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

The singleton kind-indexed data family.

Instances

TestCoercion * (Sing *)

SDecide k (KProxy k) => TestEquality k (Sing k)

data Sing Bool where

• SFalse :: (~) Bool z False => Sing Bool z
• STrue :: (~) Bool z True => Sing Bool z

data Sing Ordering where

• SLT :: (~) Ordering z LT => Sing Ordering z
• SEQ :: (~) Ordering z EQ => Sing Ordering z
• SGT :: (~) Ordering z GT => Sing Ordering z

data Sing * where

• STypeRep :: Typeable * a => Sing * a

data Sing Nat where

• SNat :: KnownNat n => Sing Nat n

data Sing Symbol where

• SSym :: KnownSymbol n => Sing Symbol n

data Sing () where

• STuple0 :: (~) () z () => Sing () z

data Sing [a0] where

• SNil :: (~) [a] z ([] a) => Sing [a] z
• SCons :: (~) [a] z ((:) a n n) => Sing a n -> Sing [a] n -> Sing [a] z

data Sing (Maybe a0) where

• SNothing :: (~) (Maybe a) z (Nothing a) => Sing (Maybe a) z
• SJust :: (~) (Maybe a) z (Just a n) => Sing a n -> Sing (Maybe a) z

data Sing (TyFun k1 k2 -> *) = SLambda {

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

}

data Sing (Either a0 b0) where

• SLeft :: (~) (Either a b) z (Left a b n) => Sing a n -> Sing (Either a b) z
• SRight :: (~) (Either a b) z (Right a b n) => Sing b n -> Sing (Either a b) z

data Sing ((,) a0 b0) where

• STuple2 :: (~) ((,) a b) z ((,) a b n n) => Sing a n -> Sing b n -> Sing ((,) a b) z

data Sing ((,,) a0 b0 c0) where

• STuple3 :: (~) ((,,) a b c) z ((,,) a b c n n n) => Sing a n -> Sing b n -> Sing c n -> Sing ((,,) a b c) z

data Sing ((,,,) a0 b0 c0 d0) where

• STuple4 :: (~) ((,,,) a b c d) z ((,,,) a b c d n n n n) => Sing a n -> Sing b n -> Sing c n -> Sing d n -> Sing ((,,,) a b c d) z

data Sing ((,,,,) a0 b0 c0 d0 e0) where

• STuple5 :: (~) ((,,,,) a b c d e) z ((,,,,) a b c d e n n n n n) => Sing a n -> Sing b n -> Sing c n -> Sing d n -> Sing e n -> Sing ((,,,,) a b c d e) z

data Sing ((,,,,,) a0 b0 c0 d0 e0 f0) where

• STuple6 :: (~) ((,,,,,) a b c d e f) z ((,,,,,) a b c d e f n n n n n n) => Sing a n -> Sing b n -> Sing c n -> Sing d n -> Sing e n -> Sing f n -> Sing ((,,,,,) a b c d e f) z

data Sing ((,,,,,,) a0 b0 c0 d0 e0 f0 g0) where

• STuple7 :: (~) ((,,,,,,) a b c d e f g) z ((,,,,,,) a b c d e f g n n n n n n n) => Sing a n -> Sing b n -> Sing c n -> Sing d n -> Sing e n -> Sing f n -> Sing g n -> 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 z = Sing z

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

Conditionals

type family If cond tru fls :: k

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

Equations

Not False = TrueSym0

Not True = FalseSym0

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

type family a :&& a :: Bool

Equations

False :&& z = FalseSym0

True :&& x = x

type family a :|| a :: Bool

Equations

False :|| x = x

True :|| z = TrueSym0

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

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

The following are derived from the function bool in Data.Bool. The extra underscore is to avoid name clashes with the type Bool.

bool_ :: forall a. a -> a -> Bool -> a

type family Bool_ a a a :: a

Equations

Bool_ fls _tru False = fls

Bool_ _fls tru True = tru

sBool_ :: forall t t t. Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply Bool_Sym0 t) t) t)

type Otherwise = (TrueSym0 :: Bool)

sOtherwise :: Sing OtherwiseSym0

Defunctionalization symbols

type TrueSym0 = True

type FalseSym0 = False

data NotSym0 l

Instances

SuppressUnusedWarnings (TyFun Bool Bool -> *) NotSym0

type Apply Bool Bool NotSym0 l0 = NotSym1 l0

type NotSym1 t = Not t

data (:&&$) l

Instances

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

type Apply (TyFun Bool Bool -> *) Bool (:&&$) l0 = (:&&$$) l0

data l :&&$$ l

Instances

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

type Apply Bool Bool ((:&&$$) l1) l0 = (:&&$$$) l1 l0

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

data (:||$) l

Instances

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

type Apply (TyFun Bool Bool -> *) Bool (:||$) l0 = (:||$$) l0

data l :||$$ l

Instances

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

type Apply Bool Bool ((:||$$) l1) l0 = (:||$$$) l1 l0

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

data Bool_Sym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k (TyFun Bool k -> *) -> *) -> *) (Bool_Sym0 k)

type Apply (TyFun k (TyFun Bool k -> *) -> *) k (Bool_Sym0 k) l0 = Bool_Sym1 k l0

data Bool_Sym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun k (TyFun Bool k -> *) -> *) (Bool_Sym1 k)

type Apply (TyFun Bool k -> *) k (Bool_Sym1 k l1) l0 = Bool_Sym2 k l1 l0

data Bool_Sym2 l l l

Instances

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

type Apply k Bool (Bool_Sym2 k l1 l2) l0 = Bool_Sym3 k l1 l2 l0

type Bool_Sym3 t t t = Bool_ t t t

type OtherwiseSym0 = Otherwise