym0 :: TyFun b6989586621679084182 (Either a6989586621679084181 b6989586621679084182) -> *)

Defined in Data.Singletons.Prelude.Instances

Methods

suppressUnusedWarnings :: ()

type Apply (RightSym0 :: TyFun b (Either a6989586621679084181 b) -> *) (l :: b)

Defined in Data.Singletons.Prelude.Instances

type Apply (RightSym0 :: TyFun b (Either a6989586621679084181 b) -> *) (l :: b) = (Right l :: Either a6989586621679084181 b)

type RightSym1 (t :: b6989586621679084182) = Right t

data Either_Sym0 (l :: TyFun (TyFun a6989586621679992217 c6989586621679992218 -> Type) (TyFun (TyFun b6989586621679992219 c6989586621679992218 -> Type) (TyFun (Either a6989586621679992217 b6989586621679992219) c6989586621679992218 -> Type) -> Type))

Instances

SuppressUnusedWarnings (Either_Sym0 :: TyFun (TyFun a6989586621679992217 c6989586621679992218 -> Type) (TyFun (TyFun b6989586621679992219 c6989586621679992218 -> Type) (TyFun (Either a6989586621679992217 b6989586621679992219) c6989586621679992218 -> Type) -> Type) -> *)

Defined in Data.Singletons.Prelude.Either

Methods

suppressUnusedWarnings :: ()

type Apply (Either_Sym0 :: TyFun (TyFun a6989586621679992217 c6989586621679992218 -> Type) (TyFun (TyFun b6989586621679992219 c6989586621679992218 -> Type) (TyFun (Either a6989586621679992217 b6989586621679992219) c6989586621679992218 -> Type) -> Type) -> *) (l :: TyFun a6989586621679992217 c6989586621679992218 -> Type)

Defined in Data.Singletons.Prelude.Either

type Apply (Either_Sym0 :: TyFun (TyFun a6989586621679992217 c6989586621679992218 -> Type) (TyFun (TyFun b6989586621679992219 c6989586621679992218 -> Type) (TyFun (Either a6989586621679992217 b6989586621679992219) c6989586621679992218 -> Type) -> Type) -> *) (l :: TyFun a6989586621679992217 c6989586621679992218 -> Type) = (Either_Sym1 l :: TyFun (TyFun b6989586621679992219 c6989586621679992218 -> Type) (TyFun (Either a6989586621679992217 b6989586621679992219) c6989586621679992218 -> Type) -> *)

data Either_Sym1 (l :: TyFun a6989586621679992217 c6989586621679992218 -> Type) (l :: TyFun (TyFun b6989586621679992219 c6989586621679992218 -> Type) (TyFun (Either a6989586621679992217 b6989586621679992219) c6989586621679992218 -> Type))

Instances

SuppressUnusedWarnings (Either_Sym1 :: (TyFun a6989586621679992217 c6989586621679992218 -> Type) -> TyFun (TyFun b6989586621679992219 c6989586621679992218 -> Type) (TyFun (Either a6989586621679992217 b6989586621679992219) c6989586621679992218 -> Type) -> *)

Defined in Data.Singletons.Prelude.Either

Methods

suppressUnusedWarnings :: ()

type Apply (Either_Sym1 l1 :: TyFun (TyFun b6989586621679992219 c6989586621679992218 -> Type) (TyFun (Either a6989586621679992217 b6989586621679992219) c6989586621679992218 -> Type) -> *) (l2 :: TyFun b6989586621679992219 c6989586621679992218 -> Type)

Defined in Data.Singletons.Prelude.Either

type Apply (Either_Sym1 l1 :: TyFun (TyFun b6989586621679992219 c6989586621679992218 -> Type) (TyFun (Either a6989586621679992217 b6989586621679992219) c6989586621679992218 -> Type) -> *) (l2 :: TyFun b6989586621679992219 c6989586621679992218 -> Type) = Either_Sym2 l1 l2

data Either_Sym2 (l :: TyFun a6989586621679992217 c6989586621679992218 -> Type) (l :: TyFun b6989586621679992219 c6989586621679992218 -> Type) (l :: TyFun (Either a6989586621679992217 b6989586621679992219) c6989586621679992218)

Instances

SuppressUnusedWarnings (Either_Sym2 :: (TyFun a6989586621679992217 c6989586621679992218 -> Type) -> (TyFun b6989586621679992219 c6989586621679992218 -> Type) -> TyFun (Either a6989586621679992217 b6989586621679992219) c6989586621679992218 -> *)

Defined in Data.Singletons.Prelude.Either

Methods

suppressUnusedWarnings :: ()

type Apply (Either_Sym2 l1 l2 :: TyFun (Either a b) c -> *) (l3 :: Either a b)

Defined in Data.Singletons.Prelude.Either

type Apply (Either_Sym2 l1 l2 :: TyFun (Either a b) c -> *) (l3 :: Either a b) = Either_ l1 l2 l3

type Either_Sym3 (t :: TyFun a6989586621679992217 c6989586621679992218 -> Type) (t :: TyFun b6989586621679992219 c6989586621679992218 -> Type) (t :: Either a6989586621679992217 b6989586621679992219) = Either_ t t t

data LeftsSym0 (l :: TyFun [Either a6989586621679993353 b6989586621679993354] [a6989586621679993353])

Instances

SuppressUnusedWarnings (LeftsSym0 :: TyFun [Either a6989586621679993353 b6989586621679993354] [a6989586621679993353] -> *)

Defined in Data.Singletons.Prelude.Either

Methods

suppressUnusedWarnings :: ()

type Apply (LeftsSym0 :: TyFun [Either a b] [a] -> *) (l :: [Either a b])

Defined in Data.Singletons.Prelude.Either

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

type LeftsSym1 (t :: [Either a6989586621679993353 b6989586621679993354]) = Lefts t

data RightsSym0 (l :: TyFun [Either a6989586621679993351 b6989586621679993352] [b6989586621679993352])

Instances

SuppressUnusedWarnings (RightsSym0 :: TyFun [Either a6989586621679993351 b6989586621679993352] [b6989586621679993352] -> *)

Defined in Data.Singletons.Prelude.Either

Methods

suppressUnusedWarnings :: ()

type Apply (RightsSym0 :: TyFun [Either a b] [b] -> *) (l :: [Either a b])

Defined in Data.Singletons.Prelude.Either

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

type RightsSym1 (t :: [Either a6989586621679993351 b6989586621679993352]) = Rights t

data IsLeftSym0 (l :: TyFun (Either a6989586621679993347 b6989586621679993348) Bool)

Instances

SuppressUnusedWarnings (IsLeftSym0 :: TyFun (Either a6989586621679993347 b6989586621679993348) Bool -> *)

Defined in Data.Singletons.Prelude.Either

Methods

suppressUnusedWarnings :: ()

type Apply (IsLeftSym0 :: TyFun (Either a b) Bool -> *) (l :: Either a b)

Defined in Data.Singletons.Prelude.Either

type Apply (IsLeftSym0 :: TyFun (Either a b) Bool -> *) (l :: Either a b) = IsLeft l

type IsLeftSym1 (t :: Either a6989586621679993347 b6989586621679993348) = IsLeft t

data IsRightSym0 (l :: TyFun (Either a6989586621679993345 b6989586621679993346) Bool)

Instances

SuppressUnusedWarnings (IsRightSym0 :: TyFun (Either a6989586621679993345 b6989586621679993346) Bool -> *)

Defined in Data.Singletons.Prelude.Either

Methods

suppressUnusedWarnings :: ()

type Apply (IsRightSym0 :: TyFun (Either a b) Bool -> *) (l :: Either a b)

Defined in Data.Singletons.Prelude.Either

type Apply (IsRightSym0 :: TyFun (Either a b) Bool -> *) (l :: Either a b) = IsRight l

type IsRightSym1 (t :: Either a6989586621679993345 b6989586621679993346) = IsRight t