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 -> *) -> ( [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.

- class HPure h 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 Prod h :: (k -> *) -> l -> *
- class (Prod (Prod h) ~ Prod h, HPure (Prod h)) => HAp h where
- hliftA :: (SingI xs, HAp h) => (forall a. f a -> f' a) -> h f xs -> h f' xs
- hliftA2 :: (SingI 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 :: (SingI 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 :: (AllMap (Prod h) c xs, SingI xs, HAp h) => Proxy c -> (forall a. c a => f a -> f' a) -> h f xs -> h f' xs
- hcliftA2 :: (AllMap (Prod h) c xs, SingI 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 :: (AllMap (Prod h) c xs, SingI 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 :: * -> *
- class HCollapse h where
- hcollapse :: SingI xs => h (K a) xs -> CollapseTo h a

- class HAp h => HSequence h where
- hsequence' :: (SingI xs, Applicative f) => h (f :.: g) xs -> f (h g xs)

- hsequence :: (SingI xs, HSequence h) => Applicative f => h f xs -> f (h I xs)
- hsequenceK :: (SingI xs, Applicative f, HSequence h) => h (K (f a)) xs -> f (h (K a) xs)

# Documentation

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

Corresponds to `pure`

directly.

*Instances:*

`hpure`

,`pure_NP`

::`SingI`

xs => (forall a. f a) ->`NP`

f xs`hpure`

,`pure_POP`

::`SingI`

xss => (forall a. f a) ->`POP`

f xss

hcpure :: (SingI xs, AllMap 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.`AllMap`

h c xs

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

is
always satisfied. Therefore, we typically define `AllMap`

h c NoConstraint xs`hpure`

separately and directly, and make it a member of the class.

*Instances:*

`hcpure`

,`cpure_NP`

:: (`SingI`

xs,`All`

c xs ) =>`Proxy`

c -> (forall a. c a => f a) ->`NP`

f xs`hcpure`

,`cpure_POP`

:: (`SingI`

xss,`All2`

c xss) =>`Proxy`

c -> (forall a. c a => f a) ->`POP`

f xss

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 Prod h :: (k -> *) -> l -> * Source

Maps a structure containing sums to the corresponding product structure.

class (Prod (Prod h) ~ Prod h, HPure (Prod h)) => HAp h where Source

A generalization of `<*>`

.

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

Corresponds to `<*>`

.

For products as well as products or products, 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

hliftA :: (SingI 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`

::`SingI`

xs => (forall a. f a -> f' a) ->`NP`

f xs ->`NP`

f' xs`hliftA`

,`liftA_NS`

::`SingI`

xs => (forall a. f a -> f' a) ->`NS`

f xs ->`NS`

f' xs`hliftA`

,`liftA_POP`

::`SingI`

xss => (forall a. f a -> f' a) ->`POP`

f xss ->`POP`

f' xss`hliftA`

,`liftA_SOP`

::`SingI`

xss => (forall a. f a -> f' a) ->`SOP`

f xss ->`SOP`

f' xss

hliftA2 :: (SingI 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`

::`SingI`

xs => (forall a. f a -> f' a -> f'' a) ->`NP`

f xs ->`NP`

f' xs ->`NP`

f'' xs`hliftA2`

,`liftA2_NS`

::`SingI`

xs => (forall a. f a -> f' a -> f'' a) ->`NP`

f xs ->`NS`

f' xs ->`NS`

f'' xs`hliftA2`

,`liftA2_POP`

::`SingI`

xss => (forall a. f a -> f' a -> f'' a) ->`POP`

f xss ->`POP`

f' xss ->`POP`

f'' xss`hliftA2`

,`liftA2_SOP`

::`SingI`

xss => (forall a. f a -> f' a -> f'' a) ->`POP`

f xss ->`SOP`

f' xss ->`SOP`

f'' xss

hliftA3 :: (SingI 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`

::`SingI`

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`

::`SingI`

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`

::`SingI`

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`

::`SingI`

xss => (forall a. f a -> f' a -> f'' a -> f''' a) ->`POP`

f xss ->`POP`

f' xss ->`SOP`

f'' xss ->`SOP`

f''' xs

hcliftA :: (AllMap (Prod h) c xs, SingI xs, HAp h) => Proxy c -> (forall a. c a => f a -> f' a) -> h f xs -> h f' xs Source

hcliftA2 :: (AllMap (Prod h) c xs, SingI 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 :: (AllMap (Prod h) c xs, SingI 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

type family CollapseTo h :: * -> * Source

Maps products to lists, and sums to identities.

type CollapseTo k [[k]] (POP k) = (:.:) * * [] [] | |

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

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

type CollapseTo k [k] (NS k) = I |

class HCollapse h where Source

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

hcollapse :: SingI 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]

class HAp h => HSequence h where Source

A generalization of `sequenceA`

.

hsequence' :: (SingI 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`

:: (`SingI`

xs ,`Applicative`

f) =>`NP`

(f`:.:`

g) xs -> f (`NP`

g xs )`hsequence'`

,`sequence'_NS`

:: (`SingI`

xs ,`Applicative`

f) =>`NS`

(f`:.:`

g) xs -> f (`NS`

g xs )`hsequence'`

,`sequence'_POP`

:: (`SingI`

xss,`Applicative`

f) =>`POP`

(f`:.:`

g) xss -> f (`POP`

g xss)`hsequence'`

,`sequence'_SOP`

:: (`SingI`

xss,`Applicative`

f) =>`SOP`

(f`:.:`

g) xss -> f (`SOP`

g xss)

hsequence :: (SingI xs, HSequence h) => Applicative f => h f xs -> f (h I xs) Source

Special case of `hsequence'`

where `g = `

.`I`

hsequenceK :: (SingI xs, Applicative f, HSequence h) => h (K (f a)) xs -> f (h (K a) xs) Source

Special case of `hsequence'`

where `g = `

.`K`

a