Generics.SOP.Classes

Classes for generalized combinators on SOP types.

In the SOP approach to generic programming, we're predominantly concerned with four structured datatypes:

  NP  :: (k -> *) -> ( [k]  -> *)   -- n-ary product
  NS  :: (k -> *) -> ( [k]  -> *)   -- n-ary sum
  POP :: (k -> *) -> ([[k]] -> *)   -- product of products
  SOP :: (k -> *) -> ([[k]] -> *)   -- sum of products

All of these have a kind that fits the following pattern:

  (k -> *) -> (l -> *)

These four types support similar interfaces. In order to allow reusing the same combinator names for all of these types, we define various classes in this module that allow the necessary generalization.

The classes typically lift concepts that exist for kinds * or * -> * to datatypes of kind (k -> *) -> (l -> *). This module also derives a number of derived combinators.

The actual instances are defined in Generics.SOP.NP and Generics.SOP.NS.

Generalized applicative functor structure

Generalized pure

class HPure (h :: (k -> *) -> l -> *) where

A generalization of pure or return to higher kinds.

Minimal complete definition

hpure, hcpure

Methods

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

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

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 AllMap h c xs states.

Morally, hpure is a special case of hcpure where the constraint is empty. However, it is in the nature of how AllMap is defined as well as current GHC limitations that it is tricky to prove to GHC in general that AllMap h c NoConstraint xs is always satisfied. Therefore, we typically define hpure separately and directly, and make it a member of the class.

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

HPure k [k] (NP k)

Methods

hpure :: SListIN (NP k) l h xs => (forall (a :: NP k). f a) -> h f xs

hcpure :: AllN (NP k) l h c xs => proxy c -> (forall (a :: NP k). c a => f a) -> h f xs

HPure k [[k]] (POP k)

Methods

hpure :: SListIN (POP k) l h xs => (forall (a :: POP k). f a) -> h f xs

hcpure :: AllN (POP k) l h c xs => proxy c -> (forall (a :: POP k). c a => f a) -> h f xs

Generalized <*>

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

Lifted functions.

Constructors

Fn

Fields

• apFn :: f a -> g a

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

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

Construct a binary lifted function.

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

Construct a ternary lifted function.

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

Construct a quarternary lifted function.

type family Same (h :: (k1 -> *) -> l1 -> *) :: (k2 -> *) -> l2 -> *

Maps a structure to the same structure.

Instances

type Same k1 [k1] k2 [k2] (NP k1)

type Same k1 [k1] k2 [k2] (NP k1) = NP k2

type Same k1 [[k1]] k2 [[k2]] (POP k1)

type Same k1 [[k1]] k2 [[k2]] (POP k1) = POP k2

type Same k1 [k1] k2 [k2] (NS k1)

type Same k1 [k1] k2 [k2] (NS k1) = NS k2

type Same k1 [[k1]] k2 [[k2]] (SOP k1)

type Same k1 [[k1]] k2 [[k2]] (SOP k1) = SOP k2

type family Prod (h :: (k -> *) -> l -> *) :: (k -> *) -> l -> *

Maps a structure containing sums to the corresponding product structure.

Instances

type Prod k [k] (NP k)

type Prod k [k] (NP k) = NP k

type Prod k [[k]] (POP k)

type Prod k [[k]] (POP k) = POP k

type Prod k [k] (NS k)

type Prod k [k] (NS k) = NP k

type Prod k [[k]] (SOP k)

type Prod k [[k]] (SOP k) = POP k

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

A generalization of <*>.

Minimal complete definition

hap

Methods

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

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

HAp k [k] (NP k)

Methods

hap :: Prod (NP k) l h ((NP k -.-> f) g) xs -> h f xs -> h g xs

HAp k [[k]] (POP k)

Methods

hap :: Prod (POP k) l h ((POP k -.-> f) g) xs -> h f xs -> h g xs

HAp k [k] (NS k)

Methods

hap :: Prod (NS k) l h ((NS k -.-> f) g) xs -> h f xs -> h g xs

HAp k [[k]] (SOP k)

Methods

hap :: Prod (SOP k) l h ((SOP k -.-> f) g) xs -> h f xs -> h g xs

Derived functions

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

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

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

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

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

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

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

Another name for hliftA3.

Since: 0.2

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

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

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

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

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

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

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

Another name for hcliftA3.

Since: 0.2

Collapsing homogeneous structures

type family CollapseTo (h :: (k -> *) -> l -> *) (x :: *) :: *

Maps products to lists, and sums to identities.

Instances

type CollapseTo k [k] (NP k) a

type CollapseTo k [k] (NP k) a = [a]

type CollapseTo k [[k]] (POP k) a

type CollapseTo k [[k]] (POP k) a = [[a]]

type CollapseTo k [k] (NS k) a

type CollapseTo k [k] (NS k) a = a

type CollapseTo k [[k]] (SOP k) a

type CollapseTo k [[k]] (SOP k) a = [a]

class HCollapse (h :: (k -> *) -> l -> *) where

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

Minimal complete definition

hcollapse

Methods

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

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

HCollapse k [k] (NP k)

Methods

hcollapse :: SListIN (NP k) l h xs => h (K (NP k) a) xs -> CollapseTo (NP k) l h a

HCollapse k [[k]] (POP k)

Methods

hcollapse :: SListIN (POP k) l h xs => h (K (POP k) a) xs -> CollapseTo (POP k) l h a

HCollapse k [k] (NS k)

Methods

hcollapse :: SListIN (NS k) l h xs => h (K (NS k) a) xs -> CollapseTo (NS k) l h a

HCollapse k [[k]] (SOP k)

Methods

hcollapse :: SListIN (SOP k) l h xs => h (K (SOP k) a) xs -> CollapseTo (SOP k) l h a

Folding and sequencing

class HTraverse_ (h :: (k -> *) -> l -> *) where

A generalization of traverse_ or foldMap.

Since: 0.3.2.0

Minimal complete definition

hctraverse_, htraverse_

Methods

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

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 ()

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

HTraverse_ k [k] (NP k)

Methods

hctraverse_ :: (AllN (NP k) l h c xs, Applicative g) => proxy c -> (forall (a :: NP k). c a => f a -> g ()) -> h f xs -> g ()

htraverse_ :: (SListIN (NP k) l h xs, Applicative g) => (forall (a :: NP k). f a -> g ()) -> h f xs -> g ()

HTraverse_ k [[k]] (POP k)

Methods

hctraverse_ :: (AllN (POP k) l h c xs, Applicative g) => proxy c -> (forall (a :: POP k). c a => f a -> g ()) -> h f xs -> g ()

htraverse_ :: (SListIN (POP k) l h xs, Applicative g) => (forall (a :: POP k). f a -> g ()) -> h f xs -> g ()

HTraverse_ k [k] (NS k)

Methods

hctraverse_ :: (AllN (NS k) l h c xs, Applicative g) => proxy c -> (forall (a :: NS k). c a => f a -> g ()) -> h f xs -> g ()

htraverse_ :: (SListIN (NS k) l h xs, Applicative g) => (forall (a :: NS k). f a -> g ()) -> h f xs -> g ()

HTraverse_ k [[k]] (SOP k)

Methods

hctraverse_ :: (AllN (SOP k) l h c xs, Applicative g) => proxy c -> (forall (a :: SOP k). c a => f a -> g ()) -> h f xs -> g ()

htraverse_ :: (SListIN (SOP k) l h xs, Applicative g) => (forall (a :: SOP k). f a -> g ()) -> h f xs -> g ()

class HAp h => HSequence (h :: (k -> *) -> l -> *) where

A generalization of sequenceA.

Minimal complete definition

hsequence', hctraverse', htraverse'

Methods

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

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)

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)

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

HSequence k [k] (NP k)

Methods

hsequence' :: (SListIN (NP k) l h xs, Applicative f) => h ((* :.: NP k) f g) xs -> f (h g xs)

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

htraverse' :: (SListIN (NP k) l h xs, Applicative g) => (forall (a :: NP k). f a -> g (f' a)) -> h f xs -> g (h f' xs)

HSequence k [[k]] (POP k)

Methods

hsequence' :: (SListIN (POP k) l h xs, Applicative f) => h ((* :.: POP k) f g) xs -> f (h g xs)

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

htraverse' :: (SListIN (POP k) l h xs, Applicative g) => (forall (a :: POP k). f a -> g (f' a)) -> h f xs -> g (h f' xs)

HSequence k [k] (NS k)

Methods

hsequence' :: (SListIN (NS k) l h xs, Applicative f) => h ((* :.: NS k) f g) xs -> f (h g xs)

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

htraverse' :: (SListIN (NS k) l h xs, Applicative g) => (forall (a :: NS k). f a -> g (f' a)) -> h f xs -> g (h f' xs)

HSequence k [[k]] (SOP k)

Methods

hsequence' :: (SListIN (SOP k) l h xs, Applicative f) => h ((* :.: SOP k) f g) xs -> f (h g xs)

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

htraverse' :: (SListIN (SOP k) l h xs, Applicative g) => (forall (a :: SOP k). f a -> g (f' a)) -> h f xs -> g (h f' xs)

Derived functions

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

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 ()

Flipped version of hctraverse_.

Since: 0.3.2.0

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

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)

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)

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)

Flipped version of hctraverse.

Since: 0.3.2.0

Indexing into sums

class HIndex (h :: (k -> *) -> l -> *) where

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

Minimal complete definition

hindex

Methods

hindex :: h f xs -> Int

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

HIndex k [k] (NS k)

Methods

hindex :: h f xs -> Int

HIndex k [[k]] (SOP k)

Methods

hindex :: h f xs -> Int

Applying all injections

type family UnProd (h :: (k -> *) -> l -> *) :: (k -> *) -> l -> *

Maps a structure containing products to the corresponding sum structure.

Since: 0.2.4.0

Instances

type UnProd k [k] (NP k)

type UnProd k [k] (NP k) = NS k

type UnProd k [[k]] (POP k)

type UnProd k [[k]] (POP k) = SOP k

class UnProd (Prod h) ~ h => HApInjs (h :: (k -> *) -> l -> *) where

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

Minimal complete definition

hapInjs

Methods

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

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

HApInjs k [k] (NS k)

Methods

hapInjs :: SListIN (NS k) l h xs => Prod (NS k) l h f xs -> [h f xs]

HApInjs k [[k]] (SOP k)

Methods

hapInjs :: SListIN (SOP k) l h xs => Prod (SOP k) l h f xs -> [h f xs]

Expanding sums to products

class HExpand (h :: (k -> *) -> l -> *) where

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

Minimal complete definition

hexpand, hcexpand

Methods

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

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

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

HExpand k [k] (NS k)

Methods

hexpand :: SListIN (NS k) l (Prod (NS k) l h) xs => (forall (x :: NS k). f x) -> h f xs -> Prod (NS k) l h f xs

hcexpand :: AllN (NS k) l (Prod (NS k) l h) c xs => proxy c -> (forall (x :: NS k). c x => f x) -> h f xs -> Prod (NS k) l h f xs

HExpand k [[k]] (SOP k)

Methods

hexpand :: SListIN (SOP k) l (Prod (SOP k) l h) xs => (forall (x :: SOP k). f x) -> h f xs -> Prod (SOP k) l h f xs

hcexpand :: AllN (SOP k) l (Prod (SOP k) l h) c xs => proxy c -> (forall (x :: SOP k). c x => f x) -> h f xs -> Prod (SOP k) l h f xs

Transformation of index lists and coercions

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

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

Minimal complete definition

htrans, hcoerce

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

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

Coerce a structure into a representationally equal structure.

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

HTrans k1 [k1] k2 [k2] (NP k1) (NP k2)

Methods

htrans :: AllZipN (NP k1) (NP k2) (NP k1) k2 (NP k2) l2 (Prod (NP k1) (NP k2) h1) c xs ys => proxy c -> (forall (x :: NP k1) (y :: k2). c x y => f x -> g y) -> h1 f xs -> h2 g ys

hcoerce :: (AllZipN (NP k1) (NP k2) (NP k1) k2 (NP k2) l2 (Prod (NP k1) (NP k2) h1) (LiftedCoercible * (NP k1) k2 f g) xs ys, HTrans (NP k1) (NP k2) k2 l2 h1 h2) => h1 f xs -> h2 g ys

HTrans k1 [[k1]] k2 [[k2]] (POP k1) (POP k2)

Methods

htrans :: AllZipN (POP k1) (POP k2) (POP k1) k2 (POP k2) l2 (Prod (POP k1) (POP k2) h1) c xs ys => proxy c -> (forall (x :: POP k1) (y :: k2). c x y => f x -> g y) -> h1 f xs -> h2 g ys

hcoerce :: (AllZipN (POP k1) (POP k2) (POP k1) k2 (POP k2) l2 (Prod (POP k1) (POP k2) h1) (LiftedCoercible * (POP k1) k2 f g) xs ys, HTrans (POP k1) (POP k2) k2 l2 h1 h2) => h1 f xs -> h2 g ys

HTrans k1 [k1] k2 [k2] (NS k1) (NS k2)

Methods

htrans :: AllZipN (NS k1) (NS k2) (NS k1) k2 (NS k2) l2 (Prod (NS k1) (NS k2) h1) c xs ys => proxy c -> (forall (x :: NS k1) (y :: k2). c x y => f x -> g y) -> h1 f xs -> h2 g ys

hcoerce :: (AllZipN (NS k1) (NS k2) (NS k1) k2 (NS k2) l2 (Prod (NS k1) (NS k2) h1) (LiftedCoercible * (NS k1) k2 f g) xs ys, HTrans (NS k1) (NS k2) k2 l2 h1 h2) => h1 f xs -> h2 g ys

HTrans k1 [[k1]] k2 [[k2]] (SOP k1) (SOP k2)

Methods

htrans :: AllZipN (SOP k1) (SOP k2) (SOP k1) k2 (SOP k2) l2 (Prod (SOP k1) (SOP k2) h1) c xs ys => proxy c -> (forall (x :: SOP k1) (y :: k2). c x y => f x -> g y) -> h1 f xs -> h2 g ys

hcoerce :: (AllZipN (SOP k1) (SOP k2) (SOP k1) k2 (SOP k2) l2 (Prod (SOP k1) (SOP k2) h1) (LiftedCoercible * (SOP k1) k2 f g) xs ys, HTrans (SOP k1) (SOP k2) k2 l2 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

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

Specialization of hcoerce.

Since: 0.3.1.0