Copyright	(C) 2013-2014 Richard Eisenberg Jan Stolarek
License	BSD-style (see LICENSE)
Maintainer	Richard Eisenberg (eir@cis.upenn.edu)
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

The `Either` singleton

data family Sing (a :: k) #

The singleton kind-indexed data family.

Instances

data Sing Bool #
data Sing Bool where SFalse :: Sing Bool z STrue :: Sing Bool z
data Sing Ordering #
data Sing Ordering where SLT :: Sing Ordering z SEQ :: Sing Ordering z SGT :: Sing Ordering z
data Sing * #
data Sing * where STypeRep :: Sing * a
data Sing Nat #
data Sing Nat where SNat :: Sing Nat n
data Sing Symbol #
data Sing Symbol where SSym :: Sing Symbol n
data Sing () #
data Sing () where STuple0 :: Sing () z
data Sing [a0] #
data Sing [a0] where SNil :: Sing [a] z SCons :: Sing [a] z
data Sing (Maybe a0) #
data Sing (Maybe a0) where SNothing :: Sing (Maybe a) z SJust :: Sing (Maybe a) z
data Sing (NonEmpty a0) #
data Sing (NonEmpty a0) where (:%\|) :: Sing (NonEmpty a) z
data Sing (Either a0 b0) #
data Sing (Either a0 b0) where SLeft :: Sing (Either a b) z SRight :: Sing (Either a b) z
data Sing (a0, b0) #
data Sing (a0, b0) where STuple2 :: Sing (a, b) z
data Sing ((~>) k1 k2) #
data Sing ((~>) k1 k2) = SLambda { applySing :: forall t. Sing k1 t -> Sing k2 ((@@) k1 k2 f t) }
data Sing (a0, b0, c0) #
data Sing (a0, b0, c0) where STuple3 :: Sing (a, b, c) z
data Sing (a0, b0, c0, d0) #
data Sing (a0, b0, c0, d0) where STuple4 :: Sing (a, b, c, d) z
data Sing (a0, b0, c0, d0, e0) #
data Sing (a0, b0, c0, d0, e0) where STuple5 :: Sing (a, b, c, d, e) z
data Sing (a0, b0, c0, d0, e0, f0) #
data Sing (a0, b0, c0, d0, e0, f0) where STuple6 :: Sing (a, b, c, d, e, f) z
data Sing (a0, b0, c0, d0, e0, f0, g0) #
data Sing (a0, b0, c0, d0, e0, f0, g0) where STuple7 :: Sing (a, b, c, d, e, f, g) z

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_ :: forall a c b. (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 _z_6989586621679761264 (Left x) = Apply f x
Either_ _z_6989586621679761268 g (Right y) = Apply g y

sEither_ :: forall t t t. 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 _z_6989586621679762609) xs) = Apply LeftsSym0 xs

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

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

Equations

Rights '[] = '[]
Rights ((:) (Left _z_6989586621679762597) xs) = Apply RightsSym0 xs
Rights ((:) (Right x) xs) = Apply (Apply (:$) x) (Apply RightsSym0 xs)

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

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

Equations

PartitionEithers a_6989586621679762551 = Apply (Apply (Apply FoldrSym0 (Apply (Apply Either_Sym0 (Let6989586621679762558LeftSym1 a_6989586621679762551)) (Let6989586621679762558RightSym1 a_6989586621679762551))) (Apply (Apply Tuple2Sym0 '[]) '[])) a_6989586621679762551

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

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

Equations

IsLeft (Left _z_6989586621679762545) = TrueSym0
IsLeft (Right _z_6989586621679762548) = FalseSym0

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

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

Equations

IsRight (Left _z_6989586621679762535) = FalseSym0
IsRight (Right _z_6989586621679762538) = TrueSym0

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

Defunctionalization symbols

data LeftSym0 l #

Instances

SuppressUnusedWarnings (TyFun a6989586621679054093 (Either a6989586621679054093 b6989586621679054094) -> *) (LeftSym0 a6989586621679054093 b6989586621679054094) #
Methods suppressUnusedWarnings :: Proxy (LeftSym0 a6989586621679054093 b6989586621679054094) t -> () #
type Apply a6989586621679054093 (Either a6989586621679054093 b6989586621679054094) (LeftSym0 a6989586621679054093 b6989586621679054094) l0 #
type Apply a6989586621679054093 (Either a6989586621679054093 b6989586621679054094) (LeftSym0 a6989586621679054093 b6989586621679054094) l0 = LeftSym1 b6989586621679054094 a6989586621679054093 l0

type LeftSym1 t = Left t #

data RightSym0 l #

Instances

SuppressUnusedWarnings (TyFun b6989586621679054094 (Either a6989586621679054093 b6989586621679054094) -> *) (RightSym0 a6989586621679054093 b6989586621679054094) #
Methods suppressUnusedWarnings :: Proxy (RightSym0 a6989586621679054093 b6989586621679054094) t -> () #
type Apply b6989586621679054094 (Either a6989586621679054093 b6989586621679054094) (RightSym0 a6989586621679054093 b6989586621679054094) l0 #
type Apply b6989586621679054094 (Either a6989586621679054093 b6989586621679054094) (RightSym0 a6989586621679054093 b6989586621679054094) l0 = RightSym1 a6989586621679054093 b6989586621679054094 l0

type RightSym1 t = Right t #

data Either_Sym0 l #

Instances

SuppressUnusedWarnings (TyFun (TyFun a6989586621679761240 c6989586621679761241 -> Type) (TyFun (TyFun b6989586621679761242 c6989586621679761241 -> Type) (TyFun (Either a6989586621679761240 b6989586621679761242) c6989586621679761241 -> Type) -> Type) -> *) (Either_Sym0 a6989586621679761240 b6989586621679761242 c6989586621679761241) #
Methods suppressUnusedWarnings :: Proxy (Either_Sym0 a6989586621679761240 b6989586621679761242 c6989586621679761241) t -> () #
type Apply (TyFun a6989586621679761240 c6989586621679761241 -> Type) (TyFun (TyFun b6989586621679761242 c6989586621679761241 -> Type) (TyFun (Either a6989586621679761240 b6989586621679761242) c6989586621679761241 -> Type) -> Type) (Either_Sym0 a6989586621679761240 b6989586621679761242 c6989586621679761241) l0 #
type Apply (TyFun a6989586621679761240 c6989586621679761241 -> Type) (TyFun (TyFun b6989586621679761242 c6989586621679761241 -> Type) (TyFun (Either a6989586621679761240 b6989586621679761242) c6989586621679761241 -> Type) -> Type) (Either_Sym0 a6989586621679761240 b6989586621679761242 c6989586621679761241) l0 = Either_Sym1 b6989586621679761242 a6989586621679761240 c6989586621679761241 l0

data Either_Sym1 l l #

Instances

SuppressUnusedWarnings ((TyFun a6989586621679761240 c6989586621679761241 -> Type) -> TyFun (TyFun b6989586621679761242 c6989586621679761241 -> Type) (TyFun (Either a6989586621679761240 b6989586621679761242) c6989586621679761241 -> Type) -> *) (Either_Sym1 b6989586621679761242 a6989586621679761240 c6989586621679761241) #
Methods suppressUnusedWarnings :: Proxy (Either_Sym1 b6989586621679761242 a6989586621679761240 c6989586621679761241) t -> () #
type Apply (TyFun b6989586621679761242 c6989586621679761241 -> Type) (TyFun (Either a6989586621679761240 b6989586621679761242) c6989586621679761241 -> Type) (Either_Sym1 b6989586621679761242 a6989586621679761240 c6989586621679761241 l0) l1 #
type Apply (TyFun b6989586621679761242 c6989586621679761241 -> Type) (TyFun (Either a6989586621679761240 b6989586621679761242) c6989586621679761241 -> Type) (Either_Sym1 b6989586621679761242 a6989586621679761240 c6989586621679761241 l0) l1 = Either_Sym2 b6989586621679761242 a6989586621679761240 c6989586621679761241 l0 l1

data Either_Sym2 l l l #

Instances

SuppressUnusedWarnings ((TyFun a6989586621679761240 c6989586621679761241 -> Type) -> (TyFun b6989586621679761242 c6989586621679761241 -> Type) -> TyFun (Either a6989586621679761240 b6989586621679761242) c6989586621679761241 -> *) (Either_Sym2 b6989586621679761242 a6989586621679761240 c6989586621679761241) #
Methods suppressUnusedWarnings :: Proxy (Either_Sym2 b6989586621679761242 a6989586621679761240 c6989586621679761241) t -> () #
type Apply (Either a6989586621679761240 b6989586621679761242) c6989586621679761241 (Either_Sym2 b6989586621679761242 a6989586621679761240 c6989586621679761241 l1 l0) l2 #
type Apply (Either a6989586621679761240 b6989586621679761242) c6989586621679761241 (Either_Sym2 b6989586621679761242 a6989586621679761240 c6989586621679761241 l1 l0) l2 = Either_Sym3 b6989586621679761242 a6989586621679761240 c6989586621679761241 l1 l0 l2

type Either_Sym3 t t t = Either_ t t t #

data LeftsSym0 l #

Instances

SuppressUnusedWarnings (TyFun [Either a6989586621679762510 b6989586621679762511] [a6989586621679762510] -> *) (LeftsSym0 b6989586621679762511 a6989586621679762510) #
Methods suppressUnusedWarnings :: Proxy (LeftsSym0 b6989586621679762511 a6989586621679762510) t -> () #
type Apply [Either a6989586621679762510 b6989586621679762511] [a6989586621679762510] (LeftsSym0 b6989586621679762511 a6989586621679762510) l0 #
type Apply [Either a6989586621679762510 b6989586621679762511] [a6989586621679762510] (LeftsSym0 b6989586621679762511 a6989586621679762510) l0 = LeftsSym1 a6989586621679762510 b6989586621679762511 l0

type LeftsSym1 t = Lefts t #

data RightsSym0 l #

Instances

SuppressUnusedWarnings (TyFun [Either a6989586621679762508 b6989586621679762509] [b6989586621679762509] -> *) (RightsSym0 a6989586621679762508 b6989586621679762509) #
Methods suppressUnusedWarnings :: Proxy (RightsSym0 a6989586621679762508 b6989586621679762509) t -> () #
type Apply [Either a6989586621679762508 b6989586621679762509] [b6989586621679762509] (RightsSym0 a6989586621679762508 b6989586621679762509) l0 #
type Apply [Either a6989586621679762508 b6989586621679762509] [b6989586621679762509] (RightsSym0 a6989586621679762508 b6989586621679762509) l0 = RightsSym1 a6989586621679762508 b6989586621679762509 l0

type RightsSym1 t = Rights t #

data IsLeftSym0 l #

Instances

SuppressUnusedWarnings (TyFun (Either a6989586621679762504 b6989586621679762505) Bool -> *) (IsLeftSym0 a6989586621679762504 b6989586621679762505) #
Methods suppressUnusedWarnings :: Proxy (IsLeftSym0 a6989586621679762504 b6989586621679762505) t -> () #
type Apply (Either a6989586621679762504 b6989586621679762505) Bool (IsLeftSym0 a6989586621679762504 b6989586621679762505) l0 #
type Apply (Either a6989586621679762504 b6989586621679762505) Bool (IsLeftSym0 a6989586621679762504 b6989586621679762505) l0 = IsLeftSym1 a6989586621679762504 b6989586621679762505 l0

type IsLeftSym1 t = IsLeft t #

data IsRightSym0 l #

Instances

SuppressUnusedWarnings (TyFun (Either a6989586621679762502 b6989586621679762503) Bool -> *) (IsRightSym0 a6989586621679762502 b6989586621679762503) #
Methods suppressUnusedWarnings :: Proxy (IsRightSym0 a6989586621679762502 b6989586621679762503) t -> () #
type Apply (Either a6989586621679762502 b6989586621679762503) Bool (IsRightSym0 a6989586621679762502 b6989586621679762503) l0 #
type Apply (Either a6989586621679762502 b6989586621679762503) Bool (IsRightSym0 a6989586621679762502 b6989586621679762503) l0 = IsRightSym1 a6989586621679762502 b6989586621679762503 l0

type IsRightSym1 t = IsRight t #

The Either singleton

Singletons from Data.Either

Defunctionalization symbols

The `Either` singleton

Singletons from `Data.Either`