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

data family Sing (a :: k)

The singleton kind-indexed data family.

Instances

data Sing (z :: Bool)

data Sing (z :: Bool) where

• SFalse :: Sing False
• STrue :: Sing True

data Sing (z :: Ordering)

data Sing (z :: Ordering) where

• SLT :: Sing LT
• SEQ :: Sing EQ
• SGT :: Sing GT

data Sing (a :: Type)

data Sing (a :: Type) = STypeRep (TypeRep a)

data Sing (n :: Nat)

data Sing (n :: Nat) where

• SNat :: Sing n

data Sing (n :: Symbol)

data Sing (n :: Symbol) where

• SSym :: Sing n

data Sing (z :: ())

data Sing (z :: ()) where

• STuple0 :: Sing ()

data Sing (z :: Void)

data Sing (z :: Void)

data Sing (z :: [a])

data Sing (z :: [a]) where

• SNil :: Sing ([] :: [k])
• SCons :: Sing (n ': n)

data Sing (z :: Maybe a)

data Sing (z :: Maybe a) where

• SNothing :: Sing (Nothing :: Maybe a)
• SJust :: Sing (Just n)

data Sing (z :: NonEmpty a)

data Sing (z :: NonEmpty a) where

• (:%|) :: Sing (n :| n)

data Sing (z :: Either a b)

data Sing (z :: Either a b) where

• SLeft :: Sing (Left n :: Either a b)
• SRight :: Sing (Right n :: Either a b)

data Sing (z :: (a, b))

data Sing (z :: (a, b)) where

• STuple2 :: Sing ((,) n n)

data Sing (f :: k1 ~> k2)

data Sing (f :: k1 ~> k2) = SLambda {

• applySing :: forall (t :: k1). Sing t -> Sing (f @@ t)

}

data Sing (z :: (a, b, c))

data Sing (z :: (a, b, c)) where

• STuple3 :: Sing ((,,) n n n)

data Sing (z :: (a, b, c, d))

data Sing (z :: (a, b, c, d)) where

• STuple4 :: Sing ((,,,) n n n n)

data Sing (z :: (a, b, c, d, e))

data Sing (z :: (a, b, c, d, e)) where

• STuple5 :: Sing ((,,,,) n n n n n)

data Sing (z :: (a, b, c, d, e, f))

data Sing (z :: (a, b, c, d, e, f)) where

• STuple6 :: Sing ((,,,,,) n n n n n n)

data Sing (z :: (a, b, c, d, e, f, g))

data Sing (z :: (a, b, c, d, e, f, g)) where

• STuple7 :: 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: 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 (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 (l :: TyFun Bool Bool)

Instances

SuppressUnusedWarnings NotSym0

Methods

suppressUnusedWarnings :: ()

type Apply NotSym0 (l :: Bool)

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

type NotSym1 (t :: Bool) = Not t

data (&&@#@$) (l :: TyFun Bool (TyFun Bool Bool -> Type))

Instances

SuppressUnusedWarnings (&&@#@$)

Methods

suppressUnusedWarnings :: ()

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

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

data (l :: Bool) &&@#@$$ (l :: TyFun Bool Bool)

Instances

SuppressUnusedWarnings (&&@#@$$)

Methods

suppressUnusedWarnings :: ()

type Apply ((&&@#@$$) l1 :: TyFun Bool Bool -> *) (l2 :: Bool)

type Apply ((&&@#@$$) l1 :: TyFun Bool Bool -> *) (l2 :: Bool) = l1 && l2

type (&&@#@$$$) (t :: Bool) (t :: Bool) = (&&) t t

data (||@#@$) (l :: TyFun Bool (TyFun Bool Bool -> Type))

Instances

SuppressUnusedWarnings (||@#@$)

Methods

suppressUnusedWarnings :: ()

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

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

data (l :: Bool) ||@#@$$ (l :: TyFun Bool Bool)

Instances

SuppressUnusedWarnings (||@#@$$)

Methods

suppressUnusedWarnings :: ()

type Apply ((||@#@$$) l1 :: TyFun Bool Bool -> *) (l2 :: Bool)

type Apply ((||@#@$$) l1 :: TyFun Bool Bool -> *) (l2 :: Bool) = l1 || l2

type (||@#@$$$) (t :: Bool) (t :: Bool) = (||) t t

data Bool_Sym0 (l :: TyFun a6989586621679289682 (TyFun a6989586621679289682 (TyFun Bool a6989586621679289682 -> Type) -> Type))

Instances

SuppressUnusedWarnings (Bool_Sym0 :: TyFun a6989586621679289682 (TyFun a6989586621679289682 (TyFun Bool a6989586621679289682 -> Type) -> Type) -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (Bool_Sym0 :: TyFun a6989586621679289682 (TyFun a6989586621679289682 (TyFun Bool a6989586621679289682 -> Type) -> Type) -> *) (l :: a6989586621679289682)

type Apply (Bool_Sym0 :: TyFun a6989586621679289682 (TyFun a6989586621679289682 (TyFun Bool a6989586621679289682 -> Type) -> Type) -> *) (l :: a6989586621679289682) = Bool_Sym1 l

data Bool_Sym1 (l :: a6989586621679289682) (l :: TyFun a6989586621679289682 (TyFun Bool a6989586621679289682 -> Type))

Instances

SuppressUnusedWarnings (Bool_Sym1 :: a6989586621679289682 -> TyFun a6989586621679289682 (TyFun Bool a6989586621679289682 -> Type) -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (Bool_Sym1 l1 :: TyFun a6989586621679289682 (TyFun Bool a6989586621679289682 -> Type) -> *) (l2 :: a6989586621679289682)

type Apply (Bool_Sym1 l1 :: TyFun a6989586621679289682 (TyFun Bool a6989586621679289682 -> Type) -> *) (l2 :: a6989586621679289682) = Bool_Sym2 l1 l2

data Bool_Sym2 (l :: a6989586621679289682) (l :: a6989586621679289682) (l :: TyFun Bool a6989586621679289682)

Instances

SuppressUnusedWarnings (Bool_Sym2 :: a6989586621679289682 -> a6989586621679289682 -> TyFun Bool a6989586621679289682 -> *)

Methods

suppressUnusedWarnings :: ()

type Apply (Bool_Sym2 l1 l2 :: TyFun Bool a -> *) (l3 :: Bool)

type Apply (Bool_Sym2 l1 l2 :: TyFun Bool a -> *) (l3 :: Bool) = Bool_ l1 l2 l3

type Bool_Sym3 (t :: a6989586621679289682) (t :: a6989586621679289682) (t :: Bool) = Bool_ t t t

type OtherwiseSym0 = Otherwise