Copyright	(C) 2013-2014 Richard Eisenberg Jan Stolarek
License	BSD-style (see LICENSE)
Maintainer	Ryan Scott
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Singletons.Prelude.Bool

Contents

The Bool singleton
Conditionals
Singletons from Data.Bool
Defunctionalization symbols

Description

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.

Synopsis

type family Sing :: k -> Type
data SBool :: Bool -> Type where
- SFalse :: SBool 'False
- STrue :: SBool 'True
type family If (cond :: Bool) (tru :: k) (fls :: k) :: k where ...
sIf :: Sing a -> Sing b -> Sing c -> Sing (If a b c)
type family Not (a :: Bool) = (res :: Bool) | res -> a where ...
sNot :: Sing a -> Sing (Not a)
type family (a :: Bool) && (b :: Bool) :: Bool where ...
type family (a :: Bool) || (b :: Bool) :: Bool where ...
(%&&) :: Sing a -> Sing b -> Sing (a && b)
(%||) :: Sing a -> Sing b -> Sing (a || b)
bool_ :: a -> a -> Bool -> a
type family Bool_ (a :: a) (a :: a) (a :: Bool) :: a where ...
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 ...
sOtherwise :: Sing (OtherwiseSym0 :: Bool)
type TrueSym0 = 'True
type FalseSym0 = 'False
data NotSym0 :: (~>) Bool Bool
type NotSym1 (a6989586621679377177 :: Bool) = Not a6989586621679377177
data (&&@#@$) :: (~>) Bool ((~>) Bool Bool)
data (&&@#@$$) (a6989586621679376645 :: Bool) :: (~>) Bool Bool
type (&&@#@$$$) (a6989586621679376645 :: Bool) (b6989586621679376646 :: Bool) = (&&) a6989586621679376645 b6989586621679376646
data (||@#@$) :: (~>) Bool ((~>) Bool Bool)
data (||@#@$$) (a6989586621679376883 :: Bool) :: (~>) Bool Bool
type (||@#@$$$) (a6989586621679376883 :: Bool) (b6989586621679376884 :: Bool) = (||) a6989586621679376883 b6989586621679376884
data Bool_Sym0 :: forall a6989586621679375883. (~>) a6989586621679375883 ((~>) a6989586621679375883 ((~>) Bool a6989586621679375883))
data Bool_Sym1 (a6989586621679375889 :: a6989586621679375883) :: (~>) a6989586621679375883 ((~>) Bool a6989586621679375883)
data Bool_Sym2 (a6989586621679375889 :: a6989586621679375883) (a6989586621679375890 :: a6989586621679375883) :: (~>) Bool a6989586621679375883
type Bool_Sym3 (a6989586621679375889 :: a6989586621679375883) (a6989586621679375890 :: a6989586621679375883) (a6989586621679375891 :: Bool) = Bool_ a6989586621679375889 a6989586621679375890 a6989586621679375891
type OtherwiseSym0 = Otherwise

The `Bool` singleton

type family Sing :: k -> Type Source #

The singleton kind-indexed type family.

Instances

Instances details

type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = SBool
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = SOrdering
type Sing Source #
Instance details Defined in Data.Singletons.TypeLits.Internal type Sing = SNat
type Sing Source #
Instance details Defined in Data.Singletons.TypeLits.Internal type Sing = SSymbol
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = STuple0
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = SVoid
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Sing = SAll
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Sing = SAny
type Sing Source #
Instance details Defined in Data.Singletons.TypeError type Sing = SErrorMessage
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = SList :: [a] -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = SMaybe :: Maybe a -> Type
type Sing Source #	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 `TypeRep`s (for instance, `TypeRep`s 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.
Instance details Defined in Data.Singletons.TypeRepTYPE type Sing = TypeRep :: TYPE rep -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Sing = SMin :: Min a -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Sing = SMax :: Max a -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Sing = SFirst :: First a -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Sing = SLast :: Last a -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Sing = SWrappedMonoid :: WrappedMonoid m -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Sing = SOption :: Option a -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = SIdentity :: Identity a -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Monoid type Sing = SFirst :: First a -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Monoid type Sing = SLast :: Last a -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Sing = SDual :: Dual a -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Sing = SSum :: Sum a -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal type Sing = SProduct :: Product a -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Ord type Sing = SDown :: Down a -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = SNonEmpty :: NonEmpty a -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = SEither :: Either a b -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = STuple2 :: (a, b) -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup type Sing = SArg :: Arg a b -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Internal type Sing = SLambda :: (k1 ~> k2) -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Internal type Sing = SWrappedSing :: WrappedSing a -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Sigma type Sing = SSigma :: Sigma s t -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = STuple3 :: (a, b, c) -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Const type Sing = SConst :: Const a b -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = STuple4 :: (a, b, c, d) -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = STuple5 :: (a, b, c, d, e) -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = STuple6 :: (a, b, c, d, e, f) -> Type
type Sing Source #
Instance details Defined in Data.Singletons.Prelude.Instances type Sing = STuple7 :: (a, b, c, d, e, f, g) -> Type

data SBool :: Bool -> Type where Source #

Constructors

SFalse :: SBool 'False
STrue :: SBool 'True

Instances

Instances details

TestCoercion SBool Source #
Instance details Defined in Data.Singletons.Prelude.Instances Methods testCoercion :: forall (a :: k) (b :: k). SBool a -> SBool b -> Maybe (Coercion a b) #
TestEquality SBool Source #
Instance details Defined in Data.Singletons.Prelude.Instances Methods testEquality :: forall (a :: k) (b :: k). SBool a -> SBool b -> Maybe (a :~: b) #
Show (SBool z) Source #
Instance details 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) Source #

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) Source #

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 Source #

Conjunction of singletons

(%||) :: Sing a -> Sing b -> Sing (a || b) infixr 2 Source #

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 Source #

type family Bool_ (a :: a) (a :: a) (a :: Bool) :: a where ... Source #

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) Source #

type family Otherwise :: Bool where ... Source #

Equations

Otherwise = TrueSym0

sOtherwise :: Sing (OtherwiseSym0 :: Bool) Source #

Defunctionalization symbols

type TrueSym0 = 'True Source #

type FalseSym0 = 'False Source #

data NotSym0 :: (~>) Bool Bool Source #

Instances

Instances details

SingI NotSym0 Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing NotSym0 Source #
SuppressUnusedWarnings NotSym0 Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply NotSym0 (a6989586621679377177 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply NotSym0 (a6989586621679377177 :: Bool) = Not a6989586621679377177

type NotSym1 (a6989586621679377177 :: Bool) = Not a6989586621679377177 Source #

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

Instances

Instances details

SingI (&&@#@$) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing (&&@#@$) Source #
SuppressUnusedWarnings (&&@#@$) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply (&&@#@$) (a6989586621679376645 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (&&@#@$) (a6989586621679376645 :: Bool) = (&&@#@$$) a6989586621679376645

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

Instances

Instances details

SingI x => SingI ((&&@#@$$) x :: TyFun Bool Bool -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing ((&&@#@$$) x) Source #
SuppressUnusedWarnings ((&&@#@$$) a6989586621679376645 :: TyFun Bool Bool -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply ((&&@#@$$) a6989586621679376645 :: TyFun Bool Bool -> Type) (b6989586621679376646 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply ((&&@#@$$) a6989586621679376645 :: TyFun Bool Bool -> Type) (b6989586621679376646 :: Bool) = a6989586621679376645 && b6989586621679376646

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

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

Instances

Instances details

SingI (\|\|@#@$) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing (\|\|@#@$) Source #
SuppressUnusedWarnings (\|\|@#@$) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply (\|\|@#@$) (a6989586621679376883 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (\|\|@#@$) (a6989586621679376883 :: Bool) = (\|\|@#@$$) a6989586621679376883

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

Instances

Instances details

SingI x => SingI ((\|\|@#@$$) x :: TyFun Bool Bool -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing ((\|\|@#@$$) x) Source #
SuppressUnusedWarnings ((\|\|@#@$$) a6989586621679376883 :: TyFun Bool Bool -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply ((\|\|@#@$$) a6989586621679376883 :: TyFun Bool Bool -> Type) (b6989586621679376884 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply ((\|\|@#@$$) a6989586621679376883 :: TyFun Bool Bool -> Type) (b6989586621679376884 :: Bool) = a6989586621679376883 \|\| b6989586621679376884

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

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

Instances

Instances details

SingI (Bool_Sym0 :: TyFun a (a ~> (Bool ~> a)) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing Bool_Sym0 Source #
SuppressUnusedWarnings (Bool_Sym0 :: TyFun a6989586621679375883 (a6989586621679375883 ~> (Bool ~> a6989586621679375883)) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply (Bool_Sym0 :: TyFun a6989586621679375883 (a6989586621679375883 ~> (Bool ~> a6989586621679375883)) -> Type) (a6989586621679375889 :: a6989586621679375883) Source #
Instance details 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) Source #

Instances

Instances details

SingI d => SingI (Bool_Sym1 d :: TyFun a (Bool ~> a) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing (Bool_Sym1 d) Source #
SuppressUnusedWarnings (Bool_Sym1 a6989586621679375889 :: TyFun a6989586621679375883 (Bool ~> a6989586621679375883) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply (Bool_Sym1 a6989586621679375889 :: TyFun a6989586621679375883 (Bool ~> a6989586621679375883) -> Type) (a6989586621679375890 :: a6989586621679375883) Source #
Instance details 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 Source #

Instances

Instances details

(SingI d1, SingI d2) => SingI (Bool_Sym2 d1 d2 :: TyFun Bool a -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing (Bool_Sym2 d1 d2) Source #
SuppressUnusedWarnings (Bool_Sym2 a6989586621679375890 a6989586621679375889 :: TyFun Bool a6989586621679375883 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply (Bool_Sym2 a6989586621679375890 a6989586621679375889 :: TyFun Bool a -> Type) (a6989586621679375891 :: Bool) Source #
Instance details 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 Source #

type OtherwiseSym0 = Otherwise Source #

'False \|\| a = a
'True \|\| a = 'True
a \|\| 'False = a
a \|\| 'True = 'True
a \|\| a = a

SingI (\|\|@#@$) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing (\|\|@#@$) Source #
SuppressUnusedWarnings (\|\|@#@$) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply (\|\|@#@$) (a6989586621679376883 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (\|\|@#@$) (a6989586621679376883 :: Bool) = (\|\|@#@$$) a6989586621679376883

SingI x => SingI ((\|\|@#@$$) x :: TyFun Bool Bool -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing ((\|\|@#@$$) x) Source #
SuppressUnusedWarnings ((\|\|@#@$$) a6989586621679376883 :: TyFun Bool Bool -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply ((\|\|@#@$$) a6989586621679376883 :: TyFun Bool Bool -> Type) (b6989586621679376884 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply ((\|\|@#@$$) a6989586621679376883 :: TyFun Bool Bool -> Type) (b6989586621679376884 :: Bool) = a6989586621679376883 \|\| b6989586621679376884

The Bool singleton

Instances

Instances

Conditionals

Singletons from Data.Bool

Defunctionalization symbols

Instances

Instances

Instances

Instances

Instances

Instances

Instances

Instances

The `Bool` singleton

Singletons from `Data.Bool`