Data.Singletons.Prelude.Bool

Defines functions and datatypes relating to the singleton for Bool, including a singletons version 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

The singleton kind-indexed type family.

Instances

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = SBool

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = SOrdering

type Sing

Defined in Data.Singletons.TypeLits.Internal

type Sing = SNat

type Sing

Defined in Data.Singletons.TypeLits.Internal

type Sing = SSymbol

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = STuple0

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = SVoid

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SAll

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SAny

type Sing

Defined in Data.Singletons.TypeError

type Sing = SErrorMessage

type Sing

Defined in Data.Singletons.Prelude.Instances

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

type Sing

Defined in Data.Singletons.Prelude.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.TypeRepTYPE

type Sing = TypeRep :: TYPE rep -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SMin :: Min a -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SMax :: Max a -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SFirst :: First a -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SLast :: Last a -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SWrappedMonoid :: WrappedMonoid m -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SOption :: Option a -> Type

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = SIdentity :: Identity a -> Type

type Sing

Defined in Data.Singletons.Prelude.Monoid

type Sing = SFirst :: First a -> Type

type Sing

Defined in Data.Singletons.Prelude.Monoid

type Sing = SLast :: Last a -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SDual :: Dual a -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SSum :: Sum a -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SProduct :: Product a -> Type

type Sing

Defined in Data.Singletons.Prelude.Ord

type Sing = SDown :: Down a -> Type

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = SNonEmpty :: NonEmpty a -> Type

type Sing

Defined in Data.Singletons.Prelude.Instances

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

type Sing

Defined in Data.Singletons.Prelude.Instances

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

type Sing

Defined in Data.Singletons.Prelude.Semigroup

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

type Sing

Defined in Data.Singletons.Internal

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

type Sing

Defined in Data.Singletons.Internal

type Sing = SWrappedSing :: WrappedSing a -> Type

type Sing

Defined in Data.Singletons.Sigma

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

type Sing

Defined in Data.Singletons.Prelude.Instances

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

type Sing

Defined in Data.Singletons.Prelude.Const

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

type Sing

Defined in Data.Singletons.Prelude.Instances

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

type Sing

Defined in Data.Singletons.Prelude.Instances

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

type Sing

Defined in Data.Singletons.Prelude.Instances

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

type Sing

Defined in Data.Singletons.Prelude.Instances

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

data SBool :: Bool -> Type where

Constructors

SFalse :: SBool 'False

STrue :: SBool 'True

Instances

TestCoercion SBool

Defined in Data.Singletons.Prelude.Instances

Methods

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

TestEquality SBool

Defined in Data.Singletons.Prelude.Instances

Methods

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

Show (SBool z)

Defined in Data.Singletons.ShowSing

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 TrueSym0 = 'True

type FalseSym0 = 'False

data NotSym0 :: (~>) Bool Bool

Instances

SingI NotSym0

Defined in Data.Singletons.Prelude.Bool

Methods

sing :: Sing NotSym0

SuppressUnusedWarnings NotSym0

Defined in Data.Singletons.Prelude.Bool

Methods

suppressUnusedWarnings :: ()

type Apply NotSym0 (a6989586621679377177 :: Bool)

Defined in Data.Singletons.Prelude.Bool

type Apply NotSym0 (a6989586621679377177 :: Bool) = Not a6989586621679377177

type NotSym1 (a6989586621679377177 :: Bool) = Not a6989586621679377177

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

Instances

SingI (&&@#@$)

Defined in Data.Singletons.Prelude.Bool

Methods

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

SuppressUnusedWarnings (&&@#@$)

Defined in Data.Singletons.Prelude.Bool

Methods

suppressUnusedWarnings :: ()

type Apply (&&@#@$) (a6989586621679376645 :: Bool)

Defined in Data.Singletons.Prelude.Bool

type Apply (&&@#@$) (a6989586621679376645 :: Bool) = (&&@#@$$) a6989586621679376645

data (&&@#@$$) (a6989586621679376645 :: Bool) :: (~>) Bool Bool infixr 3

Instances

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

Defined in Data.Singletons.Prelude.Bool

Methods

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

SuppressUnusedWarnings ((&&@#@$$) a6989586621679376645 :: TyFun Bool Bool -> Type)

Defined in Data.Singletons.Prelude.Bool

Methods

suppressUnusedWarnings :: ()

type Apply ((&&@#@$$) a6989586621679376645 :: TyFun Bool Bool -> Type) (b6989586621679376646 :: Bool)

Defined in Data.Singletons.Prelude.Bool

type Apply ((&&@#@$$) a6989586621679376645 :: TyFun Bool Bool -> Type) (b6989586621679376646 :: Bool) = a6989586621679376645 && b6989586621679376646

type (&&@#@$$$) (a6989586621679376645 :: Bool) (b6989586621679376646 :: Bool) = (&&) a6989586621679376645 b6989586621679376646

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

Instances

SingI (||@#@$)

Defined in Data.Singletons.Prelude.Bool

Methods

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

SuppressUnusedWarnings (||@#@$)

Defined in Data.Singletons.Prelude.Bool

Methods

suppressUnusedWarnings :: ()

type Apply (||@#@$) (a6989586621679376883 :: Bool)

Defined in Data.Singletons.Prelude.Bool

type Apply (||@#@$) (a6989586621679376883 :: Bool) = (||@#@$$) a6989586621679376883

data (||@#@$$) (a6989586621679376883 :: Bool) :: (~>) Bool Bool infixr 2

Instances

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

Defined in Data.Singletons.Prelude.Bool

Methods

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

SuppressUnusedWarnings ((||@#@$$) a6989586621679376883 :: TyFun Bool Bool -> Type)

Defined in Data.Singletons.Prelude.Bool

Methods

suppressUnusedWarnings :: ()

type Apply ((||@#@$$) a6989586621679376883 :: TyFun Bool Bool -> Type) (b6989586621679376884 :: Bool)

Defined in Data.Singletons.Prelude.Bool

type Apply ((||@#@$$) a6989586621679376883 :: TyFun Bool Bool -> Type) (b6989586621679376884 :: Bool) = a6989586621679376883 || b6989586621679376884

type (||@#@$$$) (a6989586621679376883 :: Bool) (b6989586621679376884 :: Bool) = (||) a6989586621679376883 b6989586621679376884

data Bool_Sym0 :: forall a6989586621679375883. (~>) a6989586621679375883 ((~>) a6989586621679375883 ((~>) Bool a6989586621679375883))

Instances

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

Defined in Data.Singletons.Prelude.Bool

Methods

sing :: Sing Bool_Sym0

SuppressUnusedWarnings (Bool_Sym0 :: TyFun a6989586621679375883 (a6989586621679375883 ~> (Bool ~> a6989586621679375883)) -> Type)

Defined in Data.Singletons.Prelude.Bool

Methods

suppressUnusedWarnings :: ()

type Apply (Bool_Sym0 :: TyFun a6989586621679375883 (a6989586621679375883 ~> (Bool ~> a6989586621679375883)) -> Type) (a6989586621679375889 :: a6989586621679375883)

Defined in Data.Singletons.Prelude.Bool

type Apply (Bool_Sym0 :: TyFun a6989586621679375883 (a6989586621679375883 ~> (Bool ~> a6989586621679375883)) -> Type) (a6989586621679375889 :: a6989586621679375883) = Bool_Sym1 a6989586621679375889

data Bool_Sym1 (a6989586621679375889 :: a6989586621679375883) :: (~>) a6989586621679375883 ((~>) Bool a6989586621679375883)

Instances

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

Defined in Data.Singletons.Prelude.Bool

Methods

sing :: Sing (Bool_Sym1 d)

SuppressUnusedWarnings (Bool_Sym1 a6989586621679375889 :: TyFun a6989586621679375883 (Bool ~> a6989586621679375883) -> Type)

Defined in Data.Singletons.Prelude.Bool

Methods

suppressUnusedWarnings :: ()

type Apply (Bool_Sym1 a6989586621679375889 :: TyFun a6989586621679375883 (Bool ~> a6989586621679375883) -> Type) (a6989586621679375890 :: a6989586621679375883)

Defined in Data.Singletons.Prelude.Bool

type Apply (Bool_Sym1 a6989586621679375889 :: TyFun a6989586621679375883 (Bool ~> a6989586621679375883) -> Type) (a6989586621679375890 :: a6989586621679375883) = Bool_Sym2 a6989586621679375889 a6989586621679375890

data Bool_Sym2 (a6989586621679375889 :: a6989586621679375883) (a6989586621679375890 :: a6989586621679375883) :: (~>) Bool a6989586621679375883

Instances

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

Defined in Data.Singletons.Prelude.Bool

Methods

sing :: Sing (Bool_Sym2 d1 d2)

SuppressUnusedWarnings (Bool_Sym2 a6989586621679375890 a6989586621679375889 :: TyFun Bool a6989586621679375883 -> Type)

Defined in Data.Singletons.Prelude.Bool

Methods

suppressUnusedWarnings :: ()

type Apply (Bool_Sym2 a6989586621679375890 a6989586621679375889 :: TyFun Bool a -> Type) (a6989586621679375891 :: Bool)

Defined in Data.Singletons.Prelude.Bool

type Apply (Bool_Sym2 a6989586621679375890 a6989586621679375889 :: TyFun Bool a -> Type) (a6989586621679375891 :: Bool) = Bool_ a6989586621679375890 a6989586621679375889 a6989586621679375891

type Bool_Sym3 (a6989586621679375889 :: a6989586621679375883) (a6989586621679375890 :: a6989586621679375883) (a6989586621679375891 :: Bool) = Bool_ a6989586621679375889 a6989586621679375890 a6989586621679375891

type OtherwiseSym0 = Otherwise