Safe Haskell | None |
---|---|

Language | Haskell2010 |

n-ary products (and products of products)

- data NP :: (k -> *) -> [k] -> * where
- newtype POP f xss = POP (NP (NP f) xss)
- unPOP :: POP f xss -> NP (NP f) xss
- pure_NP :: forall f xs. SListI xs => (forall a. f a) -> NP f xs
- pure_POP :: All SListI xss => (forall a. f a) -> POP f xss
- cpure_NP :: forall c xs proxy f. All c xs => proxy c -> (forall a. c a => f a) -> NP f xs
- cpure_POP :: forall c xss proxy f. All2 c xss => proxy c -> (forall a. c a => f a) -> POP f xss
- fromList :: SListI xs => [a] -> Maybe (NP (K a) xs)
- ap_NP :: NP (f -.-> g) xs -> NP f xs -> NP g xs
- ap_POP :: POP (f -.-> g) xss -> POP f xss -> POP g xss
- hd :: NP f (x ': xs) -> f x
- tl :: NP f (x ': xs) -> NP f xs
- type Projection f xs = 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
- liftA_NP :: SListI xs => (forall a. f a -> g a) -> NP f xs -> NP g xs
- liftA_POP :: All SListI xss => (forall a. f a -> g a) -> POP f xss -> POP g xss
- liftA2_NP :: SListI xs => (forall a. f a -> g a -> h a) -> NP f xs -> NP g xs -> NP h xs
- liftA2_POP :: All SListI xss => (forall a. f a -> g a -> h a) -> POP f xss -> POP g xss -> POP h xss
- 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
- 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
- map_NP :: SListI xs => (forall a. f a -> g a) -> NP f xs -> NP g xs
- map_POP :: All SListI xss => (forall a. f a -> g a) -> POP f xss -> POP g xss
- zipWith_NP :: SListI xs => (forall a. f a -> g a -> h a) -> NP f xs -> NP g xs -> NP h xs
- zipWith_POP :: All SListI xss => (forall a. f a -> g a -> h a) -> POP f xss -> POP g xss -> POP h xss
- 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
- 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
- cliftA_NP :: All c xs => proxy c -> (forall a. c a => f a -> g a) -> NP f xs -> NP g xs
- cliftA_POP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a) -> POP f xss -> POP g xss
- 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
- 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
- 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
- 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
- cmap_NP :: All c xs => proxy c -> (forall a. c a => f a -> g a) -> NP f xs -> NP g xs
- cmap_POP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a) -> POP f xss -> POP g xss
- 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
- 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
- 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
- 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
- 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
- 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
- collapse_NP :: NP (K a) xs -> [a]
- collapse_POP :: SListI xss => POP (K a) xss -> [[a]]
- sequence'_NP :: Applicative f => NP (f :.: g) xs -> f (NP g xs)
- sequence'_POP :: (SListI xss, Applicative f) => POP (f :.: g) xss -> f (POP g xss)
- sequence_NP :: (SListI xs, Applicative f) => NP f xs -> f (NP I xs)
- sequence_POP :: (All SListI xss, Applicative f) => POP f xss -> f (POP I xss)

# Datatypes

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

, 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.`K`

a

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 ]

HSequence [k] k (NP k) Source # | |

HCollapse [k] k (NP k) Source # | |

HAp [k] k (NP k) Source # | |

HPure [k] k (NP k) Source # | |

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

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

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

type SListIN [k] k (NP k) Source # | |

type Prod [k] k (NP k) Source # | |

type AllN [k] k (NP k) c Source # | |

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

HSequence [[k]] k (POP k) Source # | |

HCollapse [[k]] k (POP k) Source # | |

HAp [[k]] k (POP k) Source # | |

HPure [[k]] k (POP k) Source # | |

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

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

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

type SListIN [[k]] k (POP k) Source # | |

type Prod [[k]] k (POP k) Source # | |

type AllN [[k]] k (POP k) c Source # | |

type CollapseTo [[k]] k (POP k) a Source # | |

# Constructing products

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

## Construction from a list

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.

# Application

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

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 Source #

Specialization of `hap`

.

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

# Destructing products

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 #

# Lifting / mapping

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

Specialization of `hliftA`

.

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

Specialization of `hliftA`

.

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

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 Source #

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 Source #

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 Source #

Specialization of `hliftA3`

.

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

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 Source #

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 Source #

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

Specialization of `hcliftA`

.

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

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 Source #

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 Source #

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 Source #

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 Source #

Specialization of `hcliftA3`

.

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

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 Source #

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 Source #

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 Source #

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 Source #

Specialization of `hczipWith3`

, which is equivalent to `hcliftA3`

.

# Dealing with `All`

c

`All`

chcliftA' :: (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 #

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 #

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 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 Source #

Deprecated: Use `cliftA2_NP`

instead.

Specialization of `hcliftA2'`

.

# Collapsing

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

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

Specialization of `hcollapse`

.

*Example:*

`>>>`

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

(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) Source #

Specialization of `hsequence'`

.

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

Specialization of `hsequence'`

.

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

Specialization of `hsequence`

.

*Example:*

`>>>`

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

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

Specialization of `hsequence`

.

*Example:*

`>>>`

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