singletons-0.9.3: A framework for generating singleton types

Copyright(C) 2013 Richard Eisenberg
License(C) 2013 Richard Eisenberg
MaintainerRichard Eisenberg (
Safe HaskellNone




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.


The Either singleton

data family Sing a Source

The singleton kind-indexed data family.

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 zSource

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 :: cSource

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

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

type family Rights a :: [b]Source

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

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

type family IsLeft a :: BoolSource

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

type family IsRight a :: BoolSource

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