Data.Bool.Singletons

Defines functions and datatypes relating to the singleton for Bool, including singled versions of all the definitions in Data.Bool.

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

The Bool singleton

type family Sing :: k -> Type

Instances

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SAll

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SAny

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SVoid

type Sing

Defined in GHC.TypeLits.Singletons.Internal

type Sing = SNat

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SOrdering

type Sing

Defined in Data.Singletons.Base.TypeError

type Sing = SErrorMessage

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = STuple0

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SBool

type Sing

Defined in GHC.TypeLits.Singletons.Internal

type Sing = SChar

type Sing

Defined in GHC.TypeLits.Singletons.Internal

type Sing = SSymbol

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SIdentity :: Identity a -> Type

type Sing

Defined in Data.Monoid.Singletons

type Sing = SFirst :: First a -> Type

type Sing

Defined in Data.Monoid.Singletons

type Sing = SLast :: Last a -> Type

type Sing

Defined in Data.Ord.Singletons

type Sing = SDown :: Down a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SFirst :: First a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SLast :: Last a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SMax :: Max a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SMin :: Min a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SWrappedMonoid :: WrappedMonoid m -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SDual :: Dual a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SProduct :: Product a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal.Wrappers

type Sing = SSum :: Sum a -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SNonEmpty :: NonEmpty a -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SMaybe :: Maybe a -> Type

type Sing

A choice of singleton for the kind TYPE rep (for some RuntimeRep rep), an instantiation of which is the famous kind Type.

Conceivably, one could generalize this instance to `Sing @k` for any kind k, and remove all other Sing instances. We don't adopt this design, however, since it is far more convenient in practice to work with explicit singleton values than TypeReps (for instance, TypeReps are more difficult to pattern match on, and require extra runtime checks).

We cannot produce explicit singleton values for everything in TYPE rep, however, since it is an open kind, so we reach for TypeRep in this one particular case.

Defined in Data.Singletons.Base.TypeRepTYPE

type Sing = TypeRep :: TYPE rep -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SList :: [a] -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SEither :: Either a b -> Type

type Sing

Defined in Data.Proxy.Singletons

type Sing = SProxy :: Proxy t -> Type

type Sing

Defined in Data.Semigroup.Singletons

type Sing = SArg :: Arg a b -> Type

type Sing

Defined in Data.Singletons

type Sing = SWrappedSing :: WrappedSing a -> Type

type Sing

Defined in Data.Singletons

type Sing = SLambda :: (k1 ~> k2) -> Type

type Sing

Defined in Data.Singletons.Sigma

type Sing = SSigma :: Sigma s t -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = STuple2 :: (a, b) -> Type

type Sing

Defined in Data.Functor.Const.Singletons

type Sing = SConst :: Const a b -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = STuple3 :: (a, b, c) -> Type

type Sing

Defined in Data.Functor.Product.Singletons

type Sing = SProduct :: Product f g a -> Type

type Sing

Defined in Data.Functor.Sum.Singletons

type Sing = SSum :: Sum f g a -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = STuple4 :: (a, b, c, d) -> Type

type Sing

Defined in Data.Functor.Compose.Singletons

type Sing = SCompose :: Compose f g a -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = STuple5 :: (a, b, c, d, e) -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = STuple6 :: (a, b, c, d, e, f) -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = STuple7 :: (a, b, c, d, e, f, g) -> Type

data SBool (a :: Bool) where

Constructors

SFalse :: SBool 'False

STrue :: SBool 'True

Instances

TestCoercion SBool

Defined in Data.Singletons.Base.Instances

Methods

testCoercion :: forall (a :: Bool) (b :: Bool). SBool a -> SBool b -> Maybe (Coercion a b)

TestEquality SBool

Defined in Data.Singletons.Base.Instances

Methods

testEquality :: forall (a :: Bool) (b :: Bool). SBool a -> SBool b -> Maybe (a :~: b)

Show (SBool z)

Defined in Data.Singletons.Base.Instances

Methods

showsPrec :: Int -> SBool z -> ShowS

show :: SBool z -> String

showList :: [SBool z] -> ShowS

Eq (SBool z)

Defined in Data.Singletons.Base.Instances

Methods

(==) :: SBool z -> SBool z -> Bool

(/=) :: SBool z -> SBool z -> Bool

Conditionals

type family If (cond :: Bool) (tru :: k) (fls :: k) :: k where ...

Type-level If. If True a b ==> a; If False a b ==> b

Equations

If 'True (tru :: k) (fls :: k) = tru

If 'False (tru :: k) (fls :: k) = fls

sIf :: forall {k} (a :: Bool) (b :: k) (c :: k). Sing a -> Sing b -> Sing c -> Sing (If a b c)

Conditional over singletons

Singletons from Data.Bool

type family Not (a :: Bool) = (res :: Bool) | res -> a where ...

Type-level "not". An injective type family since 4.10.0.0.

Since: base-4.7.0.0

Equations

Not 'False = 'True

Not 'True = 'False

sNot :: forall (a :: Bool). Sing a -> Sing (Not a)

Negation of a singleton

type family (a :: Bool) && (b :: Bool) :: Bool where ... infixr 3

Type-level "and"

Equations

'False && a = 'False

'True && a = a

a && 'False = 'False

a && 'True = a

a && a = a

type family (a :: Bool) || (b :: Bool) :: Bool where ... infixr 2

Type-level "or"

Equations

'False || a = a

'True || a = 'True

a || 'False = a

a || 'True = 'True

a || a = a

(%&&) :: forall (a :: Bool) (b :: Bool). Sing a -> Sing b -> Sing (a && b) infixr 3

Conjunction of singletons

(%||) :: forall (a :: Bool) (b :: Bool). Sing a -> Sing b -> Sing (a || b) infixr 2

Disjunction of singletons

The following are derived from the function bool in Data.Bool. The extra underscore is to avoid name clashes with the type Bool.

bool_ :: a -> a -> Bool -> a

type family Bool_ (a1 :: a) (a2 :: a) (a3 :: Bool) :: a where ...

Equations

Bool_ (fls :: a) (_tru :: a) 'False = fls

Bool_ (_fls :: a) (tru :: a) 'True = tru

sBool_ :: forall a (t1 :: a) (t2 :: a) (t3 :: Bool). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply (Bool_Sym0 :: TyFun a (a ~> (Bool ~> a)) -> Type) t1) t2) t3)

type family Otherwise :: Bool where ...

Equations

Otherwise = TrueSym0

sOtherwise :: Sing OtherwiseSym0

Defunctionalization symbols

type family TrueSym0 :: Bool where ...

Equations

TrueSym0 = 'True

type family FalseSym0 :: Bool where ...

Equations

FalseSym0 = 'False

data IfSym0 (a :: TyFun Bool (k ~> (k ~> k)))

Instances

SingI (IfSym0 :: TyFun Bool (k ~> (k ~> k)) -> Type)

Defined in Data.Bool.Singletons

Methods

sing :: Sing (IfSym0 :: TyFun Bool (k ~> (k ~> k)) -> Type)

SuppressUnusedWarnings (IfSym0 :: TyFun Bool (k ~> (k ~> k)) -> Type)

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (IfSym0 :: TyFun Bool (k ~> (k ~> k)) -> Type) (a6989586621679133031 :: Bool)

Defined in Data.Bool.Singletons

type Apply (IfSym0 :: TyFun Bool (k ~> (k ~> k)) -> Type) (a6989586621679133031 :: Bool) = IfSym1 a6989586621679133031 :: TyFun k (k ~> k) -> Type

data IfSym1 (a6989586621679133031 :: Bool) (b :: TyFun k (k ~> k))

Instances

SingI1 (IfSym1 :: Bool -> TyFun k (k ~> k) -> Type)

Defined in Data.Bool.Singletons

Methods

liftSing :: forall (x :: Bool). Sing x -> Sing (IfSym1 x :: TyFun k (k ~> k) -> Type)

SingI c => SingI (IfSym1 c :: TyFun k (k ~> k) -> Type)

Defined in Data.Bool.Singletons

Methods

sing :: Sing (IfSym1 c :: TyFun k (k ~> k) -> Type)

SuppressUnusedWarnings (IfSym1 a6989586621679133031 :: TyFun k (k ~> k) -> Type)

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (IfSym1 a6989586621679133031 :: TyFun k (k ~> k) -> Type) (a6989586621679133032 :: k)

Defined in Data.Bool.Singletons

type Apply (IfSym1 a6989586621679133031 :: TyFun k (k ~> k) -> Type) (a6989586621679133032 :: k) = IfSym2 a6989586621679133031 a6989586621679133032

data IfSym2 (a6989586621679133031 :: Bool) (a6989586621679133032 :: k) (c :: TyFun k k)

Instances

SingI2 (IfSym2 :: Bool -> k2 -> TyFun k2 k2 -> Type)

Defined in Data.Bool.Singletons

Methods

liftSing2 :: forall (x :: Bool) (y :: k2). Sing x -> Sing y -> Sing (IfSym2 x y)

SingI c => SingI1 (IfSym2 c :: k1 -> TyFun k1 k1 -> Type)

Defined in Data.Bool.Singletons

Methods

liftSing :: forall (x :: k1). Sing x -> Sing (IfSym2 c x)

(SingI c, SingI t) => SingI (IfSym2 c t :: TyFun k k -> Type)

Defined in Data.Bool.Singletons

Methods

sing :: Sing (IfSym2 c t)

SuppressUnusedWarnings (IfSym2 a6989586621679133031 a6989586621679133032 :: TyFun k k -> Type)

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (IfSym2 a6989586621679133031 a6989586621679133032 :: TyFun k k -> Type) (a6989586621679133033 :: k)

Defined in Data.Bool.Singletons

type Apply (IfSym2 a6989586621679133031 a6989586621679133032 :: TyFun k k -> Type) (a6989586621679133033 :: k) = If a6989586621679133031 a6989586621679133032 a6989586621679133033

type family IfSym3 (a6989586621679133031 :: Bool) (a6989586621679133032 :: k) (a6989586621679133033 :: k) :: k where ...

Equations

IfSym3 a6989586621679133031 (a6989586621679133032 :: k) (a6989586621679133033 :: k) = If a6989586621679133031 a6989586621679133032 a6989586621679133033

data NotSym0 (a :: TyFun Bool Bool)

Instances

SingI NotSym0

Defined in Data.Bool.Singletons

Methods

sing :: Sing NotSym0

SuppressUnusedWarnings NotSym0

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply NotSym0 (a6989586621679132813 :: Bool)

Defined in Data.Bool.Singletons

type Apply NotSym0 (a6989586621679132813 :: Bool) = Not a6989586621679132813

type family NotSym1 (a6989586621679132813 :: Bool) :: Bool where ...

Equations

NotSym1 a6989586621679132813 = Not a6989586621679132813

data (&&@#@$) (a :: TyFun Bool (Bool ~> Bool)) infixr 3

Instances

SingI (&&@#@$)

Defined in Data.Bool.Singletons

Methods

sing :: Sing (&&@#@$)

SuppressUnusedWarnings (&&@#@$)

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (&&@#@$) (a6989586621679132115 :: Bool)

Defined in Data.Bool.Singletons

type Apply (&&@#@$) (a6989586621679132115 :: Bool) = (&&@#@$$) a6989586621679132115

data (a6989586621679132115 :: Bool) &&@#@$$ (b :: TyFun Bool Bool) infixr 3

Instances

SingI x => SingI ((&&@#@$$) x :: TyFun Bool Bool -> Type)

Defined in Data.Bool.Singletons

Methods

sing :: Sing ((&&@#@$$) x)

SuppressUnusedWarnings ((&&@#@$$) a6989586621679132115 :: TyFun Bool Bool -> Type)

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply ((&&@#@$$) a6989586621679132115 :: TyFun Bool Bool -> Type) (a6989586621679132116 :: Bool)

Defined in Data.Bool.Singletons

type Apply ((&&@#@$$) a6989586621679132115 :: TyFun Bool Bool -> Type) (a6989586621679132116 :: Bool) = a6989586621679132115 && a6989586621679132116

type family (a6989586621679132115 :: Bool) &&@#@$$$ (a6989586621679132116 :: Bool) :: Bool where ... infixr 3

Equations

a6989586621679132115 &&@#@$$$ a6989586621679132116 = a6989586621679132115 && a6989586621679132116

data (||@#@$) (a :: TyFun Bool (Bool ~> Bool)) infixr 2

Instances

SingI (||@#@$)

Defined in Data.Bool.Singletons

Methods

sing :: Sing (||@#@$)

SuppressUnusedWarnings (||@#@$)

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (||@#@$) (a6989586621679132472 :: Bool)

Defined in Data.Bool.Singletons

type Apply (||@#@$) (a6989586621679132472 :: Bool) = (||@#@$$) a6989586621679132472

data (a6989586621679132472 :: Bool) ||@#@$$ (b :: TyFun Bool Bool) infixr 2

Instances

SingI x => SingI ((||@#@$$) x :: TyFun Bool Bool -> Type)

Defined in Data.Bool.Singletons

Methods

sing :: Sing ((||@#@$$) x)

SuppressUnusedWarnings ((||@#@$$) a6989586621679132472 :: TyFun Bool Bool -> Type)

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply ((||@#@$$) a6989586621679132472 :: TyFun Bool Bool -> Type) (a6989586621679132473 :: Bool)

Defined in Data.Bool.Singletons

type Apply ((||@#@$$) a6989586621679132472 :: TyFun Bool Bool -> Type) (a6989586621679132473 :: Bool) = a6989586621679132472 || a6989586621679132473

type family (a6989586621679132472 :: Bool) ||@#@$$$ (a6989586621679132473 :: Bool) :: Bool where ... infixr 2

Equations

a6989586621679132472 ||@#@$$$ a6989586621679132473 = a6989586621679132472 || a6989586621679132473

data Bool_Sym0 (a1 :: TyFun a (a ~> (Bool ~> a)))

Instances

SingI (Bool_Sym0 :: TyFun a (a ~> (Bool ~> a)) -> Type)

Defined in Data.Bool.Singletons

Methods

sing :: Sing (Bool_Sym0 :: TyFun a (a ~> (Bool ~> a)) -> Type)

SuppressUnusedWarnings (Bool_Sym0 :: TyFun a (a ~> (Bool ~> a)) -> Type)

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (Bool_Sym0 :: TyFun a (a ~> (Bool ~> a)) -> Type) (a6989586621679130897 :: a)

Defined in Data.Bool.Singletons

type Apply (Bool_Sym0 :: TyFun a (a ~> (Bool ~> a)) -> Type) (a6989586621679130897 :: a) = Bool_Sym1 a6989586621679130897

data Bool_Sym1 (a6989586621679130897 :: a) (b :: TyFun a (Bool ~> a))

Instances

SingI1 (Bool_Sym1 :: a -> TyFun a (Bool ~> a) -> Type)

Defined in Data.Bool.Singletons

Methods

liftSing :: forall (x :: a). Sing x -> Sing (Bool_Sym1 x)

SingI d => SingI (Bool_Sym1 d :: TyFun a (Bool ~> a) -> Type)

Defined in Data.Bool.Singletons

Methods

sing :: Sing (Bool_Sym1 d)

SuppressUnusedWarnings (Bool_Sym1 a6989586621679130897 :: TyFun a (Bool ~> a) -> Type)

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (Bool_Sym1 a6989586621679130897 :: TyFun a (Bool ~> a) -> Type) (a6989586621679130898 :: a)

Defined in Data.Bool.Singletons

type Apply (Bool_Sym1 a6989586621679130897 :: TyFun a (Bool ~> a) -> Type) (a6989586621679130898 :: a) = Bool_Sym2 a6989586621679130897 a6989586621679130898

data Bool_Sym2 (a6989586621679130897 :: a) (a6989586621679130898 :: a) (c :: TyFun Bool a)

Instances

SingI2 (Bool_Sym2 :: a -> a -> TyFun Bool a -> Type)

Defined in Data.Bool.Singletons

Methods

liftSing2 :: forall (x :: a) (y :: a). Sing x -> Sing y -> Sing (Bool_Sym2 x y)

SingI d => SingI1 (Bool_Sym2 d :: a -> TyFun Bool a -> Type)

Defined in Data.Bool.Singletons

Methods

liftSing :: forall (x :: a). Sing x -> Sing (Bool_Sym2 d x)

(SingI d1, SingI d2) => SingI (Bool_Sym2 d1 d2 :: TyFun Bool a -> Type)

Defined in Data.Bool.Singletons

Methods

sing :: Sing (Bool_Sym2 d1 d2)

SuppressUnusedWarnings (Bool_Sym2 a6989586621679130897 a6989586621679130898 :: TyFun Bool a -> Type)

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (Bool_Sym2 a6989586621679130897 a6989586621679130898 :: TyFun Bool a -> Type) (a6989586621679130899 :: Bool)

Defined in Data.Bool.Singletons

type Apply (Bool_Sym2 a6989586621679130897 a6989586621679130898 :: TyFun Bool a -> Type) (a6989586621679130899 :: Bool) = Bool_ a6989586621679130897 a6989586621679130898 a6989586621679130899

type family Bool_Sym3 (a6989586621679130897 :: a) (a6989586621679130898 :: a) (a6989586621679130899 :: Bool) :: a where ...

Equations

Bool_Sym3 (a6989586621679130897 :: a) (a6989586621679130898 :: a) a6989586621679130899 = Bool_ a6989586621679130897 a6989586621679130898 a6989586621679130899

type family OtherwiseSym0 :: Bool where ...

Equations

OtherwiseSym0 = Otherwise