Copyright	(C) 2013-2014 Richard Eisenberg, Jan Stolarek
License	BSD-style (see LICENSE)
Maintainer	Richard Eisenberg (eir@cis.upenn.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

The `Bool` singleton

data family Sing a Source

The singleton kind-indexed data family.

Instances

data Sing Bool where SFalse :: (~) Bool z False => Sing Bool z STrue :: (~) Bool z True => Sing Bool z Source
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 Source
data Sing * where STypeRep :: Typeable * a => Sing * a Source
data Sing Nat where SNat :: KnownNat n => Sing Nat n Source
data Sing Symbol where SSym :: KnownSymbol n => Sing Symbol n Source
data Sing () where STuple0 :: (~) () z () => Sing () z Source
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 Source
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 Source
data Sing (TyFun k1 k2 -> *) = SLambda { applySing :: forall t. Sing k1 t -> Sing k2 ((@@) k2 k1 f t) } Source
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 Source
data Sing ((,) a0 b0) where STuple2 :: (~) ((,) a b) z ((,) a b n n) => Sing a n -> Sing b n -> Sing ((,) a b) z Source
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 Source
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 Source
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 Source
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 Source
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 Source

Though Haddock doesn't show it, the Sing instance above declares constructors

SFalse :: Sing False
STrue  :: Sing True

type SBool = (Sing :: Bool -> *) Source

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) Source

Conditional over singletons

Singletons from `Data.Bool`

type family Not a :: Bool Source

Equations

Not False = TrueSym0
Not True = FalseSym0

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

type family a :&& a :: Bool infixr 3 Source

Equations

False :&& _z_1627551223 = FalseSym0
True :&& x = x

type family a :|| a :: Bool infixr 2 Source

Equations

False :\|\| x = x
True :\|\| _z_1627551211 = TrueSym0

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

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

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 Source

type family Bool_ a a a :: a Source

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 :: a) Source

type family Otherwise :: Bool Source

Equations

Otherwise = TrueSym0

sOtherwise :: Sing (OtherwiseSym0 :: Bool) Source

Defunctionalization symbols

type TrueSym0 = True Source

type FalseSym0 = False Source

data NotSym0 l Source

Instances

SuppressUnusedWarnings (TyFun Bool Bool -> *) NotSym0 Source
type Apply Bool Bool NotSym0 l0 = NotSym1 l0 Source

type NotSym1 t = Not t Source

data (:&&$) l Source

Instances

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

data l :&&$$ l Source

Instances

SuppressUnusedWarnings (Bool -> TyFun Bool Bool -> *) (:&&$$) Source
type Apply Bool Bool ((:&&$$) l1) l0 = (:&&$$$) l1 l0 Source

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

data (:||$) l Source

Instances

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

data l :||$$ l Source

Instances

SuppressUnusedWarnings (Bool -> TyFun Bool Bool -> *) (:\|\|$$) Source
type Apply Bool Bool ((:\|\|$$) l1) l0 = (:\|\|$$$) l1 l0 Source

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

data Bool_Sym0 l Source

Instances

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

data Bool_Sym1 l l Source

Instances

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

data Bool_Sym2 l l l Source

Instances

SuppressUnusedWarnings (k -> k -> TyFun Bool k -> *) (Bool_Sym2 k) Source
type Apply k Bool (Bool_Sym2 k l1 l2) l0 = Bool_Sym3 k l1 l2 l0 Source

type Bool_Sym3 t t t = Bool_ t t t Source

type OtherwiseSym0 = Otherwise Source

The Bool singleton

Conditionals

Singletons from Data.Bool

Defunctionalization symbols

The `Bool` singleton

Singletons from `Data.Bool`