Copyright	(C) 2013-2014 Richard Eisenberg Jan Stolarek
License	BSD-style (see LICENSE)
Maintainer	Richard Eisenberg (rae@cs.brynmawr.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 [a] #
data Sing [a] where SNil :: Sing [a] z SCons :: Sing [a] z
data Sing (Maybe a) #
data Sing (Maybe a) where SNothing :: Sing (Maybe a) z SJust :: Sing (Maybe a) z
data Sing (NonEmpty a) #
data Sing (NonEmpty a) where (:%\|) :: Sing (NonEmpty a) z
data Sing (Either a b) #
data Sing (Either a b) where SLeft :: Sing (Either a b) z SRight :: Sing (Either a b) z
data Sing (a, b) #
data Sing (a, b) where STuple2 :: Sing (a, b) z
data Sing ((~>) k1 k2) #
data Sing ((~>) k1 k2) = SLambda { applySing :: forall (t :: k1). Sing k1 t -> Sing k2 ((@@) k1 k2 f t) }
data Sing (a, b, c) #
data Sing (a, b, c) where STuple3 :: Sing (a, b, c) z
data Sing (a, b, c, d) #
data Sing (a, b, c, d) where STuple4 :: Sing (a, b, c, d) z
data Sing (a, b, c, d, e) #
data Sing (a, b, c, d, e) where STuple5 :: Sing (a, b, c, d, e) z
data Sing (a, b, c, d, e, f) #
data Sing (a, b, c, d, e, f) where STuple6 :: Sing (a, b, c, d, e, f) z
data Sing (a, b, c, d, e, f, g) #
data Sing (a, b, c, d, e, f, g) 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_ :: (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_6989586621679453521 (Left x) = Apply f x
Either_ _z_6989586621679453525 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 _z_6989586621679454708) 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 _z_6989586621679454696) 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_6989586621679454650 = Apply (Apply (Apply FoldrSym0 (Apply (Apply Either_Sym0 (Let6989586621679454657LeftSym1 a_6989586621679454650)) (Let6989586621679454657RightSym1 a_6989586621679454650))) (Apply (Apply Tuple2Sym0 '[]) '[])) a_6989586621679454650

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 _z_6989586621679454644) = TrueSym0
IsLeft (Right _z_6989586621679454647) = 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 _z_6989586621679454634) = FalseSym0
IsRight (Right _z_6989586621679454637) = TrueSym0

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

Defunctionalization symbols

data LeftSym0 (l :: TyFun a6989586621679075946 (Either a6989586621679075946 b6989586621679075947)) #

Instances

SuppressUnusedWarnings (TyFun a6989586621679075946 (Either a6989586621679075946 b6989586621679075947) -> *) (LeftSym0 a6989586621679075946 b6989586621679075947) #
Methods suppressUnusedWarnings :: Proxy (LeftSym0 a6989586621679075946 b6989586621679075947) t -> () #
type Apply a (Either a b6989586621679075947) (LeftSym0 a b6989586621679075947) l #
type Apply a (Either a b6989586621679075947) (LeftSym0 a b6989586621679075947) l = Left a b6989586621679075947 l

type LeftSym1 (t :: a6989586621679075946) = Left t #

data RightSym0 (l :: TyFun b6989586621679075947 (Either a6989586621679075946 b6989586621679075947)) #

Instances

SuppressUnusedWarnings (TyFun b6989586621679075947 (Either a6989586621679075946 b6989586621679075947) -> *) (RightSym0 a6989586621679075946 b6989586621679075947) #
Methods suppressUnusedWarnings :: Proxy (RightSym0 a6989586621679075946 b6989586621679075947) t -> () #
type Apply b (Either a6989586621679075946 b) (RightSym0 a6989586621679075946 b) l #
type Apply b (Either a6989586621679075946 b) (RightSym0 a6989586621679075946 b) l = Right a6989586621679075946 b l

type RightSym1 (t :: b6989586621679075947) = Right t #

data Either_Sym0 (l :: TyFun (TyFun a6989586621679453497 c6989586621679453498 -> Type) (TyFun (TyFun b6989586621679453499 c6989586621679453498 -> Type) (TyFun (Either a6989586621679453497 b6989586621679453499) c6989586621679453498 -> Type) -> Type)) #

Instances

SuppressUnusedWarnings (TyFun (TyFun a6989586621679453497 c6989586621679453498 -> Type) (TyFun (TyFun b6989586621679453499 c6989586621679453498 -> Type) (TyFun (Either a6989586621679453497 b6989586621679453499) c6989586621679453498 -> Type) -> Type) -> *) (Either_Sym0 a6989586621679453497 b6989586621679453499 c6989586621679453498) #
Methods suppressUnusedWarnings :: Proxy (Either_Sym0 a6989586621679453497 b6989586621679453499 c6989586621679453498) t -> () #
type Apply (TyFun a6989586621679453497 c6989586621679453498 -> Type) (TyFun (TyFun b6989586621679453499 c6989586621679453498 -> Type) (TyFun (Either a6989586621679453497 b6989586621679453499) c6989586621679453498 -> Type) -> Type) (Either_Sym0 a6989586621679453497 b6989586621679453499 c6989586621679453498) l #
type Apply (TyFun a6989586621679453497 c6989586621679453498 -> Type) (TyFun (TyFun b6989586621679453499 c6989586621679453498 -> Type) (TyFun (Either a6989586621679453497 b6989586621679453499) c6989586621679453498 -> Type) -> Type) (Either_Sym0 a6989586621679453497 b6989586621679453499 c6989586621679453498) l = Either_Sym1 a6989586621679453497 b6989586621679453499 c6989586621679453498 l

data Either_Sym1 (l :: TyFun a6989586621679453497 c6989586621679453498 -> Type) (l :: TyFun (TyFun b6989586621679453499 c6989586621679453498 -> Type) (TyFun (Either a6989586621679453497 b6989586621679453499) c6989586621679453498 -> Type)) #

Instances

SuppressUnusedWarnings ((TyFun a6989586621679453497 c6989586621679453498 -> Type) -> TyFun (TyFun b6989586621679453499 c6989586621679453498 -> Type) (TyFun (Either a6989586621679453497 b6989586621679453499) c6989586621679453498 -> Type) -> *) (Either_Sym1 a6989586621679453497 b6989586621679453499 c6989586621679453498) #
Methods suppressUnusedWarnings :: Proxy (Either_Sym1 a6989586621679453497 b6989586621679453499 c6989586621679453498) t -> () #
type Apply (TyFun b6989586621679453499 c6989586621679453498 -> Type) (TyFun (Either a6989586621679453497 b6989586621679453499) c6989586621679453498 -> Type) (Either_Sym1 a6989586621679453497 b6989586621679453499 c6989586621679453498 l1) l2 #
type Apply (TyFun b6989586621679453499 c6989586621679453498 -> Type) (TyFun (Either a6989586621679453497 b6989586621679453499) c6989586621679453498 -> Type) (Either_Sym1 a6989586621679453497 b6989586621679453499 c6989586621679453498 l1) l2 = Either_Sym2 a6989586621679453497 b6989586621679453499 c6989586621679453498 l1 l2

data Either_Sym2 (l :: TyFun a6989586621679453497 c6989586621679453498 -> Type) (l :: TyFun b6989586621679453499 c6989586621679453498 -> Type) (l :: TyFun (Either a6989586621679453497 b6989586621679453499) c6989586621679453498) #

Instances

SuppressUnusedWarnings ((TyFun a6989586621679453497 c6989586621679453498 -> Type) -> (TyFun b6989586621679453499 c6989586621679453498 -> Type) -> TyFun (Either a6989586621679453497 b6989586621679453499) c6989586621679453498 -> *) (Either_Sym2 a6989586621679453497 b6989586621679453499 c6989586621679453498) #
Methods suppressUnusedWarnings :: Proxy (Either_Sym2 a6989586621679453497 b6989586621679453499 c6989586621679453498) t -> () #
type Apply (Either a b) c (Either_Sym2 a b c l1 l2) l3 #
type Apply (Either a b) c (Either_Sym2 a b c l1 l2) l3 = Either_ a b c l1 l2 l3

type Either_Sym3 (t :: TyFun a6989586621679453497 c6989586621679453498 -> Type) (t :: TyFun b6989586621679453499 c6989586621679453498 -> Type) (t :: Either a6989586621679453497 b6989586621679453499) = Either_ t t t #

data LeftsSym0 (l :: TyFun [Either a6989586621679454609 b6989586621679454610] [a6989586621679454609]) #

Instances

SuppressUnusedWarnings (TyFun [Either a6989586621679454609 b6989586621679454610] [a6989586621679454609] -> *) (LeftsSym0 b6989586621679454610 a6989586621679454609) #
Methods suppressUnusedWarnings :: Proxy (LeftsSym0 b6989586621679454610 a6989586621679454609) t -> () #
type Apply [Either a b] [a] (LeftsSym0 b a) l #
type Apply [Either a b] [a] (LeftsSym0 b a) l = Lefts b a l

type LeftsSym1 (t :: [Either a6989586621679454609 b6989586621679454610]) = Lefts t #

data RightsSym0 (l :: TyFun [Either a6989586621679454607 b6989586621679454608] [b6989586621679454608]) #

Instances

SuppressUnusedWarnings (TyFun [Either a6989586621679454607 b6989586621679454608] [b6989586621679454608] -> *) (RightsSym0 a6989586621679454607 b6989586621679454608) #
Methods suppressUnusedWarnings :: Proxy (RightsSym0 a6989586621679454607 b6989586621679454608) t -> () #
type Apply [Either a b] [b] (RightsSym0 a b) l #
type Apply [Either a b] [b] (RightsSym0 a b) l = Rights a b l

type RightsSym1 (t :: [Either a6989586621679454607 b6989586621679454608]) = Rights t #

data IsLeftSym0 (l :: TyFun (Either a6989586621679454603 b6989586621679454604) Bool) #

Instances

SuppressUnusedWarnings (TyFun (Either a6989586621679454603 b6989586621679454604) Bool -> *) (IsLeftSym0 a6989586621679454603 b6989586621679454604) #
Methods suppressUnusedWarnings :: Proxy (IsLeftSym0 a6989586621679454603 b6989586621679454604) t -> () #
type Apply (Either a b) Bool (IsLeftSym0 a b) l #
type Apply (Either a b) Bool (IsLeftSym0 a b) l = IsLeft a b l

type IsLeftSym1 (t :: Either a6989586621679454603 b6989586621679454604) = IsLeft t #

data IsRightSym0 (l :: TyFun (Either a6989586621679454601 b6989586621679454602) Bool) #

Instances

SuppressUnusedWarnings (TyFun (Either a6989586621679454601 b6989586621679454602) Bool -> *) (IsRightSym0 a6989586621679454601 b6989586621679454602) #
Methods suppressUnusedWarnings :: Proxy (IsRightSym0 a6989586621679454601 b6989586621679454602) t -> () #
type Apply (Either a b) Bool (IsRightSym0 a b) l #
type Apply (Either a b) Bool (IsRightSym0 a b) l = IsRight a b l

type IsRightSym1 (t :: Either a6989586621679454601 b6989586621679454602) = IsRight t #

The Either singleton

Singletons from Data.Either

Defunctionalization symbols

The `Either` singleton

Singletons from `Data.Either`