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
data SBool z where
- SFalse :: SBool ('False :: Bool)
- STrue :: SBool ('True :: Bool)
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 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 where ...
sOtherwise :: Sing (OtherwiseSym0 :: Bool)
type TrueSym0 = 'True :: Bool
type FalseSym0 = 'False :: Bool
data NotSym0 a6989586621679367240
type NotSym1 (a6989586621679367240 :: Bool) = Not a6989586621679367240 :: Bool
data (&&@#@$) a6989586621679366665
data a6989586621679366665 &&@#@$$ a6989586621679366666
type (&&@#@$$$) (a6989586621679366665 :: Bool) (a6989586621679366666 :: Bool) = (&&) a6989586621679366665 a6989586621679366666 :: Bool
data (||@#@$) a6989586621679366963
data a6989586621679366963 ||@#@$$ a6989586621679366964
type (||@#@$$$) (a6989586621679366963 :: Bool) (a6989586621679366964 :: Bool) = (||) a6989586621679366963 a6989586621679366964 :: Bool
data Bool_Sym0 a6989586621679365865
data Bool_Sym1 a6989586621679365865 a6989586621679365866
data Bool_Sym2 a6989586621679365865 a6989586621679365866 a6989586621679365867
type Bool_Sym3 (a6989586621679365865 :: a) (a6989586621679365866 :: a) (a6989586621679365867 :: Bool) = Bool_ a6989586621679365865 a6989586621679365866 a6989586621679365867 :: a
type OtherwiseSym0 = Otherwise :: Bool

The `Bool` singleton

type family Sing 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.Prelude.Proxy type Sing = SProxy :: Proxy t -> 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 z where Source #

Constructors

SFalse :: SBool ('False :: Bool)
STrue :: SBool ('True :: Bool)

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 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 where ... Source #

Equations

Otherwise = TrueSym0

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

Defunctionalization symbols

type TrueSym0 = 'True :: Bool Source #

type FalseSym0 = 'False :: Bool Source #

data NotSym0 a6989586621679367240 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 (a6989586621679367240 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply NotSym0 (a6989586621679367240 :: Bool) = NotSym1 a6989586621679367240

type NotSym1 (a6989586621679367240 :: Bool) = Not a6989586621679367240 :: Bool Source #

data (&&@#@$) a6989586621679366665 infixr 3 Source #

Instances

Instances details

SingI (&&@#@$) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing (&&@#@$) Source #
SuppressUnusedWarnings (&&@#@$) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply (&&@#@$) (a6989586621679366665 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (&&@#@$) (a6989586621679366665 :: Bool) = (&&@#@$$) a6989586621679366665

data a6989586621679366665 &&@#@$$ a6989586621679366666 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 ((&&@#@$$) a6989586621679366665 :: TyFun Bool Bool -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply ((&&@#@$$) a6989586621679366665 :: TyFun Bool Bool -> Type) (a6989586621679366666 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply ((&&@#@$$) a6989586621679366665 :: TyFun Bool Bool -> Type) (a6989586621679366666 :: Bool) = a6989586621679366665 &&@#@$$$ a6989586621679366666

type (&&@#@$$$) (a6989586621679366665 :: Bool) (a6989586621679366666 :: Bool) = (&&) a6989586621679366665 a6989586621679366666 :: Bool infixr 3 Source #

data (||@#@$) a6989586621679366963 infixr 2 Source #

Instances

Instances details

SingI (\|\|@#@$) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing (\|\|@#@$) Source #
SuppressUnusedWarnings (\|\|@#@$) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply (\|\|@#@$) (a6989586621679366963 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (\|\|@#@$) (a6989586621679366963 :: Bool) = (\|\|@#@$$) a6989586621679366963

data a6989586621679366963 ||@#@$$ a6989586621679366964 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 ((\|\|@#@$$) a6989586621679366963 :: TyFun Bool Bool -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply ((\|\|@#@$$) a6989586621679366963 :: TyFun Bool Bool -> Type) (a6989586621679366964 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply ((\|\|@#@$$) a6989586621679366963 :: TyFun Bool Bool -> Type) (a6989586621679366964 :: Bool) = a6989586621679366963 \|\|@#@$$$ a6989586621679366964

type (||@#@$$$) (a6989586621679366963 :: Bool) (a6989586621679366964 :: Bool) = (||) a6989586621679366963 a6989586621679366964 :: Bool infixr 2 Source #

data Bool_Sym0 a6989586621679365865 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 a (a ~> (Bool ~> a)) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply (Bool_Sym0 :: TyFun a (a ~> (Bool ~> a)) -> Type) (a6989586621679365865 :: a) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (Bool_Sym0 :: TyFun a (a ~> (Bool ~> a)) -> Type) (a6989586621679365865 :: a) = Bool_Sym1 a6989586621679365865

data Bool_Sym1 a6989586621679365865 a6989586621679365866 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 a6989586621679365865 :: TyFun a (Bool ~> a) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply (Bool_Sym1 a6989586621679365865 :: TyFun a (Bool ~> a) -> Type) (a6989586621679365866 :: a) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (Bool_Sym1 a6989586621679365865 :: TyFun a (Bool ~> a) -> Type) (a6989586621679365866 :: a) = Bool_Sym2 a6989586621679365865 a6989586621679365866

data Bool_Sym2 a6989586621679365865 a6989586621679365866 a6989586621679365867 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 a6989586621679365865 a6989586621679365866 :: TyFun Bool a -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply (Bool_Sym2 a6989586621679365865 a6989586621679365866 :: TyFun Bool a -> Type) (a6989586621679365867 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (Bool_Sym2 a6989586621679365865 a6989586621679365866 :: TyFun Bool a -> Type) (a6989586621679365867 :: Bool) = Bool_Sym3 a6989586621679365865 a6989586621679365866 a6989586621679365867

type Bool_Sym3 (a6989586621679365865 :: a) (a6989586621679365866 :: a) (a6989586621679365867 :: Bool) = Bool_ a6989586621679365865 a6989586621679365866 a6989586621679365867 :: a Source #

type OtherwiseSym0 = Otherwise :: Bool 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 (\|\|@#@$) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply (\|\|@#@$) (a6989586621679366963 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (\|\|@#@$) (a6989586621679366963 :: Bool) = (\|\|@#@$$) a6989586621679366963

SingI x => SingI ((\|\|@#@$$) x :: TyFun Bool Bool -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing ((\|\|@#@$$) x) Source #
SuppressUnusedWarnings ((\|\|@#@$$) a6989586621679366963 :: TyFun Bool Bool -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply ((\|\|@#@$$) a6989586621679366963 :: TyFun Bool Bool -> Type) (a6989586621679366964 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply ((\|\|@#@$$) a6989586621679366963 :: TyFun Bool Bool -> Type) (a6989586621679366964 :: Bool) = a6989586621679366963 \|\|@#@$$$ a6989586621679366964

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`