Portability | Rank2, MPTCs, fundeps |
---|---|

Stability | experimental |

Maintainer | Edward Kmett <ekmett@gmail.com> |

Safe Haskell | Trustworthy |

The `Wrapped`

class provides similar functionality as `Control.Newtype`

,
from the `newtype`

package, but in a more convenient and efficient form.

There are a few functions from `newtype`

that are not provided here, because
they can be done with the `Iso`

directly:

Control.Newtype.over`Sum`

f ≡`wrapping`

`Sum`

`%~`

f Control.Newtype.under`Sum`

f ≡`unwrapping`

`Sum`

`%~`

f Control.Newtype.overF`Sum`

f ≡`mapping`

(`wrapping`

`Sum`

)`%~`

f Control.Newtype.underF`Sum`

f ≡`mapping`

(`unwrapping`

`Sum`

)`%~`

f

`under`

can also be used with `wrapping`

to provide the equivalent of
`Control.Newtype.under`

. Also, most use cases don't need full polymorphism,
so only the single constructor `wrapping`

functions would be needed.

These equivalences aren't 100% honest, because `newtype`

's operators
need to rely on two `Newtype`

constraints. This means that the wrapper used
for the output is not necessarily the same as the input.

- class Wrapped s t a b | a -> s, b -> t, a t -> s, b s -> t where
- wrapping :: Wrapped s s a a => (s -> a) -> Iso s s a a
- unwrapping :: Wrapped s s a a => (s -> a) -> Iso a a s s
- wrappings :: Wrapped s t a b => (s -> a) -> (t -> b) -> Iso s t a b
- unwrappings :: Wrapped t s b a => (s -> a) -> (t -> b) -> Iso a b s t
- op :: Wrapped s s a a => (s -> a) -> a -> s
- ala :: Wrapped s s a a => (s -> a) -> ((s -> a) -> e -> a) -> e -> s
- alaf :: Wrapped s s a a => (s -> a) -> ((r -> a) -> e -> a) -> (r -> s) -> e -> s

# Documentation

class Wrapped s t a b | a -> s, b -> t, a t -> s, b s -> t whereSource

`Wrapped`

provides isomorphisms to wrap and unwrap newtypes or
data types with one constructor.

An isomorphism between s and `a`

and a related one between `t`

and `b`

, such that when `a = b`

, `s = t`

.

This is often used via `wrapping`

to aid type inference.

Wrapped Bool Bool All All | |

Wrapped Bool Bool Any Any | |

Wrapped String String PatternMatchFail PatternMatchFail | |

Wrapped String String RecSelError RecSelError | |

Wrapped String String RecConError RecConError | |

Wrapped String String RecUpdError RecUpdError | |

Wrapped String String NoMethodError NoMethodError | |

Wrapped String String AssertionFailed AssertionFailed | |

Wrapped String String ErrorCall ErrorCall | |

Wrapped a a' (Identity a) (Identity a') | |

Wrapped a b (Product a) (Product b) | |

Wrapped a b (Sum a) (Sum b) | |

Wrapped a a' (Constant a b) (Constant a' b') | |

Wrapped a b (Const a x) (Const b y) | |

Wrapped [Int] [Int] IntSet IntSet | |

Wrapped [(Int, a)] [(Int, b)] (IntMap a) (IntMap b) | |

Wrapped [a] [b] (Seq a) (Seq b) | |

(Ord a, Ord b) => Wrapped [a] [b] (Set a) (Set b) | |

(Hashable a, Eq a, Hashable b, Eq b) => Wrapped [a] [b] (HashSet a) (HashSet b) | Use |

Wrapped [a] [b] (ZipList a) (ZipList b) | |

Wrapped (Maybe a) (Maybe b) (Last a) (Last b) | |

Wrapped (Maybe a) (Maybe b) (First a) (First b) | |

(Ord k, Ord k') => Wrapped [(k, a)] [(k', b)] (Map k a) (Map k' b) | |

(Hashable k, Eq k, Hashable k', Eq k') => Wrapped [(k, a)] [(k', b)] (HashMap k a) (HashMap k' b) | Use |

Wrapped (f a) (f' a') (Reverse f a) (Reverse f' a') | |

Wrapped (m (Maybe a)) (m' (Maybe a')) (MaybeT m a) (MaybeT m' a') | |

Wrapped (m [a]) (m' [a']) (ListT m a) (ListT m' a') | |

(Applicative f, Applicative g) => Wrapped (f a) (g b) (Lift f a) (Lift g b) | |

Wrapped (m a) (m' a') (IdentityT m a) (IdentityT m' a') | |

Wrapped (f a) (f' a') (Backwards f a) (Backwards f' a') | |

Wrapped (m a) (n b) (WrappedMonad m a) (WrappedMonad n b) | |

Wrapped (w (m -> a)) (w' (m' -> a')) (TracedT m w a) (TracedT m' w' a') | |

Wrapped (m (a, w)) (m' (a', w')) (WriterT w m a) (WriterT w' m' a') | |

Wrapped (m (a, w)) (m' (a', w')) (WriterT w m a) (WriterT w' m' a') | |

Wrapped (m (Either e a)) (m' (Either e' a')) (ErrorT e m a) (ErrorT e' m' a') | |

Wrapped (f (g a)) (f' (g' a')) (Compose f g a) (Compose f' g' a') | |

Wrapped (a -> a) (b -> b) (Endo a) (Endo b) | |

(ArrowApply m, ArrowApply n) => Wrapped (m () a) (n () b) (ArrowMonad m a) (ArrowMonad n b) | |

Wrapped ((a -> m r) -> m r) ((a' -> m' r') -> m' r') (ContT r m a) (ContT r' m' a') | |

Wrapped (s -> m (a, s)) (s' -> m' (a', s')) (StateT s m a) (StateT s' m' a') | |

Wrapped (s -> m (a, s)) (s' -> m' (a', s')) (StateT s m a) (StateT s' m' a') | |

Wrapped (r -> m a) (r' -> m' a') (ReaderT r m a) (ReaderT r' m' a') | |

Wrapped (a -> m b) (u -> n v) (Kleisli m a b) (Kleisli n u v) | |

Wrapped (Either (f a) (g a)) (Either (f' a') (g' a')) (Coproduct f g a) (Coproduct f' g' a') | |

Wrapped (a b c) (u v w) (WrappedArrow a b c) (WrappedArrow u v w) | |

Wrapped (r -> s -> m (a, s, w)) (r' -> s' -> m' (a', s', w')) (RWST r w s m a) (RWST r' w' s' m' a') | |

Wrapped (r -> s -> m (a, s, w)) (r' -> s' -> m' (a', s', w')) (RWST r w s m a) (RWST r' w' s' m' a') |

wrapping :: Wrapped s s a a => (s -> a) -> Iso s s a aSource

This is a convenient version of `wrapped`

with an argument that's ignored.

The argument is used to specify which newtype the user intends to wrap by using the constructor for that newtype.

The user supplied function is *ignored*, merely its type is used.

unwrapping :: Wrapped s s a a => (s -> a) -> Iso a a s sSource

This is a convenient version of `unwrapped`

with an argument that's ignored.

The argument is used to specify which newtype the user intends to *remove*
by using the constructor for that newtype.

The user supplied function is *ignored*, merely its type is used.

wrappings :: Wrapped s t a b => (s -> a) -> (t -> b) -> Iso s t a bSource

This is a convenient version of `wrapped`

with two arguments that are ignored.

These arguments are used to which newtype the user intends to wrap and should both be the same constructor. This redundancy is necessary in order to find the full polymorphic isomorphism family.

The user supplied functions are *ignored*, merely their types are used.

unwrappings :: Wrapped t s b a => (s -> a) -> (t -> b) -> Iso a b s tSource

This is a convenient version of `unwrapped`

with two arguments that are ignored.

These arguments are used to which newtype the user intends to remove and should both be the same constructor. This redundancy is necessary in order to find the full polymorphic isomorphism family.

The user supplied functions are *ignored*, merely their types are used.

ala :: Wrapped s s a a => (s -> a) -> ((s -> a) -> e -> a) -> e -> sSource

This combinator is based on `ala`

from Conor McBride's work on Epigram.

As with `wrapping`

, the user supplied function for the newtype is *ignored*.

`>>>`

10`ala Sum foldMap [1,2,3,4]`

`>>>`

True`ala All foldMap [True,True]`

`>>>`

False`ala All foldMap [True,False]`

`>>>`

False`ala Any foldMap [False,False]`

`>>>`

True`ala Any foldMap [True,False]`

`>>>`

10`ala Sum foldMap [1,2,3,4]`

`>>>`

24`ala Product foldMap [1,2,3,4]`