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 Bool

data Sing Bool where

• SFalse :: Sing Bool z
• STrue :: Sing Bool z

data Sing Ordering

data Sing Ordering where

• SLT :: Sing Ordering z
• SEQ :: Sing Ordering z
• SGT :: Sing Ordering z

data Sing *

data Sing * where

• STypeRep :: Sing * a

data Sing Nat

data Sing Nat where

• SNat :: Sing Nat n

data Sing Symbol

data Sing Symbol where

• SSym :: Sing Symbol n

data Sing ()

data Sing () where

• STuple0 :: Sing () z

data Sing [a]

data Sing [a] where

• SNil :: Sing [a] z
• SCons :: Sing [a] z

data Sing (Maybe a)

data Sing (Maybe a) where

• SNothing :: Sing (Maybe a) z
• SJust :: Sing (Maybe a) z

data Sing (NonEmpty a)

data Sing (NonEmpty a) where

• (:%|) :: Sing (NonEmpty a) z

data Sing (Either a b)

data Sing (Either a b) where

• SLeft :: Sing (Either a b) z
• SRight :: Sing (Either a b) z

data Sing (a, b)

data Sing (a, b) where

• STuple2 :: Sing (a, b) z

data Sing ((~>) k1 k2)

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

• applySing :: forall (t :: k1). Sing k1 t -> Sing k2 ((@@) k1 k2 f t)

}

data Sing (a, b, c)

data Sing (a, b, c) where

• STuple3 :: Sing (a, b, c) z

data Sing (a, b, c, d)

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

• STuple4 :: Sing (a, b, c, d) z

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

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

• STuple5 :: Sing (a, b, c, d, e) z

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

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

• STuple6 :: Sing (a, b, c, d, e, f) z

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

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

• STuple7 :: Sing (a, b, c, d, e, f, g) z

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 k (cond :: Bool) (tru :: k) (fls :: k) :: k where ...

Type-level If. If True a b ==> a; If False a b ==> b

Equations

If k True tru fls = tru

If k False tru fls = 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) :: Bool where ...

Equations

Not False = TrueSym0

Not True = FalseSym0

sNot :: forall (t :: Bool). Sing t -> Sing (Apply NotSym0 t :: Bool)

type family (a :: Bool) :&& (a :: Bool) :: Bool where ... infixr 3

Equations

False :&& _z_6989586621679274680 = FalseSym0

True :&& x = x

type family (a :: Bool) :|| (a :: Bool) :: Bool where ... infixr 2

Equations

False :|| x = x

True :|| _z_6989586621679274668 = TrueSym0

(%:&&) :: forall (t :: Bool) (t :: Bool). Sing t -> Sing t -> Sing (Apply (Apply (:&&$) t) t :: Bool) infixr 3

(%:||) :: forall (t :: Bool) (t :: Bool). Sing t -> Sing t -> Sing (Apply (Apply (:||$) t) t :: Bool) infixr 2

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 (TyFun Bool Bool -> *) NotSym0

Methods

suppressUnusedWarnings :: Proxy NotSym0 t -> ()

type Apply Bool Bool NotSym0 l

type Apply Bool Bool NotSym0 l = Not l

type NotSym1 (t :: Bool) = Not t

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

Instances

SuppressUnusedWarnings (TyFun Bool (TyFun Bool Bool -> Type) -> *) (:&&$)

Methods

suppressUnusedWarnings :: Proxy (:&&$) t -> ()

type Apply Bool (TyFun Bool Bool -> Type) (:&&$) l

type Apply Bool (TyFun Bool Bool -> Type) (:&&$) l = (:&&$$) l

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

Instances

SuppressUnusedWarnings (Bool -> TyFun Bool Bool -> *) (:&&$$)

Methods

suppressUnusedWarnings :: Proxy (:&&$$) t -> ()

type Apply Bool Bool ((:&&$$) l1) l2

type Apply Bool Bool ((:&&$$) l1) l2 = (:&&) l1 l2

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

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

Instances

SuppressUnusedWarnings (TyFun Bool (TyFun Bool Bool -> Type) -> *) (:||$)

Methods

suppressUnusedWarnings :: Proxy (:||$) t -> ()

type Apply Bool (TyFun Bool Bool -> Type) (:||$) l

type Apply Bool (TyFun Bool Bool -> Type) (:||$) l = (:||$$) l

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

Instances

SuppressUnusedWarnings (Bool -> TyFun Bool Bool -> *) (:||$$)

Methods

suppressUnusedWarnings :: Proxy (:||$$) t -> ()

type Apply Bool Bool ((:||$$) l1) l2

type Apply Bool Bool ((:||$$) l1) l2 = (:||) l1 l2

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

data Bool_Sym0 (l :: TyFun a6989586621679274033 (TyFun a6989586621679274033 (TyFun Bool a6989586621679274033 -> Type) -> Type))

Instances

SuppressUnusedWarnings (TyFun a6989586621679274033 (TyFun a6989586621679274033 (TyFun Bool a6989586621679274033 -> Type) -> Type) -> *) (Bool_Sym0 a6989586621679274033)

Methods

suppressUnusedWarnings :: Proxy (Bool_Sym0 a6989586621679274033) t -> ()

type Apply a6989586621679274033 (TyFun a6989586621679274033 (TyFun Bool a6989586621679274033 -> Type) -> Type) (Bool_Sym0 a6989586621679274033) l

type Apply a6989586621679274033 (TyFun a6989586621679274033 (TyFun Bool a6989586621679274033 -> Type) -> Type) (Bool_Sym0 a6989586621679274033) l = Bool_Sym1 a6989586621679274033 l

data Bool_Sym1 (l :: a6989586621679274033) (l :: TyFun a6989586621679274033 (TyFun Bool a6989586621679274033 -> Type))

Instances

SuppressUnusedWarnings (a6989586621679274033 -> TyFun a6989586621679274033 (TyFun Bool a6989586621679274033 -> Type) -> *) (Bool_Sym1 a6989586621679274033)

Methods

suppressUnusedWarnings :: Proxy (Bool_Sym1 a6989586621679274033) t -> ()

type Apply a6989586621679274033 (TyFun Bool a6989586621679274033 -> Type) (Bool_Sym1 a6989586621679274033 l1) l2

type Apply a6989586621679274033 (TyFun Bool a6989586621679274033 -> Type) (Bool_Sym1 a6989586621679274033 l1) l2 = Bool_Sym2 a6989586621679274033 l1 l2

data Bool_Sym2 (l :: a6989586621679274033) (l :: a6989586621679274033) (l :: TyFun Bool a6989586621679274033)

Instances

SuppressUnusedWarnings (a6989586621679274033 -> a6989586621679274033 -> TyFun Bool a6989586621679274033 -> *) (Bool_Sym2 a6989586621679274033)

Methods

suppressUnusedWarnings :: Proxy (Bool_Sym2 a6989586621679274033) t -> ()

type Apply Bool a (Bool_Sym2 a l1 l2) l3

type Apply Bool a (Bool_Sym2 a l1 l2) l3 = Bool_ a l1 l2 l3

type Bool_Sym3 (t :: a6989586621679274033) (t :: a6989586621679274033) (t :: Bool) = Bool_ t t t

type OtherwiseSym0 = Otherwise