singletons-2.6: A framework for generating singleton types
Copyright(C) 2013-2014 Richard Eisenberg Jan Stolarek
LicenseBSD-style (see LICENSE)
MaintainerRyan Scott
Stabilityexperimental
Portabilitynon-portable
Safe HaskellNone
LanguageHaskell2010

Data.Singletons.Prelude.Bool

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

The Bool singleton

type family Sing :: k -> Type Source #

The singleton kind-indexed type family.

Instances

Instances details
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = SBool
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = SOrdering
type Sing Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Sing = SNat
type Sing Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Sing = SSymbol
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = STuple0
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = SVoid
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SAll
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SAny
type Sing Source # 
Instance details

Defined in Data.Singletons.TypeError

type Sing = SErrorMessage
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = SList :: [a] -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = SMaybe :: Maybe a -> Type
type Sing Source #

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` 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 TypeReps (for instance, TypeReps 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

type Sing = TypeRep :: TYPE rep -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = SNonEmpty :: NonEmpty a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

type Sing = SDown :: Down a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = SIdentity :: Identity a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SFirst :: First a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SLast :: Last a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SMax :: Max a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SMin :: Min a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SOption :: Option a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SWrappedMonoid :: WrappedMonoid m -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SDual :: Dual a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SProduct :: Product a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SSum :: Sum a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

type Sing = SFirst :: First a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

type Sing = SLast :: Last a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = SEither :: Either a b -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = STuple2 :: (a, b) -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Internal

type Sing = SLambda :: (k1 ~> k2) -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Internal

type Sing = SWrappedSing :: WrappedSing a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup

type Sing = SArg :: Arg a b -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Sigma

type Sing = SSigma :: Sigma s t -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = STuple3 :: (a, b, c) -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Const

type Sing = SConst :: Const a b -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = STuple4 :: (a, b, c, d) -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = STuple5 :: (a, b, c, d, e) -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = STuple6 :: (a, b, c, d, e, f) -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = STuple7 :: (a, b, c, d, e, f, g) -> Type

data SBool :: Bool -> Type where Source #

Constructors

SFalse :: SBool 'False 
STrue :: SBool 'True 

Instances

Instances details
TestCoercion SBool Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testCoercion :: forall (a :: k) (b :: k). SBool a -> SBool b -> Maybe (Coercion a b)

TestEquality SBool Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testEquality :: forall (a :: k) (b :: k). SBool a -> SBool b -> Maybe (a :~: b)

Show (SBool z) 
Instance details

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> SBool z -> ShowS

show :: SBool z -> String

showList :: [SBool z] -> ShowS

Conditionals

type family If (cond :: Bool) (tru :: k) (fls :: k) :: k where ... #

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 ... #

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 ... #

Equations

'False && a = 'False 
'True && a = a 
a && 'False = 'False 
a && 'True = a 
a && a = a 

type family (a :: Bool) || (b :: Bool) :: Bool where ... #

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 a (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 :: (~>) Bool Bool Source #

Instances

Instances details
SingI NotSym0 Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

Methods

sing :: Sing NotSym0 Source #

SuppressUnusedWarnings NotSym0 Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

Methods

suppressUnusedWarnings :: () Source #

type Apply NotSym0 (a6989586621679372930 :: Bool) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

type Apply NotSym0 (a6989586621679372930 :: Bool) = Not a6989586621679372930

type NotSym1 (a6989586621679372930 :: Bool) = Not a6989586621679372930 Source #

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

Instances

Instances details
SingI (&&@#@$) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

Methods

sing :: Sing (&&@#@$) Source #

SuppressUnusedWarnings (&&@#@$) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

Methods

suppressUnusedWarnings :: () Source #

type Apply (&&@#@$) (a6989586621679372398 :: Bool) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

type Apply (&&@#@$) (a6989586621679372398 :: Bool) = (&&@#@$$) a6989586621679372398

data (&&@#@$$) (a6989586621679372398 :: Bool) :: (~>) Bool Bool infixr 3 Source #

Instances

Instances details
SingI x => SingI ((&&@#@$$) x :: TyFun Bool Bool -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

Methods

sing :: Sing ((&&@#@$$) x) Source #

SuppressUnusedWarnings ((&&@#@$$) a6989586621679372398 :: TyFun Bool Bool -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

Methods

suppressUnusedWarnings :: () Source #

type Apply ((&&@#@$$) a6989586621679372398 :: TyFun Bool Bool -> Type) (b6989586621679372399 :: Bool) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

type Apply ((&&@#@$$) a6989586621679372398 :: TyFun Bool Bool -> Type) (b6989586621679372399 :: Bool) = a6989586621679372398 && b6989586621679372399

type (&&@#@$$$) (a6989586621679372398 :: Bool) (b6989586621679372399 :: Bool) = (&&) a6989586621679372398 b6989586621679372399 Source #

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

Instances

Instances details
SingI (||@#@$) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

Methods

sing :: Sing (||@#@$) Source #

SuppressUnusedWarnings (||@#@$) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

Methods

suppressUnusedWarnings :: () Source #

type Apply (||@#@$) (a6989586621679372636 :: Bool) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

type Apply (||@#@$) (a6989586621679372636 :: Bool) = (||@#@$$) a6989586621679372636

data (||@#@$$) (a6989586621679372636 :: Bool) :: (~>) Bool Bool infixr 2 Source #

Instances

Instances details
SingI x => SingI ((||@#@$$) x :: TyFun Bool Bool -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

Methods

sing :: Sing ((||@#@$$) x) Source #

SuppressUnusedWarnings ((||@#@$$) a6989586621679372636 :: TyFun Bool Bool -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

Methods

suppressUnusedWarnings :: () Source #

type Apply ((||@#@$$) a6989586621679372636 :: TyFun Bool Bool -> Type) (b6989586621679372637 :: Bool) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

type Apply ((||@#@$$) a6989586621679372636 :: TyFun Bool Bool -> Type) (b6989586621679372637 :: Bool) = a6989586621679372636 || b6989586621679372637

type (||@#@$$$) (a6989586621679372636 :: Bool) (b6989586621679372637 :: Bool) = (||) a6989586621679372636 b6989586621679372637 Source #

data Bool_Sym0 :: forall a6989586621679371636. (~>) a6989586621679371636 ((~>) a6989586621679371636 ((~>) Bool a6989586621679371636)) Source #

Instances

Instances details
SingI (Bool_Sym0 :: TyFun a (a ~> (Bool ~> a)) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

Methods

sing :: Sing Bool_Sym0 Source #

SuppressUnusedWarnings (Bool_Sym0 :: TyFun a6989586621679371636 (a6989586621679371636 ~> (Bool ~> a6989586621679371636)) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

Methods

suppressUnusedWarnings :: () Source #

type Apply (Bool_Sym0 :: TyFun a6989586621679371636 (a6989586621679371636 ~> (Bool ~> a6989586621679371636)) -> Type) (a6989586621679371642 :: a6989586621679371636) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

type Apply (Bool_Sym0 :: TyFun a6989586621679371636 (a6989586621679371636 ~> (Bool ~> a6989586621679371636)) -> Type) (a6989586621679371642 :: a6989586621679371636) = Bool_Sym1 a6989586621679371642

data Bool_Sym1 (a6989586621679371642 :: a6989586621679371636) :: (~>) a6989586621679371636 ((~>) Bool a6989586621679371636) Source #

Instances

Instances details
SingI d => SingI (Bool_Sym1 d :: TyFun a (Bool ~> a) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

Methods

sing :: Sing (Bool_Sym1 d) Source #

SuppressUnusedWarnings (Bool_Sym1 a6989586621679371642 :: TyFun a6989586621679371636 (Bool ~> a6989586621679371636) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

Methods

suppressUnusedWarnings :: () Source #

type Apply (Bool_Sym1 a6989586621679371642 :: TyFun a6989586621679371636 (Bool ~> a6989586621679371636) -> Type) (a6989586621679371643 :: a6989586621679371636) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

type Apply (Bool_Sym1 a6989586621679371642 :: TyFun a6989586621679371636 (Bool ~> a6989586621679371636) -> Type) (a6989586621679371643 :: a6989586621679371636) = Bool_Sym2 a6989586621679371642 a6989586621679371643

data Bool_Sym2 (a6989586621679371642 :: a6989586621679371636) (a6989586621679371643 :: a6989586621679371636) :: (~>) Bool a6989586621679371636 Source #

Instances

Instances details
(SingI d1, SingI d2) => SingI (Bool_Sym2 d1 d2 :: TyFun Bool a -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

Methods

sing :: Sing (Bool_Sym2 d1 d2) Source #

SuppressUnusedWarnings (Bool_Sym2 a6989586621679371643 a6989586621679371642 :: TyFun Bool a6989586621679371636 -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

Methods

suppressUnusedWarnings :: () Source #

type Apply (Bool_Sym2 a6989586621679371643 a6989586621679371642 :: TyFun Bool a -> Type) (a6989586621679371644 :: Bool) Source # 
Instance details

Defined in Data.Singletons.Prelude.Bool

type Apply (Bool_Sym2 a6989586621679371643 a6989586621679371642 :: TyFun Bool a -> Type) (a6989586621679371644 :: Bool) = Bool_ a6989586621679371643 a6989586621679371642 a6989586621679371644

type Bool_Sym3 (a6989586621679371642 :: a6989586621679371636) (a6989586621679371643 :: a6989586621679371636) (a6989586621679371644 :: Bool) = Bool_ a6989586621679371642 a6989586621679371643 a6989586621679371644 Source #

type OtherwiseSym0 = Otherwise Source #