Reviewing

This is a limited form of a Prism that can only be used for re operations.

Like with a Getter, there are no laws to state for a Review.

You can generate a Review by using unto. You can also use any Prism or Iso directly as a Review.

A Simple Review

If you see this in a signature for a function, the function is expecting a Review (in practice, this usually means a Prism).

A Simple AReview

An analogue of to for review.

 unto :: (b -> t) -> Review' t b

 unto = un . to

Turn a Getter around to get a Review

 un = unto . view
 unto = un . to

>>> un (to length) # [1,2,3]
3

Turn a Prism or Iso around to build a Getter.

If you have an Iso, from is a more powerful version of this function that will return an Iso instead of a mere Getter.

>>> 5 ^.re _Left
Left 5

>>> 6 ^.re (_Left.unto succ)
Left 7

 review  ≡ view  . re
 reviews ≡ views . re
 reuse   ≡ use   . re
 reuses  ≡ uses  . re

 re :: Prism s t a b -> Getter b t
 re :: Iso s t a b   -> Getter b t

This can be used to turn an Iso or Prism around and view a value (or the current environment) through it the other way.

 review ≡ view . re
 review . unto ≡ id

>>> review _Left "mustard"
Left "mustard"

>>> review (unto succ) 5
6

Usually review is used in the (->) Monad with a Prism or Iso, in which case it may be useful to think of it as having one of these more restricted type signatures:

 review :: Iso' s a   -> a -> s
 review :: Prism' s a -> a -> s

However, when working with a Monad transformer stack, it is sometimes useful to be able to review the current environment, in which case one of these more slightly more liberal type signatures may be beneficial to think of it as having:

 review :: MonadReader a m => Iso' s a   -> m s
 review :: MonadReader a m => Prism' s a -> m s

This can be used to turn an Iso or Prism around and view a value (or the current environment) through it the other way, applying a function.

 reviews ≡ views . re
 reviews (unto f) g ≡ g . f

>>> reviews _Left isRight "mustard"
False

>>> reviews (unto succ) (*2) 3
8

Usually this function is used in the (->) Monad with a Prism or Iso, in which case it may be useful to think of it as having one of these more restricted type signatures:

 reviews :: Iso' s a   -> (s -> r) -> a -> r
 reviews :: Prism' s a -> (s -> r) -> a -> r

However, when working with a Monad transformer stack, it is sometimes useful to be able to review the current environment, in which case one of these more slightly more liberal type signatures may be beneficial to think of it as having:

 reviews :: MonadReader a m => Iso' s a   -> (s -> r) -> m r
 reviews :: MonadReader a m => Prism' s a -> (s -> r) -> m r

This can be used to turn an Iso or Prism around and use a value (or the current environment) through it the other way.

 reuse ≡ use . re
 reuse . unto ≡ gets

>>> evalState (reuse _Left) 5
Left 5

>>> evalState (reuse (unto succ)) 5
6

 reuse :: MonadState a m => Prism' s a -> m s
 reuse :: MonadState a m => Iso' s a   -> m s

This can be used to turn an Iso or Prism around and use the current state through it the other way, applying a function.

 reuses ≡ uses . re
 reuses (unto f) g ≡ gets (g . f)

>>> evalState (reuses _Left isLeft) (5 :: Int)
True

 reuses :: MonadState a m => Prism' s a -> (s -> r) -> m r
 reuses :: MonadState a m => Iso' s a   -> (s -> r) -> m r

An infix alias for review.

 unto f # x ≡ f x
 l # x ≡ x ^. re l

This is commonly used when using a Prism as a smart constructor.

>>> _Left # 4
Left 4

But it can be used for any Prism

>>> base 16 # 123
"7b"

 (#) :: Iso'      s a -> a -> s
 (#) :: Prism'    s a -> a -> s
 (#) :: Review'   s a -> a -> s
 (#) :: Equality' s a -> a -> s

Minimal definition either bimap or first and second

Formally, the class Bifunctor represents a bifunctor from Hask -> Hask.

Intuitively it is a bifunctor where both the first and second arguments are covariant.

You can define a Bifunctor by either defining bimap or by defining both first and second.

If you supply bimap, you should ensure that:

bimap id id ≡ id

If you supply first and second, ensure:

 first id ≡ id
 second id ≡ id

If you supply both, you should also ensure:

bimap f g ≡ first f . second g

These ensure by parametricity:

 bimap  (f . g) (h . i) ≡ bimap f h . bimap g i
 first  (f . g) ≡ first  f . first  g
 second (f . g) ≡ second f . second g

This is a profunctor used internally to implement Review

It plays a role similar to that of Accessor or Const do for Control.Lens.Getter

This class is provided mostly for backwards compatibility with lens 3.8, but it can also shorten type signatures.