Safe Haskell | None |
---|---|
Language | Haskell2010 |
n-ary sums (and sums of products)
Synopsis
- data NS :: (k -> Type) -> [k] -> Type where
- newtype SOP (f :: k -> Type) (xss :: [[k]]) = SOP (NS (NP f) xss)
- unSOP :: SOP f xss -> NS (NP f) xss
- 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
- apInjs_NP :: SListI xs => NP f xs -> [NS f xs]
- apInjs'_NP :: SListI xs => NP f xs -> NP (K (NS f xs)) xs
- apInjs_POP :: SListI xss => POP f xss -> [SOP f xss]
- apInjs'_POP :: SListI xss => POP f xss -> NP (K (SOP f xss)) xss
- unZ :: NS f '[x] -> f x
- index_NS :: forall f xs. NS f xs -> Int
- index_SOP :: SOP f xs -> Int
- type Ejection (f :: k -> Type) (xs :: [k]) = K (NS f xs) -.-> (Maybe :.: f)
- ejections :: forall xs f. SListI xs => NP (Ejection f xs) xs
- shiftEjection :: forall f x xs a. Ejection f xs a -> Ejection f (x ': xs) a
- ap_NS :: NP (f -.-> g) xs -> NS f xs -> NS g xs
- ap_SOP :: POP (f -.-> g) xss -> SOP f xss -> SOP g xss
- liftA_NS :: SListI xs => (forall a. f a -> g a) -> NS f xs -> NS g xs
- liftA_SOP :: All SListI xss => (forall a. f a -> g a) -> SOP f xss -> SOP g xss
- liftA2_NS :: SListI xs => (forall a. f a -> g a -> h a) -> NP f xs -> NS g xs -> NS h xs
- liftA2_SOP :: All SListI xss => (forall a. f a -> g a -> h a) -> POP f xss -> SOP g xss -> SOP h xss
- cliftA_NS :: All c xs => proxy c -> (forall a. c a => f a -> g a) -> NS f xs -> NS g xs
- cliftA_SOP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a) -> SOP f xss -> SOP g xss
- cliftA2_NS :: All c xs => proxy c -> (forall a. c a => f a -> g a -> h a) -> NP f xs -> NS g xs -> NS h xs
- cliftA2_SOP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a -> h a) -> POP f xss -> SOP g xss -> SOP h xss
- map_NS :: SListI xs => (forall a. f a -> g a) -> NS f xs -> NS g xs
- map_SOP :: All SListI xss => (forall a. f a -> g a) -> SOP f xss -> SOP g xss
- cmap_NS :: All c xs => proxy c -> (forall a. c a => f a -> g a) -> NS f xs -> NS g xs
- cmap_SOP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a) -> SOP f xss -> SOP g xss
- cliftA2'_NS :: All2 c xss => proxy c -> (forall xs. All c xs => f xs -> g xs -> h xs) -> NP f xss -> NS g xss -> NS h 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
- collapse_NS :: NS (K a) xs -> a
- collapse_SOP :: SListI xss => SOP (K a) xss -> [a]
- ctraverse__NS :: forall c proxy xs f g. All c xs => proxy c -> (forall a. c a => f a -> g ()) -> NS f xs -> g ()
- ctraverse__SOP :: forall c proxy xss f g. (All2 c xss, Applicative g) => proxy c -> (forall a. c a => f a -> g ()) -> SOP f xss -> g ()
- traverse__NS :: forall xs f g. SListI xs => (forall a. f a -> g ()) -> NS f xs -> g ()
- traverse__SOP :: forall xss f g. (SListI2 xss, Applicative g) => (forall a. f a -> g ()) -> SOP f xss -> g ()
- cfoldMap_NS :: forall c proxy f xs m. All c xs => proxy c -> (forall a. c a => f a -> m) -> NS f xs -> m
- cfoldMap_SOP :: (All2 c xs, Monoid m) => proxy c -> (forall a. c a => f a -> m) -> SOP f xs -> m
- sequence'_NS :: Applicative f => NS (f :.: g) xs -> f (NS g xs)
- sequence'_SOP :: (SListI xss, Applicative f) => SOP (f :.: g) xss -> f (SOP g xss)
- sequence_NS :: (SListI xs, Applicative f) => NS f xs -> f (NS I xs)
- sequence_SOP :: (All SListI xss, Applicative f) => SOP f xss -> f (SOP I xss)
- ctraverse'_NS :: forall c proxy xs f f' g. (All c xs, Functor g) => proxy c -> (forall a. c a => f a -> g (f' a)) -> NS f xs -> g (NS f' xs)
- 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)
- traverse'_NS :: forall xs f f' g. (SListI xs, Functor g) => (forall a. f a -> g (f' a)) -> NS f xs -> g (NS f' xs)
- traverse'_SOP :: (SListI2 xss, Applicative g) => (forall a. f a -> g (f' a)) -> SOP f xss -> g (SOP f' xss)
- ctraverse_NS :: (All c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g a) -> NP f xs -> g (NP I xs)
- ctraverse_SOP :: (All2 c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g a) -> POP f xs -> g (POP I xs)
- cata_NS :: forall r f xs. (forall y ys. f y -> r (y ': ys)) -> (forall y ys. r ys -> r (y ': ys)) -> NS f xs -> r xs
- ccata_NS :: forall c proxy r f xs. All c xs => proxy c -> (forall y ys. c y => f y -> r (y ': ys)) -> (forall y ys. c y => r ys -> r (y ': ys)) -> NS f xs -> r xs
- ana_NS :: forall s f xs. SListI xs => (forall r. s '[] -> r) -> (forall y ys. s (y ': ys) -> Either (f y) (s ys)) -> s xs -> NS f xs
- cana_NS :: forall c proxy s f xs. All c xs => proxy c -> (forall r. s '[] -> r) -> (forall y ys. c y => s (y ': ys) -> Either (f y) (s ys)) -> s xs -> NS f xs
- expand_NS :: forall f xs. SListI xs => (forall x. f x) -> NS f xs -> NP f xs
- cexpand_NS :: forall c proxy f xs. All c xs => proxy c -> (forall x. c x => f x) -> NS f xs -> NP f xs
- expand_SOP :: forall f xss. All SListI xss => (forall x. f x) -> SOP f xss -> POP f xss
- cexpand_SOP :: forall c proxy f xss. All2 c xss => proxy c -> (forall x. c x => f x) -> SOP f xss -> POP f xss
- trans_NS :: AllZip c xs ys => proxy c -> (forall x y. c x y => f x -> g y) -> NS f xs -> NS g ys
- trans_SOP :: AllZip2 c xss yss => proxy c -> (forall x y. c x y => f x -> g y) -> SOP f xss -> SOP g yss
- coerce_NS :: forall f g xs ys. AllZip (LiftedCoercible f g) xs ys => NS f xs -> NS g ys
- coerce_SOP :: forall f g xss yss. AllZip2 (LiftedCoercible f g) xss yss => SOP f xss -> SOP g yss
- fromI_NS :: forall f xs ys. AllZip (LiftedCoercible I f) xs ys => NS I xs -> NS f ys
- fromI_SOP :: forall f xss yss. AllZip2 (LiftedCoercible I f) xss yss => SOP I xss -> SOP f yss
- toI_NS :: forall f xs ys. AllZip (LiftedCoercible f I) xs ys => NS f xs -> NS I ys
- toI_SOP :: forall f xss yss. AllZip2 (LiftedCoercible f I) xss yss => SOP f xss -> SOP I yss
Datatypes
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
, 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.K
a
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 ]
Instances
HTrans (NS :: (k1 -> Type) -> [k1] -> Type) (NS :: (k2 -> Type) -> [k2] -> Type) Source # | |
Defined in Data.SOP.NS 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 # | |
HApInjs (NS :: (k -> Type) -> [k] -> Type) Source # | |
HIndex (NS :: (k -> Type) -> [k] -> Type) Source # | |
HSequence (NS :: (k -> Type) -> [k] -> Type) Source # | |
Defined in Data.SOP.NS 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 # | |
Defined in Data.SOP.NS 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 # | |
Defined in Data.SOP.NS | |
HAp (NS :: (k -> Type) -> [k] -> Type) Source # | |
All (Compose Eq f) xs => Eq (NS f xs) Source # | |
(All (Compose Eq f) xs, All (Compose Ord f) xs) => Ord (NS f xs) Source # | |
All (Compose Show f) xs => Show (NS f xs) Source # | |
All (Compose NFData f) xs => NFData (NS f xs) Source # | Since: 0.2.5.0 |
Defined in Data.SOP.NS | |
type Same (NS :: (k1 -> Type) -> [k1] -> Type) Source # | |
type SListIN (NS :: (k -> Type) -> [k] -> Type) Source # | |
Defined in Data.SOP.NS | |
type Prod (NS :: (k -> Type) -> [k] -> Type) Source # | |
type AllN (NS :: (k -> Type) -> [k] -> Type) (c :: k -> Constraint) Source # | |
Defined in Data.SOP.NS | |
type CollapseTo (NS :: (k -> Type) -> [k] -> Type) a Source # | |
Defined in Data.SOP.NS |
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
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.SOP
I
Instances
HTrans (SOP :: (k1 -> Type) -> [[k1]] -> Type) (SOP :: (k2 -> Type) -> [[k2]] -> Type) Source # | |
Defined in Data.SOP.NS 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 # | |
HApInjs (SOP :: (k -> Type) -> [[k]] -> Type) Source # | |
HIndex (SOP :: (k -> Type) -> [[k]] -> Type) Source # | |
HSequence (SOP :: (k -> Type) -> [[k]] -> Type) Source # | |
Defined in Data.SOP.NS 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 # | |
Defined in Data.SOP.NS 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 # | |
Defined in Data.SOP.NS | |
HAp (SOP :: (k -> Type) -> [[k]] -> Type) Source # | |
Eq (NS (NP f) xss) => Eq (SOP f xss) Source # | |
Ord (NS (NP f) xss) => Ord (SOP f xss) Source # | |
Defined in Data.SOP.NS | |
Show (NS (NP f) xss) => Show (SOP f xss) Source # | |
NFData (NS (NP f) xss) => NFData (SOP f xss) Source # | Since: 0.2.5.0 |
Defined in Data.SOP.NS | |
type Same (SOP :: (k1 -> Type) -> [[k1]] -> Type) Source # | |
type SListIN (SOP :: (k -> Type) -> [[k]] -> Type) Source # | |
Defined in Data.SOP.NS | |
type Prod (SOP :: (k -> Type) -> [[k]] -> Type) Source # | |
type AllN (SOP :: (k -> Type) -> [[k]] -> Type) (c :: k -> Constraint) Source # | |
Defined in Data.SOP.NS | |
type CollapseTo (SOP :: (k -> Type) -> [[k]] -> Type) a Source # | |
Defined in Data.SOP.NS |
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.
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)))]
apInjs'_POP :: SListI xss => POP f xss -> NP (K (SOP f xss)) xss Source #
apInjs_POP
without hcollapse
.
Example:
>>>
apInjs'_POP (POP ((I 'x' :* Nil) :* (I True :* I 2 :* Nil) :* Nil))
K (SOP (Z (I 'x' :* Nil))) :* K (SOP (S (Z (I True :* I 2 :* Nil)))) :* Nil
Since: 0.2.5.0
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
index_NS :: forall f xs. NS f xs -> Int Source #
Obtain the index from an n-ary sum.
An n-nary sum represents a choice between n different options. This function returns an integer between 0 and n - 1 indicating the option chosen by the given value.
Examples:
>>>
index_NS (S (S (Z (I False))))
2>>>
index_NS (Z (K ()))
0
Since: 0.2.4.0
index_SOP :: SOP f xs -> Int Source #
Obtain the index from an n-ary sum of products.
An n-nary sum represents a choice between n different options. This function returns an integer between 0 and n - 1 indicating the option chosen by the given value.
Specification:
index_SOP
=index_NS
.
unSOP
Example:
>>>
index_SOP (SOP (S (Z (I True :* I 'x' :* Nil))))
1
Since: 0.2.4.0
type Ejection (f :: k -> Type) (xs :: [k]) = K (NS f xs) -.-> (Maybe :.: f) Source #
The type of ejections from an n-ary sum.
An ejection is the pattern matching function for one part of the n-ary sum.
It is the opposite of an Injection
.
Since: 0.5.0.0
ejections :: forall xs f. SListI xs => NP (Ejection f xs) xs Source #
Compute all ejections from an n-ary sum.
Each element of the resulting product contains one of the ejections.
Since: 0.5.0.0
shiftEjection :: forall f x xs a. Ejection f xs a -> Ejection f (x ': xs) a Source #
Since: 0.5.0.0
Application
Lifting / mapping
liftA_NS :: SListI xs => (forall a. f a -> g a) -> NS f xs -> NS g xs Source #
Specialization of hliftA
.
liftA_SOP :: All SListI xss => (forall a. f a -> g a) -> SOP f xss -> SOP g xss Source #
Specialization of hliftA
.
liftA2_NS :: SListI xs => (forall a. f a -> g a -> h a) -> NP f xs -> NS g xs -> NS h xs Source #
Specialization of hliftA2
.
liftA2_SOP :: All SListI xss => (forall a. f a -> g a -> h a) -> POP f xss -> SOP g xss -> SOP h xss Source #
Specialization of hliftA2
.
cliftA_NS :: All c xs => proxy c -> (forall a. c a => f a -> g a) -> NS f xs -> NS g xs Source #
Specialization of hcliftA
.
cliftA_SOP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a) -> SOP f xss -> SOP g xss Source #
Specialization of hcliftA
.
cliftA2_NS :: All c xs => proxy c -> (forall a. c a => f a -> g a -> h a) -> NP f xs -> NS g xs -> NS h xs Source #
Specialization of hcliftA2
.
cliftA2_SOP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a -> h a) -> POP f xss -> SOP g xss -> SOP h xss Source #
Specialization of hcliftA2
.
cmap_SOP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a) -> SOP f xss -> SOP g xss Source #
Dealing with
All
c
All
ccliftA2'_NS :: All2 c xss => proxy c -> (forall xs. All c xs => f xs -> g xs -> h xs) -> NP f xss -> NS g xss -> NS h xss Source #
Deprecated: Use cliftA2_NS
instead.
Specialization of hcliftA2'
.
Comparison
:: 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
:: 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
:: 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
:: 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
Folding and sequencing
ctraverse__NS :: forall c proxy xs f g. All c xs => proxy c -> (forall a. c a => f a -> g ()) -> NS f xs -> g () Source #
ctraverse__SOP :: forall c proxy xss f g. (All2 c xss, Applicative g) => proxy c -> (forall a. c a => f a -> g ()) -> SOP f xss -> g () Source #
Specialization of hctraverse_
.
Since: 0.3.2.0
traverse__NS :: forall xs f g. SListI xs => (forall a. f a -> g ()) -> NS f xs -> g () Source #
traverse__SOP :: forall xss f g. (SListI2 xss, Applicative g) => (forall a. f a -> g ()) -> SOP f xss -> g () Source #
Specialization of htraverse_
.
Since: 0.3.2.0
cfoldMap_NS :: forall c proxy f xs m. All c xs => proxy c -> (forall a. c a => f a -> m) -> NS f xs -> m Source #
cfoldMap_SOP :: (All2 c xs, Monoid m) => proxy c -> (forall a. c a => f a -> m) -> SOP f xs -> m Source #
Specialization of hcfoldMap
.
Since: 0.3.2.0
sequence'_NS :: Applicative f => NS (f :.: g) xs -> f (NS g xs) Source #
Specialization of hsequence'
.
sequence'_SOP :: (SListI xss, Applicative f) => SOP (f :.: g) xss -> f (SOP g xss) Source #
Specialization of hsequence'
.
sequence_NS :: (SListI xs, Applicative f) => NS f xs -> f (NS I xs) Source #
Specialization of hsequence
.
sequence_SOP :: (All SListI xss, Applicative f) => SOP f xss -> f (SOP I xss) Source #
Specialization of hsequence
.
ctraverse'_NS :: forall c proxy xs f f' g. (All c xs, Functor g) => proxy c -> (forall a. c a => f a -> g (f' a)) -> NS f xs -> g (NS f' xs) Source #
Specialization of hctraverse'
.
Note: as NS
has exactly one element, the Functor
constraint is enough.
Since: 0.3.2.0
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) Source #
Specialization of hctraverse'
.
Since: 0.3.2.0
traverse'_NS :: forall xs f f' g. (SListI xs, Functor g) => (forall a. f a -> g (f' a)) -> NS f xs -> g (NS f' xs) Source #
Specialization of htraverse'
.
Note: as NS
has exactly one element, the Functor
constraint is enough.
Since: 0.3.2.0
traverse'_SOP :: (SListI2 xss, Applicative g) => (forall a. f a -> g (f' a)) -> SOP f xss -> g (SOP f' xss) Source #
Specialization of htraverse'
.
Since: 0.3.2.0
ctraverse_NS :: (All c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g a) -> NP f xs -> g (NP I xs) Source #
Specialization of hctraverse
.
Since: 0.3.2.0
ctraverse_SOP :: (All2 c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g a) -> POP f xs -> g (POP I xs) Source #
Specialization of hctraverse
.
Since: 0.3.2.0
Catamorphism and anamorphism
cata_NS :: forall r f xs. (forall y ys. f y -> r (y ': ys)) -> (forall y ys. r ys -> r (y ': ys)) -> NS f xs -> r xs Source #
ccata_NS :: forall c proxy r f xs. All c xs => proxy c -> (forall y ys. c y => f y -> r (y ': ys)) -> (forall y ys. c y => r ys -> r (y ': ys)) -> NS f xs -> r xs Source #
Constrained catamorphism for NS
.
Since: 0.2.3.0
ana_NS :: forall s f xs. SListI xs => (forall r. s '[] -> r) -> (forall y ys. s (y ': ys) -> Either (f y) (s ys)) -> s xs -> NS f xs Source #
Anamorphism for NS
.
Since: 0.2.3.0
cana_NS :: forall c proxy s f xs. All c xs => proxy c -> (forall r. s '[] -> r) -> (forall y ys. c y => s (y ': ys) -> Either (f y) (s ys)) -> s xs -> NS f xs Source #
Constrained anamorphism for NS
.
Since: 0.2.3.0
Expanding sums to products
expand_NS :: forall f xs. SListI xs => (forall x. f x) -> NS f xs -> NP f xs Source #
Specialization of hexpand
.
Since: 0.2.5.0
cexpand_NS :: forall c proxy f xs. All c xs => proxy c -> (forall x. c x => f x) -> NS f xs -> NP f xs Source #
Specialization of hcexpand
.
Since: 0.2.5.0
expand_SOP :: forall f xss. All SListI xss => (forall x. f x) -> SOP f xss -> POP f xss Source #
Specialization of hexpand
.
Since: 0.2.5.0
cexpand_SOP :: forall c proxy f xss. All2 c xss => proxy c -> (forall x. c x => f x) -> SOP f xss -> POP f xss Source #
Specialization of hcexpand
.
Since: 0.2.5.0
Transformation of index lists and coercions
trans_NS :: AllZip c xs ys => proxy c -> (forall x y. c x y => f x -> g y) -> NS f xs -> NS g ys Source #
Specialization of htrans
.
Since: 0.3.1.0
trans_SOP :: AllZip2 c xss yss => proxy c -> (forall x y. c x y => f x -> g y) -> SOP f xss -> SOP g yss Source #
Specialization of htrans
.
Since: 0.3.1.0
coerce_NS :: forall f g xs ys. AllZip (LiftedCoercible f g) xs ys => NS f xs -> NS g ys Source #
Specialization of hcoerce
.
Since: 0.3.1.0
coerce_SOP :: forall f g xss yss. AllZip2 (LiftedCoercible f g) xss yss => SOP f xss -> SOP g yss Source #
Specialization of hcoerce
.
Since: 0.3.1.0
fromI_NS :: forall f xs ys. AllZip (LiftedCoercible I f) xs ys => NS I xs -> NS f ys Source #
Specialization of hfromI
.
Since: 0.3.1.0
fromI_SOP :: forall f xss yss. AllZip2 (LiftedCoercible I f) xss yss => SOP I xss -> SOP f yss Source #
Specialization of hfromI
.
Since: 0.3.1.0