Data.Singletons.Prelude.Maybe

Defines functions and datatypes relating to the singleton for Maybe, including a singletons version of all the definitions in Data.Maybe.

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.Maybe. Also, please excuse the apparent repeated variable names. This is due to an interaction between Template Haskell and Haddock.

Documentation

data family Sing (a :: k)

The singleton kind-indexed data family.

Instances

data Sing (z :: Bool)

data Sing (z :: Bool) where

• SFalse :: Sing False
• STrue :: Sing True

data Sing (z :: Ordering)

data Sing (z :: Ordering) where

• SLT :: Sing LT
• SEQ :: Sing EQ
• SGT :: Sing GT

data Sing (a :: Type)

data Sing (a :: Type) = STypeRep (TypeRep a)

data Sing (n :: Nat)

data Sing (n :: Nat) where

• SNat :: Sing n

data Sing (n :: Symbol)

data Sing (n :: Symbol) where

• SSym :: Sing n

data Sing (z :: ())

data Sing (z :: ()) where

• STuple0 :: Sing ()

data Sing (z :: Void)

data Sing (z :: Void)

data Sing (z :: [a])

data Sing (z :: [a]) where

• SNil :: Sing ([] :: [k])
• SCons :: Sing (n ': n)

data Sing (z :: Maybe a)

data Sing (z :: Maybe a) where

• SNothing :: Sing (Nothing :: Maybe a)
• SJust :: Sing (Just n)

data Sing (z :: NonEmpty a)

data Sing (z :: NonEmpty a) where

• (:%|) :: Sing (n :| n)

data Sing (z :: Either a b)

data Sing (z :: Either a b) where

• SLeft :: Sing (Left n :: Either a b)
• SRight :: Sing (Right n :: Either a b)

data Sing (z :: (a, b))

data Sing (z :: (a, b)) where

• STuple2 :: Sing ((,) n n)

data Sing (f :: k1 ~> k2)

data Sing (f :: k1 ~> k2) = SLambda {

• applySing :: forall (t :: k1). Sing t -> Sing (f @@ t)

}

data Sing (z :: (a, b, c))

data Sing (z :: (a, b, c)) where

• STuple3 :: Sing ((,,) n n n)

data Sing (z :: (a, b, c, d))

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

• STuple4 :: Sing ((,,,) n n n n)

data Sing (z :: (a, b, c, d, e))

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

• STuple5 :: Sing ((,,,,) n n n n n)

data Sing (z :: (a, b, c, d, e, f))

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

• STuple6 :: Sing ((,,,,,) n n n n n n)

data Sing (z :: (a, b, c, d, e, f, g))

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

• STuple7 :: Sing ((,,,,,,) n n n n n n n)

Though Haddock doesn't show it, the Sing instance above declares constructors

SNothing :: Sing Nothing
SJust    :: Sing a -> Sing (Just a)

type SMaybe = (Sing :: Maybe a -> Type)

SBool is a kind-restricted synonym for Sing: type SMaybe (a :: Maybe k) = Sing a

Singletons from Data.Maybe

maybe_ :: b -> (a -> b) -> Maybe a -> b

type family Maybe_ (a :: b) (a :: TyFun a b -> Type) (a :: Maybe a) :: b where ...

Equations

Maybe_ n _ Nothing = n

Maybe_ _ f (Just x) = Apply f x

sMaybe_ :: forall (t :: b) (t :: TyFun a b -> Type) (t :: Maybe a). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply Maybe_Sym0 t) t) t :: b)

The preceding two definitions are derived from the function maybe in Data.Maybe. The extra underscore is to avoid name clashes with the type Maybe.

type family IsJust (a :: Maybe a) :: Bool where ...

Equations

IsJust Nothing = FalseSym0

IsJust (Just _) = TrueSym0

sIsJust :: forall (t :: Maybe a). Sing t -> Sing (Apply IsJustSym0 t :: Bool)

type family IsNothing (a :: Maybe a) :: Bool where ...

Equations

IsNothing Nothing = TrueSym0

IsNothing (Just _) = FalseSym0

sIsNothing :: forall (t :: Maybe a). Sing t -> Sing (Apply IsNothingSym0 t :: Bool)

type family FromJust (a :: Maybe a) :: a where ...

Equations

FromJust Nothing = Apply ErrorSym0 "Maybe.fromJust: Nothing"

FromJust (Just x) = x

sFromJust :: forall (t :: Maybe a). Sing t -> Sing (Apply FromJustSym0 t :: a)

type family FromMaybe (a :: a) (a :: Maybe a) :: a where ...

Equations

FromMaybe d x = Case_6989586621679404659 d x x

sFromMaybe :: forall (t :: a) (t :: Maybe a). Sing t -> Sing t -> Sing (Apply (Apply FromMaybeSym0 t) t :: a)

type family ListToMaybe (a :: [a]) :: Maybe a where ...

Equations

ListToMaybe '[] = NothingSym0

ListToMaybe ((:) a _) = Apply JustSym0 a

sListToMaybe :: forall (t :: [a]). Sing t -> Sing (Apply ListToMaybeSym0 t :: Maybe a)

type family MaybeToList (a :: Maybe a) :: [a] where ...

Equations

MaybeToList Nothing = '[]

MaybeToList (Just x) = Apply (Apply (:@#@$) x) '[]

sMaybeToList :: forall (t :: Maybe a). Sing t -> Sing (Apply MaybeToListSym0 t :: [a])

type family CatMaybes (a :: [Maybe a]) :: [a] where ...

Equations

CatMaybes '[] = '[]

CatMaybes ((:) (Just x) xs) = Apply (Apply (:@#@$) x) (Apply CatMaybesSym0 xs)

CatMaybes ((:) Nothing xs) = Apply CatMaybesSym0 xs

sCatMaybes :: forall (t :: [Maybe a]). Sing t -> Sing (Apply CatMaybesSym0 t :: [a])

type family MapMaybe (a :: TyFun a (Maybe b) -> Type) (a :: [a]) :: [b] where ...

Equations

MapMaybe _ '[] = '[]

MapMaybe f ((:) x xs) = Case_6989586621679404627 f x xs (Let6989586621679404614Scrutinee_6989586621679404457Sym3 f x xs)

sMapMaybe :: forall (t :: TyFun a (Maybe b) -> Type) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply MapMaybeSym0 t) t :: [b])

Defunctionalization symbols

type NothingSym0 = Nothing

data JustSym0 (l :: TyFun a3530822107858468865 (Maybe a3530822107858468865))

Instances

SuppressUnusedWarnings (JustSym0 :: TyFun a3530822107858468865 (Maybe a3530822107858468865) -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (JustSym0 :: TyFun a (Maybe a) -> *) (l :: a)

type Apply (JustSym0 :: TyFun a (Maybe a) -> *) (l :: a) = Just l

type JustSym1 (t :: a3530822107858468865) = Just t

data Maybe_Sym0 (l :: TyFun b6989586621679403309 (TyFun (TyFun a6989586621679403310 b6989586621679403309 -> Type) (TyFun (Maybe a6989586621679403310) b6989586621679403309 -> Type) -> Type))

Instances

SuppressUnusedWarnings (Maybe_Sym0 :: TyFun b6989586621679403309 (TyFun (TyFun a6989586621679403310 b6989586621679403309 -> Type) (TyFun (Maybe a6989586621679403310) b6989586621679403309 -> Type) -> Type) -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (Maybe_Sym0 :: TyFun b6989586621679403309 (TyFun (TyFun a6989586621679403310 b6989586621679403309 -> Type) (TyFun (Maybe a6989586621679403310) b6989586621679403309 -> Type) -> Type) -> *) (l :: b6989586621679403309)

type Apply (Maybe_Sym0 :: TyFun b6989586621679403309 (TyFun (TyFun a6989586621679403310 b6989586621679403309 -> Type) (TyFun (Maybe a6989586621679403310) b6989586621679403309 -> Type) -> Type) -> *) (l :: b6989586621679403309) = (Maybe_Sym1 l :: TyFun (TyFun a6989586621679403310 b6989586621679403309 -> Type) (TyFun (Maybe a6989586621679403310) b6989586621679403309 -> Type) -> *)

data Maybe_Sym1 (l :: b6989586621679403309) (l :: TyFun (TyFun a6989586621679403310 b6989586621679403309 -> Type) (TyFun (Maybe a6989586621679403310) b6989586621679403309 -> Type))

Instances

SuppressUnusedWarnings (Maybe_Sym1 :: b6989586621679403309 -> TyFun (TyFun a6989586621679403310 b6989586621679403309 -> Type) (TyFun (Maybe a6989586621679403310) b6989586621679403309 -> Type) -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (Maybe_Sym1 l1 :: TyFun (TyFun a6989586621679403310 b6989586621679403309 -> Type) (TyFun (Maybe a6989586621679403310) b6989586621679403309 -> Type) -> *) (l2 :: TyFun a6989586621679403310 b6989586621679403309 -> Type)

type Apply (Maybe_Sym1 l1 :: TyFun (TyFun a6989586621679403310 b6989586621679403309 -> Type) (TyFun (Maybe a6989586621679403310) b6989586621679403309 -> Type) -> *) (l2 :: TyFun a6989586621679403310 b6989586621679403309 -> Type) = Maybe_Sym2 l1 l2

data Maybe_Sym2 (l :: b6989586621679403309) (l :: TyFun a6989586621679403310 b6989586621679403309 -> Type) (l :: TyFun (Maybe a6989586621679403310) b6989586621679403309)

Instances

SuppressUnusedWarnings (Maybe_Sym2 :: b6989586621679403309 -> (TyFun a6989586621679403310 b6989586621679403309 -> Type) -> TyFun (Maybe a6989586621679403310) b6989586621679403309 -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (Maybe_Sym2 l1 l2 :: TyFun (Maybe a) b -> *) (l3 :: Maybe a)

type Apply (Maybe_Sym2 l1 l2 :: TyFun (Maybe a) b -> *) (l3 :: Maybe a) = Maybe_ l1 l2 l3

type Maybe_Sym3 (t :: b6989586621679403309) (t :: TyFun a6989586621679403310 b6989586621679403309 -> Type) (t :: Maybe a6989586621679403310) = Maybe_ t t t

data IsJustSym0 (l :: TyFun (Maybe a6989586621679404430) Bool)

Instances

SuppressUnusedWarnings (IsJustSym0 :: TyFun (Maybe a6989586621679404430) Bool -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (IsJustSym0 :: TyFun (Maybe a) Bool -> *) (l :: Maybe a)

type Apply (IsJustSym0 :: TyFun (Maybe a) Bool -> *) (l :: Maybe a) = IsJust l

type IsJustSym1 (t :: Maybe a6989586621679404430) = IsJust t

data IsNothingSym0 (l :: TyFun (Maybe a6989586621679404429) Bool)

Instances

SuppressUnusedWarnings (IsNothingSym0 :: TyFun (Maybe a6989586621679404429) Bool -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (IsNothingSym0 :: TyFun (Maybe a) Bool -> *) (l :: Maybe a)

type Apply (IsNothingSym0 :: TyFun (Maybe a) Bool -> *) (l :: Maybe a) = IsNothing l

type IsNothingSym1 (t :: Maybe a6989586621679404429) = IsNothing t

data FromJustSym0 (l :: TyFun (Maybe a6989586621679404428) a6989586621679404428)

Instances

SuppressUnusedWarnings (FromJustSym0 :: TyFun (Maybe a6989586621679404428) a6989586621679404428 -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (FromJustSym0 :: TyFun (Maybe a) a -> *) (l :: Maybe a)

type Apply (FromJustSym0 :: TyFun (Maybe a) a -> *) (l :: Maybe a) = FromJust l

type FromJustSym1 (t :: Maybe a6989586621679404428) = FromJust t

data FromMaybeSym0 (l :: TyFun a6989586621679404427 (TyFun (Maybe a6989586621679404427) a6989586621679404427 -> Type))

Instances

SuppressUnusedWarnings (FromMaybeSym0 :: TyFun a6989586621679404427 (TyFun (Maybe a6989586621679404427) a6989586621679404427 -> Type) -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (FromMaybeSym0 :: TyFun a6989586621679404427 (TyFun (Maybe a6989586621679404427) a6989586621679404427 -> Type) -> *) (l :: a6989586621679404427)

type Apply (FromMaybeSym0 :: TyFun a6989586621679404427 (TyFun (Maybe a6989586621679404427) a6989586621679404427 -> Type) -> *) (l :: a6989586621679404427) = FromMaybeSym1 l

data FromMaybeSym1 (l :: a6989586621679404427) (l :: TyFun (Maybe a6989586621679404427) a6989586621679404427)

Instances

SuppressUnusedWarnings (FromMaybeSym1 :: a6989586621679404427 -> TyFun (Maybe a6989586621679404427) a6989586621679404427 -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (FromMaybeSym1 l1 :: TyFun (Maybe a) a -> *) (l2 :: Maybe a)

type Apply (FromMaybeSym1 l1 :: TyFun (Maybe a) a -> *) (l2 :: Maybe a) = FromMaybe l1 l2

type FromMaybeSym2 (t :: a6989586621679404427) (t :: Maybe a6989586621679404427) = FromMaybe t t

data ListToMaybeSym0 (l :: TyFun [a6989586621679404425] (Maybe a6989586621679404425))

Instances

SuppressUnusedWarnings (ListToMaybeSym0 :: TyFun [a6989586621679404425] (Maybe a6989586621679404425) -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (ListToMaybeSym0 :: TyFun [a] (Maybe a) -> *) (l :: [a])

type Apply (ListToMaybeSym0 :: TyFun [a] (Maybe a) -> *) (l :: [a]) = ListToMaybe l

type ListToMaybeSym1 (t :: [a6989586621679404425]) = ListToMaybe t

data MaybeToListSym0 (l :: TyFun (Maybe a6989586621679404426) [a6989586621679404426])

Instances

SuppressUnusedWarnings (MaybeToListSym0 :: TyFun (Maybe a6989586621679404426) [a6989586621679404426] -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (MaybeToListSym0 :: TyFun (Maybe a) [a] -> *) (l :: Maybe a)

type Apply (MaybeToListSym0 :: TyFun (Maybe a) [a] -> *) (l :: Maybe a) = MaybeToList l

type MaybeToListSym1 (t :: Maybe a6989586621679404426) = MaybeToList t

data CatMaybesSym0 (l :: TyFun [Maybe a6989586621679404424] [a6989586621679404424])

Instances

SuppressUnusedWarnings (CatMaybesSym0 :: TyFun [Maybe a6989586621679404424] [a6989586621679404424] -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (CatMaybesSym0 :: TyFun [Maybe a] [a] -> *) (l :: [Maybe a])

type Apply (CatMaybesSym0 :: TyFun [Maybe a] [a] -> *) (l :: [Maybe a]) = CatMaybes l

type CatMaybesSym1 (t :: [Maybe a6989586621679404424]) = CatMaybes t

data MapMaybeSym0 (l :: TyFun (TyFun a6989586621679404422 (Maybe b6989586621679404423) -> Type) (TyFun [a6989586621679404422] [b6989586621679404423] -> Type))

Instances

SuppressUnusedWarnings (MapMaybeSym0 :: TyFun (TyFun a6989586621679404422 (Maybe b6989586621679404423) -> Type) (TyFun [a6989586621679404422] [b6989586621679404423] -> Type) -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (MapMaybeSym0 :: TyFun (TyFun a6989586621679404422 (Maybe b6989586621679404423) -> Type) (TyFun [a6989586621679404422] [b6989586621679404423] -> Type) -> *) (l :: TyFun a6989586621679404422 (Maybe b6989586621679404423) -> Type)

type Apply (MapMaybeSym0 :: TyFun (TyFun a6989586621679404422 (Maybe b6989586621679404423) -> Type) (TyFun [a6989586621679404422] [b6989586621679404423] -> Type) -> *) (l :: TyFun a6989586621679404422 (Maybe b6989586621679404423) -> Type) = MapMaybeSym1 l

data MapMaybeSym1 (l :: TyFun a6989586621679404422 (Maybe b6989586621679404423) -> Type) (l :: TyFun [a6989586621679404422] [b6989586621679404423])

Instances

SuppressUnusedWarnings (MapMaybeSym1 :: (TyFun a6989586621679404422 (Maybe b6989586621679404423) -> Type) -> TyFun [a6989586621679404422] [b6989586621679404423] -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (MapMaybeSym1 l1 :: TyFun [a] [b] -> *) (l2 :: [a])

type Apply (MapMaybeSym1 l1 :: TyFun [a] [b] -> *) (l2 :: [a]) = MapMaybe l1 l2

type MapMaybeSym2 (t :: TyFun a6989586621679404422 (Maybe b6989586621679404423) -> Type) (t :: [a6989586621679404422]) = MapMaybe t t