singletons-1.0: 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 Source

The singleton kind-indexed data family.

Instances

TestCoercion * (Sing *) 
SDecide k (KProxy k) => TestEquality k (Sing k) 
data Sing Bool where 
data Sing Ordering where 
data Sing * where 
data Sing Nat where 
data Sing Symbol where 
data Sing () where 
data Sing [a0] where 
data Sing (Maybe a0) where 
data Sing (TyFun k1 k2 -> *) = SLambda {} 
data Sing (Either a0 b0) where 
data Sing ((,) a0 b0) where 
data Sing ((,,) a0 b0 c0) where 
data Sing ((,,,) a0 b0 c0 d0) where 
data Sing ((,,,,) a0 b0 c0 d0 e0) where 
data Sing ((,,,,,) a0 b0 c0 d0 e0 f0) where 
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 z = Sing z Source

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 Source

type family Either_ a a a :: c Source

Equations

Either_ f z (Left x) = Apply f x 
Either_ z 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) 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) = Apply (Apply (:$) x) (Apply LeftsSym0 xs) 
Lefts ((:) (Right z) xs) = Apply LeftsSym0 xs 

sLefts :: forall t. Sing t -> Sing (Apply LeftsSym0 t) Source

type family Rights a :: [] b Source

Equations

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

sRights :: forall t. Sing t -> Sing (Apply RightsSym0 t) Source

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

Equations

PartitionEithers a_1627864927 = Apply (Apply (Apply FoldrSym0 (Apply (Apply Either_Sym0 (Let_1627864934LeftSym1 a_1627864927)) (Let_1627864934RightSym1 a_1627864927))) (Apply (Apply Tuple2Sym0 []) [])) a_1627864927 

sPartitionEithers :: forall t. Sing t -> Sing (Apply PartitionEithersSym0 t) Source

type family IsLeft a :: Bool Source

Equations

IsLeft (Left z) = TrueSym0 
IsLeft (Right z) = FalseSym0 

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

type family IsRight a :: Bool Source

Equations

IsRight (Left z) = FalseSym0 
IsRight (Right z) = TrueSym0 

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

Defunctionalization symbols

data LeftSym0 l Source

Instances

SuppressUnusedWarnings (TyFun k (Either k k) -> *) (LeftSym0 k k) 
type Apply (Either k k1) k (LeftSym0 k1 k) l0 = LeftSym1 k k1 l0 

type LeftSym1 t = Left t Source

data RightSym0 l Source

Instances

SuppressUnusedWarnings (TyFun k (Either k k) -> *) (RightSym0 k k) 
type Apply (Either k k1) k1 (RightSym0 k k1) l0 = RightSym1 k k1 l0 

type RightSym1 t = Right t Source

data Either_Sym0 l Source

Instances

SuppressUnusedWarnings (TyFun (TyFun k k -> *) (TyFun (TyFun k k -> *) (TyFun (Either k k) k -> *) -> *) -> *) (Either_Sym0 k k k) 
type Apply (TyFun (TyFun k2 k -> *) (TyFun (Either k1 k2) k -> *) -> *) (TyFun k1 k -> *) (Either_Sym0 k2 k k1) l0 = Either_Sym1 k k1 k2 l0 

data Either_Sym1 l l Source

Instances

SuppressUnusedWarnings ((TyFun k k -> *) -> TyFun (TyFun k k -> *) (TyFun (Either k k) k -> *) -> *) (Either_Sym1 k k k) 
type Apply (TyFun (Either k2 k) k1 -> *) (TyFun k k1 -> *) (Either_Sym1 k1 k2 k l1) l0 = Either_Sym2 k1 k2 k l1 l0 

data Either_Sym2 l l l Source

Instances

SuppressUnusedWarnings ((TyFun k k -> *) -> (TyFun k k -> *) -> TyFun (Either k k) k -> *) (Either_Sym2 k k k) 
type Apply k (Either k1 k2) (Either_Sym2 k k1 k2 l1 l2) l0 = Either_Sym3 k k1 k2 l1 l2 l0 

type Either_Sym3 t t t = Either_ t t t Source

data LeftsSym0 l Source

Instances

SuppressUnusedWarnings (TyFun [Either k k] [k] -> *) (LeftsSym0 k k) 
type Apply [k] [Either k k1] (LeftsSym0 k k1) l0 = LeftsSym1 k k1 l0 

type LeftsSym1 t = Lefts t Source

data RightsSym0 l Source

Instances

SuppressUnusedWarnings (TyFun [Either k k] [k] -> *) (RightsSym0 k k) 
type Apply [k] [Either k1 k] (RightsSym0 k1 k) l0 = RightsSym1 k1 k l0 

type RightsSym1 t = Rights t Source

data IsLeftSym0 l Source

Instances

SuppressUnusedWarnings (TyFun (Either k k) Bool -> *) (IsLeftSym0 k k) 
type Apply Bool (Either k k1) (IsLeftSym0 k k1) l0 = IsLeftSym1 k k1 l0 

type IsLeftSym1 t = IsLeft t Source

data IsRightSym0 l Source

Instances

SuppressUnusedWarnings (TyFun (Either k k) Bool -> *) (IsRightSym0 k k) 
type Apply Bool (Either k k1) (IsRightSym0 k k1) l0 = IsRightSym1 k k1 l0 

type IsRightSym1 t = IsRight t Source