Safe Haskell	None
Language	Haskell2010

Data.SOP

Contents

n-ary datatypes
Combinators
Utilities

Description

Main module of sop-core

Synopsis

data NP :: (k -> Type) -> [k] -> Type where
- Nil :: NP f '[]
- (:*) :: f x -> NP f xs -> NP f (x ': xs)
data NS :: (k -> Type) -> [k] -> Type where
- Z :: f x -> NS f (x ': xs)
- S :: NS f xs -> NS f (x ': xs)
newtype SOP (f :: k -> Type) (xss :: [[k]]) = SOP (NS (NP f) xss)
unSOP :: SOP f xss -> NS (NP f) xss
newtype POP (f :: k -> Type) (xss :: [[k]]) = POP (NP (NP f) xss)
unPOP :: POP f xss -> NP (NP f) xss
class HPure (h :: (k -> Type) -> l -> Type) where
- hpure :: SListIN h xs => (forall a. f a) -> h f xs
- hcpure :: AllN h c xs => proxy c -> (forall a. c a => f a) -> h f xs
hd :: NP f (x ': xs) -> f x
tl :: NP f (x ': xs) -> NP f xs
type Projection (f :: k -> Type) (xs :: [k]) = K (NP f xs) -.-> f
projections :: forall xs f. SListI xs => NP (Projection f xs) xs
shiftProjection :: Projection f xs a -> Projection f (x ': xs) a
newtype (f -.-> g) a = Fn {
- apFn :: f a -> g a
}
fn :: (f a -> f' a) -> (f -.-> f') a
fn_2 :: (f a -> f' a -> f'' a) -> (f -.-> (f' -.-> f'')) a
fn_3 :: (f a -> f' a -> f'' a -> f''' a) -> (f -.-> (f' -.-> (f'' -.-> f'''))) a
fn_4 :: (f a -> f' a -> f'' a -> f''' a -> f'''' a) -> (f -.-> (f' -.-> (f'' -.-> (f''' -.-> f'''')))) a
type family Prod (h :: (k -> Type) -> l -> Type) :: (k -> Type) -> l -> Type
class (Prod (Prod h) ~ Prod h, HPure (Prod h)) => HAp (h :: (k -> Type) -> l -> Type) where
- hap :: Prod h (f -.-> g) xs -> h f xs -> h g xs
hliftA :: (SListIN (Prod h) xs, HAp h) => (forall a. f a -> f' a) -> h f xs -> h f' xs
hliftA2 :: (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall a. f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs
hliftA3 :: (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall a. f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs
hcliftA :: (AllN (Prod h) c xs, HAp h) => proxy c -> (forall a. c a => f a -> f' a) -> h f xs -> h f' xs
hcliftA2 :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. c a => f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs
hcliftA3 :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. c a => f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs
hmap :: (SListIN (Prod h) xs, HAp h) => (forall a. f a -> f' a) -> h f xs -> h f' xs
hzipWith :: (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall a. f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs
hzipWith3 :: (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall a. f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs
hcmap :: (AllN (Prod h) c xs, HAp h) => proxy c -> (forall a. c a => f a -> f' a) -> h f xs -> h f' xs
hczipWith :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. c a => f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs
hczipWith3 :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. c a => f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs
type Injection (f :: k -> Type) (xs :: [k]) = f -.-> K (NS f xs)
injections :: forall xs f. SListI xs => NP (Injection f xs) xs
shift :: Injection f xs a -> Injection f (x ': xs) a
shiftInjection :: Injection f xs a -> Injection f (x ': xs) a
type family UnProd (h :: (k -> Type) -> l -> Type) :: (k -> Type) -> l -> Type
class UnProd (Prod h) ~ h => HApInjs (h :: (k -> Type) -> l -> Type) where
- hapInjs :: SListIN h xs => Prod h f xs -> [h f xs]
apInjs_NP :: SListI xs => NP f xs -> [NS f xs]
apInjs_POP :: SListI xss => POP f xss -> [SOP f xss]
unZ :: NS f '[x] -> f x
class HIndex (h :: (k -> Type) -> l -> Type) where
- hindex :: h f xs -> Int
hcliftA' :: (All2 c xss, Prod h ~ NP, HAp h) => proxy c -> (forall xs. All c xs => f xs -> f' xs) -> h f xss -> h f' xss
hcliftA2' :: (All2 c xss, Prod h ~ NP, HAp h) => proxy c -> (forall xs. All c xs => f xs -> f' xs -> f'' xs) -> Prod h f xss -> h f' xss -> h f'' xss
hcliftA3' :: (All2 c xss, Prod h ~ NP, HAp h) => proxy c -> (forall xs. All c xs => f xs -> f' xs -> f'' xs -> f''' xs) -> Prod h f xss -> Prod h f' xss -> h f'' xss -> h f''' xss
compare_NS :: forall r f g xs. r -> (forall x. f x -> g x -> r) -> r -> NS f xs -> NS g xs -> r
ccompare_NS :: forall c proxy r f g xs. All c xs => proxy c -> r -> (forall x. c x => f x -> g x -> r) -> r -> NS f xs -> NS g xs -> r
compare_SOP :: forall r f g xss. r -> (forall xs. NP f xs -> NP g xs -> r) -> r -> SOP f xss -> SOP g xss -> r
ccompare_SOP :: forall c proxy r f g xss. All2 c xss => proxy c -> r -> (forall xs. All c xs => NP f xs -> NP g xs -> r) -> r -> SOP f xss -> SOP g xss -> r
type family CollapseTo (h :: (k -> Type) -> l -> Type) (x :: Type) :: Type
class HCollapse (h :: (k -> Type) -> l -> Type) where
- hcollapse :: SListIN h xs => h (K a) xs -> CollapseTo h a
class HTraverse_ (h :: (k -> Type) -> l -> Type) where
- hctraverse_ :: (AllN h c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g ()) -> h f xs -> g ()
- htraverse_ :: (SListIN h xs, Applicative g) => (forall a. f a -> g ()) -> h f xs -> g ()
hcfoldMap :: (HTraverse_ h, AllN h c xs, Monoid m) => proxy c -> (forall a. c a => f a -> m) -> h f xs -> m
hcfor_ :: (HTraverse_ h, AllN h c xs, Applicative g) => proxy c -> h f xs -> (forall a. c a => f a -> g ()) -> g ()
class HAp h => HSequence (h :: (k -> Type) -> l -> Type) where
- hsequence' :: (SListIN h xs, Applicative f) => h (f :.: g) xs -> f (h g xs)
- hctraverse' :: (AllN h c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g (f' a)) -> h f xs -> g (h f' xs)
- htraverse' :: (SListIN h xs, Applicative g) => (forall a. f a -> g (f' a)) -> h f xs -> g (h f' xs)
hsequence :: (SListIN h xs, SListIN (Prod h) xs, HSequence h) => Applicative f => h f xs -> f (h I xs)
hsequenceK :: (SListIN h xs, SListIN (Prod h) xs, Applicative f, HSequence h) => h (K (f a)) xs -> f (h (K a) xs)
hctraverse :: (HSequence h, AllN h c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g a) -> h f xs -> g (h I xs)
hcfor :: (HSequence h, AllN h c xs, Applicative g) => proxy c -> h f xs -> (forall a. c a => f a -> g a) -> g (h I xs)
class HExpand (h :: (k -> Type) -> l -> Type) where
- hexpand :: SListIN (Prod h) xs => (forall x. f x) -> h f xs -> Prod h f xs
- hcexpand :: AllN (Prod h) c xs => proxy c -> (forall x. c x => f x) -> h f xs -> Prod h f xs
class (Same h1 ~ h2, Same h2 ~ h1) => HTrans (h1 :: (k1 -> Type) -> l1 -> Type) (h2 :: (k2 -> Type) -> l2 -> Type) where
- htrans :: AllZipN (Prod h1) c xs ys => proxy c -> (forall x y. c x y => f x -> g y) -> h1 f xs -> h2 g ys
- hcoerce :: (AllZipN (Prod h1) (LiftedCoercible f g) xs ys, HTrans h1 h2) => h1 f xs -> h2 g ys
hfromI :: (AllZipN (Prod h1) (LiftedCoercible I f) xs ys, HTrans h1 h2) => h1 I xs -> h2 f ys
htoI :: (AllZipN (Prod h1) (LiftedCoercible f I) xs ys, HTrans h1 h2) => h1 f xs -> h2 I ys
fromList :: SListI xs => [a] -> Maybe (NP (K a) xs)
newtype K (a :: Type) (b :: k) = K a
unK :: K a b -> a
newtype I (a :: Type) = I a
unI :: I a -> a
newtype ((f :: l -> Type) :.: (g :: k -> l)) (p :: k) = Comp (f (g p))
unComp :: (f :.: g) p -> f (g p)
mapII :: (a -> b) -> I a -> I b
mapIK :: (a -> b) -> I a -> K b c
mapKI :: (a -> b) -> K a c -> I b
mapKK :: (a -> b) -> K a c -> K b d
mapIII :: (a -> b -> c) -> I a -> I b -> I c
mapIIK :: (a -> b -> c) -> I a -> I b -> K c d
mapIKI :: (a -> b -> c) -> I a -> K b d -> I c
mapIKK :: (a -> b -> c) -> I a -> K b d -> K c e
mapKII :: (a -> b -> c) -> K a d -> I b -> I c
mapKIK :: (a -> b -> c) -> K a d -> I b -> K c e
mapKKI :: (a -> b -> c) -> K a d -> K b e -> I c
mapKKK :: (a -> b -> c) -> K a d -> K b e -> K c f
class (AllF c xs, SListI xs) => All (c :: k -> Constraint) (xs :: [k])
type All2 c = All (All c)
cpara_SList :: All c xs => proxy c -> r '[] -> (forall y ys. (c y, All c ys) => r ys -> r (y ': ys)) -> r xs
ccase_SList :: All c xs => proxy c -> r '[] -> (forall y ys. (c y, All c ys) => r (y ': ys)) -> r xs
class (SListI xs, SListI ys, SameShapeAs xs ys, SameShapeAs ys xs, AllZipF c xs ys) => AllZip (c :: a -> b -> Constraint) (xs :: [a]) (ys :: [b])
class (AllZipF (AllZip f) xss yss, SListI xss, SListI yss, SameShapeAs xss yss, SameShapeAs yss xss) => AllZip2 f xss yss
type family AllN (h :: (k -> Type) -> l -> Type) (c :: k -> Constraint) :: l -> Constraint
type family AllZipN (h :: (k -> Type) -> l -> Type) (c :: k1 -> k2 -> Constraint) :: l1 -> l2 -> Constraint
class f (g x) => Compose f g x
class (f x, g x) => And f g x
class Top x
class Coercible (f x) (g y) => LiftedCoercible f g x y
type family SameShapeAs (xs :: [a]) (ys :: [b]) :: Constraint where ...
data SList :: [k] -> Type where
- SNil :: SList '[]
- SCons :: SListI xs => SList (x ': xs)
type SListI = All Top
type SListI2 = All SListI
sList :: SListI xs => SList xs
para_SList :: SListI xs => r '[] -> (forall y ys. SListI ys => r ys -> r (y ': ys)) -> r xs
case_SList :: SListI xs => r '[] -> (forall y ys. SListI ys => r (y ': ys)) -> r xs
data Shape :: [k] -> Type where
- ShapeNil :: Shape '[]
- ShapeCons :: SListI xs => Shape xs -> Shape (x ': xs)
shape :: forall (xs :: [k]). SListI xs => Shape xs
lengthSList :: forall (xs :: [k]) proxy. SListI xs => proxy xs -> Int
data Proxy (t :: k) = Proxy

n-ary datatypes

data NP :: (k -> Type) -> [k] -> Type where Source #

An n-ary product.

The product is parameterized by a type constructor f and indexed by a type-level list xs. The length of the list determines the number of elements in the product, and if the i-th element of the list is of type x, then the i-th element of the product is of type f x.

The constructor names are chosen to resemble the names of the list constructors.

Two common instantiations of f are the identity functor I and the constant functor K. For I, the product becomes a heterogeneous list, where the type-level list describes the types of its components. For K a, the product becomes a homogeneous list, where the contents of the type-level list are ignored, but its length still specifies the number of elements.

In the context of the SOP approach to generic programming, an n-ary product describes the structure of the arguments of a single data constructor.

Examples:

I 'x'    :* I True  :* Nil  ::  NP I       '[ Char, Bool ]
K 0      :* K 1     :* Nil  ::  NP (K Int) '[ Char, Bool ]
Just 'x' :* Nothing :* Nil  ::  NP Maybe   '[ Char, Bool ]

Constructors

Nil :: NP f '[]
(:*) :: f x -> NP f xs -> NP f (x ': xs) infixr 5

Instances

Instances details

HTrans (NP :: (k1 -> Type) -> [k1] -> Type) (NP :: (k2 -> Type) -> [k2] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN (Prod NP) c xs ys => proxy c -> (forall (x :: k10) (y :: k20). c x y => f x -> g y) -> NP f xs -> NP g ys Source # hcoerce :: forall (f :: k10 -> Type) (g :: k20 -> Type) (xs :: l1) (ys :: l2). (AllZipN (Prod NP) (LiftedCoercible f g) xs ys, HTrans NP NP) => NP f xs -> NP g ys Source #
HSequence (NP :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hsequence' :: forall (xs :: l) f (g :: k0 -> Type). (SListIN NP xs, Applicative f) => NP (f :.: g) xs -> f (NP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. (AllN NP c xs, Applicative g) => proxy c -> (forall (a :: k0). c a => f a -> g (f' a)) -> NP f xs -> g (NP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. (SListIN NP xs, Applicative g) => (forall (a :: k0). f a -> g (f' a)) -> NP f xs -> g (NP f' xs) Source #
HTraverse_ (NP :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hctraverse_ :: forall c (xs :: l) g proxy f. (AllN NP c xs, Applicative g) => proxy c -> (forall (a :: k0). c a => f a -> g ()) -> NP f xs -> g () Source # htraverse_ :: forall (xs :: l) g f. (SListIN NP xs, Applicative g) => (forall (a :: k0). f a -> g ()) -> NP f xs -> g () Source #
HCollapse (NP :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hcollapse :: forall (xs :: l) a. SListIN NP xs => NP (K a) xs -> CollapseTo NP a Source #
HAp (NP :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hap :: forall (f :: k0 -> Type) (g :: k0 -> Type) (xs :: l). Prod NP (f -.-> g) xs -> NP f xs -> NP g xs Source #
HPure (NP :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hpure :: forall (xs :: l) f. SListIN NP xs => (forall (a :: k0). f a) -> NP f xs Source # hcpure :: forall c (xs :: l) proxy f. AllN NP c xs => proxy c -> (forall (a :: k0). c a => f a) -> NP f xs Source #
All (Compose Eq f) xs => Eq (NP f xs) Source #
Instance details Defined in Data.SOP.NP Methods (==) :: NP f xs -> NP f xs -> Bool # (/=) :: NP f xs -> NP f xs -> Bool #
(All (Compose Eq f) xs, All (Compose Ord f) xs) => Ord (NP f xs) Source #
Instance details Defined in Data.SOP.NP Methods compare :: NP f xs -> NP f xs -> Ordering # (<) :: NP f xs -> NP f xs -> Bool # (<=) :: NP f xs -> NP f xs -> Bool # (>) :: NP f xs -> NP f xs -> Bool # (>=) :: NP f xs -> NP f xs -> Bool # max :: NP f xs -> NP f xs -> NP f xs # min :: NP f xs -> NP f xs -> NP f xs #
All (Compose Show f) xs => Show (NP f xs) Source #
Instance details Defined in Data.SOP.NP Methods showsPrec :: Int -> NP f xs -> ShowS # show :: NP f xs -> String # showList :: [NP f xs] -> ShowS #
All (Compose Semigroup f) xs => Semigroup (NP f xs) Source #	Since: 0.4.0.0
Instance details Defined in Data.SOP.NP Methods (<>) :: NP f xs -> NP f xs -> NP f xs # sconcat :: NonEmpty (NP f xs) -> NP f xs # stimes :: Integral b => b -> NP f xs -> NP f xs #
(All (Compose Monoid f) xs, All (Compose Semigroup f) xs) => Monoid (NP f xs) Source #	Since: 0.4.0.0
Instance details Defined in Data.SOP.NP Methods mempty :: NP f xs # mappend :: NP f xs -> NP f xs -> NP f xs # mconcat :: [NP f xs] -> NP f xs #
All (Compose NFData f) xs => NFData (NP f xs) Source #	Since: 0.2.5.0
Instance details Defined in Data.SOP.NP Methods rnf :: NP f xs -> () #
type AllZipN (NP :: (k -> Type) -> [k] -> Type) (c :: a -> b -> Constraint) Source #
Instance details Defined in Data.SOP.NP type AllZipN (NP :: (k -> Type) -> [k] -> Type) (c :: a -> b -> Constraint) = AllZip c
type Same (NP :: (k1 -> Type) -> [k1] -> Type) Source #
Instance details Defined in Data.SOP.NP type Same (NP :: (k1 -> Type) -> [k1] -> Type) = NP :: (k2 -> Type) -> [k2] -> Type
type SListIN (NP :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NP type SListIN (NP :: (k -> Type) -> [k] -> Type) = SListI :: [k] -> Constraint
type UnProd (NP :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS type UnProd (NP :: (k -> Type) -> [k] -> Type) = NS :: (k -> Type) -> [k] -> Type
type Prod (NP :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NP type Prod (NP :: (k -> Type) -> [k] -> Type) = NP :: (k -> Type) -> [k] -> Type
type AllN (NP :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) Source #
Instance details Defined in Data.SOP.NP type AllN (NP :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) = All c
type CollapseTo (NP :: (k -> Type) -> [k] -> Type) a Source #
Instance details Defined in Data.SOP.NP type CollapseTo (NP :: (k -> Type) -> [k] -> Type) a = [a]

data NS :: (k -> Type) -> [k] -> Type where Source #

An n-ary sum.

The sum is parameterized by a type constructor f and indexed by a type-level list xs. The length of the list determines the number of choices in the sum and if the i-th element of the list is of type x, then the i-th choice of the sum is of type f x.

The constructor names are chosen to resemble Peano-style natural numbers, i.e., Z is for "zero", and S is for "successor". Chaining S and Z chooses the corresponding component of the sum.

Examples:

Z         :: f x -> NS f (x ': xs)
S . Z     :: f y -> NS f (x ': y ': xs)
S . S . Z :: f z -> NS f (x ': y ': z ': xs)
...

Note that empty sums (indexed by an empty list) have no non-bottom elements.

Two common instantiations of f are the identity functor I and the constant functor K. For I, the sum becomes a direct generalization of the Either type to arbitrarily many choices. For K a, the result is a homogeneous choice type, where the contents of the type-level list are ignored, but its length specifies the number of options.

In the context of the SOP approach to generic programming, an n-ary sum describes the top-level structure of a datatype, which is a choice between all of its constructors.

Examples:

Z (I 'x')      :: NS I       '[ Char, Bool ]
S (Z (I True)) :: NS I       '[ Char, Bool ]
S (Z (K 1))    :: NS (K Int) '[ Char, Bool ]

Constructors

Z :: f x -> NS f (x ': xs)
S :: NS f xs -> NS f (x ': xs)

Instances

Instances details

HTrans (NS :: (k1 -> Type) -> [k1] -> Type) (NS :: (k2 -> Type) -> [k2] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN (Prod NS) c xs ys => proxy c -> (forall (x :: k10) (y :: k20). c x y => f x -> g y) -> NS f xs -> NS g ys Source # hcoerce :: forall (f :: k10 -> Type) (g :: k20 -> Type) (xs :: l1) (ys :: l2). (AllZipN (Prod NS) (LiftedCoercible f g) xs ys, HTrans NS NS) => NS f xs -> NS g ys Source #
HExpand (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hexpand :: forall (xs :: l) f. SListIN (Prod NS) xs => (forall (x :: k0). f x) -> NS f xs -> Prod NS f xs Source # hcexpand :: forall c (xs :: l) proxy f. AllN (Prod NS) c xs => proxy c -> (forall (x :: k0). c x => f x) -> NS f xs -> Prod NS f xs Source #
HApInjs (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hapInjs :: forall (xs :: l) (f :: k0 -> Type). SListIN NS xs => Prod NS f xs -> [NS f xs] Source #
HIndex (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hindex :: forall (f :: k0 -> Type) (xs :: l). NS f xs -> Int Source #
HSequence (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hsequence' :: forall (xs :: l) f (g :: k0 -> Type). (SListIN NS xs, Applicative f) => NS (f :.: g) xs -> f (NS g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. (AllN NS c xs, Applicative g) => proxy c -> (forall (a :: k0). c a => f a -> g (f' a)) -> NS f xs -> g (NS f' xs) Source # htraverse' :: forall (xs :: l) g f f'. (SListIN NS xs, Applicative g) => (forall (a :: k0). f a -> g (f' a)) -> NS f xs -> g (NS f' xs) Source #
HTraverse_ (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hctraverse_ :: forall c (xs :: l) g proxy f. (AllN NS c xs, Applicative g) => proxy c -> (forall (a :: k0). c a => f a -> g ()) -> NS f xs -> g () Source # htraverse_ :: forall (xs :: l) g f. (SListIN NS xs, Applicative g) => (forall (a :: k0). f a -> g ()) -> NS f xs -> g () Source #
HCollapse (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hcollapse :: forall (xs :: l) a. SListIN NS xs => NS (K a) xs -> CollapseTo NS a Source #
HAp (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hap :: forall (f :: k0 -> Type) (g :: k0 -> Type) (xs :: l). Prod NS (f -.-> g) xs -> NS f xs -> NS g xs Source #
All (Compose Eq f) xs => Eq (NS f xs) Source #
Instance details Defined in Data.SOP.NS Methods (==) :: NS f xs -> NS f xs -> Bool # (/=) :: NS f xs -> NS f xs -> Bool #
(All (Compose Eq f) xs, All (Compose Ord f) xs) => Ord (NS f xs) Source #
Instance details Defined in Data.SOP.NS Methods compare :: NS f xs -> NS f xs -> Ordering # (<) :: NS f xs -> NS f xs -> Bool # (<=) :: NS f xs -> NS f xs -> Bool # (>) :: NS f xs -> NS f xs -> Bool # (>=) :: NS f xs -> NS f xs -> Bool # max :: NS f xs -> NS f xs -> NS f xs # min :: NS f xs -> NS f xs -> NS f xs #
All (Compose Show f) xs => Show (NS f xs) Source #
Instance details Defined in Data.SOP.NS Methods showsPrec :: Int -> NS f xs -> ShowS # show :: NS f xs -> String # showList :: [NS f xs] -> ShowS #
All (Compose NFData f) xs => NFData (NS f xs) Source #	Since: 0.2.5.0
Instance details Defined in Data.SOP.NS Methods rnf :: NS f xs -> () #
type Same (NS :: (k1 -> Type) -> [k1] -> Type) Source #
Instance details Defined in Data.SOP.NS type Same (NS :: (k1 -> Type) -> [k1] -> Type) = NS :: (k2 -> Type) -> [k2] -> Type
type SListIN (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS type SListIN (NS :: (k -> Type) -> [k] -> Type) = SListI :: [k] -> Constraint
type Prod (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS type Prod (NS :: (k -> Type) -> [k] -> Type) = NP :: (k -> Type) -> [k] -> Type
type AllN (NS :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) Source #
Instance details Defined in Data.SOP.NS type AllN (NS :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) = All c
type CollapseTo (NS :: (k -> Type) -> [k] -> Type) a Source #
Instance details Defined in Data.SOP.NS type CollapseTo (NS :: (k -> Type) -> [k] -> Type) a = a

newtype SOP (f :: k -> Type) (xss :: [[k]]) Source #

A sum of products.

This is a 'newtype' for an NS of an NP. The elements of the (inner) products are applications of the parameter f. The type SOP is indexed by the list of lists that determines the sizes of both the (outer) sum and all the (inner) products, as well as the types of all the elements of the inner products.

A SOP I reflects the structure of a normal Haskell datatype. The sum structure represents the choice between the different constructors, the product structure represents the arguments of each constructor.

Constructors

SOP (NS (NP f) xss)

Instances

Instances details

HTrans (SOP :: (k1 -> Type) -> [[k1]] -> Type) (SOP :: (k2 -> Type) -> [[k2]] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN (Prod SOP) c xs ys => proxy c -> (forall (x :: k10) (y :: k20). c x y => f x -> g y) -> SOP f xs -> SOP g ys Source # hcoerce :: forall (f :: k10 -> Type) (g :: k20 -> Type) (xs :: l1) (ys :: l2). (AllZipN (Prod SOP) (LiftedCoercible f g) xs ys, HTrans SOP SOP) => SOP f xs -> SOP g ys Source #
HExpand (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hexpand :: forall (xs :: l) f. SListIN (Prod SOP) xs => (forall (x :: k0). f x) -> SOP f xs -> Prod SOP f xs Source # hcexpand :: forall c (xs :: l) proxy f. AllN (Prod SOP) c xs => proxy c -> (forall (x :: k0). c x => f x) -> SOP f xs -> Prod SOP f xs Source #
HApInjs (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hapInjs :: forall (xs :: l) (f :: k0 -> Type). SListIN SOP xs => Prod SOP f xs -> [SOP f xs] Source #
HIndex (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hindex :: forall (f :: k0 -> Type) (xs :: l). SOP f xs -> Int Source #
HSequence (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hsequence' :: forall (xs :: l) f (g :: k0 -> Type). (SListIN SOP xs, Applicative f) => SOP (f :.: g) xs -> f (SOP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. (AllN SOP c xs, Applicative g) => proxy c -> (forall (a :: k0). c a => f a -> g (f' a)) -> SOP f xs -> g (SOP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. (SListIN SOP xs, Applicative g) => (forall (a :: k0). f a -> g (f' a)) -> SOP f xs -> g (SOP f' xs) Source #
HTraverse_ (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hctraverse_ :: forall c (xs :: l) g proxy f. (AllN SOP c xs, Applicative g) => proxy c -> (forall (a :: k0). c a => f a -> g ()) -> SOP f xs -> g () Source # htraverse_ :: forall (xs :: l) g f. (SListIN SOP xs, Applicative g) => (forall (a :: k0). f a -> g ()) -> SOP f xs -> g () Source #
HCollapse (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hcollapse :: forall (xs :: l) a. SListIN SOP xs => SOP (K a) xs -> CollapseTo SOP a Source #
HAp (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hap :: forall (f :: k0 -> Type) (g :: k0 -> Type) (xs :: l). Prod SOP (f -.-> g) xs -> SOP f xs -> SOP g xs Source #
Eq (NS (NP f) xss) => Eq (SOP f xss) Source #
Instance details Defined in Data.SOP.NS Methods (==) :: SOP f xss -> SOP f xss -> Bool # (/=) :: SOP f xss -> SOP f xss -> Bool #
Ord (NS (NP f) xss) => Ord (SOP f xss) Source #
Instance details Defined in Data.SOP.NS Methods compare :: SOP f xss -> SOP f xss -> Ordering # (<) :: SOP f xss -> SOP f xss -> Bool # (<=) :: SOP f xss -> SOP f xss -> Bool # (>) :: SOP f xss -> SOP f xss -> Bool # (>=) :: SOP f xss -> SOP f xss -> Bool # max :: SOP f xss -> SOP f xss -> SOP f xss # min :: SOP f xss -> SOP f xss -> SOP f xss #
Show (NS (NP f) xss) => Show (SOP f xss) Source #
Instance details Defined in Data.SOP.NS Methods showsPrec :: Int -> SOP f xss -> ShowS # show :: SOP f xss -> String # showList :: [SOP f xss] -> ShowS #
NFData (NS (NP f) xss) => NFData (SOP f xss) Source #	Since: 0.2.5.0
Instance details Defined in Data.SOP.NS Methods rnf :: SOP f xss -> () #
type Same (SOP :: (k1 -> Type) -> [[k1]] -> Type) Source #
Instance details Defined in Data.SOP.NS type Same (SOP :: (k1 -> Type) -> [[k1]] -> Type) = SOP :: (k2 -> Type) -> [[k2]] -> Type
type SListIN (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS type SListIN (SOP :: (k -> Type) -> [[k]] -> Type) = SListI2 :: [[k]] -> Constraint
type Prod (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS type Prod (SOP :: (k -> Type) -> [[k]] -> Type) = POP :: (k -> Type) -> [[k]] -> Type
type AllN (SOP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) Source #
Instance details Defined in Data.SOP.NS type AllN (SOP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) = All2 c
type CollapseTo (SOP :: (k -> Type) -> [[k]] -> Type) a Source #
Instance details Defined in Data.SOP.NS type CollapseTo (SOP :: (k -> Type) -> [[k]] -> Type) a = [a]

unSOP :: SOP f xss -> NS (NP f) xss Source #

Unwrap a sum of products.

newtype POP (f :: k -> Type) (xss :: [[k]]) Source #

A product of products.

This is a 'newtype' for an NP of an NP. The elements of the inner products are applications of the parameter f. The type POP is indexed by the list of lists that determines the lengths of both the outer and all the inner products, as well as the types of all the elements of the inner products.

A POP is reminiscent of a two-dimensional table (but the inner lists can all be of different length). In the context of the SOP approach to generic programming, a POP is useful to represent information that is available for all arguments of all constructors of a datatype.

Constructors

POP (NP (NP f) xss)

Instances

Instances details

HTrans (POP :: (k1 -> Type) -> [[k1]] -> Type) (POP :: (k2 -> Type) -> [[k2]] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN (Prod POP) c xs ys => proxy c -> (forall (x :: k10) (y :: k20). c x y => f x -> g y) -> POP f xs -> POP g ys Source # hcoerce :: forall (f :: k10 -> Type) (g :: k20 -> Type) (xs :: l1) (ys :: l2). (AllZipN (Prod POP) (LiftedCoercible f g) xs ys, HTrans POP POP) => POP f xs -> POP g ys Source #
HSequence (POP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hsequence' :: forall (xs :: l) f (g :: k0 -> Type). (SListIN POP xs, Applicative f) => POP (f :.: g) xs -> f (POP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. (AllN POP c xs, Applicative g) => proxy c -> (forall (a :: k0). c a => f a -> g (f' a)) -> POP f xs -> g (POP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. (SListIN POP xs, Applicative g) => (forall (a :: k0). f a -> g (f' a)) -> POP f xs -> g (POP f' xs) Source #
HTraverse_ (POP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hctraverse_ :: forall c (xs :: l) g proxy f. (AllN POP c xs, Applicative g) => proxy c -> (forall (a :: k0). c a => f a -> g ()) -> POP f xs -> g () Source # htraverse_ :: forall (xs :: l) g f. (SListIN POP xs, Applicative g) => (forall (a :: k0). f a -> g ()) -> POP f xs -> g () Source #
HCollapse (POP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hcollapse :: forall (xs :: l) a. SListIN POP xs => POP (K a) xs -> CollapseTo POP a Source #
HAp (POP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hap :: forall (f :: k0 -> Type) (g :: k0 -> Type) (xs :: l). Prod POP (f -.-> g) xs -> POP f xs -> POP g xs Source #
HPure (POP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hpure :: forall (xs :: l) f. SListIN POP xs => (forall (a :: k0). f a) -> POP f xs Source # hcpure :: forall c (xs :: l) proxy f. AllN POP c xs => proxy c -> (forall (a :: k0). c a => f a) -> POP f xs Source #
Eq (NP (NP f) xss) => Eq (POP f xss) Source #
Instance details Defined in Data.SOP.NP Methods (==) :: POP f xss -> POP f xss -> Bool # (/=) :: POP f xss -> POP f xss -> Bool #
Ord (NP (NP f) xss) => Ord (POP f xss) Source #
Instance details Defined in Data.SOP.NP Methods compare :: POP f xss -> POP f xss -> Ordering # (<) :: POP f xss -> POP f xss -> Bool # (<=) :: POP f xss -> POP f xss -> Bool # (>) :: POP f xss -> POP f xss -> Bool # (>=) :: POP f xss -> POP f xss -> Bool # max :: POP f xss -> POP f xss -> POP f xss # min :: POP f xss -> POP f xss -> POP f xss #
Show (NP (NP f) xss) => Show (POP f xss) Source #
Instance details Defined in Data.SOP.NP Methods showsPrec :: Int -> POP f xss -> ShowS # show :: POP f xss -> String # showList :: [POP f xss] -> ShowS #
Semigroup (NP (NP f) xss) => Semigroup (POP f xss) Source #	Since: 0.4.0.0
Instance details Defined in Data.SOP.NP Methods (<>) :: POP f xss -> POP f xss -> POP f xss # sconcat :: NonEmpty (POP f xss) -> POP f xss # stimes :: Integral b => b -> POP f xss -> POP f xss #
Monoid (NP (NP f) xss) => Monoid (POP f xss) Source #	Since: 0.4.0.0
Instance details Defined in Data.SOP.NP Methods mempty :: POP f xss # mappend :: POP f xss -> POP f xss -> POP f xss # mconcat :: [POP f xss] -> POP f xss #
NFData (NP (NP f) xss) => NFData (POP f xss) Source #	Since: 0.2.5.0
Instance details Defined in Data.SOP.NP Methods rnf :: POP f xss -> () #
type AllZipN (POP :: (k -> Type) -> [[k]] -> Type) (c :: a -> b -> Constraint) Source #
Instance details Defined in Data.SOP.NP type AllZipN (POP :: (k -> Type) -> [[k]] -> Type) (c :: a -> b -> Constraint) = AllZip2 c
type Same (POP :: (k1 -> Type) -> [[k1]] -> Type) Source #
Instance details Defined in Data.SOP.NP type Same (POP :: (k1 -> Type) -> [[k1]] -> Type) = POP :: (k2 -> Type) -> [[k2]] -> Type
type SListIN (POP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NP type SListIN (POP :: (k -> Type) -> [[k]] -> Type) = SListI2 :: [[k]] -> Constraint
type UnProd (POP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS type UnProd (POP :: (k -> Type) -> [[k]] -> Type) = SOP :: (k -> Type) -> [[k]] -> Type
type Prod (POP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NP type Prod (POP :: (k -> Type) -> [[k]] -> Type) = POP :: (k -> Type) -> [[k]] -> Type
type AllN (POP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) Source #
Instance details Defined in Data.SOP.NP type AllN (POP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) = All2 c
type CollapseTo (POP :: (k -> Type) -> [[k]] -> Type) a Source #
Instance details Defined in Data.SOP.NP type CollapseTo (POP :: (k -> Type) -> [[k]] -> Type) a = [[a]]

unPOP :: POP f xss -> NP (NP f) xss Source #

Unwrap a product of products.

Combinators

Constructing products

class HPure (h :: (k -> Type) -> l -> Type) where Source #

A generalization of pure or return to higher kinds.

Methods

hpure :: SListIN h xs => (forall a. f a) -> h f xs Source #

Corresponds to pure directly.

Instances:

hpure, pure_NP  :: SListI  xs  => (forall a. f a) -> NP  f xs
hpure, pure_POP :: SListI2 xss => (forall a. f a) -> POP f xss

hcpure :: AllN h c xs => proxy c -> (forall a. c a => f a) -> h f xs Source #

A variant of hpure that allows passing in a constrained argument.

Calling hcpure f s where s :: h f xs causes f to be applied at all the types that are contained in xs. Therefore, the constraint c has to be satisfied for all elements of xs, which is what AllN h c xs states.

Instances:

hcpure, cpure_NP  :: (All  c xs ) => proxy c -> (forall a. c a => f a) -> NP  f xs
hcpure, cpure_POP :: (All2 c xss) => proxy c -> (forall a. c a => f a) -> POP f xss

Instances

Instances details

HPure (NP :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hpure :: forall (xs :: l) f. SListIN NP xs => (forall (a :: k0). f a) -> NP f xs Source # hcpure :: forall c (xs :: l) proxy f. AllN NP c xs => proxy c -> (forall (a :: k0). c a => f a) -> NP f xs Source #
HPure (POP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hpure :: forall (xs :: l) f. SListIN POP xs => (forall (a :: k0). f a) -> POP f xs Source # hcpure :: forall c (xs :: l) proxy f. AllN POP c xs => proxy c -> (forall (a :: k0). c a => f a) -> POP f xs Source #

Destructing products

hd :: NP f (x ': xs) -> f x Source #

Obtain the head of an n-ary product.

Since: 0.2.1.0

tl :: NP f (x ': xs) -> NP f xs Source #

Obtain the tail of an n-ary product.

Since: 0.2.1.0

type Projection (f :: k -> Type) (xs :: [k]) = K (NP f xs) -.-> f Source #

The type of projections from an n-ary product.

A projection is a function from the n-ary product to a single element.

projections :: forall xs f. SListI xs => NP (Projection f xs) xs Source #

Compute all projections from an n-ary product.

Each element of the resulting product contains one of the projections.

shiftProjection :: Projection f xs a -> Projection f (x ': xs) a Source #

Application

newtype (f -.-> g) a infixr 1 Source #

Lifted functions.

Constructors

Fn
Fields apFn :: f a -> g a

fn :: (f a -> f' a) -> (f -.-> f') a Source #

Construct a lifted function.

Same as Fn. Only available for uniformity with the higher-arity versions.

fn_2 :: (f a -> f' a -> f'' a) -> (f -.-> (f' -.-> f'')) a Source #

Construct a binary lifted function.

fn_3 :: (f a -> f' a -> f'' a -> f''' a) -> (f -.-> (f' -.-> (f'' -.-> f'''))) a Source #

Construct a ternary lifted function.

fn_4 :: (f a -> f' a -> f'' a -> f''' a -> f'''' a) -> (f -.-> (f' -.-> (f'' -.-> (f''' -.-> f'''')))) a Source #

Construct a quarternary lifted function.

type family Prod (h :: (k -> Type) -> l -> Type) :: (k -> Type) -> l -> Type Source #

Maps a structure containing sums to the corresponding product structure.

Instances

Instances details

type Prod (NP :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NP type Prod (NP :: (k -> Type) -> [k] -> Type) = NP :: (k -> Type) -> [k] -> Type
type Prod (POP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NP type Prod (POP :: (k -> Type) -> [[k]] -> Type) = POP :: (k -> Type) -> [[k]] -> Type
type Prod (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS type Prod (NS :: (k -> Type) -> [k] -> Type) = NP :: (k -> Type) -> [k] -> Type
type Prod (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS type Prod (SOP :: (k -> Type) -> [[k]] -> Type) = POP :: (k -> Type) -> [[k]] -> Type

class (Prod (Prod h) ~ Prod h, HPure (Prod h)) => HAp (h :: (k -> Type) -> l -> Type) where Source #

A generalization of <*>.

Methods

hap :: Prod h (f -.-> g) xs -> h f xs -> h g xs Source #

Corresponds to <*>.

For products (NP) as well as products of products (POP), the correspondence is rather direct. We combine a structure containing (lifted) functions and a compatible structure containing corresponding arguments into a compatible structure containing results.

The same combinator can also be used to combine a product structure of functions with a sum structure of arguments, which then results in another sum structure of results. The sum structure determines which part of the product structure will be used.

Instances:

hap, ap_NP  :: NP  (f -.-> g) xs  -> NP  f xs  -> NP  g xs
hap, ap_NS  :: NP  (f -.-> g) xs  -> NS  f xs  -> NS  g xs
hap, ap_POP :: POP (f -.-> g) xss -> POP f xss -> POP g xss
hap, ap_SOP :: POP (f -.-> g) xss -> SOP f xss -> SOP g xss

Instances

Instances details

HAp (NP :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hap :: forall (f :: k0 -> Type) (g :: k0 -> Type) (xs :: l). Prod NP (f -.-> g) xs -> NP f xs -> NP g xs Source #
HAp (POP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hap :: forall (f :: k0 -> Type) (g :: k0 -> Type) (xs :: l). Prod POP (f -.-> g) xs -> POP f xs -> POP g xs Source #
HAp (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hap :: forall (f :: k0 -> Type) (g :: k0 -> Type) (xs :: l). Prod NS (f -.-> g) xs -> NS f xs -> NS g xs Source #
HAp (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hap :: forall (f :: k0 -> Type) (g :: k0 -> Type) (xs :: l). Prod SOP (f -.-> g) xs -> SOP f xs -> SOP g xs Source #

Lifting / mapping

hliftA :: (SListIN (Prod h) xs, HAp h) => (forall a. f a -> f' a) -> h f xs -> h f' xs Source #

A generalized form of liftA, which in turn is a generalized map.

Takes a lifted function and applies it to every element of a structure while preserving its shape.

Specification:

hliftA f xs = hpure (fn f) ` hap ` xs

Instances:

hliftA, liftA_NP  :: SListI  xs  => (forall a. f a -> f' a) -> NP  f xs  -> NP  f' xs
hliftA, liftA_NS  :: SListI  xs  => (forall a. f a -> f' a) -> NS  f xs  -> NS  f' xs
hliftA, liftA_POP :: SListI2 xss => (forall a. f a -> f' a) -> POP f xss -> POP f' xss
hliftA, liftA_SOP :: SListI2 xss => (forall a. f a -> f' a) -> SOP f xss -> SOP f' xss

hliftA2 :: (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall a. f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs Source #

A generalized form of liftA2, which in turn is a generalized zipWith.

Takes a lifted binary function and uses it to combine two structures of equal shape into a single structure.

It either takes two product structures to a product structure, or one product and one sum structure to a sum structure.

Specification:

hliftA2 f xs ys = hpure (fn_2 f) ` hap ` xs ` hap ` ys

Instances:

hliftA2, liftA2_NP  :: SListI  xs  => (forall a. f a -> f' a -> f'' a) -> NP  f xs  -> NP  f' xs  -> NP  f'' xs
hliftA2, liftA2_NS  :: SListI  xs  => (forall a. f a -> f' a -> f'' a) -> NP  f xs  -> NS  f' xs  -> NS  f'' xs
hliftA2, liftA2_POP :: SListI2 xss => (forall a. f a -> f' a -> f'' a) -> POP f xss -> POP f' xss -> POP f'' xss
hliftA2, liftA2_SOP :: SListI2 xss => (forall a. f a -> f' a -> f'' a) -> POP f xss -> SOP f' xss -> SOP f'' xss

hliftA3 :: (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall a. f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs Source #

A generalized form of liftA3, which in turn is a generalized zipWith3.

Takes a lifted ternary function and uses it to combine three structures of equal shape into a single structure.

It either takes three product structures to a product structure, or two product structures and one sum structure to a sum structure.

Specification:

hliftA3 f xs ys zs = hpure (fn_3 f) ` hap ` xs ` hap ` ys ` hap ` zs

Instances:

hliftA3, liftA3_NP  :: SListI  xs  => (forall a. f a -> f' a -> f'' a -> f''' a) -> NP  f xs  -> NP  f' xs  -> NP  f'' xs  -> NP  f''' xs
hliftA3, liftA3_NS  :: SListI  xs  => (forall a. f a -> f' a -> f'' a -> f''' a) -> NP  f xs  -> NP  f' xs  -> NS  f'' xs  -> NS  f''' xs
hliftA3, liftA3_POP :: SListI2 xss => (forall a. f a -> f' a -> f'' a -> f''' a) -> POP f xss -> POP f' xss -> POP f'' xss -> POP f''' xs
hliftA3, liftA3_SOP :: SListI2 xss => (forall a. f a -> f' a -> f'' a -> f''' a) -> POP f xss -> POP f' xss -> SOP f'' xss -> SOP f''' xs

hcliftA :: (AllN (Prod h) c xs, HAp h) => proxy c -> (forall a. c a => f a -> f' a) -> h f xs -> h f' xs Source #

Variant of hliftA that takes a constrained function.

Specification:

hcliftA p f xs = hcpure p (fn f) ` hap ` xs

hcliftA2 :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. c a => f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs Source #

Variant of hcliftA2 that takes a constrained function.

Specification:

hcliftA2 p f xs ys = hcpure p (fn_2 f) ` hap ` xs ` hap ` ys

hcliftA3 :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. c a => f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs Source #

Variant of hcliftA3 that takes a constrained function.

Specification:

hcliftA3 p f xs ys zs = hcpure p (fn_3 f) ` hap ` xs ` hap ` ys ` hap ` zs

hmap :: (SListIN (Prod h) xs, HAp h) => (forall a. f a -> f' a) -> h f xs -> h f' xs Source #

Another name for hliftA.

Since: 0.2

hzipWith :: (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall a. f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs Source #

Another name for hliftA2.

Since: 0.2

hzipWith3 :: (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall a. f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs Source #

Another name for hliftA3.

Since: 0.2

hcmap :: (AllN (Prod h) c xs, HAp h) => proxy c -> (forall a. c a => f a -> f' a) -> h f xs -> h f' xs Source #

Another name for hcliftA.

Since: 0.2

hczipWith :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. c a => f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs Source #

Another name for hcliftA2.

Since: 0.2

hczipWith3 :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. c a => f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs Source #

Another name for hcliftA3.

Since: 0.2

Constructing sums

type Injection (f :: k -> Type) (xs :: [k]) = f -.-> K (NS f xs) Source #

The type of injections into an n-ary sum.

If you expand the type synonyms and newtypes involved, you get

Injection f xs a = (f -.-> K (NS f xs)) a ~= f a -> K (NS f xs) a ~= f a -> NS f xs

If we pick a to be an element of xs, this indeed corresponds to an injection into the sum.

injections :: forall xs f. SListI xs => NP (Injection f xs) xs Source #

Compute all injections into an n-ary sum.

Each element of the resulting product contains one of the injections.

shift :: Injection f xs a -> Injection f (x ': xs) a Source #

Deprecated: Use shiftInjection instead.

Shift an injection.

Given an injection, return an injection into a sum that is one component larger.

shiftInjection :: Injection f xs a -> Injection f (x ': xs) a Source #

Shift an injection.

Given an injection, return an injection into a sum that is one component larger.

type family UnProd (h :: (k -> Type) -> l -> Type) :: (k -> Type) -> l -> Type Source #

Maps a structure containing products to the corresponding sum structure.

Since: 0.2.4.0

Instances

Instances details

type UnProd (NP :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS type UnProd (NP :: (k -> Type) -> [k] -> Type) = NS :: (k -> Type) -> [k] -> Type
type UnProd (POP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS type UnProd (POP :: (k -> Type) -> [[k]] -> Type) = SOP :: (k -> Type) -> [[k]] -> Type

class UnProd (Prod h) ~ h => HApInjs (h :: (k -> Type) -> l -> Type) where Source #

A class for applying all injections corresponding to a sum-like structure to a table containing suitable arguments.

Methods

hapInjs :: SListIN h xs => Prod h f xs -> [h f xs] Source #

For a given table (product-like structure), produce a list where each element corresponds to the application of an injection function into the corresponding sum-like structure.

Instances:

hapInjs, apInjs_NP  :: SListI  xs  => NP  f xs -> [NS  f xs ]
hapInjs, apInjs_SOP :: SListI2 xss => POP f xs -> [SOP f xss]

Examples:

>>> hapInjs (I 'x' :* I True :* I 2 :* Nil) :: [NS I '[Char, Bool, Int]]
[Z (I 'x'),S (Z (I True)),S (S (Z (I 2)))]

>>> hapInjs (POP ((I 'x' :* Nil) :* (I True :* I 2 :* Nil) :* Nil)) :: [SOP I '[ '[Char], '[Bool, Int]]]
[SOP (Z (I 'x' :* Nil)),SOP (S (Z (I True :* I 2 :* Nil)))]

Unfortunately the type-signatures are required in GHC-7.10 and older.

Since: 0.2.4.0

Instances

Instances details

HApInjs (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hapInjs :: forall (xs :: l) (f :: k0 -> Type). SListIN NS xs => Prod NS f xs -> [NS f xs] Source #
HApInjs (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hapInjs :: forall (xs :: l) (f :: k0 -> Type). SListIN SOP xs => Prod SOP f xs -> [SOP f xs] Source #

apInjs_NP :: SListI xs => NP f xs -> [NS f xs] Source #

Apply injections to a product.

Given a product containing all possible choices, produce a list of sums by applying each injection to the appropriate element.

Example:

>>> apInjs_NP (I 'x' :* I True :* I 2 :* Nil)
[Z (I 'x'),S (Z (I True)),S (S (Z (I 2)))]

apInjs_POP :: SListI xss => POP f xss -> [SOP f xss] Source #

Apply injections to a product of product.

This operates on the outer product only. Given a product containing all possible choices (that are products), produce a list of sums (of products) by applying each injection to the appropriate element.

Example:

>>> apInjs_POP (POP ((I 'x' :* Nil) :* (I True :* I 2 :* Nil) :* Nil))
[SOP (Z (I 'x' :* Nil)),SOP (S (Z (I True :* I 2 :* Nil)))]

Destructing sums

unZ :: NS f '[x] -> f x Source #

Extract the payload from a unary sum.

For larger sums, this function would be partial, so it is only provided with a rather restrictive type.

Example:

>>> unZ (Z (I 'x'))
I 'x'

Since: 0.2.2.0

class HIndex (h :: (k -> Type) -> l -> Type) where Source #

A class for determining which choice in a sum-like structure a value represents.

Methods

hindex :: h f xs -> Int Source #

If h is a sum-like structure representing a choice between n different options, and x is a value of type h f xs, then hindex x returns a number between 0 and n - 1 representing the index of the choice made by x.

Instances:

hindex, index_NS  :: NS  f xs -> Int
hindex, index_SOP :: SOP f xs -> Int

Examples:

>>> hindex (S (S (Z (I False))))
2
>>> hindex (Z (K ()))
0
>>> hindex (SOP (S (Z (I True :* I 'x' :* Nil))))
1

Since: 0.2.4.0

Instances

Instances details

HIndex (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hindex :: forall (f :: k0 -> Type) (xs :: l). NS f xs -> Int Source #
HIndex (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hindex :: forall (f :: k0 -> Type) (xs :: l). SOP f xs -> Int Source #

Dealing with `All c`

hcliftA' :: (All2 c xss, Prod h ~ NP, HAp h) => proxy c -> (forall xs. All c xs => f xs -> f' xs) -> h f xss -> h f' xss Source #

Deprecated: Use hcliftA or hcmap instead.

Lift a constrained function operating on a list-indexed structure to a function on a list-of-list-indexed structure.

This is a variant of hcliftA.

Specification:

hcliftA' p f xs = hpure (fn_2 $ \ AllDictC -> f) ` hap ` allDict_NP p ` hap ` xs

Instances:

hcliftA' :: All2 c xss => proxy c -> (forall xs. All c xs => f xs -> f' xs) -> NP f xss -> NP f' xss
hcliftA' :: All2 c xss => proxy c -> (forall xs. All c xs => f xs -> f' xs) -> NS f xss -> NS f' xss

hcliftA2' :: (All2 c xss, Prod h ~ NP, HAp h) => proxy c -> (forall xs. All c xs => f xs -> f' xs -> f'' xs) -> Prod h f xss -> h f' xss -> h f'' xss Source #

Deprecated: Use hcliftA2 or hczipWith instead.

Like hcliftA', but for binary functions.

hcliftA3' :: (All2 c xss, Prod h ~ NP, HAp h) => proxy c -> (forall xs. All c xs => f xs -> f' xs -> f'' xs -> f''' xs) -> Prod h f xss -> Prod h f' xss -> h f'' xss -> h f''' xss Source #

Deprecated: Use hcliftA3 or hczipWith3 instead.

Like hcliftA', but for ternary functions.

Comparison

compare_NS Source #

Arguments

:: forall r f g xs. r	what to do if first is smaller
-> (forall x. f x -> g x -> r)	what to do if both are equal
-> r	what to do if first is larger
-> NS f xs
-> NS g xs
-> r

Compare two sums with respect to the choice they are making.

A value that chooses the first option is considered smaller than one that chooses the second option.

If the choices are different, then either the first (if the first is smaller than the second) or the third (if the first is larger than the second) argument are called. If both choices are equal, then the second argument is called, which has access to the elements contained in the sums.

Since: 0.3.2.0

ccompare_NS Source #

Arguments

:: forall c proxy r f g xs. All c xs
=> proxy c
-> r	what to do if first is smaller
-> (forall x. c x => f x -> g x -> r)	what to do if both are equal
-> r	what to do if first is larger
-> NS f xs
-> NS g xs
-> r

Constrained version of compare_NS.

Since: 0.3.2.0

compare_SOP Source #

Arguments

:: forall r f g xss. r	what to do if first is smaller
-> (forall xs. NP f xs -> NP g xs -> r)	what to do if both are equal
-> r	what to do if first is larger
-> SOP f xss
-> SOP g xss
-> r

Compare two sums of products with respect to the choice in the sum they are making.

Only the sum structure is used for comparison. This is a small wrapper around ccompare_NS for a common special case.

Since: 0.3.2.0

ccompare_SOP Source #

Arguments

:: forall c proxy r f g xss. All2 c xss
=> proxy c
-> r	what to do if first is smaller
-> (forall xs. All c xs => NP f xs -> NP g xs -> r)	what to do if both are equal
-> r	what to do if first is larger
-> SOP f xss
-> SOP g xss
-> r

Constrained version of compare_SOP.

Since: 0.3.2.0

Collapsing

type family CollapseTo (h :: (k -> Type) -> l -> Type) (x :: Type) :: Type Source #

Maps products to lists, and sums to identities.

Instances

Instances details

type CollapseTo (NP :: (k -> Type) -> [k] -> Type) a Source #
Instance details Defined in Data.SOP.NP type CollapseTo (NP :: (k -> Type) -> [k] -> Type) a = [a]
type CollapseTo (POP :: (k -> Type) -> [[k]] -> Type) a Source #
Instance details Defined in Data.SOP.NP type CollapseTo (POP :: (k -> Type) -> [[k]] -> Type) a = [[a]]
type CollapseTo (NS :: (k -> Type) -> [k] -> Type) a Source #
Instance details Defined in Data.SOP.NS type CollapseTo (NS :: (k -> Type) -> [k] -> Type) a = a
type CollapseTo (SOP :: (k -> Type) -> [[k]] -> Type) a Source #
Instance details Defined in Data.SOP.NS type CollapseTo (SOP :: (k -> Type) -> [[k]] -> Type) a = [a]

class HCollapse (h :: (k -> Type) -> l -> Type) where Source #

A class for collapsing a heterogeneous structure into a homogeneous one.

Methods

hcollapse :: SListIN h xs => h (K a) xs -> CollapseTo h a Source #

Collapse a heterogeneous structure with homogeneous elements into a homogeneous structure.

If a heterogeneous structure is instantiated to the constant functor K, then it is in fact homogeneous. This function maps such a value to a simpler Haskell datatype reflecting that. An NS (K a) contains a single a, and an NP (K a) contains a list of as.

Instances:

hcollapse, collapse_NP  :: NP  (K a) xs  ->  [a]
hcollapse, collapse_NS  :: NS  (K a) xs  ->   a
hcollapse, collapse_POP :: POP (K a) xss -> [[a]]
hcollapse, collapse_SOP :: SOP (K a) xss ->  [a]

Instances

Instances details

HCollapse (NP :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hcollapse :: forall (xs :: l) a. SListIN NP xs => NP (K a) xs -> CollapseTo NP a Source #
HCollapse (POP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hcollapse :: forall (xs :: l) a. SListIN POP xs => POP (K a) xs -> CollapseTo POP a Source #
HCollapse (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hcollapse :: forall (xs :: l) a. SListIN NS xs => NS (K a) xs -> CollapseTo NS a Source #
HCollapse (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hcollapse :: forall (xs :: l) a. SListIN SOP xs => SOP (K a) xs -> CollapseTo SOP a Source #

Folding and sequencing

class HTraverse_ (h :: (k -> Type) -> l -> Type) where Source #

A generalization of traverse_ or foldMap.

Since: 0.3.2.0

Methods

hctraverse_ :: (AllN h c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g ()) -> h f xs -> g () Source #

Corresponds to traverse_.

Instances:

hctraverse_, ctraverse__NP  :: (All  c xs , Applicative g) => proxy c -> (forall a. c a => f a -> g ()) -> NP  f xs  -> g ()
hctraverse_, ctraverse__NS  :: (All2 c xs , Applicative g) => proxy c -> (forall a. c a => f a -> g ()) -> NS  f xs  -> g ()
hctraverse_, ctraverse__POP :: (All  c xss, Applicative g) => proxy c -> (forall a. c a => f a -> g ()) -> POP f xss -> g ()
hctraverse_, ctraverse__SOP :: (All2 c xss, Applicative g) => proxy c -> (forall a. c a => f a -> g ()) -> SOP f xss -> g ()

Since: 0.3.2.0

htraverse_ :: (SListIN h xs, Applicative g) => (forall a. f a -> g ()) -> h f xs -> g () Source #

Unconstrained version of hctraverse_.

Instances:

traverse_, traverse__NP  :: (SListI  xs , Applicative g) => (forall a. f a -> g ()) -> NP  f xs  -> g ()
traverse_, traverse__NS  :: (SListI  xs , Applicative g) => (forall a. f a -> g ()) -> NS  f xs  -> g ()
traverse_, traverse__POP :: (SListI2 xss, Applicative g) => (forall a. f a -> g ()) -> POP f xss -> g ()
traverse_, traverse__SOP :: (SListI2 xss, Applicative g) => (forall a. f a -> g ()) -> SOP f xss -> g ()

Since: 0.3.2.0

Instances

Instances details

HTraverse_ (NP :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hctraverse_ :: forall c (xs :: l) g proxy f. (AllN NP c xs, Applicative g) => proxy c -> (forall (a :: k0). c a => f a -> g ()) -> NP f xs -> g () Source # htraverse_ :: forall (xs :: l) g f. (SListIN NP xs, Applicative g) => (forall (a :: k0). f a -> g ()) -> NP f xs -> g () Source #
HTraverse_ (POP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hctraverse_ :: forall c (xs :: l) g proxy f. (AllN POP c xs, Applicative g) => proxy c -> (forall (a :: k0). c a => f a -> g ()) -> POP f xs -> g () Source # htraverse_ :: forall (xs :: l) g f. (SListIN POP xs, Applicative g) => (forall (a :: k0). f a -> g ()) -> POP f xs -> g () Source #
HTraverse_ (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hctraverse_ :: forall c (xs :: l) g proxy f. (AllN NS c xs, Applicative g) => proxy c -> (forall (a :: k0). c a => f a -> g ()) -> NS f xs -> g () Source # htraverse_ :: forall (xs :: l) g f. (SListIN NS xs, Applicative g) => (forall (a :: k0). f a -> g ()) -> NS f xs -> g () Source #
HTraverse_ (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hctraverse_ :: forall c (xs :: l) g proxy f. (AllN SOP c xs, Applicative g) => proxy c -> (forall (a :: k0). c a => f a -> g ()) -> SOP f xs -> g () Source # htraverse_ :: forall (xs :: l) g f. (SListIN SOP xs, Applicative g) => (forall (a :: k0). f a -> g ()) -> SOP f xs -> g () Source #

hcfoldMap :: (HTraverse_ h, AllN h c xs, Monoid m) => proxy c -> (forall a. c a => f a -> m) -> h f xs -> m Source #

Special case of hctraverse_.

Since: 0.3.2.0

hcfor_ :: (HTraverse_ h, AllN h c xs, Applicative g) => proxy c -> h f xs -> (forall a. c a => f a -> g ()) -> g () Source #

Flipped version of hctraverse_.

Since: 0.3.2.0

class HAp h => HSequence (h :: (k -> Type) -> l -> Type) where Source #

A generalization of sequenceA.

Methods

hsequence' :: (SListIN h xs, Applicative f) => h (f :.: g) xs -> f (h g xs) Source #

Corresponds to sequenceA.

Lifts an applicative functor out of a structure.

Instances:

hsequence', sequence'_NP  :: (SListI  xs , Applicative f) => NP  (f :.: g) xs  -> f (NP  g xs )
hsequence', sequence'_NS  :: (SListI  xs , Applicative f) => NS  (f :.: g) xs  -> f (NS  g xs )
hsequence', sequence'_POP :: (SListI2 xss, Applicative f) => POP (f :.: g) xss -> f (POP g xss)
hsequence', sequence'_SOP :: (SListI2 xss, Applicative f) => SOP (f :.: g) xss -> f (SOP g xss)

hctraverse' :: (AllN h c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g (f' a)) -> h f xs -> g (h f' xs) Source #

Corresponds to traverse.

Instances:

hctraverse', ctraverse'_NP  :: (All  c xs , Applicative g) => proxy c -> (forall a. c a => f a -> g (f' a)) -> NP  f xs  -> g (NP  f' xs )
hctraverse', ctraverse'_NS  :: (All2 c xs , Applicative g) => proxy c -> (forall a. c a => f a -> g (f' a)) -> NS  f xs  -> g (NS  f' xs )
hctraverse', ctraverse'_POP :: (All  c xss, Applicative g) => proxy c -> (forall a. c a => f a -> g (f' a)) -> POP f xss -> g (POP f' xss)
hctraverse', ctraverse'_SOP :: (All2 c xss, Applicative g) => proxy c -> (forall a. c a => f a -> g (f' a)) -> SOP f xss -> g (SOP f' xss)

Since: 0.3.2.0

htraverse' :: (SListIN h xs, Applicative g) => (forall a. f a -> g (f' a)) -> h f xs -> g (h f' xs) Source #

Unconstrained variant of htraverse`.

Instances:

htraverse', traverse'_NP  :: (SListI  xs , Applicative g) => (forall a. c a => f a -> g (f' a)) -> NP  f xs  -> g (NP  f' xs )
htraverse', traverse'_NS  :: (SListI2 xs , Applicative g) => (forall a. c a => f a -> g (f' a)) -> NS  f xs  -> g (NS  f' xs )
htraverse', traverse'_POP :: (SListI  xss, Applicative g) => (forall a. c a => f a -> g (f' a)) -> POP f xss -> g (POP f' xss)
htraverse', traverse'_SOP :: (SListI2 xss, Applicative g) => (forall a. c a => f a -> g (f' a)) -> SOP f xss -> g (SOP f' xss)

Since: 0.3.2.0

Instances

Instances details

HSequence (NP :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hsequence' :: forall (xs :: l) f (g :: k0 -> Type). (SListIN NP xs, Applicative f) => NP (f :.: g) xs -> f (NP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. (AllN NP c xs, Applicative g) => proxy c -> (forall (a :: k0). c a => f a -> g (f' a)) -> NP f xs -> g (NP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. (SListIN NP xs, Applicative g) => (forall (a :: k0). f a -> g (f' a)) -> NP f xs -> g (NP f' xs) Source #
HSequence (POP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods hsequence' :: forall (xs :: l) f (g :: k0 -> Type). (SListIN POP xs, Applicative f) => POP (f :.: g) xs -> f (POP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. (AllN POP c xs, Applicative g) => proxy c -> (forall (a :: k0). c a => f a -> g (f' a)) -> POP f xs -> g (POP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. (SListIN POP xs, Applicative g) => (forall (a :: k0). f a -> g (f' a)) -> POP f xs -> g (POP f' xs) Source #
HSequence (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hsequence' :: forall (xs :: l) f (g :: k0 -> Type). (SListIN NS xs, Applicative f) => NS (f :.: g) xs -> f (NS g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. (AllN NS c xs, Applicative g) => proxy c -> (forall (a :: k0). c a => f a -> g (f' a)) -> NS f xs -> g (NS f' xs) Source # htraverse' :: forall (xs :: l) g f f'. (SListIN NS xs, Applicative g) => (forall (a :: k0). f a -> g (f' a)) -> NS f xs -> g (NS f' xs) Source #
HSequence (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hsequence' :: forall (xs :: l) f (g :: k0 -> Type). (SListIN SOP xs, Applicative f) => SOP (f :.: g) xs -> f (SOP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. (AllN SOP c xs, Applicative g) => proxy c -> (forall (a :: k0). c a => f a -> g (f' a)) -> SOP f xs -> g (SOP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. (SListIN SOP xs, Applicative g) => (forall (a :: k0). f a -> g (f' a)) -> SOP f xs -> g (SOP f' xs) Source #

hsequence :: (SListIN h xs, SListIN (Prod h) xs, HSequence h) => Applicative f => h f xs -> f (h I xs) Source #

Special case of hsequence' where g = I.

hsequenceK :: (SListIN h xs, SListIN (Prod h) xs, Applicative f, HSequence h) => h (K (f a)) xs -> f (h (K a) xs) Source #

Special case of hsequence' where g = K a.

hctraverse :: (HSequence h, AllN h c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g a) -> h f xs -> g (h I xs) Source #

Special case of hctraverse' where f' = I.

Since: 0.3.2.0

hcfor :: (HSequence h, AllN h c xs, Applicative g) => proxy c -> h f xs -> (forall a. c a => f a -> g a) -> g (h I xs) Source #

Flipped version of hctraverse.

Since: 0.3.2.0

Expanding sums to products

class HExpand (h :: (k -> Type) -> l -> Type) where Source #

A class for expanding sum structures into corresponding product structures, filling in the slots not targeted by the sum with default values.

Since: 0.2.5.0

Methods

hexpand :: SListIN (Prod h) xs => (forall x. f x) -> h f xs -> Prod h f xs Source #

Expand a given sum structure into a corresponding product structure by placing the value contained in the sum into the corresponding position in the product, and using the given default value for all other positions.

Instances:

hexpand, expand_NS  :: SListI xs   => (forall x . f x) -> NS  f xs  -> NP  f xs
hexpand, expand_SOP :: SListI2 xss => (forall x . f x) -> SOP f xss -> POP f xss

Examples:

>>> hexpand Nothing (S (Z (Just 3))) :: NP Maybe '[Char, Int, Bool]
Nothing :* Just 3 :* Nothing :* Nil
>>> hexpand [] (SOP (S (Z ([1,2] :* "xyz" :* Nil)))) :: POP [] '[ '[Bool], '[Int, Char] ]
POP (([] :* Nil) :* ([1,2] :* "xyz" :* Nil) :* Nil)

Since: 0.2.5.0

hcexpand :: AllN (Prod h) c xs => proxy c -> (forall x. c x => f x) -> h f xs -> Prod h f xs Source #

Variant of hexpand that allows passing a constrained default.

Instances:

hcexpand, cexpand_NS  :: All  c xs  => proxy c -> (forall x . c x => f x) -> NS  f xs  -> NP  f xs
hcexpand, cexpand_SOP :: All2 c xss => proxy c -> (forall x . c x => f x) -> SOP f xss -> POP f xss

Examples:

>>> hcexpand (Proxy :: Proxy Bounded) (I minBound) (S (Z (I 20))) :: NP I '[Bool, Int, Ordering]
I False :* I 20 :* I LT :* Nil
>>> hcexpand (Proxy :: Proxy Num) (I 0) (SOP (S (Z (I 1 :* I 2 :* Nil)))) :: POP I '[ '[Double], '[Int, Int] ]
POP ((I 0.0 :* Nil) :* (I 1 :* I 2 :* Nil) :* Nil)

Since: 0.2.5.0

Instances

Instances details

HExpand (NS :: (k -> Type) -> [k] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hexpand :: forall (xs :: l) f. SListIN (Prod NS) xs => (forall (x :: k0). f x) -> NS f xs -> Prod NS f xs Source # hcexpand :: forall c (xs :: l) proxy f. AllN (Prod NS) c xs => proxy c -> (forall (x :: k0). c x => f x) -> NS f xs -> Prod NS f xs Source #
HExpand (SOP :: (k -> Type) -> [[k]] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods hexpand :: forall (xs :: l) f. SListIN (Prod SOP) xs => (forall (x :: k0). f x) -> SOP f xs -> Prod SOP f xs Source # hcexpand :: forall c (xs :: l) proxy f. AllN (Prod SOP) c xs => proxy c -> (forall (x :: k0). c x => f x) -> SOP f xs -> Prod SOP f xs Source #

Transformation of index lists and coercions

class (Same h1 ~ h2, Same h2 ~ h1) => HTrans (h1 :: (k1 -> Type) -> l1 -> Type) (h2 :: (k2 -> Type) -> l2 -> Type) where Source #

A class for transforming structures into related structures with a different index list, as long as the index lists have the same shape and the elements and interpretation functions are suitably related.

Since: 0.3.1.0

Methods

htrans :: AllZipN (Prod h1) c xs ys => proxy c -> (forall x y. c x y => f x -> g y) -> h1 f xs -> h2 g ys Source #

Transform a structure into a related structure given a conversion function for the elements.

Since: 0.3.1.0

hcoerce :: (AllZipN (Prod h1) (LiftedCoercible f g) xs ys, HTrans h1 h2) => h1 f xs -> h2 g ys Source #

Safely coerce a structure into a representationally equal structure.

This is a special case of htrans, but can be implemented more efficiently; for example in terms of unsafeCoerce.

Examples:

>>> hcoerce (I (Just LT) :* I (Just 'x') :* I (Just True) :* Nil) :: NP Maybe '[Ordering, Char, Bool]
Just LT :* Just 'x' :* Just True :* Nil
>>> hcoerce (SOP (Z (K True :* K False :* Nil))) :: SOP I '[ '[Bool, Bool], '[Bool] ]
SOP (Z (I True :* I False :* Nil))

Since: 0.3.1.0

Instances

Instances details

HTrans (NP :: (k1 -> Type) -> [k1] -> Type) (NP :: (k2 -> Type) -> [k2] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN (Prod NP) c xs ys => proxy c -> (forall (x :: k10) (y :: k20). c x y => f x -> g y) -> NP f xs -> NP g ys Source # hcoerce :: forall (f :: k10 -> Type) (g :: k20 -> Type) (xs :: l1) (ys :: l2). (AllZipN (Prod NP) (LiftedCoercible f g) xs ys, HTrans NP NP) => NP f xs -> NP g ys Source #
HTrans (POP :: (k1 -> Type) -> [[k1]] -> Type) (POP :: (k2 -> Type) -> [[k2]] -> Type) Source #
Instance details Defined in Data.SOP.NP Methods htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN (Prod POP) c xs ys => proxy c -> (forall (x :: k10) (y :: k20). c x y => f x -> g y) -> POP f xs -> POP g ys Source # hcoerce :: forall (f :: k10 -> Type) (g :: k20 -> Type) (xs :: l1) (ys :: l2). (AllZipN (Prod POP) (LiftedCoercible f g) xs ys, HTrans POP POP) => POP f xs -> POP g ys Source #
HTrans (NS :: (k1 -> Type) -> [k1] -> Type) (NS :: (k2 -> Type) -> [k2] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN (Prod NS) c xs ys => proxy c -> (forall (x :: k10) (y :: k20). c x y => f x -> g y) -> NS f xs -> NS g ys Source # hcoerce :: forall (f :: k10 -> Type) (g :: k20 -> Type) (xs :: l1) (ys :: l2). (AllZipN (Prod NS) (LiftedCoercible f g) xs ys, HTrans NS NS) => NS f xs -> NS g ys Source #
HTrans (SOP :: (k1 -> Type) -> [[k1]] -> Type) (SOP :: (k2 -> Type) -> [[k2]] -> Type) Source #
Instance details Defined in Data.SOP.NS Methods htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN (Prod SOP) c xs ys => proxy c -> (forall (x :: k10) (y :: k20). c x y => f x -> g y) -> SOP f xs -> SOP g ys Source # hcoerce :: forall (f :: k10 -> Type) (g :: k20 -> Type) (xs :: l1) (ys :: l2). (AllZipN (Prod SOP) (LiftedCoercible f g) xs ys, HTrans SOP SOP) => SOP f xs -> SOP g ys Source #

hfromI :: (AllZipN (Prod h1) (LiftedCoercible I f) xs ys, HTrans h1 h2) => h1 I xs -> h2 f ys Source #

Specialization of hcoerce.

Since: 0.3.1.0

htoI :: (AllZipN (Prod h1) (LiftedCoercible f I) xs ys, HTrans h1 h2) => h1 f xs -> h2 I ys Source #

Specialization of hcoerce.

Since: 0.3.1.0

Partial operations

fromList :: SListI xs => [a] -> Maybe (NP (K a) xs) Source #

Construct a homogeneous n-ary product from a normal Haskell list.

Returns Nothing if the length of the list does not exactly match the expected size of the product.

Utilities

Basic functors

newtype K (a :: Type) (b :: k) Source #

The constant type functor.

Like Constant, but kind-polymorphic in its second argument and with a shorter name.

Constructors

K a

Instances

Instances details

Eq2 (K :: Type -> Type -> Type) Source #	Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> K a c -> K b d -> Bool #
Ord2 (K :: Type -> Type -> Type) Source #	Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> K a c -> K b d -> Ordering #
Read2 (K :: Type -> Type -> Type) Source #	Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (K a b) # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [K a b] # liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (K a b) # liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [K a b] #
Show2 (K :: Type -> Type -> Type) Source #	Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> K a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [K a b] -> ShowS #
NFData2 (K :: Type -> Type -> Type) Source #	Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftRnf2 :: (a -> ()) -> (b -> ()) -> K a b -> () #
Functor (K a :: Type -> Type) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods fmap :: (a0 -> b) -> K a a0 -> K a b # (<$) :: a0 -> K a b -> K a a0 #
Monoid a => Applicative (K a :: Type -> Type) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods pure :: a0 -> K a a0 # (<>) :: K a (a0 -> b) -> K a a0 -> K a b # liftA2 :: (a0 -> b -> c) -> K a a0 -> K a b -> K a c # (>) :: K a a0 -> K a b -> K a b # (<*) :: K a a0 -> K a b -> K a a0 #
Foldable (K a :: Type -> Type) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods fold :: Monoid m => K a m -> m # foldMap :: Monoid m => (a0 -> m) -> K a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> K a a0 -> m # foldr :: (a0 -> b -> b) -> b -> K a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> K a a0 -> b # foldl :: (b -> a0 -> b) -> b -> K a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> K a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> K a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> K a a0 -> a0 # toList :: K a a0 -> [a0] # null :: K a a0 -> Bool # length :: K a a0 -> Int # elem :: Eq a0 => a0 -> K a a0 -> Bool # maximum :: Ord a0 => K a a0 -> a0 # minimum :: Ord a0 => K a a0 -> a0 # sum :: Num a0 => K a a0 -> a0 # product :: Num a0 => K a a0 -> a0 #
Traversable (K a :: Type -> Type) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods traverse :: Applicative f => (a0 -> f b) -> K a a0 -> f (K a b) # sequenceA :: Applicative f => K a (f a0) -> f (K a a0) # mapM :: Monad m => (a0 -> m b) -> K a a0 -> m (K a b) # sequence :: Monad m => K a (m a0) -> m (K a a0) #
Eq a => Eq1 (K a :: Type -> Type) Source #	Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftEq :: (a0 -> b -> Bool) -> K a a0 -> K a b -> Bool #
Ord a => Ord1 (K a :: Type -> Type) Source #	Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftCompare :: (a0 -> b -> Ordering) -> K a a0 -> K a b -> Ordering #
Read a => Read1 (K a :: Type -> Type) Source #	Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (K a a0) # liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [K a a0] # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (K a a0) # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [K a a0] #
Show a => Show1 (K a :: Type -> Type) Source #	Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> K a a0 -> ShowS # liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [K a a0] -> ShowS #
NFData a => NFData1 (K a :: Type -> Type) Source #	Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftRnf :: (a0 -> ()) -> K a a0 -> () #
Eq a => Eq (K a b) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods (==) :: K a b -> K a b -> Bool # (/=) :: K a b -> K a b -> Bool #
Ord a => Ord (K a b) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods compare :: K a b -> K a b -> Ordering # (<) :: K a b -> K a b -> Bool # (<=) :: K a b -> K a b -> Bool # (>) :: K a b -> K a b -> Bool # (>=) :: K a b -> K a b -> Bool # max :: K a b -> K a b -> K a b # min :: K a b -> K a b -> K a b #
Read a => Read (K a b) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods readsPrec :: Int -> ReadS (K a b) # readList :: ReadS [K a b] # readPrec :: ReadPrec (K a b) # readListPrec :: ReadPrec [K a b] #
Show a => Show (K a b) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods showsPrec :: Int -> K a b -> ShowS # show :: K a b -> String # showList :: [K a b] -> ShowS #
Generic (K a b) Source #
Instance details Defined in Data.SOP.BasicFunctors Associated Types type Rep (K a b) :: Type -> Type # Methods from :: K a b -> Rep (K a b) x # to :: Rep (K a b) x -> K a b #
Semigroup a => Semigroup (K a b) Source #	Since: 0.4.0.0
Instance details Defined in Data.SOP.BasicFunctors Methods (<>) :: K a b -> K a b -> K a b # sconcat :: NonEmpty (K a b) -> K a b # stimes :: Integral b0 => b0 -> K a b -> K a b #
Monoid a => Monoid (K a b) Source #	Since: 0.4.0.0
Instance details Defined in Data.SOP.BasicFunctors Methods mempty :: K a b # mappend :: K a b -> K a b -> K a b # mconcat :: [K a b] -> K a b #
NFData a => NFData (K a b) Source #	Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods rnf :: K a b -> () #
type Rep (K a b) Source #
Instance details Defined in Data.SOP.BasicFunctors type Rep (K a b) = D1 ('MetaData "K" "Data.SOP.BasicFunctors" "sop-core-0.5.0.0-8Z2mcN5MN4PKIxdMlK1cP6" 'True) (C1 ('MetaCons "K" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

unK :: K a b -> a Source #

Extract the contents of a K value.

newtype I (a :: Type) Source #

The identity type functor.

Like Identity, but with a shorter name.

Constructors

I a

Instances

Instances details

Monad I Source #
Instance details Defined in Data.SOP.BasicFunctors Methods (>>=) :: I a -> (a -> I b) -> I b # (>>) :: I a -> I b -> I b # return :: a -> I a #
Functor I Source #
Instance details Defined in Data.SOP.BasicFunctors Methods fmap :: (a -> b) -> I a -> I b # (<$) :: a -> I b -> I a #
Applicative I Source #
Instance details Defined in Data.SOP.BasicFunctors Methods pure :: a -> I a # (<>) :: I (a -> b) -> I a -> I b # liftA2 :: (a -> b -> c) -> I a -> I b -> I c # (>) :: I a -> I b -> I b # (<*) :: I a -> I b -> I a #
Foldable I Source #
Instance details Defined in Data.SOP.BasicFunctors Methods fold :: Monoid m => I m -> m # foldMap :: Monoid m => (a -> m) -> I a -> m # foldMap' :: Monoid m => (a -> m) -> I a -> m # foldr :: (a -> b -> b) -> b -> I a -> b # foldr' :: (a -> b -> b) -> b -> I a -> b # foldl :: (b -> a -> b) -> b -> I a -> b # foldl' :: (b -> a -> b) -> b -> I a -> b # foldr1 :: (a -> a -> a) -> I a -> a # foldl1 :: (a -> a -> a) -> I a -> a # toList :: I a -> [a] # null :: I a -> Bool # length :: I a -> Int # elem :: Eq a => a -> I a -> Bool # maximum :: Ord a => I a -> a # minimum :: Ord a => I a -> a # sum :: Num a => I a -> a # product :: Num a => I a -> a #
Traversable I Source #
Instance details Defined in Data.SOP.BasicFunctors Methods traverse :: Applicative f => (a -> f b) -> I a -> f (I b) # sequenceA :: Applicative f => I (f a) -> f (I a) # mapM :: Monad m => (a -> m b) -> I a -> m (I b) # sequence :: Monad m => I (m a) -> m (I a) #
Eq1 I Source #	Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftEq :: (a -> b -> Bool) -> I a -> I b -> Bool #
Ord1 I Source #	Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftCompare :: (a -> b -> Ordering) -> I a -> I b -> Ordering #
Read1 I Source #	Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (I a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [I a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (I a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [I a] #
Show1 I Source #	Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> I a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [I a] -> ShowS #
NFData1 I Source #	Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftRnf :: (a -> ()) -> I a -> () #
Eq a => Eq (I a) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods (==) :: I a -> I a -> Bool # (/=) :: I a -> I a -> Bool #
Ord a => Ord (I a) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods compare :: I a -> I a -> Ordering # (<) :: I a -> I a -> Bool # (<=) :: I a -> I a -> Bool # (>) :: I a -> I a -> Bool # (>=) :: I a -> I a -> Bool # max :: I a -> I a -> I a # min :: I a -> I a -> I a #
Read a => Read (I a) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods readsPrec :: Int -> ReadS (I a) # readList :: ReadS [I a] # readPrec :: ReadPrec (I a) # readListPrec :: ReadPrec [I a] #
Show a => Show (I a) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods showsPrec :: Int -> I a -> ShowS # show :: I a -> String # showList :: [I a] -> ShowS #
Generic (I a) Source #
Instance details Defined in Data.SOP.BasicFunctors Associated Types type Rep (I a) :: Type -> Type # Methods from :: I a -> Rep (I a) x # to :: Rep (I a) x -> I a #
Semigroup a => Semigroup (I a) Source #	Since: 0.4.0.0
Instance details Defined in Data.SOP.BasicFunctors Methods (<>) :: I a -> I a -> I a # sconcat :: NonEmpty (I a) -> I a # stimes :: Integral b => b -> I a -> I a #
Monoid a => Monoid (I a) Source #	Since: 0.4.0.0
Instance details Defined in Data.SOP.BasicFunctors Methods mempty :: I a # mappend :: I a -> I a -> I a # mconcat :: [I a] -> I a #
NFData a => NFData (I a) Source #	Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods rnf :: I a -> () #
type Rep (I a) Source #
Instance details Defined in Data.SOP.BasicFunctors type Rep (I a) = D1 ('MetaData "I" "Data.SOP.BasicFunctors" "sop-core-0.5.0.0-8Z2mcN5MN4PKIxdMlK1cP6" 'True) (C1 ('MetaCons "I" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

unI :: I a -> a Source #

Extract the contents of an I value.

newtype ((f :: l -> Type) :.: (g :: k -> l)) (p :: k) infixr 7 Source #

Composition of functors.

Like Compose, but kind-polymorphic and with a shorter name.

Constructors

Comp (f (g p))

Instances

Instances details

(Functor f, Functor g) => Functor (f :.: g) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b # (<$) :: a -> (f :.: g) b -> (f :.: g) a #
(Applicative f, Applicative g) => Applicative (f :.: g) Source #	Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods pure :: a -> (f :.: g) a # (<>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b # liftA2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c # (>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b # (<*) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a #
(Foldable f, Foldable g) => Foldable (f :.: g) Source #	Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods fold :: Monoid m => (f :.: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a # toList :: (f :.: g) a -> [a] # null :: (f :.: g) a -> Bool # length :: (f :.: g) a -> Int # elem :: Eq a => a -> (f :.: g) a -> Bool # maximum :: Ord a => (f :.: g) a -> a # minimum :: Ord a => (f :.: g) a -> a # sum :: Num a => (f :.: g) a -> a # product :: Num a => (f :.: g) a -> a #
(Traversable f, Traversable g) => Traversable (f :.: g) Source #	Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) # sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a) # mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) # sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) #
(Eq1 f, Eq1 g) => Eq1 (f :.: g) Source #	Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftEq :: (a -> b -> Bool) -> (f :.: g) a -> (f :.: g) b -> Bool #
(Ord1 f, Ord1 g) => Ord1 (f :.: g) Source #	Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftCompare :: (a -> b -> Ordering) -> (f :.: g) a -> (f :.: g) b -> Ordering #
(Read1 f, Read1 g) => Read1 (f :.: g) Source #	Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS ((f :.: g) a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [(f :.: g) a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec ((f :.: g) a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [(f :.: g) a] #
(Show1 f, Show1 g) => Show1 (f :.: g) Source #	Since: 0.2.4.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> (f :.: g) a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [(f :.: g) a] -> ShowS #
(NFData1 f, NFData1 g) => NFData1 (f :.: g) Source #	Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods liftRnf :: (a -> ()) -> (f :.: g) a -> () #
(Eq1 f, Eq1 g, Eq a) => Eq ((f :.: g) a) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods (==) :: (f :.: g) a -> (f :.: g) a -> Bool # (/=) :: (f :.: g) a -> (f :.: g) a -> Bool #
(Ord1 f, Ord1 g, Ord a) => Ord ((f :.: g) a) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods compare :: (f :.: g) a -> (f :.: g) a -> Ordering # (<) :: (f :.: g) a -> (f :.: g) a -> Bool # (<=) :: (f :.: g) a -> (f :.: g) a -> Bool # (>) :: (f :.: g) a -> (f :.: g) a -> Bool # (>=) :: (f :.: g) a -> (f :.: g) a -> Bool # max :: (f :.: g) a -> (f :.: g) a -> (f :.: g) a # min :: (f :.: g) a -> (f :.: g) a -> (f :.: g) a #
(Read1 f, Read1 g, Read a) => Read ((f :.: g) a) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods readsPrec :: Int -> ReadS ((f :.: g) a) # readList :: ReadS [(f :.: g) a] # readPrec :: ReadPrec ((f :.: g) a) # readListPrec :: ReadPrec [(f :.: g) a] #
(Show1 f, Show1 g, Show a) => Show ((f :.: g) a) Source #
Instance details Defined in Data.SOP.BasicFunctors Methods showsPrec :: Int -> (f :.: g) a -> ShowS # show :: (f :.: g) a -> String # showList :: [(f :.: g) a] -> ShowS #
Generic ((f :.: g) p) Source #
Instance details Defined in Data.SOP.BasicFunctors Associated Types type Rep ((f :.: g) p) :: Type -> Type # Methods from :: (f :.: g) p -> Rep ((f :.: g) p) x # to :: Rep ((f :.: g) p) x -> (f :.: g) p #
Semigroup (f (g x)) => Semigroup ((f :.: g) x) Source #	Since: 0.4.0.0
Instance details Defined in Data.SOP.BasicFunctors Methods (<>) :: (f :.: g) x -> (f :.: g) x -> (f :.: g) x # sconcat :: NonEmpty ((f :.: g) x) -> (f :.: g) x # stimes :: Integral b => b -> (f :.: g) x -> (f :.: g) x #
Monoid (f (g x)) => Monoid ((f :.: g) x) Source #	Since: 0.4.0.0
Instance details Defined in Data.SOP.BasicFunctors Methods mempty :: (f :.: g) x # mappend :: (f :.: g) x -> (f :.: g) x -> (f :.: g) x # mconcat :: [(f :.: g) x] -> (f :.: g) x #
NFData (f (g a)) => NFData ((f :.: g) a) Source #	Since: 0.2.5.0
Instance details Defined in Data.SOP.BasicFunctors Methods rnf :: (f :.: g) a -> () #
type Rep ((f :.: g) p) Source #
Instance details Defined in Data.SOP.BasicFunctors type Rep ((f :.: g) p) = D1 ('MetaData ":.:" "Data.SOP.BasicFunctors" "sop-core-0.5.0.0-8Z2mcN5MN4PKIxdMlK1cP6" 'True) (C1 ('MetaCons "Comp" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f (g p)))))

unComp :: (f :.: g) p -> f (g p) Source #

Extract the contents of a Comp value.

Mapping functions

mapII :: (a -> b) -> I a -> I b Source #

Lift the given function.

Since: 0.2.5.0

mapIK :: (a -> b) -> I a -> K b c Source #

Lift the given function.

Since: 0.2.5.0

mapKI :: (a -> b) -> K a c -> I b Source #

Lift the given function.

Since: 0.2.5.0

mapKK :: (a -> b) -> K a c -> K b d Source #

Lift the given function.

Since: 0.2.5.0

mapIII :: (a -> b -> c) -> I a -> I b -> I c Source #

Lift the given function.

Since: 0.2.5.0

mapIIK :: (a -> b -> c) -> I a -> I b -> K c d Source #

Lift the given function.

Since: 0.2.5.0

mapIKI :: (a -> b -> c) -> I a -> K b d -> I c Source #

Lift the given function.

Since: 0.2.5.0

mapIKK :: (a -> b -> c) -> I a -> K b d -> K c e Source #

Lift the given function.

Since: 0.2.5.0

mapKII :: (a -> b -> c) -> K a d -> I b -> I c Source #

Lift the given function.

Since: 0.2.5.0

mapKIK :: (a -> b -> c) -> K a d -> I b -> K c e Source #

Lift the given function.

Since: 0.2.5.0

mapKKI :: (a -> b -> c) -> K a d -> K b e -> I c Source #

Lift the given function.

Since: 0.2.5.0

mapKKK :: (a -> b -> c) -> K a d -> K b e -> K c f Source #

Lift the given function.

Since: 0.2.5.0

Mapping constraints

class (AllF c xs, SListI xs) => All (c :: k -> Constraint) (xs :: [k]) Source #

Require a constraint for every element of a list.

If you have a datatype that is indexed over a type-level list, then you can use All to indicate that all elements of that type-level list must satisfy a given constraint.

Example: The constraint

All Eq '[ Int, Bool, Char ]

is equivalent to the constraint

(Eq Int, Eq Bool, Eq Char)

Example: A type signature such as

f :: All Eq xs => NP I xs -> ...

means that f can assume that all elements of the n-ary product satisfy Eq.

Note on superclasses: ghc cannot deduce superclasses from All constraints. You might expect the following to compile

class (Eq a) => MyClass a

foo :: (All Eq xs) => NP f xs -> z
foo = [..]

bar :: (All MyClass xs) => NP f xs -> x
bar = foo

but it will fail with an error saying that it was unable to deduce the class constraint AllF Eq xs (or similar) in the definition of bar. In cases like this you can use Dict from Data.SOP.Dict to prove conversions between constraints. See this answer on SO for more details.

Minimal complete definition

cpara_SList

Instances

Instances details

All (c :: k -> Constraint) ('[] :: [k]) Source #
Instance details Defined in Data.SOP.Constraint Methods cpara_SList :: proxy c -> r '[] -> (forall (y :: k0) (ys :: [k0]). (c y, All c ys) => r ys -> r (y ': ys)) -> r '[] Source #
(c x, All c xs) => All (c :: a -> Constraint) (x ': xs :: [a]) Source #
Instance details Defined in Data.SOP.Constraint Methods cpara_SList :: proxy c -> r '[] -> (forall (y :: k) (ys :: [k]). (c y, All c ys) => r ys -> r (y ': ys)) -> r (x ': xs) Source #

type All2 c = All (All c) Source #

Require a constraint for every element of a list of lists.

If you have a datatype that is indexed over a type-level list of lists, then you can use All2 to indicate that all elements of the inner lists must satisfy a given constraint.

Example: The constraint

All2 Eq '[ '[ Int ], '[ Bool, Char ] ]

is equivalent to the constraint

(Eq Int, Eq Bool, Eq Char)

Example: A type signature such as

f :: All2 Eq xss => SOP I xs -> ...

means that f can assume that all elements of the sum of product satisfy Eq.

Since 0.4.0.0, this is merely a synonym for 'All (All c)'.

Since: 0.4.0.0

cpara_SList :: All c xs => proxy c -> r '[] -> (forall y ys. (c y, All c ys) => r ys -> r (y ': ys)) -> r xs Source #

Constrained paramorphism for a type-level list.

The advantage of writing functions in terms of cpara_SList is that they are then typically not recursive, and can be unfolded statically if the type-level list is statically known.

Since: 0.4.0.0

ccase_SList :: All c xs => proxy c -> r '[] -> (forall y ys. (c y, All c ys) => r (y ': ys)) -> r xs Source #

Constrained case distinction on a type-level list.

Since: 0.4.0.0

class (SListI xs, SListI ys, SameShapeAs xs ys, SameShapeAs ys xs, AllZipF c xs ys) => AllZip (c :: a -> b -> Constraint) (xs :: [a]) (ys :: [b]) Source #

Require a constraint pointwise for every pair of elements from two lists.

Example: The constraint

All (~) '[ Int, Bool, Char ] '[ a, b, c ]

is equivalent to the constraint

(Int ~ a, Bool ~ b, Char ~ c)

Since: 0.3.1.0

Instances

Instances details

(SListI xs, SListI ys, SameShapeAs xs ys, SameShapeAs ys xs, AllZipF c xs ys) => AllZip (c :: a -> b -> Constraint) (xs :: [a]) (ys :: [b]) Source #
Instance details Defined in Data.SOP.Constraint

class (AllZipF (AllZip f) xss yss, SListI xss, SListI yss, SameShapeAs xss yss, SameShapeAs yss xss) => AllZip2 f xss yss Source #

Require a constraint pointwise for every pair of elements from two lists of lists.

Instances

Instances details

(AllZipF (AllZip f) xss yss, SListI xss, SListI yss, SameShapeAs xss yss, SameShapeAs yss xss) => AllZip2 (f :: a -> b -> Constraint) (xss :: [[a]]) (yss :: [[b]]) Source #
Instance details Defined in Data.SOP.Constraint

type family AllN (h :: (k -> Type) -> l -> Type) (c :: k -> Constraint) :: l -> Constraint Source #

A generalization of All and All2.

The family AllN expands to All or All2 depending on whether the argument is indexed by a list or a list of lists.

Instances

Instances details

type AllN (NP :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) Source #
Instance details Defined in Data.SOP.NP type AllN (NP :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) = All c
type AllN (POP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) Source #
Instance details Defined in Data.SOP.NP type AllN (POP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) = All2 c
type AllN (NS :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) Source #
Instance details Defined in Data.SOP.NS type AllN (NS :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) = All c
type AllN (SOP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) Source #
Instance details Defined in Data.SOP.NS type AllN (SOP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) = All2 c

type family AllZipN (h :: (k -> Type) -> l -> Type) (c :: k1 -> k2 -> Constraint) :: l1 -> l2 -> Constraint Source #

A generalization of AllZip and AllZip2.

The family AllZipN expands to AllZip or AllZip2 depending on whther the argument is indexed by a list or a list of lists.

Instances

Instances details

type AllZipN (NP :: (k -> Type) -> [k] -> Type) (c :: a -> b -> Constraint) Source #
Instance details Defined in Data.SOP.NP type AllZipN (NP :: (k -> Type) -> [k] -> Type) (c :: a -> b -> Constraint) = AllZip c
type AllZipN (POP :: (k -> Type) -> [[k]] -> Type) (c :: a -> b -> Constraint) Source #
Instance details Defined in Data.SOP.NP type AllZipN (POP :: (k -> Type) -> [[k]] -> Type) (c :: a -> b -> Constraint) = AllZip2 c

Other constraints

class f (g x) => Compose f g x infixr 9 Source #

Composition of constraints.

Note that the result of the composition must be a constraint, and therefore, in Compose f g, the kind of f is k -> Constraint. The kind of g, however, is l -> k and can thus be a normal type constructor.

A typical use case is in connection with All on an NP or an NS. For example, in order to denote that all elements on an NP f xs satisfy Show, we can say All (Compose Show f) xs.

Since: 0.2

Instances

Instances details

f (g x) => Compose (f :: k1 -> Constraint) (g :: k2 -> k1) (x :: k2) Source #
Instance details Defined in Data.SOP.Constraint

class (f x, g x) => And f g x infixl 7 Source #

Pairing of constraints.

Since: 0.2

Instances

Instances details

(f x, g x) => And (f :: k -> Constraint) (g :: k -> Constraint) (x :: k) Source #
Instance details Defined in Data.SOP.Constraint

class Top x Source #

A constraint that can always be satisfied.

Since: 0.2

Instances

Instances details

Top (x :: k) Source #
Instance details Defined in Data.SOP.Constraint

class Coercible (f x) (g y) => LiftedCoercible f g x y Source #

The constraint LiftedCoercible f g x y is equivalent to Coercible (f x) (g y).

Since: 0.3.1.0

Instances

Instances details

Coercible (f x) (g y) => LiftedCoercible (f :: k1 -> k2) (g :: k3 -> k2) (x :: k1) (y :: k3) Source #
Instance details Defined in Data.SOP.Constraint

type family SameShapeAs (xs :: [a]) (ys :: [b]) :: Constraint where ... Source #

Type family that forces a type-level list to be of the same shape as the given type-level list.

Since 0.5.0.0, this only tests the top-level structure of the list, and is intended to be used in conjunction with a separate construct (such as the AllZip, AllZipF combination to tie the recursive knot). The reason is that making SameShapeAs directly recursive leads to quadratic compile times.

The main use of this constraint is to help type inference to learn something about otherwise unknown type-level lists.

Since: 0.5.0.0

Equations

SameShapeAs '[] ys = ys ~ '[]
SameShapeAs (x ': xs) ys = ys ~ (Head ys ': Tail ys)

Singletons

data SList :: [k] -> Type where Source #

Explicit singleton list.

A singleton list can be used to reveal the structure of a type-level list argument that the function is quantified over. For every type-level list xs, there is one non-bottom value of type SList xs.

Note that these singleton lists are polymorphic in the list elements; we do not require a singleton representation for them.

Since: 0.2

Constructors

SNil :: SList '[]
SCons :: SListI xs => SList (x ': xs)

Instances

Instances details

Eq (SList xs) Source #
Instance details Defined in Data.SOP.Sing Methods (==) :: SList xs -> SList xs -> Bool # (/=) :: SList xs -> SList xs -> Bool #
Ord (SList xs) Source #
Instance details Defined in Data.SOP.Sing Methods compare :: SList xs -> SList xs -> Ordering # (<) :: SList xs -> SList xs -> Bool # (<=) :: SList xs -> SList xs -> Bool # (>) :: SList xs -> SList xs -> Bool # (>=) :: SList xs -> SList xs -> Bool # max :: SList xs -> SList xs -> SList xs # min :: SList xs -> SList xs -> SList xs #
Show (SList xs) Source #
Instance details Defined in Data.SOP.Sing Methods showsPrec :: Int -> SList xs -> ShowS # show :: SList xs -> String # showList :: [SList xs] -> ShowS #

type SListI = All Top Source #

Implicit singleton list.

A singleton list can be used to reveal the structure of a type-level list argument that the function is quantified over.

Since 0.4.0.0, this is now defined in terms of All. A singleton list provides a witness for a type-level list where the elements need not satisfy any additional constraints.

Since: 0.4.0.0

type SListI2 = All SListI Source #

Require a singleton for every inner list in a list of lists.

sList :: SListI xs => SList xs Source #

Get hold of an explicit singleton (that one can then pattern match on) for a type-level list

para_SList :: SListI xs => r '[] -> (forall y ys. SListI ys => r ys -> r (y ': ys)) -> r xs Source #

Paramorphism for a type-level list.

Since: 0.4.0.0

case_SList :: SListI xs => r '[] -> (forall y ys. SListI ys => r (y ': ys)) -> r xs Source #

Case distinction on a type-level list.

Since: 0.4.0.0

Shape of type-level lists

data Shape :: [k] -> Type where Source #

Occasionally it is useful to have an explicit, term-level, representation of type-level lists (esp because of https://ghc.haskell.org/trac/ghc/ticket/9108 )

Constructors

ShapeNil :: Shape '[]
ShapeCons :: SListI xs => Shape xs -> Shape (x ': xs)

Instances

Instances details

Eq (Shape xs) Source #
Instance details Defined in Data.SOP.Sing Methods (==) :: Shape xs -> Shape xs -> Bool # (/=) :: Shape xs -> Shape xs -> Bool #
Ord (Shape xs) Source #
Instance details Defined in Data.SOP.Sing Methods compare :: Shape xs -> Shape xs -> Ordering # (<) :: Shape xs -> Shape xs -> Bool # (<=) :: Shape xs -> Shape xs -> Bool # (>) :: Shape xs -> Shape xs -> Bool # (>=) :: Shape xs -> Shape xs -> Bool # max :: Shape xs -> Shape xs -> Shape xs # min :: Shape xs -> Shape xs -> Shape xs #
Show (Shape xs) Source #
Instance details Defined in Data.SOP.Sing Methods showsPrec :: Int -> Shape xs -> ShowS # show :: Shape xs -> String # showList :: [Shape xs] -> ShowS #

shape :: forall (xs :: [k]). SListI xs => Shape xs Source #

The shape of a type-level list.

lengthSList :: forall (xs :: [k]) proxy. SListI xs => proxy xs -> Int Source #

The length of a type-level list.

Since: 0.2

Re-exports

data Proxy (t :: k) #

Proxy is a type that holds no data, but has a phantom parameter of arbitrary type (or even kind). Its use is to provide type information, even though there is no value available of that type (or it may be too costly to create one).

Historically, Proxy :: Proxy a is a safer alternative to the undefined :: a idiom.

>>> Proxy :: Proxy (Void, Int -> Int)
Proxy

Proxy can even hold types of higher kinds,

>>> Proxy :: Proxy Either
Proxy

>>> Proxy :: Proxy Functor
Proxy

>>> Proxy :: Proxy complicatedStructure
Proxy

Constructors

Proxy

Instances

Instances details

Generic1 (Proxy :: k -> Type)	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Associated Types type Rep1 Proxy :: k -> Type # Methods from1 :: forall (a :: k0). Proxy a -> Rep1 Proxy a # to1 :: forall (a :: k0). Rep1 Proxy a -> Proxy a #
Monad (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods (>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b # (>>) :: Proxy a -> Proxy b -> Proxy b # return :: a -> Proxy a #
Functor (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods fmap :: (a -> b) -> Proxy a -> Proxy b # (<$) :: a -> Proxy b -> Proxy a #
Applicative (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods pure :: a -> Proxy a # (<>) :: Proxy (a -> b) -> Proxy a -> Proxy b # liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c # (>) :: Proxy a -> Proxy b -> Proxy b # (<*) :: Proxy a -> Proxy b -> Proxy a #
Foldable (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Proxy m -> m # foldMap :: Monoid m => (a -> m) -> Proxy a -> m # foldMap' :: Monoid m => (a -> m) -> Proxy a -> m # foldr :: (a -> b -> b) -> b -> Proxy a -> b # foldr' :: (a -> b -> b) -> b -> Proxy a -> b # foldl :: (b -> a -> b) -> b -> Proxy a -> b # foldl' :: (b -> a -> b) -> b -> Proxy a -> b # foldr1 :: (a -> a -> a) -> Proxy a -> a # foldl1 :: (a -> a -> a) -> Proxy a -> a # toList :: Proxy a -> [a] # null :: Proxy a -> Bool # length :: Proxy a -> Int # elem :: Eq a => a -> Proxy a -> Bool # maximum :: Ord a => Proxy a -> a # minimum :: Ord a => Proxy a -> a # sum :: Num a => Proxy a -> a # product :: Num a => Proxy a -> a #
Traversable (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Proxy a -> f (Proxy b) # sequenceA :: Applicative f => Proxy (f a) -> f (Proxy a) # mapM :: Monad m => (a -> m b) -> Proxy a -> m (Proxy b) # sequence :: Monad m => Proxy (m a) -> m (Proxy a) #
Eq1 (Proxy :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq :: (a -> b -> Bool) -> Proxy a -> Proxy b -> Bool #
Ord1 (Proxy :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftCompare :: (a -> b -> Ordering) -> Proxy a -> Proxy b -> Ordering #
Read1 (Proxy :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Proxy a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Proxy a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Proxy a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Proxy a] #
Show1 (Proxy :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Proxy a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Proxy a] -> ShowS #
Alternative (Proxy :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods empty :: Proxy a # (<\|>) :: Proxy a -> Proxy a -> Proxy a # some :: Proxy a -> Proxy [a] # many :: Proxy a -> Proxy [a] #
MonadPlus (Proxy :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods mzero :: Proxy a # mplus :: Proxy a -> Proxy a -> Proxy a #
NFData1 (Proxy :: Type -> Type)	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> Proxy a -> () #
Bounded (Proxy t)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods minBound :: Proxy t # maxBound :: Proxy t #
Enum (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods succ :: Proxy s -> Proxy s # pred :: Proxy s -> Proxy s # toEnum :: Int -> Proxy s # fromEnum :: Proxy s -> Int # enumFrom :: Proxy s -> [Proxy s] # enumFromThen :: Proxy s -> Proxy s -> [Proxy s] # enumFromTo :: Proxy s -> Proxy s -> [Proxy s] # enumFromThenTo :: Proxy s -> Proxy s -> Proxy s -> [Proxy s] #
Eq (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods (==) :: Proxy s -> Proxy s -> Bool # (/=) :: Proxy s -> Proxy s -> Bool #
Ord (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods compare :: Proxy s -> Proxy s -> Ordering # (<) :: Proxy s -> Proxy s -> Bool # (<=) :: Proxy s -> Proxy s -> Bool # (>) :: Proxy s -> Proxy s -> Bool # (>=) :: Proxy s -> Proxy s -> Bool # max :: Proxy s -> Proxy s -> Proxy s # min :: Proxy s -> Proxy s -> Proxy s #
Read (Proxy t)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods readsPrec :: Int -> ReadS (Proxy t) # readList :: ReadS [Proxy t] # readPrec :: ReadPrec (Proxy t) # readListPrec :: ReadPrec [Proxy t] #
Show (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods showsPrec :: Int -> Proxy s -> ShowS # show :: Proxy s -> String # showList :: [Proxy s] -> ShowS #
Ix (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods range :: (Proxy s, Proxy s) -> [Proxy s] # index :: (Proxy s, Proxy s) -> Proxy s -> Int # unsafeIndex :: (Proxy s, Proxy s) -> Proxy s -> Int # inRange :: (Proxy s, Proxy s) -> Proxy s -> Bool # rangeSize :: (Proxy s, Proxy s) -> Int # unsafeRangeSize :: (Proxy s, Proxy s) -> Int #
Generic (Proxy t)	Since: base-4.6.0.0
Instance details Defined in GHC.Generics Associated Types type Rep (Proxy t) :: Type -> Type # Methods from :: Proxy t -> Rep (Proxy t) x # to :: Rep (Proxy t) x -> Proxy t #
Semigroup (Proxy s)	Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods (<>) :: Proxy s -> Proxy s -> Proxy s # sconcat :: NonEmpty (Proxy s) -> Proxy s # stimes :: Integral b => b -> Proxy s -> Proxy s #
Monoid (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods mempty :: Proxy s # mappend :: Proxy s -> Proxy s -> Proxy s # mconcat :: [Proxy s] -> Proxy s #
NFData (Proxy a)	Since: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Proxy a -> () #
type Rep1 (Proxy :: k -> Type)
Instance details Defined in GHC.Generics type Rep1 (Proxy :: k -> Type) = D1 ('MetaData "Proxy" "Data.Proxy" "base" 'False) (C1 ('MetaCons "Proxy" 'PrefixI 'False) (U1 :: k -> Type))
type Rep (Proxy t)
Instance details Defined in GHC.Generics type Rep (Proxy t) = D1 ('MetaData "Proxy" "Data.Proxy" "base" 'False) (C1 ('MetaCons "Proxy" 'PrefixI 'False) (U1 :: Type -> Type))

n-ary datatypes

Instances

Instances

Instances

Instances

Combinators

Constructing products

Instances

Destructing products

Application

Instances

Instances

Lifting / mapping

Constructing sums

Instances

Instances

Destructing sums

Instances

Dealing with All c

Comparison

Collapsing

Instances

Instances

Folding and sequencing

Instances

Instances

Expanding sums to products

Instances

Transformation of index lists and coercions

Instances

Partial operations

Utilities

Basic functors

Instances

Instances

Instances

Mapping functions

Mapping constraints

Instances

Instances

Instances

Instances

Instances

Other constraints

Instances

Instances

Instances

Instances

Singletons

Instances

Shape of type-level lists

Instances

Re-exports

Instances

Dealing with `All c`