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

data family Sing :: k -> Type
type SBool = (Sing :: Bool -> Type)
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 (a6989586621679378735 :: Bool) = Not a6989586621679378735
data (&&@#@$) :: (~>) Bool ((~>) Bool Bool)
data (&&@#@$$) (a6989586621679378194 :: Bool) :: (~>) Bool Bool
type (&&@#@$$$) (a6989586621679378194 :: Bool) (b6989586621679378195 :: Bool) = (&&) a6989586621679378194 b6989586621679378195
data (||@#@$) :: (~>) Bool ((~>) Bool Bool)
data (||@#@$$) (a6989586621679378435 :: Bool) :: (~>) Bool Bool
type (||@#@$$$) (a6989586621679378435 :: Bool) (b6989586621679378436 :: Bool) = (||) a6989586621679378435 b6989586621679378436
data Bool_Sym0 :: forall a6989586621679377443. (~>) a6989586621679377443 ((~>) a6989586621679377443 ((~>) Bool a6989586621679377443))
data Bool_Sym1 (a6989586621679377449 :: a6989586621679377443) :: (~>) a6989586621679377443 ((~>) Bool a6989586621679377443)
data Bool_Sym2 (a6989586621679377449 :: a6989586621679377443) (a6989586621679377450 :: a6989586621679377443) :: (~>) Bool a6989586621679377443
type Bool_Sym3 (a6989586621679377449 :: a6989586621679377443) (a6989586621679377450 :: a6989586621679377443) (a6989586621679377451 :: Bool) = Bool_ a6989586621679377449 a6989586621679377450 a6989586621679377451
type OtherwiseSym0 = Otherwise

The `Bool` singleton

data family Sing :: k -> Type #

The singleton kind-indexed data family.

Instances

SDecide k => TestCoercion (Sing :: k -> Type) #
Instance details Defined in Data.Singletons.Decide Methods testCoercion :: Sing a -> Sing b -> Maybe (Coercion a b) #
SDecide k => TestEquality (Sing :: k -> Type) #
Instance details Defined in Data.Singletons.Decide Methods testEquality :: Sing a -> Sing b -> Maybe (a :~: b) #
Show (SSymbol s) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> SSymbol s -> ShowS # show :: SSymbol s -> String # showList :: [SSymbol s] -> ShowS #
Show (SNat n) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> SNat n -> ShowS # show :: SNat n -> String # showList :: [SNat n] -> ShowS #
Eq (Sing a) #
Instance details Defined in Data.Singletons.TypeRepTYPE Methods (==) :: Sing a -> Sing a -> Bool # (/=) :: Sing a -> Sing a -> Bool #
Ord (Sing a) #
Instance details Defined in Data.Singletons.TypeRepTYPE Methods compare :: Sing a -> Sing a -> Ordering # (<) :: Sing a -> Sing a -> Bool # (<=) :: Sing a -> Sing a -> Bool # (>) :: Sing a -> Sing a -> Bool # (>=) :: Sing a -> Sing a -> Bool # max :: Sing a -> Sing a -> Sing a # min :: Sing a -> Sing a -> Sing a #
Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing [a]) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing b) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
Show (Sing a) #
Instance details Defined in Data.Singletons.TypeRepTYPE Methods showsPrec :: Int -> Sing a -> ShowS # show :: Sing a -> String # showList :: [Sing a] -> ShowS #
Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing b) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing b, ShowSing c) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing b, ShowSing c, ShowSing d) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing b, ShowSing c, ShowSing d, ShowSing e) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing b, ShowSing c, ShowSing d, ShowSing e, ShowSing f) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing b, ShowSing c, ShowSing d, ShowSing e, ShowSing f, ShowSing g) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing b) => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing m => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing (Maybe a) => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing (Maybe a) => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Monoid Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing (Maybe a) => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Monoid Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing Bool => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing Bool => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
ShowSing a => Show (Sing z) #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
(ShowSing a, ShowSing [a]) => Show (Sing z) #
Instance details Defined in Data.Singletons.ShowSing Methods showsPrec :: Int -> Sing z -> ShowS # show :: Sing z -> String # showList :: [Sing z] -> ShowS #
data Sing (a :: Bool) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (a :: Bool) where SFalse :: forall (a :: Bool). Sing False STrue :: forall (a :: Bool). Sing True
data Sing (a :: Ordering) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (a :: Ordering) where SLT :: forall (a :: Ordering). Sing LT SEQ :: forall (a :: Ordering). Sing EQ SGT :: forall (a :: Ordering). Sing GT
data Sing (n :: Nat) #
Instance details Defined in Data.Singletons.TypeLits.Internal data Sing (n :: Nat) where SNat :: forall (n :: Nat). KnownNat n => Sing n
data Sing (n :: Symbol) #
Instance details Defined in Data.Singletons.TypeLits.Internal data Sing (n :: Symbol) where SSym :: forall (n :: Symbol). KnownSymbol n => Sing n
data Sing (a :: ()) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (a :: ()) where STuple0 :: forall (a :: ()). Sing ()
data Sing (a :: Void) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (a :: Void)
data Sing (a :: All) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (a :: All) where SAll :: forall (a :: All) (n :: Bool). {..} -> Sing (All n)
data Sing (a :: Any) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (a :: Any) where SAny :: forall (a :: Any) (n :: Bool). {..} -> Sing (Any n)
data Sing (a :: PErrorMessage) #
Instance details Defined in Data.Singletons.TypeError data Sing (a :: PErrorMessage) where SText :: forall (a :: PErrorMessage) (t :: Symbol). Sing t -> Sing (Text t) SShowType :: forall (a :: PErrorMessage) t (ty :: t). Sing ty -> Sing (ShowType ty :: ErrorMessage' Symbol) (:%<>:) :: forall (a :: PErrorMessage) (e1 :: ErrorMessage' Symbol) (e2 :: ErrorMessage' Symbol). Sing e1 -> Sing e2 -> Sing (e1 :<>: e2) (:%$$:) :: forall (a :: PErrorMessage) (e1 :: ErrorMessage' Symbol) (e2 :: ErrorMessage' Symbol). Sing e1 -> Sing e2 -> Sing (e1 :$$: e2)
data Sing (b :: [a]) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (b :: [a]) where SNil :: forall k (b :: [k]). Sing ([] :: [k]) SCons :: forall a (b :: [a]) (n :: a) (n :: [a]). Sing n -> Sing n -> Sing (n ': n)
data Sing (b :: Maybe a) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (b :: Maybe a) where SNothing :: forall a (b :: Maybe a). Sing (Nothing :: Maybe a) SJust :: forall a (b :: Maybe a) (n :: a). Sing n -> Sing (Just n)
newtype Sing (a :: TYPE rep) #	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 -> Type` 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 newtype Sing (a :: TYPE rep) = STypeRep (TypeRep a)
data Sing (b :: Min a) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (b :: Min a) where SMin :: forall a (b :: Min a) (n :: a). {..} -> Sing (Min n)
data Sing (b :: Max a) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (b :: Max a) where SMax :: forall a (b :: Max a) (n :: a). {..} -> Sing (Max n)
data Sing (b :: First a) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (b :: First a) where SFirst :: forall a (b :: First a) (n :: a). {..} -> Sing (First n)
data Sing (b :: Last a) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (b :: Last a) where SLast :: forall a (b :: Last a) (n :: a). {..} -> Sing (Last n)
data Sing (a :: WrappedMonoid m) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (a :: WrappedMonoid m) where SWrapMonoid :: forall m (a :: WrappedMonoid m) (n :: m). {..} -> Sing (WrapMonoid n)
data Sing (b :: Option a) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (b :: Option a) where SOption :: forall a (b :: Option a) (n :: Maybe a). {..} -> Sing (Option n)
data Sing (b :: Identity a) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (b :: Identity a) where SIdentity :: forall a (b :: Identity a) (n :: a). {..} -> Sing (Identity n)
data Sing (b :: First a) #
Instance details Defined in Data.Singletons.Prelude.Monoid data Sing (b :: First a) where SFirst :: forall a (b :: First a) (n :: Maybe a). {..} -> Sing (First n)
data Sing (b :: Last a) #
Instance details Defined in Data.Singletons.Prelude.Monoid data Sing (b :: Last a) where SLast :: forall a (b :: Last a) (n :: Maybe a). {..} -> Sing (Last n)
data Sing (b :: Dual a) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (b :: Dual a) where SDual :: forall a (b :: Dual a) (n :: a). {..} -> Sing (Dual n)
data Sing (b :: Sum a) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (b :: Sum a) where SSum :: forall a (b :: Sum a) (n :: a). {..} -> Sing (Sum n)
data Sing (b :: Product a) #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal data Sing (b :: Product a) where SProduct :: forall a (b :: Product a) (n :: a). {..} -> Sing (Product n)
data Sing (b :: Down a) #
Instance details Defined in Data.Singletons.Prelude.Ord data Sing (b :: Down a) where SDown :: forall a (b :: Down a) (n :: a). Sing n -> Sing (Down n)
data Sing (b :: NonEmpty a) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (b :: NonEmpty a) where (:%\|) :: forall a (b :: NonEmpty a) (n :: a) (n :: [a]). Sing n -> Sing n -> Sing (n :\| n)
data Sing (c :: Either a b) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (c :: Either a b) where SLeft :: forall a b (c :: Either a b) (n :: a). Sing n -> Sing (Left n :: Either a b) SRight :: forall a b (c :: Either a b) (n :: b). Sing n -> Sing (Right n :: Either a b)
data Sing (c :: (a, b)) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (c :: (a, b)) where STuple2 :: forall a b (c :: (a, b)) (n :: a) (n :: b). Sing n -> Sing n -> Sing ((,) n n)
data Sing (c :: Arg a b) #
Instance details Defined in Data.Singletons.Prelude.Semigroup data Sing (c :: Arg a b) where SArg :: forall a b (c :: Arg a b) (n :: a) (n :: b). Sing n -> Sing n -> Sing (Arg n n)
newtype Sing (f :: k1 ~> k2) #
Instance details Defined in Data.Singletons.Internal newtype Sing (f :: k1 ~> k2) = SLambda { applySing :: forall (t :: k1). Sing t -> Sing (f @@ t) }
data Sing (d :: (a, b, c)) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (d :: (a, b, c)) where STuple3 :: forall a b c (d :: (a, b, c)) (n :: a) (n :: b) (n :: c). Sing n -> Sing n -> Sing n -> Sing ((,,) n n n)
data Sing (c :: Const a b) #
Instance details Defined in Data.Singletons.Prelude.Const data Sing (c :: Const a b) where SConst :: forall k a (b :: k) (c :: Const a b) (a :: a). {..} -> Sing (Const a :: Const a b)
data Sing (e :: (a, b, c, d)) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (e :: (a, b, c, d)) where STuple4 :: forall a b c d (e :: (a, b, c, d)) (n :: a) (n :: b) (n :: c) (n :: d). Sing n -> Sing n -> Sing n -> Sing n -> Sing ((,,,) n n n n)
data Sing (f :: (a, b, c, d, e)) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (f :: (a, b, c, d, e)) where STuple5 :: forall a b c d e (f :: (a, b, c, d, e)) (n :: a) (n :: b) (n :: c) (n :: d) (n :: e). Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing ((,,,,) n n n n n)
data Sing (g :: (a, b, c, d, e, f)) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (g :: (a, b, c, d, e, f)) where STuple6 :: forall a b c d e f (g :: (a, b, c, d, e, f)) (n :: a) (n :: b) (n :: c) (n :: d) (n :: e) (n :: f). Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing ((,,,,,) n n n n n n)
data Sing (h :: (a, b, c, d, e, f, g)) #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (h :: (a, b, c, d, e, f, g)) where STuple7 :: forall a b c d e f g (h :: (a, b, c, d, e, f, g)) (n :: a) (n :: b) (n :: c) (n :: d) (n :: e) (n :: f) (n :: g). Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing n -> Sing ((,,,,,,) n n n n n n n)

Though Haddock doesn't show it, the Sing instance above declares constructors

SFalse :: Sing False
STrue  :: Sing True

type SBool = (Sing :: Bool -> Type) #

SBool is a kind-restricted synonym for Sing: type SBool (a :: Bool) = Sing a

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 #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing NotSym0 #
SuppressUnusedWarnings NotSym0 #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () #
type Apply NotSym0 (a6989586621679378735 :: Bool) #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply NotSym0 (a6989586621679378735 :: Bool) = Not a6989586621679378735

type NotSym1 (a6989586621679378735 :: Bool) = Not a6989586621679378735 #

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

Instances

SingI (&&@#@$) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing (&&@#@$) #
SuppressUnusedWarnings (&&@#@$) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () #
type Apply (&&@#@$) (a6989586621679378194 :: Bool) #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (&&@#@$) (a6989586621679378194 :: Bool) = (&&@#@$$) a6989586621679378194

data (&&@#@$$) (a6989586621679378194 :: Bool) :: (~>) Bool Bool infixr 3 #

Instances

SingI x => SingI ((&&@#@$$) x :: TyFun Bool Bool -> Type) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing ((&&@#@$$) x) #
SuppressUnusedWarnings ((&&@#@$$) a6989586621679378194 :: TyFun Bool Bool -> Type) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () #
type Apply ((&&@#@$$) a6989586621679378194 :: TyFun Bool Bool -> Type) (b6989586621679378195 :: Bool) #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply ((&&@#@$$) a6989586621679378194 :: TyFun Bool Bool -> Type) (b6989586621679378195 :: Bool) = a6989586621679378194 && b6989586621679378195

type (&&@#@$$$) (a6989586621679378194 :: Bool) (b6989586621679378195 :: Bool) = (&&) a6989586621679378194 b6989586621679378195 #

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

Instances

SingI (\|\|@#@$) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing (\|\|@#@$) #
SuppressUnusedWarnings (\|\|@#@$) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () #
type Apply (\|\|@#@$) (a6989586621679378435 :: Bool) #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (\|\|@#@$) (a6989586621679378435 :: Bool) = (\|\|@#@$$) a6989586621679378435

data (||@#@$$) (a6989586621679378435 :: Bool) :: (~>) Bool Bool infixr 2 #

Instances

SingI x => SingI ((\|\|@#@$$) x :: TyFun Bool Bool -> Type) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing ((\|\|@#@$$) x) #
SuppressUnusedWarnings ((\|\|@#@$$) a6989586621679378435 :: TyFun Bool Bool -> Type) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () #
type Apply ((\|\|@#@$$) a6989586621679378435 :: TyFun Bool Bool -> Type) (b6989586621679378436 :: Bool) #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply ((\|\|@#@$$) a6989586621679378435 :: TyFun Bool Bool -> Type) (b6989586621679378436 :: Bool) = a6989586621679378435 \|\| b6989586621679378436

type (||@#@$$$) (a6989586621679378435 :: Bool) (b6989586621679378436 :: Bool) = (||) a6989586621679378435 b6989586621679378436 #

data Bool_Sym0 :: forall a6989586621679377443. (~>) a6989586621679377443 ((~>) a6989586621679377443 ((~>) Bool a6989586621679377443)) #

Instances

SingI (Bool_Sym0 :: TyFun a (a ~> (Bool ~> a)) -> Type) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing Bool_Sym0 #
SuppressUnusedWarnings (Bool_Sym0 :: TyFun a6989586621679377443 (a6989586621679377443 ~> (Bool ~> a6989586621679377443)) -> Type) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () #
type Apply (Bool_Sym0 :: TyFun a6989586621679377443 (a6989586621679377443 ~> (Bool ~> a6989586621679377443)) -> Type) (a6989586621679377449 :: a6989586621679377443) #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (Bool_Sym0 :: TyFun a6989586621679377443 (a6989586621679377443 ~> (Bool ~> a6989586621679377443)) -> Type) (a6989586621679377449 :: a6989586621679377443) = Bool_Sym1 a6989586621679377449

data Bool_Sym1 (a6989586621679377449 :: a6989586621679377443) :: (~>) a6989586621679377443 ((~>) Bool a6989586621679377443) #

Instances

SingI d => SingI (Bool_Sym1 d :: TyFun a (Bool ~> a) -> Type) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing (Bool_Sym1 d) #
SuppressUnusedWarnings (Bool_Sym1 a6989586621679377449 :: TyFun a6989586621679377443 (Bool ~> a6989586621679377443) -> Type) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () #
type Apply (Bool_Sym1 a6989586621679377449 :: TyFun a6989586621679377443 (Bool ~> a6989586621679377443) -> Type) (a6989586621679377450 :: a6989586621679377443) #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (Bool_Sym1 a6989586621679377449 :: TyFun a6989586621679377443 (Bool ~> a6989586621679377443) -> Type) (a6989586621679377450 :: a6989586621679377443) = Bool_Sym2 a6989586621679377449 a6989586621679377450

data Bool_Sym2 (a6989586621679377449 :: a6989586621679377443) (a6989586621679377450 :: a6989586621679377443) :: (~>) Bool a6989586621679377443 #

Instances

(SingI d1, SingI d2) => SingI (Bool_Sym2 d1 d2 :: TyFun Bool a -> Type) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing (Bool_Sym2 d1 d2) #
SuppressUnusedWarnings (Bool_Sym2 a6989586621679377450 a6989586621679377449 :: TyFun Bool a6989586621679377443 -> Type) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () #
type Apply (Bool_Sym2 a6989586621679377450 a6989586621679377449 :: TyFun Bool a -> Type) (a6989586621679377451 :: Bool) #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (Bool_Sym2 a6989586621679377450 a6989586621679377449 :: TyFun Bool a -> Type) (a6989586621679377451 :: Bool) = Bool_ a6989586621679377450 a6989586621679377449 a6989586621679377451

type Bool_Sym3 (a6989586621679377449 :: a6989586621679377443) (a6989586621679377450 :: a6989586621679377443) (a6989586621679377451 :: Bool) = Bool_ a6989586621679377449 a6989586621679377450 a6989586621679377451 #

type OtherwiseSym0 = Otherwise #

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

SingI (\|\|@#@$) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing (\|\|@#@$) #
SuppressUnusedWarnings (\|\|@#@$) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () #
type Apply (\|\|@#@$) (a6989586621679378435 :: Bool) #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (\|\|@#@$) (a6989586621679378435 :: Bool) = (\|\|@#@$$) a6989586621679378435

SingI x => SingI ((\|\|@#@$$) x :: TyFun Bool Bool -> Type) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods sing :: Sing ((\|\|@#@$$) x) #
SuppressUnusedWarnings ((\|\|@#@$$) a6989586621679378435 :: TyFun Bool Bool -> Type) #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () #
type Apply ((\|\|@#@$$) a6989586621679378435 :: TyFun Bool Bool -> Type) (b6989586621679378436 :: Bool) #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply ((\|\|@#@$$) a6989586621679378435 :: TyFun Bool Bool -> Type) (b6989586621679378436 :: Bool) = a6989586621679378435 \|\| b6989586621679378436

The Bool singleton

Conditionals

Singletons from Data.Bool

Defunctionalization symbols

The `Bool` singleton

Singletons from `Data.Bool`