Data.Functor.Product.Singletons

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

The Product singleton

type family Sing :: k -> Type

Instances

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SAll

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SAny

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SVoid

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SOrdering

type Sing

Defined in Data.Singletons.Base.TypeError

type Sing = SErrorMessage

type Sing

Defined in GHC.TypeLits.Singletons.Internal

type Sing = SNat

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = STuple0

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SBool

type Sing

Defined in GHC.TypeLits.Singletons.Internal

type Sing = SChar

type Sing

Defined in GHC.TypeLits.Singletons.Internal

type Sing = SSymbol

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SIdentity :: Identity a -> Type

type Sing

Defined in Data.Monoid.Singletons

type Sing = SFirst :: First a -> Type

type Sing

Defined in Data.Monoid.Singletons

type Sing = SLast :: Last a -> Type

type Sing

Defined in Data.Ord.Singletons

type Sing = SDown :: Down a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SFirst :: First a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SLast :: Last a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SMax :: Max a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SMin :: Min a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SWrappedMonoid :: WrappedMonoid m -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SDual :: Dual a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SProduct :: Product a -> Type

type Sing

Defined in Data.Semigroup.Singletons.Internal

type Sing = SSum :: Sum a -> Type

type Sing

Defined in Data.Singletons.Base.Instances

type Sing = SNonEmpty :: NonEmpty a -> Type

type Sing

Defined in Data.Singletons.Base.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.Base.TypeRepTYPE

type Sing = TypeRep :: TYPE rep -> Type

type Sing

Defined in Data.Singletons.Base.Instances

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

type Sing

Defined in Data.Singletons.Base.Instances

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

type Sing

Defined in Data.Proxy.Singletons

type Sing = SProxy :: Proxy t -> Type

type Sing

Defined in Data.Semigroup.Singletons

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

type Sing

Defined in Data.Singletons

type Sing = SWrappedSing :: WrappedSing a -> Type

type Sing

Defined in Data.Singletons

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

type Sing

Defined in Data.Singletons.Base.Instances

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

type Sing

Defined in Data.Functor.Const.Singletons

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

type Sing

Defined in Data.Singletons.Base.Instances

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

type Sing

Defined in Data.Functor.Product.Singletons

type Sing = SProduct :: Product f g a -> Type

type Sing

Defined in Data.Functor.Sum.Singletons

type Sing = SSum :: Sum f g a -> Type

type Sing

Defined in Data.Singletons.Base.Instances

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

type Sing

Defined in Data.Functor.Compose.Singletons

type Sing = SCompose :: Compose f g a -> Type

type Sing

Defined in Data.Singletons.Base.Instances

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

type Sing

Defined in Data.Singletons.Base.Instances

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

type Sing

Defined in Data.Singletons.Base.Instances

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

data SProduct :: Product f g a -> Type where

Constructors

SPair :: forall f g a (x :: f a) (y :: g a). Sing x -> Sing y -> SProduct ('Pair @f @g @a x y)

Defunctionalization symbols

data PairSym0 z

Instances

SingI (PairSym0 :: TyFun (f a) (g a ~> Product f g a) -> Type)

Defined in Data.Functor.Product.Singletons

Methods

sing :: Sing PairSym0

type Apply (PairSym0 :: TyFun (f a) (g a ~> Product f g a) -> Type) (x :: f a)

Defined in Data.Functor.Product.Singletons

type Apply (PairSym0 :: TyFun (f a) (g a ~> Product f g a) -> Type) (x :: f a) = PairSym1 x :: TyFun (g a) (Product f g a) -> Type

data PairSym1 fa z

Instances

SingI1 (PairSym1 :: f a -> TyFun (g a) (Product f g a) -> Type)

Defined in Data.Functor.Product.Singletons

Methods

liftSing :: forall (x :: k1). Sing x -> Sing (PairSym1 x)

SingI x => SingI (PairSym1 x :: TyFun (g a) (Product f g a) -> Type)

Defined in Data.Functor.Product.Singletons

Methods

sing :: Sing (PairSym1 x)

type Apply (PairSym1 x :: TyFun (g a) (Product f g a) -> Type) (y :: g a)

Defined in Data.Functor.Product.Singletons

type Apply (PairSym1 x :: TyFun (g a) (Product f g a) -> Type) (y :: g a) = 'Pair x y

type family PairSym2 x y where ...

Equations

PairSym2 x y = 'Pair x y

Orphan instances

PAlternative (Product f g :: k -> Type)

Associated Types

type Empty :: f a

type arg <|> arg1 :: f a

PMonadPlus (Product f g :: k -> Type)

Associated Types

type Mzero :: m a

type Mplus arg arg1 :: m a

SingI2 ('Pair :: f a -> g a -> Product f g a)

Methods

liftSing2 :: forall (x :: k1) (y :: k2). Sing x -> Sing y -> Sing ('Pair x y)

SingI x => SingI1 ('Pair x :: g a -> Product f g a)

Methods

liftSing :: forall (x0 :: k1). Sing x0 -> Sing ('Pair x x0)

PApplicative (Product f g)

Associated Types

type Pure arg :: f a

type arg <*> arg1 :: f b

type LiftA2 arg arg1 arg2 :: f c

type arg *> arg1 :: f b

type arg <* arg1 :: f a

PFunctor (Product f g)

Associated Types

type Fmap arg arg1 :: f b

type arg <$ arg1 :: f a

PMonad (Product f g)

Associated Types

type arg >>= arg1 :: m b

type arg >> arg1 :: m b

type Return arg :: m a

(SAlternative f, SAlternative g) => SAlternative (Product f g)

Methods

sEmpty :: Sing EmptySym0

(%<|>) :: forall a (t1 :: Product f g a) (t2 :: Product f g a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<|>@#@$) t1) t2)

(SApplicative f, SApplicative g) => SApplicative (Product f g)

Methods

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

(%<*>) :: forall a b (t1 :: Product f g (a ~> b)) (t2 :: Product f g a). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<*>@#@$) t1) t2)

sLiftA2 :: forall a b c (t1 :: a ~> (b ~> c)) (t2 :: Product f g a) (t3 :: Product f g b). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply LiftA2Sym0 t1) t2) t3)

(%*>) :: forall a b (t1 :: Product f g a) (t2 :: Product f g b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (*>@#@$) t1) t2)

(%<*) :: forall a b (t1 :: Product f g a) (t2 :: Product f g b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<*@#@$) t1) t2)

(SFunctor f, SFunctor g) => SFunctor (Product f g)

Methods

sFmap :: forall a b (t1 :: a ~> b) (t2 :: Product f g a). Sing t1 -> Sing t2 -> Sing (Apply (Apply FmapSym0 t1) t2)

(%<$) :: forall a b (t1 :: a) (t2 :: Product f g b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (<$@#@$) t1) t2)

(SMonad f, SMonad g) => SMonad (Product f g)

Methods

(%>>=) :: forall a b (t1 :: Product f g a) (t2 :: a ~> Product f g b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>>=@#@$) t1) t2)

(%>>) :: forall a b (t1 :: Product f g a) (t2 :: Product f g b). Sing t1 -> Sing t2 -> Sing (Apply (Apply (>>@#@$) t1) t2)

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

(SMonadPlus f, SMonadPlus g) => SMonadPlus (Product f g)

Methods

sMzero :: Sing MzeroSym0

sMplus :: forall a (t1 :: Product f g a) (t2 :: Product f g a). Sing t1 -> Sing t2 -> Sing (Apply (Apply MplusSym0 t1) t2)

PMonadZip (Product f g)

Associated Types

type Mzip arg arg1 :: m (a, b)

type MzipWith arg arg1 arg2 :: m c

type Munzip arg :: (m a, m b)

(SMonadZip f, SMonadZip g) => SMonadZip (Product f g)

Methods

sMzip :: forall a b (t1 :: Product f g a) (t2 :: Product f g b). Sing t1 -> Sing t2 -> Sing (Apply (Apply MzipSym0 t1) t2)

sMzipWith :: forall a b c (t1 :: a ~> (b ~> c)) (t2 :: Product f g a) (t3 :: Product f g b). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply MzipWithSym0 t1) t2) t3)

sMunzip :: forall a b (t :: Product f g (a, b)). Sing t -> Sing (Apply MunzipSym0 t)

PFoldable (Product f g)

Associated Types

type Fold arg :: m

type FoldMap arg arg1 :: m

type Foldr arg arg1 arg2 :: b

type Foldr' arg arg1 arg2 :: b

type Foldl arg arg1 arg2 :: b

type Foldl' arg arg1 arg2 :: b

type Foldr1 arg arg1 :: a

type Foldl1 arg arg1 :: a

type ToList arg :: [a]

type Null arg :: Bool

type Length arg :: Natural

type Elem arg arg1 :: Bool

type Maximum arg :: a

type Minimum arg :: a

type Sum arg :: a

type Product arg :: a

(SFoldable f, SFoldable g) => SFoldable (Product f g)

Methods

sFold :: forall m (t1 :: Product f g m). SMonoid m => Sing t1 -> Sing (Apply FoldSym0 t1)

sFoldMap :: forall a m (t1 :: a ~> m) (t2 :: Product f g a). SMonoid m => Sing t1 -> Sing t2 -> Sing (Apply (Apply FoldMapSym0 t1) t2)

sFoldr :: forall a b (t1 :: a ~> (b ~> b)) (t2 :: b) (t3 :: Product f g a). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply FoldrSym0 t1) t2) t3)

sFoldr' :: forall a b (t1 :: a ~> (b ~> b)) (t2 :: b) (t3 :: Product f g a). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply Foldr'Sym0 t1) t2) t3)

sFoldl :: forall b a (t1 :: b ~> (a ~> b)) (t2 :: b) (t3 :: Product f g a). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply FoldlSym0 t1) t2) t3)

sFoldl' :: forall b a (t1 :: b ~> (a ~> b)) (t2 :: b) (t3 :: Product f g a). Sing t1 -> Sing t2 -> Sing t3 -> Sing (Apply (Apply (Apply Foldl'Sym0 t1) t2) t3)

sFoldr1 :: forall a (t1 :: a ~> (a ~> a)) (t2 :: Product f g a). Sing t1 -> Sing t2 -> Sing (Apply (Apply Foldr1Sym0 t1) t2)

sFoldl1 :: forall a (t1 :: a ~> (a ~> a)) (t2 :: Product f g a). Sing t1 -> Sing t2 -> Sing (Apply (Apply Foldl1Sym0 t1) t2)

sToList :: forall a (t1 :: Product f g a). Sing t1 -> Sing (Apply ToListSym0 t1)

sNull :: forall a (t1 :: Product f g a). Sing t1 -> Sing (Apply NullSym0 t1)

sLength :: forall a (t1 :: Product f g a). Sing t1 -> Sing (Apply LengthSym0 t1)

sElem :: forall a (t1 :: a) (t2 :: Product f g a). SEq a => Sing t1 -> Sing t2 -> Sing (Apply (Apply ElemSym0 t1) t2)

sMaximum :: forall a (t1 :: Product f g a). SOrd a => Sing t1 -> Sing (Apply MaximumSym0 t1)

sMinimum :: forall a (t1 :: Product f g a). SOrd a => Sing t1 -> Sing (Apply MinimumSym0 t1)

sSum :: forall a (t1 :: Product f g a). SNum a => Sing t1 -> Sing (Apply SumSym0 t1)

sProduct :: forall a (t1 :: Product f g a). SNum a => Sing t1 -> Sing (Apply ProductSym0 t1)

PTraversable (Product f g)

Associated Types

type Traverse arg arg1 :: f (t b)

type SequenceA arg :: f (t a)

type MapM arg arg1 :: m (t b)

type Sequence arg :: m (t a)

(STraversable f, STraversable g) => STraversable (Product f g)

Methods

sTraverse :: forall a (f0 :: Type -> Type) b (t1 :: a ~> f0 b) (t2 :: Product f g a). SApplicative f0 => Sing t1 -> Sing t2 -> Sing (Apply (Apply TraverseSym0 t1) t2)

sSequenceA :: forall (f0 :: Type -> Type) a (t1 :: Product f g (f0 a)). SApplicative f0 => Sing t1 -> Sing (Apply SequenceASym0 t1)

sMapM :: forall a (m :: Type -> Type) b (t1 :: a ~> m b) (t2 :: Product f g a). SMonad m => Sing t1 -> Sing t2 -> Sing (Apply (Apply MapMSym0 t1) t2)

sSequence :: forall (m :: Type -> Type) a (t1 :: Product f g (m a)). SMonad m => Sing t1 -> Sing (Apply SequenceSym0 t1)

(SingI x, SingI y) => SingI ('Pair x y :: Product f g a)

Methods

sing :: Sing ('Pair x y)