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

Language | Haskell2010 |

Classes for generalized combinators on SOP types.

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

`NP`

:: (k ->`Type`

) -> ( [k] ->`Type`

) -- n-ary product`NS`

:: (k ->`Type`

) -> ( [k] ->`Type`

) -- n-ary sum`POP`

:: (k ->`Type`

) -> ([[k]] ->`Type`

) -- product of products`SOP`

:: (k ->`Type`

) -> ([[k]] ->`Type`

) -- sum of products

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

(k ->`Type`

) -> (l ->`Type`

)

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
`Type`

to datatypes of kind `Type`

-> `Type`

`(k -> `

. This module
also derives a number of derived combinators.`Type`

) -> (l -> `Type`

)

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

## Synopsis

- class HPure (h :: (k -> Type) -> l -> Type) where
- 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 Same (h :: (k1 -> Type) -> l1 -> Type) :: (k2 -> Type) -> l2 -> Type
- 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
- 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
- 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
- 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
- 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 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 ()

- 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)

- 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 ()
- 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 HIndex (h :: (k -> Type) -> l -> Type) where
- type family UnProd (h :: (k -> Type) -> l -> Type) :: (k -> Type) -> l -> Type
- class UnProd (Prod h) ~ h => HApInjs (h :: (k -> Type) -> l -> Type) where
- class HExpand (h :: (k -> Type) -> l -> Type) where
- class (Same h1 ~ h2, Same h2 ~ h1) => HTrans (h1 :: (k1 -> Type) -> l1 -> Type) (h2 :: (k2 -> Type) -> l2 -> Type) where
- 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

# Generalized applicative functor structure

## Generalized

`pure`

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

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

where `hcpure`

f s`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

states.`AllN`

h c xs

*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

## Generalized

`<*>`

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 Same (h :: (k1 -> Type) -> l1 -> Type) :: (k2 -> Type) -> l2 -> Type Source #

Maps a structure to the same structure.

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

Maps a structure containing sums to the corresponding product structure.

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

A generalization of `<*>`

.

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

## Derived functions

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

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*

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 #

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 #

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 #

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*

# Collapsing homogeneous structures

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

Maps products to lists, and sums to identities.

#### Instances

type CollapseTo (NP :: (k -> Type) -> [k] -> Type) a Source # | |

Defined in Data.SOP.NP | |

type CollapseTo (POP :: (k -> Type) -> [[k]] -> Type) a Source # | |

Defined in Data.SOP.NP | |

type CollapseTo (NS :: (k -> Type) -> [k] -> Type) a Source # | |

Defined in Data.SOP.NS | |

type CollapseTo (SOP :: (k -> Type) -> [[k]] -> Type) a Source # | |

Defined in Data.SOP.NS |

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

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

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

contains a single `NS`

(`K`

a)`a`

, and an

contains
a list of `NP`

(`K`

a)`a`

s.

*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 (NP :: (k -> Type) -> [k] -> Type) Source # | |

Defined in Data.SOP.NP | |

HCollapse (POP :: (k -> Type) -> [[k]] -> Type) Source # | |

Defined in Data.SOP.NP | |

HCollapse (NS :: (k -> Type) -> [k] -> Type) Source # | |

Defined in Data.SOP.NS | |

HCollapse (SOP :: (k -> Type) -> [[k]] -> Type) Source # | |

Defined in Data.SOP.NS |

# Folding and sequencing

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

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

HTraverse_ (NP :: (k -> Type) -> [k] -> Type) Source # | |

Defined in Data.SOP.NP 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 # | |

Defined in Data.SOP.NP 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 # | |

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 # | |

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 # |

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

A generalization of `sequenceA`

.

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 `hctraverse`

`.

*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 (NP :: (k -> Type) -> [k] -> Type) Source # | |

Defined in Data.SOP.NP 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 # | |

Defined in Data.SOP.NP 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 # | |

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 # | |

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 # |

## Derived functions

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*

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*

# Indexing into sums

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

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

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

returns a number between
`hindex`

x`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:*

`>>>`

2`hindex (S (S (Z (I False))))`

`>>>`

0`hindex (Z (K ()))`

`>>>`

1`hindex (SOP (S (Z (I True :* I 'x' :* Nil))))`

*Since: 0.2.4.0*

#### Instances

# Applying all injections

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*

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.

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:*

`>>>`

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

`>>>`

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

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

*Since: 0.2.4.0*

# 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*

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:*

`>>>`

Nothing :* Just 3 :* Nothing :* Nil`hexpand Nothing (S (Z (Just 3))) :: NP Maybe '[Char, Int, Bool]`

`>>>`

POP (([] :* Nil) :* ([1,2] :* "xyz" :* Nil) :* Nil)`hexpand [] (SOP (S (Z ([1,2] :* "xyz" :* Nil)))) :: POP [] '[ '[Bool], '[Int, Char] ]`

*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:*

`>>>`

I False :* I 20 :* I LT :* Nil`hcexpand (Proxy :: Proxy Bounded) (I minBound) (S (Z (I 20))) :: NP I '[Bool, Int, Ordering]`

`>>>`

POP ((I 0.0 :* Nil) :* (I 1 :* I 2 :* Nil) :* Nil)`hcexpand (Proxy :: Proxy Num) (I 0) (SOP (S (Z (I 1 :* I 2 :* Nil)))) :: POP I '[ '[Double], '[Int, Int] ]`

*Since: 0.2.5.0*

# 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*

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 => 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:*

`>>>`

Just LT :* Just 'x' :* Just True :* Nil`hcoerce (I (Just LT) :* I (Just 'x') :* I (Just True) :* Nil) :: NP Maybe '[Ordering, Char, Bool]`

`>>>`

SOP (Z (I True :* I False :* Nil))`hcoerce (SOP (Z (K True :* K False :* Nil))) :: SOP I '[ '[Bool, Bool], '[Bool] ]`

*Since: 0.3.1.0*

#### Instances

HTrans (NP :: (k1 -> Type) -> [k1] -> Type) (NP :: (k2 -> Type) -> [k2] -> Type) Source # | |

Defined in Data.SOP.NP 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 => NP f xs -> NP g ys Source # | |

HTrans (POP :: (k1 -> Type) -> [[k1]] -> Type) (POP :: (k2 -> Type) -> [[k2]] -> Type) Source # | |

Defined in Data.SOP.NP 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 => POP f xs -> POP g ys Source # | |

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 => NS f xs -> NS g ys Source # | |

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 => SOP f xs -> SOP g ys Source # |