Copyright	(C) 2013-2014 Richard Eisenberg Jan Stolarek
License	BSD-style (see LICENSE)
Maintainer	Richard Eisenberg (rae@cs.brynmawr.edu)
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 (a :: k)
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 (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 (l :: TyFun Bool Bool)
type NotSym1 (t :: Bool) = Not t
data (&&@#@$) (l :: TyFun Bool (TyFun Bool Bool -> Type))
data (l :: Bool) &&@#@$$ (l :: TyFun Bool Bool)
type (&&@#@$$$) (t :: Bool) (t :: Bool) = (&&) t t
data (||@#@$) (l :: TyFun Bool (TyFun Bool Bool -> Type))
data (l :: Bool) ||@#@$$ (l :: TyFun Bool Bool)
type (||@#@$$$) (t :: Bool) (t :: Bool) = (||) t t
data Bool_Sym0 (l :: TyFun a6989586621679308852 (TyFun a6989586621679308852 (TyFun Bool a6989586621679308852 -> Type) -> Type))
data Bool_Sym1 (l :: a6989586621679308852) (l :: TyFun a6989586621679308852 (TyFun Bool a6989586621679308852 -> Type))
data Bool_Sym2 (l :: a6989586621679308852) (l :: a6989586621679308852) (l :: TyFun Bool a6989586621679308852)
type Bool_Sym3 (t :: a6989586621679308852) (t :: a6989586621679308852) (t :: Bool) = Bool_ t t t
type OtherwiseSym0 = Otherwise

The `Bool` singleton

data family Sing (a :: k) Source #

The singleton kind-indexed data family.

Instances

SDecide k => TestCoercion (Sing :: k -> *) #
Instance details Defined in Data.Singletons.Decide Methods testCoercion :: Sing a -> Sing b -> Maybe (Coercion a b) #
SDecide k => TestEquality (Sing :: k -> *) #
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.TypeRepStar Methods (==) :: Sing a -> Sing a -> Bool # (/=) :: Sing a -> Sing a -> Bool #
Ord (Sing a) #
Instance details Defined in Data.Singletons.TypeRepStar 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.TypeRepStar 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, 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 (z :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (z :: Bool) where SFalse :: Sing False STrue :: Sing True
data Sing (z :: Ordering) Source #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (z :: Ordering) where SLT :: Sing LT SEQ :: Sing EQ SGT :: Sing GT
data Sing (a :: Type) Source #
Instance details Defined in Data.Singletons.TypeRepStar data Sing (a :: Type) = STypeRep (TypeRep a)
data Sing (n :: Nat) Source #
Instance details Defined in Data.Singletons.TypeLits.Internal data Sing (n :: Nat) where SNat :: Sing n
data Sing (n :: Symbol) Source #
Instance details Defined in Data.Singletons.TypeLits.Internal data Sing (n :: Symbol) where SSym :: Sing n
data Sing (z :: ()) Source #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (z :: ()) where STuple0 :: Sing ()
data Sing (z :: Void) Source #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (z :: Void)
data Sing (z :: [a]) Source #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (z :: [a]) where SNil :: Sing ([] :: [k]) SCons :: Sing (n ': n)
data Sing (z :: Maybe a) Source #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (z :: Maybe a) where SNothing :: Sing (Nothing :: Maybe a) SJust :: Sing (Just n)
data Sing (z :: NonEmpty a) Source #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (z :: NonEmpty a) where (:%\|) :: Sing (n :\| n)
data Sing (z :: Either a b) Source #
Instance details Defined in Data.Singletons.Prelude.Instances 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)) Source #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (z :: (a, b)) where STuple2 :: Sing ((,) n n)
data Sing (f :: k1 ~> k2) Source #
Instance details Defined in Data.Singletons.Internal data Sing (f :: k1 ~> k2) = SLambda { applySing :: forall (t :: k1). Sing t -> Sing (f @@ t) }
data Sing (z :: (a, b, c)) Source #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (z :: (a, b, c)) where STuple3 :: Sing ((,,) n n n)
data Sing (z :: (a, b, c, d)) Source #
Instance details Defined in Data.Singletons.Prelude.Instances data Sing (z :: (a, b, c, d)) where STuple4 :: Sing ((,,,) n n n n)
data Sing (z :: (a, b, c, d, e)) Source #
Instance details Defined in Data.Singletons.Prelude.Instances 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)) Source #
Instance details Defined in Data.Singletons.Prelude.Instances 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)) Source #
Instance details Defined in Data.Singletons.Prelude.Instances 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) Source #

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) 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 :: a) (a :: Bool) :: a where ... Source #

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) Source #

type family Otherwise :: Bool where ... Source #

Equations

Otherwise = TrueSym0

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

Defunctionalization symbols

type TrueSym0 = True Source #

type FalseSym0 = False Source #

data NotSym0 (l :: TyFun Bool Bool) Source #

Instances

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

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

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

Instances

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

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

Instances

SuppressUnusedWarnings (&&@#@$$) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply ((&&@#@$$) l1 :: TyFun Bool Bool -> *) (l2 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply ((&&@#@$$) l1 :: TyFun Bool Bool -> *) (l2 :: Bool) = l1 && l2

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

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

Instances

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

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

Instances

SuppressUnusedWarnings (\|\|@#@$$) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply ((\|\|@#@$$) l1 :: TyFun Bool Bool -> *) (l2 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply ((\|\|@#@$$) l1 :: TyFun Bool Bool -> *) (l2 :: Bool) = l1 \|\| l2

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

data Bool_Sym0 (l :: TyFun a6989586621679308852 (TyFun a6989586621679308852 (TyFun Bool a6989586621679308852 -> Type) -> Type)) Source #

Instances

SuppressUnusedWarnings (Bool_Sym0 :: TyFun a6989586621679308852 (TyFun a6989586621679308852 (TyFun Bool a6989586621679308852 -> Type) -> Type) -> *) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply (Bool_Sym0 :: TyFun a6989586621679308852 (TyFun a6989586621679308852 (TyFun Bool a6989586621679308852 -> Type) -> Type) -> *) (l :: a6989586621679308852) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (Bool_Sym0 :: TyFun a6989586621679308852 (TyFun a6989586621679308852 (TyFun Bool a6989586621679308852 -> Type) -> Type) -> *) (l :: a6989586621679308852) = Bool_Sym1 l

data Bool_Sym1 (l :: a6989586621679308852) (l :: TyFun a6989586621679308852 (TyFun Bool a6989586621679308852 -> Type)) Source #

Instances

SuppressUnusedWarnings (Bool_Sym1 :: a6989586621679308852 -> TyFun a6989586621679308852 (TyFun Bool a6989586621679308852 -> Type) -> *) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply (Bool_Sym1 l1 :: TyFun a6989586621679308852 (TyFun Bool a6989586621679308852 -> Type) -> *) (l2 :: a6989586621679308852) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (Bool_Sym1 l1 :: TyFun a6989586621679308852 (TyFun Bool a6989586621679308852 -> Type) -> *) (l2 :: a6989586621679308852) = Bool_Sym2 l1 l2

data Bool_Sym2 (l :: a6989586621679308852) (l :: a6989586621679308852) (l :: TyFun Bool a6989586621679308852) Source #

Instances

SuppressUnusedWarnings (Bool_Sym2 :: a6989586621679308852 -> a6989586621679308852 -> TyFun Bool a6989586621679308852 -> *) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply (Bool_Sym2 l1 l2 :: TyFun Bool a -> *) (l3 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply (Bool_Sym2 l1 l2 :: TyFun Bool a -> *) (l3 :: Bool) = Bool_ l1 l2 l3

type Bool_Sym3 (t :: a6989586621679308852) (t :: a6989586621679308852) (t :: Bool) = Bool_ t t t Source #

type OtherwiseSym0 = Otherwise Source #

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

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

SuppressUnusedWarnings (\|\|@#@$$) Source #
Instance details Defined in Data.Singletons.Prelude.Bool Methods suppressUnusedWarnings :: () Source #
type Apply ((\|\|@#@$$) l1 :: TyFun Bool Bool -> *) (l2 :: Bool) Source #
Instance details Defined in Data.Singletons.Prelude.Bool type Apply ((\|\|@#@$$) l1 :: TyFun Bool Bool -> *) (l2 :: Bool) = l1 \|\| l2

The Bool singleton

Conditionals

Singletons from Data.Bool

Defunctionalization symbols

The `Bool` singleton

Singletons from `Data.Bool`