singletons-2.2: A framework for generating singleton types

Copyright(C) 2013-2014 Richard Eisenberg Jan Stolarek
LicenseBSD-style (see LICENSE)
MaintainerRichard Eisenberg (eir@cis.upenn.edu)
Stabilityexperimental
Portabilitynon-portable
Safe HaskellNone
LanguageHaskell2010

Data.Singletons.Prelude.Either

Contents

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
data Sing Ordering # 
data Sing * # 
data Sing * where
data Sing Nat # 
data Sing Nat where
data Sing Symbol # 
data Sing Symbol where
data Sing () # 
data Sing () where
data Sing [a0] # 
data Sing [a0] where
data Sing (Maybe a0) # 
data Sing (Maybe a0) where
data Sing (NonEmpty a0) # 
data Sing (NonEmpty a0) where
data Sing (Either a0 b0) # 
data Sing (Either a0 b0) where
data Sing (a0, b0) # 
data Sing (a0, b0) where
data Sing ((~>) k1 k2) # 
data Sing ((~>) k1 k2) = SLambda {}
data Sing (a0, b0, c0) # 
data Sing (a0, b0, c0) where
data Sing (a0, b0, c0, d0) # 
data Sing (a0, b0, c0, d0) where
data Sing (a0, b0, c0, d0, e0) # 
data Sing (a0, b0, c0, d0, e0) where
data Sing (a0, b0, c0, d0, e0, f0) # 
data Sing (a0, b0, c0, d0, e0, f0) where
data Sing (a0, b0, c0, d0, e0, f0, g0) # 
data Sing (a0, b0, c0, d0, e0, f0, g0) where

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_6989586621679958206 (Left x) = Apply f x 
Either_ _z_6989586621679958210 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_6989586621679959551) 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_6989586621679959539) 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_6989586621679959493 = Apply (Apply (Apply FoldrSym0 (Apply (Apply Either_Sym0 (Let6989586621679959500LeftSym1 a_6989586621679959493)) (Let6989586621679959500RightSym1 a_6989586621679959493))) (Apply (Apply Tuple2Sym0 '[]) '[])) a_6989586621679959493 

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

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

Equations

IsLeft (Left _z_6989586621679959487) = TrueSym0 
IsLeft (Right _z_6989586621679959490) = FalseSym0 

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

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

Equations

IsRight (Left _z_6989586621679959477) = FalseSym0 
IsRight (Right _z_6989586621679959480) = 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 a6989586621679958182 c6989586621679958183 -> Type) (TyFun (TyFun b6989586621679958184 c6989586621679958183 -> Type) (TyFun (Either a6989586621679958182 b6989586621679958184) c6989586621679958183 -> Type) -> Type) -> *) (Either_Sym0 a6989586621679958182 b6989586621679958184 c6989586621679958183) # 

Methods

suppressUnusedWarnings :: Proxy (Either_Sym0 a6989586621679958182 b6989586621679958184 c6989586621679958183) t -> () #

type Apply (TyFun a6989586621679958182 c6989586621679958183 -> Type) (TyFun (TyFun b6989586621679958184 c6989586621679958183 -> Type) (TyFun (Either a6989586621679958182 b6989586621679958184) c6989586621679958183 -> Type) -> Type) (Either_Sym0 a6989586621679958182 b6989586621679958184 c6989586621679958183) l0 # 
type Apply (TyFun a6989586621679958182 c6989586621679958183 -> Type) (TyFun (TyFun b6989586621679958184 c6989586621679958183 -> Type) (TyFun (Either a6989586621679958182 b6989586621679958184) c6989586621679958183 -> Type) -> Type) (Either_Sym0 a6989586621679958182 b6989586621679958184 c6989586621679958183) l0 = Either_Sym1 b6989586621679958184 a6989586621679958182 c6989586621679958183 l0

data Either_Sym1 l l #

Instances

SuppressUnusedWarnings ((TyFun a6989586621679958182 c6989586621679958183 -> Type) -> TyFun (TyFun b6989586621679958184 c6989586621679958183 -> Type) (TyFun (Either a6989586621679958182 b6989586621679958184) c6989586621679958183 -> Type) -> *) (Either_Sym1 b6989586621679958184 a6989586621679958182 c6989586621679958183) # 

Methods

suppressUnusedWarnings :: Proxy (Either_Sym1 b6989586621679958184 a6989586621679958182 c6989586621679958183) t -> () #

type Apply (TyFun b6989586621679958184 c6989586621679958183 -> Type) (TyFun (Either a6989586621679958182 b6989586621679958184) c6989586621679958183 -> Type) (Either_Sym1 b6989586621679958184 a6989586621679958182 c6989586621679958183 l0) l1 # 
type Apply (TyFun b6989586621679958184 c6989586621679958183 -> Type) (TyFun (Either a6989586621679958182 b6989586621679958184) c6989586621679958183 -> Type) (Either_Sym1 b6989586621679958184 a6989586621679958182 c6989586621679958183 l0) l1 = Either_Sym2 b6989586621679958184 a6989586621679958182 c6989586621679958183 l0 l1

data Either_Sym2 l l l #

Instances

SuppressUnusedWarnings ((TyFun a6989586621679958182 c6989586621679958183 -> Type) -> (TyFun b6989586621679958184 c6989586621679958183 -> Type) -> TyFun (Either a6989586621679958182 b6989586621679958184) c6989586621679958183 -> *) (Either_Sym2 b6989586621679958184 a6989586621679958182 c6989586621679958183) # 

Methods

suppressUnusedWarnings :: Proxy (Either_Sym2 b6989586621679958184 a6989586621679958182 c6989586621679958183) t -> () #

type Apply (Either a6989586621679958182 b6989586621679958184) c6989586621679958183 (Either_Sym2 b6989586621679958184 a6989586621679958182 c6989586621679958183 l1 l0) l2 # 
type Apply (Either a6989586621679958182 b6989586621679958184) c6989586621679958183 (Either_Sym2 b6989586621679958184 a6989586621679958182 c6989586621679958183 l1 l0) l2 = Either_Sym3 b6989586621679958184 a6989586621679958182 c6989586621679958183 l1 l0 l2

type Either_Sym3 t t t = Either_ t t t #

data LeftsSym0 l #

Instances

SuppressUnusedWarnings (TyFun [Either a6989586621679959452 b6989586621679959453] [a6989586621679959452] -> *) (LeftsSym0 b6989586621679959453 a6989586621679959452) # 

Methods

suppressUnusedWarnings :: Proxy (LeftsSym0 b6989586621679959453 a6989586621679959452) t -> () #

type Apply [Either a6989586621679959452 b6989586621679959453] [a6989586621679959452] (LeftsSym0 b6989586621679959453 a6989586621679959452) l0 # 
type Apply [Either a6989586621679959452 b6989586621679959453] [a6989586621679959452] (LeftsSym0 b6989586621679959453 a6989586621679959452) l0 = LeftsSym1 a6989586621679959452 b6989586621679959453 l0

type LeftsSym1 t = Lefts t #

data RightsSym0 l #

Instances

SuppressUnusedWarnings (TyFun [Either a6989586621679959450 b6989586621679959451] [b6989586621679959451] -> *) (RightsSym0 a6989586621679959450 b6989586621679959451) # 

Methods

suppressUnusedWarnings :: Proxy (RightsSym0 a6989586621679959450 b6989586621679959451) t -> () #

type Apply [Either a6989586621679959450 b6989586621679959451] [b6989586621679959451] (RightsSym0 a6989586621679959450 b6989586621679959451) l0 # 
type Apply [Either a6989586621679959450 b6989586621679959451] [b6989586621679959451] (RightsSym0 a6989586621679959450 b6989586621679959451) l0 = RightsSym1 a6989586621679959450 b6989586621679959451 l0

type RightsSym1 t = Rights t #

data IsLeftSym0 l #

Instances

SuppressUnusedWarnings (TyFun (Either a6989586621679959446 b6989586621679959447) Bool -> *) (IsLeftSym0 a6989586621679959446 b6989586621679959447) # 

Methods

suppressUnusedWarnings :: Proxy (IsLeftSym0 a6989586621679959446 b6989586621679959447) t -> () #

type Apply (Either a6989586621679959446 b6989586621679959447) Bool (IsLeftSym0 a6989586621679959446 b6989586621679959447) l0 # 
type Apply (Either a6989586621679959446 b6989586621679959447) Bool (IsLeftSym0 a6989586621679959446 b6989586621679959447) l0 = IsLeftSym1 a6989586621679959446 b6989586621679959447 l0

type IsLeftSym1 t = IsLeft t #

data IsRightSym0 l #

Instances

SuppressUnusedWarnings (TyFun (Either a6989586621679959444 b6989586621679959445) Bool -> *) (IsRightSym0 a6989586621679959444 b6989586621679959445) # 

Methods

suppressUnusedWarnings :: Proxy (IsRightSym0 a6989586621679959444 b6989586621679959445) t -> () #

type Apply (Either a6989586621679959444 b6989586621679959445) Bool (IsRightSym0 a6989586621679959444 b6989586621679959445) l0 # 
type Apply (Either a6989586621679959444 b6989586621679959445) Bool (IsRightSym0 a6989586621679959444 b6989586621679959445) l0 = IsRightSym1 a6989586621679959444 b6989586621679959445 l0

type IsRightSym1 t = IsRight t #