singletons-2.4.1: A framework for generating singleton types

Copyright(C) 2013-2014 Richard Eisenberg Jan Stolarek
LicenseBSD-style (see LICENSE)
MaintainerRichard Eisenberg (rae@cs.brynmawr.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
SDecide k => TestCoercion (Sing :: k -> *) # 
Instance details

Defined in Data.Singletons.Decide

Methods

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

SDecide k => TestEquality (Sing :: k -> *) # 
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.TypeRepStar

Methods

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

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

Ord (Sing a) # 
Instance details

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) # 
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.TypeRepStar

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, 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 (z :: Bool) # 
Instance details

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: Bool) where
data Sing (z :: Ordering) # 
Instance details

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: Ordering) where
data Sing (a :: Type) # 
Instance details

Defined in Data.Singletons.TypeRepStar

data Sing (a :: Type) = STypeRep (TypeRep a)
data Sing (n :: Nat) # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

data Sing (n :: Nat) where
data Sing (n :: Symbol) # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

data Sing (n :: Symbol) where
data Sing (z :: ()) # 
Instance details

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: ()) where
data Sing (z :: Void) # 
Instance details

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: Void)
data Sing (z :: [a]) # 
Instance details

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: [a]) where
data Sing (z :: Maybe a) # 
Instance details

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: Maybe a) where
data Sing (z :: NonEmpty a) # 
Instance details

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: NonEmpty a) where
data Sing (z :: Either a b) # 
Instance details

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: Either a b) where
data Sing (z :: (a, b)) # 
Instance details

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: (a, b)) where
data Sing (f :: k1 ~> k2) # 
Instance details

Defined in Data.Singletons.Internal

data Sing (f :: k1 ~> k2) = SLambda {}
data Sing (z :: (a, b, c)) # 
Instance details

Defined in Data.Singletons.Prelude.Instances

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

Defined in Data.Singletons.Prelude.Instances

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

Defined in Data.Singletons.Prelude.Instances

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

Defined in Data.Singletons.Prelude.Instances

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

Defined in Data.Singletons.Prelude.Instances

data Sing (z :: (a, b, c, d, e, f, g)) 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_ :: (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_6989586621679942164 = Apply (Apply (Apply FoldrSym0 (Apply (Apply Either_Sym0 (Let6989586621679942171LeftSym1 a_6989586621679942164)) (Let6989586621679942171RightSym1 a_6989586621679942164))) (Apply (Apply Tuple2Sym0 '[]) '[])) a_6989586621679942164 

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 a6989586621679083190 (Either a6989586621679083190 b6989586621679083191)) #

Instances
SuppressUnusedWarnings (LeftSym0 :: TyFun a6989586621679083190 (Either a6989586621679083190 b6989586621679083191) -> *) # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Apply (LeftSym0 :: TyFun a (Either a b6989586621679083191) -> *) (l :: a) # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Apply (LeftSym0 :: TyFun a (Either a b6989586621679083191) -> *) (l :: a) = (Left l :: Either a b6989586621679083191)

type LeftSym1 (t :: a6989586621679083190) = Left t #

data RightSym0 (l :: TyFun b6989586621679083191 (Either a6989586621679083190 b6989586621679083191)) #

Instances
SuppressUnusedWarnings (RightSym0 :: TyFun b6989586621679083191 (Either a6989586621679083190 b6989586621679083191) -> *) # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Apply (RightSym0 :: TyFun b (Either a6989586621679083190 b) -> *) (l :: b) # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Apply (RightSym0 :: TyFun b (Either a6989586621679083190 b) -> *) (l :: b) = (Right l :: Either a6989586621679083190 b)

type RightSym1 (t :: b6989586621679083191) = Right t #

data Either_Sym0 (l :: TyFun (TyFun a6989586621679940661 c6989586621679940662 -> Type) (TyFun (TyFun b6989586621679940663 c6989586621679940662 -> Type) (TyFun (Either a6989586621679940661 b6989586621679940663) c6989586621679940662 -> Type) -> Type)) #

Instances
SuppressUnusedWarnings (Either_Sym0 :: TyFun (TyFun a6989586621679940661 c6989586621679940662 -> Type) (TyFun (TyFun b6989586621679940663 c6989586621679940662 -> Type) (TyFun (Either a6989586621679940661 b6989586621679940663) c6989586621679940662 -> Type) -> Type) -> *) # 
Instance details

Defined in Data.Singletons.Prelude.Either

type Apply (Either_Sym0 :: TyFun (TyFun a6989586621679940661 c6989586621679940662 -> Type) (TyFun (TyFun b6989586621679940663 c6989586621679940662 -> Type) (TyFun (Either a6989586621679940661 b6989586621679940663) c6989586621679940662 -> Type) -> Type) -> *) (l :: TyFun a6989586621679940661 c6989586621679940662 -> Type) # 
Instance details

Defined in Data.Singletons.Prelude.Either

type Apply (Either_Sym0 :: TyFun (TyFun a6989586621679940661 c6989586621679940662 -> Type) (TyFun (TyFun b6989586621679940663 c6989586621679940662 -> Type) (TyFun (Either a6989586621679940661 b6989586621679940663) c6989586621679940662 -> Type) -> Type) -> *) (l :: TyFun a6989586621679940661 c6989586621679940662 -> Type) = (Either_Sym1 l :: TyFun (TyFun b6989586621679940663 c6989586621679940662 -> Type) (TyFun (Either a6989586621679940661 b6989586621679940663) c6989586621679940662 -> Type) -> *)

data Either_Sym1 (l :: TyFun a6989586621679940661 c6989586621679940662 -> Type) (l :: TyFun (TyFun b6989586621679940663 c6989586621679940662 -> Type) (TyFun (Either a6989586621679940661 b6989586621679940663) c6989586621679940662 -> Type)) #

Instances
SuppressUnusedWarnings (Either_Sym1 :: (TyFun a6989586621679940661 c6989586621679940662 -> Type) -> TyFun (TyFun b6989586621679940663 c6989586621679940662 -> Type) (TyFun (Either a6989586621679940661 b6989586621679940663) c6989586621679940662 -> Type) -> *) # 
Instance details

Defined in Data.Singletons.Prelude.Either

type Apply (Either_Sym1 l1 :: TyFun (TyFun b6989586621679940663 c6989586621679940662 -> Type) (TyFun (Either a6989586621679940661 b6989586621679940663) c6989586621679940662 -> Type) -> *) (l2 :: TyFun b6989586621679940663 c6989586621679940662 -> Type) # 
Instance details

Defined in Data.Singletons.Prelude.Either

type Apply (Either_Sym1 l1 :: TyFun (TyFun b6989586621679940663 c6989586621679940662 -> Type) (TyFun (Either a6989586621679940661 b6989586621679940663) c6989586621679940662 -> Type) -> *) (l2 :: TyFun b6989586621679940663 c6989586621679940662 -> Type) = Either_Sym2 l1 l2

data Either_Sym2 (l :: TyFun a6989586621679940661 c6989586621679940662 -> Type) (l :: TyFun b6989586621679940663 c6989586621679940662 -> Type) (l :: TyFun (Either a6989586621679940661 b6989586621679940663) c6989586621679940662) #

Instances
SuppressUnusedWarnings (Either_Sym2 :: (TyFun a6989586621679940661 c6989586621679940662 -> Type) -> (TyFun b6989586621679940663 c6989586621679940662 -> Type) -> TyFun (Either a6989586621679940661 b6989586621679940663) c6989586621679940662 -> *) # 
Instance details

Defined in Data.Singletons.Prelude.Either

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

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 a6989586621679940661 c6989586621679940662 -> Type) (t :: TyFun b6989586621679940663 c6989586621679940662 -> Type) (t :: Either a6989586621679940661 b6989586621679940663) = Either_ t t t #

data LeftsSym0 (l :: TyFun [Either a6989586621679941797 b6989586621679941798] [a6989586621679941797]) #

Instances
SuppressUnusedWarnings (LeftsSym0 :: TyFun [Either a6989586621679941797 b6989586621679941798] [a6989586621679941797] -> *) # 
Instance details

Defined in Data.Singletons.Prelude.Either

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

Defined in Data.Singletons.Prelude.Either

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

type LeftsSym1 (t :: [Either a6989586621679941797 b6989586621679941798]) = Lefts t #

data RightsSym0 (l :: TyFun [Either a6989586621679941795 b6989586621679941796] [b6989586621679941796]) #

Instances
SuppressUnusedWarnings (RightsSym0 :: TyFun [Either a6989586621679941795 b6989586621679941796] [b6989586621679941796] -> *) # 
Instance details

Defined in Data.Singletons.Prelude.Either

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

Defined in Data.Singletons.Prelude.Either

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

type RightsSym1 (t :: [Either a6989586621679941795 b6989586621679941796]) = Rights t #

data IsLeftSym0 (l :: TyFun (Either a6989586621679941791 b6989586621679941792) Bool) #

Instances
SuppressUnusedWarnings (IsLeftSym0 :: TyFun (Either a6989586621679941791 b6989586621679941792) Bool -> *) # 
Instance details

Defined in Data.Singletons.Prelude.Either

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

Defined in Data.Singletons.Prelude.Either

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

type IsLeftSym1 (t :: Either a6989586621679941791 b6989586621679941792) = IsLeft t #

data IsRightSym0 (l :: TyFun (Either a6989586621679941789 b6989586621679941790) Bool) #

Instances
SuppressUnusedWarnings (IsRightSym0 :: TyFun (Either a6989586621679941789 b6989586621679941790) Bool -> *) # 
Instance details

Defined in Data.Singletons.Prelude.Either

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

Defined in Data.Singletons.Prelude.Either

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

type IsRightSym1 (t :: Either a6989586621679941789 b6989586621679941790) = IsRight t #