Generics.SOP.Classes

generics-sop-0.3.1.0: Generic Programming using True Sums of Products

Safe Haskell | None
Language | Haskell2010

Generics.SOP.Classes

Contents

- Generalized applicative functor structure
  - Generalized `pure`
  - Generalized `<*>`
  - Derived functions
- Collapsing homogeneous structures
- Sequencing effects
  - Derived functions
- Indexing into sums
- Applying all injections
- Expanding sums to products
- Transformation of index lists and coercions

Description

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.

Synopsis

- 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 Same (h :: (k1 -> *) -> l1 -> *) :: (k2 -> *) -> l2 -> *
- type family Prod (h :: (k -> *) -> l -> *) :: (k -> *) -> l -> *
- class (Prod (Prod h) ~ Prod h, HPure (Prod h)) => HAp h 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 -> *) -> l -> *) (x :: *) :: *
- class HCollapse h where
- class HAp h => HSequence h where
- 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)
- class HIndex h where
- type family UnProd (h :: (k -> *) -> l -> *) :: (k -> *) -> l -> *
- class UnProd (Prod h) ~ h => HApInjs h where
- class HExpand h where
- class (Same h1 ~ h2, Same h2 ~ h1) => HTrans h1 h2 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 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 (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 #
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 #

## 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 [[k2]] k2 [[k1]] k1 (POP k1) # |
type Same [[k2]] k2 [[k1]] k1 (POP k1) = POP k2
type Same [[k2]] k2 [[k1]] k1 (SOP k1) # |
type Same [[k2]] k2 [[k1]] k1 (SOP k1) = SOP k2
type Same [k2] k2 [k1] k1 (NP k1) # |
type Same [k2] k2 [k1] k1 (NP k1) = NP k2
type Same [k2] k2 [k1] k1 (NS k1) # |
type Same [k2] k2 [k1] k1 (NS k1) = NS k2

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

Maps a structure containing sums to the corresponding product structure.

Instances

type Prod [[k]] k (POP k) # |
type Prod [[k]] k (POP k) = POP k
type Prod [[k]] k (SOP k) # |
type Prod [[k]] k (SOP k) = POP k
type Prod [k] k (NP k) # |
type Prod [k] k (NP k) = NP k
type Prod [k] k (NS k) # |
type Prod [k] k (NS k) = NP k

class (Prod (Prod h) ~ Prod h, HPure (Prod h)) => HAp h 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 (POP k) # |
Methods hap :: Prod (POP k) k h ((k -.-> f) g) xs -> h f xs -> h g xs #
HAp [[k]] k (SOP k) # |
Methods hap :: Prod (SOP k) k h ((k -.-> f) g) xs -> h f xs -> h g xs #
HAp [k] k (NP k) # |
Methods hap :: Prod (NP k) k h ((k -.-> f) g) xs -> h f xs -> h g xs #
HAp [k] k (NS k) # |
Methods hap :: Prod (NS k) k h ((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 (POP k) a # |
type CollapseTo [[k]] k (POP k) a = [[a]]
type CollapseTo [[k]] k (SOP k) a # |
type CollapseTo [[k]] k (SOP k) a = [a]
type CollapseTo [k] k (NP k) a # |
type CollapseTo [k] k (NP k) a = [a]
type CollapseTo [k] k (NS k) a # |
type CollapseTo [k] k (NS k) a = a

class HCollapse h 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 `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 [[k]] k (POP k) # |
Methods hcollapse :: SListIN (POP k) k h xs => h (K k a) xs -> CollapseTo (POP k) k h a #
HCollapse [[k]] k (SOP k) # |
Methods hcollapse :: SListIN (SOP k) k h xs => h (K k a) xs -> CollapseTo (SOP k) k h a #
HCollapse [k] k (NP k) # |
Methods hcollapse :: SListIN (NP k) k h xs => h (K k a) xs -> CollapseTo (NP k) k h a #
HCollapse [k] k (NS k) # |
Methods hcollapse :: SListIN (NS k) k h xs => h (K k a) xs -> CollapseTo (NS k) k h a #

# Sequencing effects

class HAp h => HSequence h where #

A generalization of `sequenceA`.

Minimal complete definition

hsequence'

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)

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) #
HSequence [[k]] k (SOP k) # |
Methods hsequence' :: (SListIN (SOP k) k h xs, Applicative f) => h ((k :.: *) f g) xs -> f (h g xs) #
HSequence [k] k (NP k) # |
Methods hsequence' :: (SListIN (NP k) k h xs, Applicative f) => h ((k :.: *) f g) xs -> f (h g xs) #
HSequence [k] k (NS k) # |
Methods hsequence' :: (SListIN (NS k) k h xs, Applicative f) => h ((k :.: *) f g) xs -> f (h g xs) #

## Derived functions

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`.

# Indexing into sums

class HIndex h 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 (SOP k) # |
Methods hindex :: h f xs -> Int #
HIndex [k] k (NS 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 (POP k) # |
type UnProd [[k]] k (POP k) = SOP k
type UnProd [k] k (NP k) # |
type UnProd [k] k (NP k) = NS k

class UnProd (Prod h) ~ h => HApInjs h 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)
    [Z (I 'x'), S (Z (I True)), S (S (Z (I 2)))]

    >>> hapInjs (POP ((I 'x' :* Nil) :* (I True :* I 2 :* Nil) :* Nil)
    [SOP (Z (I 'x' :* Nil)), SOP (S (Z (I True :* (I 2 :* Nil))))]

Since: 0.2.4.0

Instances

HApInjs [[k]] k (SOP k) # |
Methods hapInjs :: SListIN (SOP k) k h xs => Prod (SOP k) k h f xs -> [h f xs] #
HApInjs [k] k (NS k) # |
Methods hapInjs :: SListIN (NS k) k h xs => Prod (NS k) k h f xs -> [h f xs] #

# Expanding sums to products

class HExpand h 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 (SOP k) # |
Methods hexpand :: SListIN (SOP k) k (Prod (SOP k) k h) xs => (forall x. f x) -> h f xs -> Prod (SOP k) k h f xs # hcexpand :: AllN (SOP k) k (Prod (SOP k) k h) c xs => proxy c -> (forall x. c x => f x) -> h f xs -> Prod (SOP k) k h f xs #
HExpand [k] k (NS k) # |
Methods hexpand :: SListIN (NS k) k (Prod (NS k) k h) xs => (forall x. f x) -> h f xs -> Prod (NS k) k h f xs # hcexpand :: AllN (NS k) k (Prod (NS k) k h) c xs => proxy c -> (forall x. c x => f x) -> h f xs -> Prod (NS k) k h f xs #

# Transformation of index lists and coercions

class (Same h1 ~ h2, Same h2 ~ h1) => HTrans h1 h2 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 [[k2]] k2 [[k1]] k1 (POP k1) (POP k2) # |
Methods htrans :: AllZipN (POP k1) l1 (POP k2) k1 l1 k1 (Prod l1 k1 h1) c xs ys => proxy c -> (forall x y. c x y => f x -> g y) -> h1 f xs -> h2 g ys # hcoerce :: (AllZipN (POP k1) l1 (POP k2) k1 l1 k1 (Prod l1 k1 h1) (LiftedCoercible (POP k2) * k1 f g) xs ys, HTrans (POP k1) (POP k2) l1 k1 h1 h2) => h1 f xs -> h2 g ys #
HTrans [[k2]] k2 [[k1]] k1 (SOP k1) (SOP k2) # |
Methods htrans :: AllZipN (SOP k1) l1 (SOP k2) k1 l1 k1 (Prod l1 k1 h1) c xs ys => proxy c -> (forall x y. c x y => f x -> g y) -> h1 f xs -> h2 g ys # hcoerce :: (AllZipN (SOP k1) l1 (SOP k2) k1 l1 k1 (Prod l1 k1 h1) (LiftedCoercible (SOP k2) * k1 f g) xs ys, HTrans (SOP k1) (SOP k2) l1 k1 h1 h2) => h1 f xs -> h2 g ys #
HTrans [k2] k2 [k1] k1 (NP k1) (NP k2) # |
Methods htrans :: AllZipN (NP k1) l1 (NP k2) k1 l1 k1 (Prod l1 k1 h1) c xs ys => proxy c -> (forall x y. c x y => f x -> g y) -> h1 f xs -> h2 g ys # hcoerce :: (AllZipN (NP k1) l1 (NP k2) k1 l1 k1 (Prod l1 k1 h1) (LiftedCoercible (NP k2) * k1 f g) xs ys, HTrans (NP k1) (NP k2) l1 k1 h1 h2) => h1 f xs -> h2 g ys #
HTrans [k2] k2 [k1] k1 (NS k1) (NS k2) # |
Methods htrans :: AllZipN (NS k1) l1 (NS k2) k1 l1 k1 (Prod l1 k1 h1) c xs ys => proxy c -> (forall x y. c x y => f x -> g y) -> h1 f xs -> h2 g ys # hcoerce :: (AllZipN (NS k1) l1 (NS k2) k1 l1 k1 (Prod l1 k1 h1) (LiftedCoercible (NS k2) * k1 f g) xs ys, HTrans (NS k1) (NS k2) l1 k1 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