Copyright	(C) 2013 Richard Eisenberg
License	BSD-style (see LICENSE)
Maintainer	Richard Eisenberg (eir@cis.upenn.edu)
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Singletons.Either

Contents

The Either singleton
Singletons from Data.Either

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 Source

The singleton kind-indexed data family.

Instances

TestCoercion * (Sing *)
SDecide k (KProxy k) => TestEquality k (Sing k)
data Sing Bool where SFalse :: (~) Bool z False => Sing Bool z STrue :: (~) Bool z True => Sing Bool z
data Sing Ordering where SLT :: (~) Ordering z LT => Sing Ordering z SEQ :: (~) Ordering z EQ => Sing Ordering z SGT :: (~) Ordering z GT => Sing Ordering z
data Sing * where STypeRep :: Typeable * a => Sing * a
data Sing Nat where SNat :: KnownNat n => Sing Nat n
data Sing Symbol where SSym :: KnownSymbol n => Sing Symbol n
data Sing () where STuple0 :: (~) () z () => Sing () z
data Sing [a0] where SNil :: (~) [a] z ([] a) => Sing [a] z SCons :: (~) [a] z ((:) a n n) => Sing a n -> Sing [a] n -> Sing [a] z
data Sing (Maybe a0) where SNothing :: (~) (Maybe a) z (Nothing a) => Sing (Maybe a) z SJust :: (~) (Maybe a) z (Just a n) => Sing a n -> Sing (Maybe a) z
data Sing (Either a0 b0) where SLeft :: (~) (Either a b) z (Left a b n) => Sing a n -> Sing (Either a b) z SRight :: (~) (Either a b) z (Right a b n) => Sing b n -> Sing (Either a b) z
data Sing ((,) a0 b0) where STuple2 :: (~) ((,) a b) z ((,) a b n n) => Sing a n -> Sing b n -> Sing ((,) a b) z
data Sing ((,,) a0 b0 c0) where STuple3 :: (~) ((,,) a b c) z ((,,) a b c n n n) => Sing a n -> Sing b n -> Sing c n -> Sing ((,,) a b c) z
data Sing ((,,,) a0 b0 c0 d0) where STuple4 :: (~) ((,,,) a b c d) z ((,,,) a b c d n n n n) => Sing a n -> Sing b n -> Sing c n -> Sing d n -> Sing ((,,,) a b c d) z
data Sing ((,,,,) a0 b0 c0 d0 e0) where STuple5 :: (~) ((,,,,) a b c d e) z ((,,,,) a b c d e n n n n n) => Sing a n -> Sing b n -> Sing c n -> Sing d n -> Sing e n -> Sing ((,,,,) a b c d e) z
data Sing ((,,,,,) a0 b0 c0 d0 e0 f0) where STuple6 :: (~) ((,,,,,) a b c d e f) z ((,,,,,) a b c d e f n n n n n n) => Sing a n -> Sing b n -> Sing c n -> Sing d n -> Sing e n -> Sing f n -> Sing ((,,,,,) a b c d e f) z
data Sing ((,,,,,,) a0 b0 c0 d0 e0 f0 g0) where STuple7 :: (~) ((,,,,,,) a b c d e f g) z ((,,,,,,) a b c d e f g n n n n n n n) => Sing a n -> Sing b n -> Sing c n -> Sing d n -> Sing e n -> Sing f n -> Sing g n -> 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 z = Sing z Source

SEither is a kind-restricted synonym for Sing: type SEither (a :: Either x y) = Sing a

Singletons from `Data.Either`

type family Either_ a a a :: c Source

Equations

Either_ f z (Left x) = f x
Either_ z g (Right y) = g y

sEither_ :: forall t t t. (forall t. Sing t -> Sing (t t)) -> (forall t. Sing t -> Sing (t t)) -> Sing t -> Sing (Either_ t t t) Source

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 :: [a] Source

Equations

Lefts [] = `[]`
Lefts ((:) (Left x) xs) = (:) x (Lefts xs)
Lefts ((:) (Right z) xs) = Lefts xs

sLefts :: forall t. Sing t -> Sing (Lefts t) Source

type family Rights a :: [b] Source

Equations

Rights [] = `[]`
Rights ((:) (Left z) xs) = Rights xs
Rights ((:) (Right x) xs) = (:) x (Rights xs)

sRights :: forall t. Sing t -> Sing (Rights t) Source

type family PartitionEithers a :: ([a], [b]) Source

Equations

PartitionEithers es = PartitionEithers_aux `(`[]`, `[]`)` es

sPartitionEithers :: forall t. Sing t -> Sing (PartitionEithers t) Source

type family IsLeft a :: Bool Source

Equations

IsLeft (Left z) = True
IsLeft (Right z) = False

sIsLeft :: forall t. Sing t -> Sing (IsLeft t) Source

type family IsRight a :: Bool Source

Equations

IsRight (Left z) = False
IsRight (Right z) = True

sIsRight :: forall t. Sing t -> Sing (IsRight t) Source

The Either singleton

Singletons from Data.Either

The `Either` singleton

Singletons from `Data.Either`