Generics.SOP.NP

n-ary products (and products of products)

Datatypes

data NP :: (k -> *) -> [k] -> * where

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

HSequence [k] k (NP k)

Methods

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

HCollapse [k] k (NP k)

Methods

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

HAp [k] k (NP k)

Methods

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

HPure [k] k (NP k)

Methods

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

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

All k (Compose * k Eq f) xs => Eq (NP k f xs)

Methods

(==) :: NP k f xs -> NP k f xs -> Bool

(/=) :: NP k f xs -> NP k f xs -> Bool

(All k (Compose * k Eq f) xs, All k (Compose * k Ord f) xs) => Ord (NP k f xs)

Methods

compare :: NP k f xs -> NP k f xs -> Ordering

(<) :: NP k f xs -> NP k f xs -> Bool

(<=) :: NP k f xs -> NP k f xs -> Bool

(>) :: NP k f xs -> NP k f xs -> Bool

(>=) :: NP k f xs -> NP k f xs -> Bool

max :: NP k f xs -> NP k f xs -> NP k f xs

min :: NP k f xs -> NP k f xs -> NP k f xs

All k (Compose * k Show f) xs => Show (NP k f xs)

Methods

showsPrec :: Int -> NP k f xs -> ShowS

show :: NP k f xs -> String

showList :: [NP k f xs] -> ShowS

type SListIN [k] k (NP k)

type SListIN [k] k (NP k) = SListI k

type Prod [k] k (NP k)

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

type AllN [k] k (NP k) c

type AllN [k] k (NP k) c = All k c

type CollapseTo [k] k (NP k) a

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

newtype POP f xss

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

HSequence [[k]] k (POP k)

Methods

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

HCollapse [[k]] k (POP k)

Methods

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

HAp [[k]] k (POP k)

Methods

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

HPure [[k]] k (POP k)

Methods

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

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

Eq (NP [k] (NP k f) xss) => Eq (POP k f xss)

Methods

(==) :: POP k f xss -> POP k f xss -> Bool

(/=) :: POP k f xss -> POP k f xss -> Bool

Ord (NP [k] (NP k f) xss) => Ord (POP k f xss)

Methods

compare :: POP k f xss -> POP k f xss -> Ordering

(<) :: POP k f xss -> POP k f xss -> Bool

(<=) :: POP k f xss -> POP k f xss -> Bool

(>) :: POP k f xss -> POP k f xss -> Bool

(>=) :: POP k f xss -> POP k f xss -> Bool

max :: POP k f xss -> POP k f xss -> POP k f xss

min :: POP k f xss -> POP k f xss -> POP k f xss

Show (NP [k] (NP k f) xss) => Show (POP k f xss)

Methods

showsPrec :: Int -> POP k f xss -> ShowS

show :: POP k f xss -> String

showList :: [POP k f xss] -> ShowS

type SListIN [[k]] k (POP k)

type SListIN [[k]] k (POP k) = SListI2 k

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

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

type AllN [[k]] k (POP k) c

type AllN [[k]] k (POP k) c = All2 k c

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

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

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

Unwrap a product of products.

Constructing products

pure_NP :: forall f xs. SListI xs => (forall a. f a) -> NP f xs

Specialization of hpure.

The call pure_NP x generates a product that contains x in every element position.

Example:

>>> pure_NP [] :: NP [] '[Char, Bool]
"" :* [] :* Nil
>>> pure_NP (K 0) :: NP (K Int) '[Double, Int, String]
K 0 :* K 0 :* K 0 :* Nil

pure_POP :: All SListI xss => (forall a. f a) -> POP f xss

Specialization of hpure.

The call pure_POP x generates a product of products that contains x in every element position.

cpure_NP :: forall c xs proxy f. All c xs => proxy c -> (forall a. c a => f a) -> NP f xs

Specialization of hcpure.

The call cpure_NP p x generates a product that contains x in every element position.

cpure_POP :: forall c xss proxy f. All2 c xss => proxy c -> (forall a. c a => f a) -> POP f xss

Specialization of hcpure.

The call cpure_NP p x generates a product of products that contains x in every element position.

Construction from a list

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

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.

Application

ap_NP :: NP (f -.-> g) xs -> NP f xs -> NP g xs

Specialization of hap.

Applies a product of (lifted) functions pointwise to a product of suitable arguments.

ap_POP :: POP (f -.-> g) xss -> POP f xss -> POP g xss

Specialization of hap.

Applies a product of (lifted) functions pointwise to a product of suitable arguments.

Destructing products

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

Obtain the head of an n-ary product.

Since: 0.2.1.0

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

Obtain the tail of an n-ary product.

Since: 0.2.1.0

type Projection f xs = K (NP f xs) -.-> f

The type of projections from an n-ary product.

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

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

Lifting / mapping

liftA_NP :: SListI xs => (forall a. f a -> g a) -> NP f xs -> NP g xs

Specialization of hliftA.

liftA_POP :: All SListI xss => (forall a. f a -> g a) -> POP f xss -> POP g xss

Specialization of hliftA.

liftA2_NP :: SListI xs => (forall a. f a -> g a -> h a) -> NP f xs -> NP g xs -> NP h xs

Specialization of hliftA2.

liftA2_POP :: All SListI xss => (forall a. f a -> g a -> h a) -> POP f xss -> POP g xss -> POP h xss

Specialization of hliftA2.

liftA3_NP :: SListI xs => (forall a. f a -> g a -> h a -> i a) -> NP f xs -> NP g xs -> NP h xs -> NP i xs

Specialization of hliftA3.

liftA3_POP :: All SListI xss => (forall a. f a -> g a -> h a -> i a) -> POP f xss -> POP g xss -> POP h xss -> POP i xss

Specialization of hliftA3.

map_NP :: SListI xs => (forall a. f a -> g a) -> NP f xs -> NP g xs

Specialization of hmap, which is equivalent to hliftA.

map_POP :: All SListI xss => (forall a. f a -> g a) -> POP f xss -> POP g xss

Specialization of hmap, which is equivalent to hliftA.

zipWith_NP :: SListI xs => (forall a. f a -> g a -> h a) -> NP f xs -> NP g xs -> NP h xs

Specialization of hzipWith, which is equivalent to hliftA2.

zipWith_POP :: All SListI xss => (forall a. f a -> g a -> h a) -> POP f xss -> POP g xss -> POP h xss

Specialization of hzipWith, which is equivalent to hliftA2.

zipWith3_NP :: SListI xs => (forall a. f a -> g a -> h a -> i a) -> NP f xs -> NP g xs -> NP h xs -> NP i xs

Specialization of hzipWith3, which is equivalent to hliftA3.

zipWith3_POP :: All SListI xss => (forall a. f a -> g a -> h a -> i a) -> POP f xss -> POP g xss -> POP h xss -> POP i xss

Specialization of hzipWith3, which is equivalent to hliftA3.

cliftA_NP :: All c xs => proxy c -> (forall a. c a => f a -> g a) -> NP f xs -> NP g xs

Specialization of hcliftA.

cliftA_POP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a) -> POP f xss -> POP g xss

Specialization of hcliftA.

cliftA2_NP :: All c xs => proxy c -> (forall a. c a => f a -> g a -> h a) -> NP f xs -> NP g xs -> NP h xs

Specialization of hcliftA2.

cliftA2_POP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a -> h a) -> POP f xss -> POP g xss -> POP h xss

Specialization of hcliftA2.

cliftA3_NP :: All c xs => proxy c -> (forall a. c a => f a -> g a -> h a -> i a) -> NP f xs -> NP g xs -> NP h xs -> NP i xs

Specialization of hcliftA3.

cliftA3_POP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a -> h a -> i a) -> POP f xss -> POP g xss -> POP h xss -> POP i xss

Specialization of hcliftA3.

cmap_NP :: All c xs => proxy c -> (forall a. c a => f a -> g a) -> NP f xs -> NP g xs

Specialization of hcmap, which is equivalent to hcliftA.

cmap_POP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a) -> POP f xss -> POP g xss

Specialization of hcmap, which is equivalent to hcliftA.

czipWith_NP :: All c xs => proxy c -> (forall a. c a => f a -> g a -> h a) -> NP f xs -> NP g xs -> NP h xs

Specialization of hczipWith, which is equivalent to hcliftA2.

czipWith_POP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a -> h a) -> POP f xss -> POP g xss -> POP h xss

Specialization of hczipWith, which is equivalent to hcliftA2.

czipWith3_NP :: All c xs => proxy c -> (forall a. c a => f a -> g a -> h a -> i a) -> NP f xs -> NP g xs -> NP h xs -> NP i xs

Specialization of hczipWith3, which is equivalent to hcliftA3.

czipWith3_POP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a -> h a -> i a) -> POP f xss -> POP g xss -> POP h xss -> POP i xss

Specialization of hczipWith3, which is equivalent to hcliftA3.

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

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

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

Deprecated: Use hcliftA3 or hczipWith3 instead.

Like hcliftA', but for ternay functions.

cliftA2'_NP :: All2 c xss => proxy c -> (forall xs. All c xs => f xs -> g xs -> h xs) -> NP f xss -> NP g xss -> NP h xss

Deprecated: Use cliftA2_NP instead.

Specialization of hcliftA2'.

Collapsing

collapse_NP :: NP (K a) xs -> [a]

Specialization of hcollapse.

Example:

>>> collapse_NP (K 1 :* K 2 :* K 3 :* Nil)
[1,2,3]

collapse_POP :: SListI xss => POP (K a) xss -> [[a]]

Specialization of hcollapse.

Example:

>>> collapse_POP (POP ((K 'a' :* Nil) :* (K 'b' :* K 'c' :* Nil) :* Nil) :: POP (K Char) '[ '[(a :: *)], '[b, c] ])
["a", "bc"]

(The type signature is only necessary in this case to fix the kind of the type variables.)

Sequencing

sequence'_NP :: Applicative f => NP (f :.: g) xs -> f (NP g xs)

Specialization of hsequence'.

sequence'_POP :: (SListI xss, Applicative f) => POP (f :.: g) xss -> f (POP g xss)

Specialization of hsequence'.

sequence_NP :: (SListI xs, Applicative f) => NP f xs -> f (NP I xs)

Specialization of hsequence.

Example:

>>> sequence_NP (Just 1 :* Just 2 :* Nil)
Just (I 1 :* I 2 :* Nil)

sequence_POP :: (All SListI xss, Applicative f) => POP f xss -> f (POP I xss)

Specialization of hsequence.

Example:

>>> sequence_POP (POP ((Just 1 :* Nil) :* (Just 2 :* Just 3 :* Nil) :* Nil))
Just (POP ((I 1 :* Nil) :* ((I 2 :* (I 3 :* Nil)) :* Nil)))