Data.Singletons.Prelude.Identity

Exports the promoted and singled versions of the Identity data type.

The Identity singleton

type family Sing

The singleton kind-indexed type family.

Instances

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = SBool

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = SOrdering

type Sing

Defined in Data.Singletons.TypeLits.Internal

type Sing = SNat

type Sing

Defined in Data.Singletons.TypeLits.Internal

type Sing = SSymbol

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = STuple0

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = SVoid

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SAll

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SAny

type Sing

Defined in Data.Singletons.TypeError

type Sing = SErrorMessage

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = SList :: [a] -> Type

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = SMaybe :: Maybe a -> Type

type Sing

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.

Defined in Data.Singletons.TypeRepTYPE

type Sing = TypeRep :: TYPE rep -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SMin :: Min a -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SMax :: Max a -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SFirst :: First a -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SLast :: Last a -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SWrappedMonoid :: WrappedMonoid m -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SOption :: Option a -> Type

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = SIdentity :: Identity a -> Type

type Sing

Defined in Data.Singletons.Prelude.Monoid

type Sing = SFirst :: First a -> Type

type Sing

Defined in Data.Singletons.Prelude.Monoid

type Sing = SLast :: Last a -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SDual :: Dual a -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SSum :: Sum a -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SProduct :: Product a -> Type

type Sing

Defined in Data.Singletons.Prelude.Ord

type Sing = SDown :: Down a -> Type

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = SNonEmpty :: NonEmpty a -> Type

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = SEither :: Either a b -> Type

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = STuple2 :: (a, b) -> Type

type Sing

Defined in Data.Singletons.Prelude.Semigroup

type Sing = SArg :: Arg a b -> Type

type Sing

Defined in Data.Singletons.Prelude.Proxy

type Sing = SProxy :: Proxy t -> Type

type Sing

Defined in Data.Singletons.Internal

type Sing = SLambda :: (k1 ~> k2) -> Type

type Sing

Defined in Data.Singletons.Internal

type Sing = SWrappedSing :: WrappedSing a -> Type

type Sing

Defined in Data.Singletons.Sigma

type Sing = SSigma :: Sigma s t -> Type

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = STuple3 :: (a, b, c) -> Type

type Sing

Defined in Data.Singletons.Prelude.Const

type Sing = SConst :: Const a b -> Type

type Sing

Defined in Data.Singletons.Prelude.Instances

type Sing = STuple4 :: (a, b, c, d) -> Type

type Sing

Defined in Data.Singletons.Prelude.Instances

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

type Sing

Defined in Data.Singletons.Prelude.Instances

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

type Sing

Defined in Data.Singletons.Prelude.Instances

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

data SIdentity z where

Constructors

SIdentity :: forall (a :: Type) (n :: a). (Sing n) -> SIdentity ('Identity n :: Identity (a :: Type))

Instances

SDecide a => TestCoercion (SIdentity :: Identity a -> Type)

Defined in Data.Singletons.Prelude.Instances

Methods

testCoercion :: forall (a0 :: k) (b :: k). SIdentity a0 -> SIdentity b -> Maybe (Coercion a0 b)

SDecide a => TestEquality (SIdentity :: Identity a -> Type)

Defined in Data.Singletons.Prelude.Instances

Methods

testEquality :: forall (a0 :: k) (b :: k). SIdentity a0 -> SIdentity b -> Maybe (a0 :~: b)

ShowSing a => Show (SIdentity z)

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> SIdentity z -> ShowS

show :: SIdentity z -> String

showList :: [SIdentity z] -> ShowS

type family RunIdentity a where ...

Equations

RunIdentity ('Identity field) = field

sRunIdentity :: forall (a :: Type) (t :: Identity (a :: Type)). Sing t -> Sing (Apply RunIdentitySym0 t :: a)

Defunctionalization symbols

data IdentitySym0 a6989586621679304610

Instances

SingI (IdentitySym0 :: TyFun a (Identity a) -> Type)

Defined in Data.Singletons.Prelude.Instances

Methods

sing :: Sing IdentitySym0

SuppressUnusedWarnings (IdentitySym0 :: TyFun a (Identity a) -> Type)

Defined in Data.Singletons.Prelude.Instances

Methods

suppressUnusedWarnings :: ()

type Apply (IdentitySym0 :: TyFun a (Identity a) -> Type) (a6989586621679304610 :: a)

Defined in Data.Singletons.Prelude.Instances

type Apply (IdentitySym0 :: TyFun a (Identity a) -> Type) (a6989586621679304610 :: a) = IdentitySym1 a6989586621679304610

type IdentitySym1 (a6989586621679304610 :: a) = 'Identity a6989586621679304610 :: Identity (a :: Type)

data RunIdentitySym0 a6989586621679304613

Instances

SingI (RunIdentitySym0 :: TyFun (Identity a) a -> Type)

Defined in Data.Singletons.Prelude.Instances

Methods

sing :: Sing RunIdentitySym0

SuppressUnusedWarnings (RunIdentitySym0 :: TyFun (Identity a) a -> Type)

Defined in Data.Singletons.Prelude.Instances

Methods

suppressUnusedWarnings :: ()

type Apply (RunIdentitySym0 :: TyFun (Identity a) a -> Type) (a6989586621679304613 :: Identity a)

Defined in Data.Singletons.Prelude.Instances

type Apply (RunIdentitySym0 :: TyFun (Identity a) a -> Type) (a6989586621679304613 :: Identity a) = RunIdentitySym1 a6989586621679304613

type RunIdentitySym1 (a6989586621679304613 :: Identity (a :: Type)) = RunIdentity a6989586621679304613 :: a

Orphan instances

SMonad Identity

Methods

(%>>=) :: forall a b (t :: Identity a) (t :: a ~> Identity b). Sing t -> Sing t -> Sing (Apply (Apply (>>=@#@$) t) t)

(%>>) :: forall a b (t :: Identity a) (t :: Identity b). Sing t -> Sing t -> Sing (Apply (Apply (>>@#@$) t) t)

sReturn :: forall a (t :: a). Sing t -> Sing (Apply ReturnSym0 t)

SApplicative Identity

Methods

sPure :: forall a (t :: a). Sing t -> Sing (Apply PureSym0 t)

(%<*>) :: forall a b (t :: Identity (a ~> b)) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply (<*>@#@$) t) t)

sLiftA2 :: forall a b c (t :: a ~> (b ~> c)) (t :: Identity a) (t :: Identity b). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply LiftA2Sym0 t) t) t)

(%*>) :: forall a b (t :: Identity a) (t :: Identity b). Sing t -> Sing t -> Sing (Apply (Apply (*>@#@$) t) t)

(%<*) :: forall a b (t :: Identity a) (t :: Identity b). Sing t -> Sing t -> Sing (Apply (Apply (<*@#@$) t) t)

SFunctor Identity

Methods

sFmap :: forall a b (t :: a ~> b) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply FmapSym0 t) t)

(%<$) :: forall a b (t :: a) (t :: Identity b). Sing t -> Sing t -> Sing (Apply (Apply (<$@#@$) t) t)

PMonad Identity

Associated Types

type arg >>= arg :: m b

type arg >> arg :: m b

type Return arg :: m a

PApplicative Identity

Associated Types

type Pure arg :: f a

type arg <*> arg :: f b

type LiftA2 arg arg arg :: f c

type arg *> arg :: f b

type arg <* arg :: f a

PFunctor Identity

Associated Types

type Fmap arg arg :: f b

type arg <$ arg :: f a

SFoldable Identity

Methods

sFold :: forall m (t :: Identity m). SMonoid m => Sing t -> Sing (Apply FoldSym0 t)

sFoldMap :: forall a m (t :: a ~> m) (t :: Identity a). SMonoid m => Sing t -> Sing t -> Sing (Apply (Apply FoldMapSym0 t) t)

sFoldr :: forall a b (t :: a ~> (b ~> b)) (t :: b) (t :: Identity a). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply FoldrSym0 t) t) t)

sFoldr' :: forall a b (t :: a ~> (b ~> b)) (t :: b) (t :: Identity a). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply Foldr'Sym0 t) t) t)

sFoldl :: forall b a (t :: b ~> (a ~> b)) (t :: b) (t :: Identity a). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply FoldlSym0 t) t) t)

sFoldl' :: forall b a (t :: b ~> (a ~> b)) (t :: b) (t :: Identity a). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply Foldl'Sym0 t) t) t)

sFoldr1 :: forall a (t :: a ~> (a ~> a)) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply Foldr1Sym0 t) t)

sFoldl1 :: forall a (t :: a ~> (a ~> a)) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply Foldl1Sym0 t) t)

sToList :: forall a (t :: Identity a). Sing t -> Sing (Apply ToListSym0 t)

sNull :: forall a (t :: Identity a). Sing t -> Sing (Apply NullSym0 t)

sLength :: forall a (t :: Identity a). Sing t -> Sing (Apply LengthSym0 t)

sElem :: forall a (t :: a) (t :: Identity a). SEq a => Sing t -> Sing t -> Sing (Apply (Apply ElemSym0 t) t)

sMaximum :: forall a (t :: Identity a). SOrd a => Sing t -> Sing (Apply MaximumSym0 t)

sMinimum :: forall a (t :: Identity a). SOrd a => Sing t -> Sing (Apply MinimumSym0 t)

sSum :: forall a (t :: Identity a). SNum a => Sing t -> Sing (Apply SumSym0 t)

sProduct :: forall a (t :: Identity a). SNum a => Sing t -> Sing (Apply ProductSym0 t)

PFoldable Identity

Associated Types

type Fold arg :: m

type FoldMap arg arg :: m

type Foldr arg arg arg :: b

type Foldr' arg arg arg :: b

type Foldl arg arg arg :: b

type Foldl' arg arg arg :: b

type Foldr1 arg arg :: a

type Foldl1 arg arg :: a

type ToList arg :: [a]

type Null arg :: Bool

type Length arg :: Nat

type Elem arg arg :: Bool

type Maximum arg :: a

type Minimum arg :: a

type Sum arg :: a

type Product arg :: a

SNum a => SNum (Identity a)

Methods

(%+) :: forall (t :: Identity a) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply (+@#@$) t) t)

(%-) :: forall (t :: Identity a) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply (-@#@$) t) t)

(%*) :: forall (t :: Identity a) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply (*@#@$) t) t)

sNegate :: forall (t :: Identity a). Sing t -> Sing (Apply NegateSym0 t)

sAbs :: forall (t :: Identity a). Sing t -> Sing (Apply AbsSym0 t)

sSignum :: forall (t :: Identity a). Sing t -> Sing (Apply SignumSym0 t)

sFromInteger :: forall (t :: Nat). Sing t -> Sing (Apply FromIntegerSym0 t)

PNum (Identity a)

Associated Types

type arg + arg :: a

type arg - arg :: a

type arg * arg :: a

type Negate arg :: a

type Abs arg :: a

type Signum arg :: a

type FromInteger arg :: a

SEnum a => SEnum (Identity a)

Methods

sSucc :: forall (t :: Identity a). Sing t -> Sing (Apply SuccSym0 t)

sPred :: forall (t :: Identity a). Sing t -> Sing (Apply PredSym0 t)

sToEnum :: forall (t :: Nat). Sing t -> Sing (Apply ToEnumSym0 t)

sFromEnum :: forall (t :: Identity a). Sing t -> Sing (Apply FromEnumSym0 t)

sEnumFromTo :: forall (t :: Identity a) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply EnumFromToSym0 t) t)

sEnumFromThenTo :: forall (t :: Identity a) (t :: Identity a) (t :: Identity a). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply EnumFromThenToSym0 t) t) t)

PEnum (Identity a)

Associated Types

type Succ arg :: a

type Pred arg :: a

type ToEnum arg :: a

type FromEnum arg :: Nat

type EnumFromTo arg arg :: [a]

type EnumFromThenTo arg arg arg :: [a]

SSemigroup a => SSemigroup (Identity a)

Methods

(%<>) :: forall (t :: Identity a) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply (<>@#@$) t) t)

sSconcat :: forall (t :: NonEmpty (Identity a)). Sing t -> Sing (Apply SconcatSym0 t)

PSemigroup (Identity a)

Associated Types

type arg <> arg :: a

type Sconcat arg :: a

SShow a => SShow (Identity a)

Methods

sShowsPrec :: forall (t :: Nat) (t :: Identity a) (t :: Symbol). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply ShowsPrecSym0 t) t) t)

sShow_ :: forall (t :: Identity a). Sing t -> Sing (Apply Show_Sym0 t)

sShowList :: forall (t :: [Identity a]) (t :: Symbol). Sing t -> Sing t -> Sing (Apply (Apply ShowListSym0 t) t)

PShow (Identity a)

Associated Types

type ShowsPrec arg arg arg :: Symbol

type Show_ arg :: Symbol

type ShowList arg arg :: Symbol

SMonoid a => SMonoid (Identity a)

Methods

sMempty :: Sing MemptySym0

sMappend :: forall (t :: Identity a) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply MappendSym0 t) t)

sMconcat :: forall (t :: [Identity a]). Sing t -> Sing (Apply MconcatSym0 t)

PMonoid (Identity a)

Associated Types

type Mempty :: a

type Mappend arg arg :: a

type Mconcat arg :: a