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

type Sing = SAll

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SAny

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SVoid

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 GHC.TypeLits.Singletons.Internal

type Sing = SNat

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

type Sing = SFirst :: First a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SLast :: Last a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SMax :: Max a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SMin :: Min a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SWrappedMonoid :: WrappedMonoid m -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SDual :: Dual a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SProduct :: Product a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal

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.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 :: Bool -> Type where

Constructors

SFalse :: SBool ('False :: Bool)

STrue :: SBool ('True :: Bool)

Instances

TestCoercion SBool

Defined in Data.Singletons.Base.Instances

Methods

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

TestEquality SBool

Defined in Data.Singletons.Base.Instances

Methods

testEquality :: forall (a :: k) (b :: k). 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

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 :: 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 :: 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

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

Conjunction of singletons

(%||) :: 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_ (a :: a) (a :: a) (a :: Bool) :: a where ...

Equations

Bool_ fls _tru 'False = fls

Bool_ _fls tru 'True = tru

sBool_ :: forall a (t :: a) (t :: a) (t :: Bool). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply Bool_Sym0 t) t) t :: a)

type family Otherwise :: Bool where ...

Equations

Otherwise = TrueSym0

sOtherwise :: Sing (OtherwiseSym0 :: Bool)

Defunctionalization symbols

type family TrueSym0 :: Bool where ...

Equations

TrueSym0 = 'True

type family FalseSym0 :: Bool where ...

Equations

FalseSym0 = 'False

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

Instances

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

Defined in Data.Bool.Singletons

Methods

sing :: Sing IfSym0

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

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (IfSym0 :: TyFun Bool (k ~> (k ~> k)) -> Type) (a6989586621679141394 :: Bool)

Defined in Data.Bool.Singletons

type Apply (IfSym0 :: TyFun Bool (k ~> (k ~> k)) -> Type) (a6989586621679141394 :: Bool) = IfSym1 a6989586621679141394 :: TyFun k (k ~> k) -> Type

data IfSym1 (a6989586621679141394 :: Bool) :: (~>) k ((~>) k k)

Instances

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

Defined in Data.Bool.Singletons

Methods

liftSing :: forall (x :: k1). Sing x -> Sing (IfSym1 x)

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

Defined in Data.Bool.Singletons

Methods

sing :: Sing (IfSym1 c)

SuppressUnusedWarnings (IfSym1 a6989586621679141394 :: TyFun k (k ~> k) -> Type)

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (IfSym1 a6989586621679141394 :: TyFun k (k ~> k) -> Type) (a6989586621679141395 :: k)

Defined in Data.Bool.Singletons

type Apply (IfSym1 a6989586621679141394 :: TyFun k (k ~> k) -> Type) (a6989586621679141395 :: k) = IfSym2 a6989586621679141394 a6989586621679141395

data IfSym2 (a6989586621679141394 :: Bool) (a6989586621679141395 :: k) :: (~>) k k

Instances

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

Defined in Data.Bool.Singletons

Methods

liftSing2 :: forall (x :: k1) (y :: k20). 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 :: k10). 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 a6989586621679141394 a6989586621679141395 :: TyFun k k -> Type)

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (IfSym2 a6989586621679141394 a6989586621679141395 :: TyFun k k -> Type) (a6989586621679141396 :: k)

Defined in Data.Bool.Singletons

type Apply (IfSym2 a6989586621679141394 a6989586621679141395 :: TyFun k k -> Type) (a6989586621679141396 :: k) = If a6989586621679141394 a6989586621679141395 a6989586621679141396

type family IfSym3 (a6989586621679141394 :: Bool) (a6989586621679141395 :: k) (a6989586621679141396 :: k) :: k where ...

Equations

IfSym3 a6989586621679141394 a6989586621679141395 a6989586621679141396 = If a6989586621679141394 a6989586621679141395 a6989586621679141396

data NotSym0 :: (~>) 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 (a6989586621679141194 :: Bool)

Defined in Data.Bool.Singletons

type Apply NotSym0 (a6989586621679141194 :: Bool) = Not a6989586621679141194

type family NotSym1 (a6989586621679141194 :: Bool) :: Bool where ...

Equations

NotSym1 a6989586621679141194 = Not a6989586621679141194

data (&&@#@$) :: (~>) 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 (&&@#@$) (a6989586621679140549 :: Bool)

Defined in Data.Bool.Singletons

type Apply (&&@#@$) (a6989586621679140549 :: Bool) = (&&@#@$$) a6989586621679140549

data (&&@#@$$) (a6989586621679140549 :: Bool) :: (~>) Bool Bool infixr 3

Instances

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

Defined in Data.Bool.Singletons

Methods

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

SuppressUnusedWarnings ((&&@#@$$) a6989586621679140549 :: TyFun Bool Bool -> Type)

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply ((&&@#@$$) a6989586621679140549 :: TyFun Bool Bool -> Type) (a6989586621679140550 :: Bool)

Defined in Data.Bool.Singletons

type Apply ((&&@#@$$) a6989586621679140549 :: TyFun Bool Bool -> Type) (a6989586621679140550 :: Bool) = a6989586621679140549 && a6989586621679140550

type family (a6989586621679140549 :: Bool) &&@#@$$$ (a6989586621679140550 :: Bool) :: Bool where ... infixr 3

Equations

a6989586621679140549 &&@#@$$$ a6989586621679140550 = (&&) a6989586621679140549 a6989586621679140550

data (||@#@$) :: (~>) 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 (||@#@$) (a6989586621679140880 :: Bool)

Defined in Data.Bool.Singletons

type Apply (||@#@$) (a6989586621679140880 :: Bool) = (||@#@$$) a6989586621679140880

data (||@#@$$) (a6989586621679140880 :: Bool) :: (~>) Bool Bool infixr 2

Instances

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

Defined in Data.Bool.Singletons

Methods

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

SuppressUnusedWarnings ((||@#@$$) a6989586621679140880 :: TyFun Bool Bool -> Type)

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply ((||@#@$$) a6989586621679140880 :: TyFun Bool Bool -> Type) (a6989586621679140881 :: Bool)

Defined in Data.Bool.Singletons

type Apply ((||@#@$$) a6989586621679140880 :: TyFun Bool Bool -> Type) (a6989586621679140881 :: Bool) = a6989586621679140880 || a6989586621679140881

type family (a6989586621679140880 :: Bool) ||@#@$$$ (a6989586621679140881 :: Bool) :: Bool where ... infixr 2

Equations

a6989586621679140880 ||@#@$$$ a6989586621679140881 = (||) a6989586621679140880 a6989586621679140881

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

Instances

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

Defined in Data.Bool.Singletons

Methods

sing :: Sing Bool_Sym0

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) (a6989586621679139245 :: a)

Defined in Data.Bool.Singletons

type Apply (Bool_Sym0 :: TyFun a (a ~> (Bool ~> a)) -> Type) (a6989586621679139245 :: a) = Bool_Sym1 a6989586621679139245

data Bool_Sym1 (a6989586621679139245 :: a) :: (~>) a ((~>) Bool a)

Instances

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

Defined in Data.Bool.Singletons

Methods

liftSing :: forall (x :: k1). 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 a6989586621679139245 :: TyFun a (Bool ~> a) -> Type)

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (Bool_Sym1 a6989586621679139245 :: TyFun a (Bool ~> a) -> Type) (a6989586621679139246 :: a)

Defined in Data.Bool.Singletons

type Apply (Bool_Sym1 a6989586621679139245 :: TyFun a (Bool ~> a) -> Type) (a6989586621679139246 :: a) = Bool_Sym2 a6989586621679139245 a6989586621679139246

data Bool_Sym2 (a6989586621679139245 :: a) (a6989586621679139246 :: a) :: (~>) Bool a

Instances

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

Defined in Data.Bool.Singletons

Methods

liftSing2 :: forall (x :: k1) (y :: k2). 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 :: k1). 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 a6989586621679139245 a6989586621679139246 :: TyFun Bool a -> Type)

Defined in Data.Bool.Singletons

Methods

suppressUnusedWarnings :: ()

type Apply (Bool_Sym2 a6989586621679139245 a6989586621679139246 :: TyFun Bool a -> Type) (a6989586621679139247 :: Bool)

Defined in Data.Bool.Singletons

type Apply (Bool_Sym2 a6989586621679139245 a6989586621679139246 :: TyFun Bool a -> Type) (a6989586621679139247 :: Bool) = Bool_ a6989586621679139245 a6989586621679139246 a6989586621679139247

type family Bool_Sym3 (a6989586621679139245 :: a) (a6989586621679139246 :: a) (a6989586621679139247 :: Bool) :: a where ...

Equations

Bool_Sym3 a6989586621679139245 a6989586621679139246 a6989586621679139247 = Bool_ a6989586621679139245 a6989586621679139246 a6989586621679139247

type family OtherwiseSym0 :: Bool where ...

Equations

OtherwiseSym0 = Otherwise