Obtain a View from an arbitrary function.

to f . to g ≡ to (g . f)
a ^. to f ≡ f a

>>> ("hello","world") ^. to snd
"world"

>>> 5 ^. to succ
6

>>> (0, -5) ^. second' . to abs
5

to :: (s -> a) -> View s a

Obtain a Review from an arbitrary function.

from ≡ re . to

>>> review (from Prelude.length) [1,2,3]
3

from :: (b -> t) -> Review t b

TODO: Document

cloneView :: Monoid a => AView a s a -> Fold s a

TODO: Document

Obtain a constant-valued (index-preserving) View from an arbitrary value.

This can be useful as a second case failing a Fold e.g. foo failing like 0

like a . like b ≡ like b
a ^. like b ≡ b
a ^. like b ≡ a ^. to (const b)

like :: a -> View s a

Obtain a constant-valued (index-preserving) Review from an arbitrary value.

relike a . relike b ≡ relike a
relike a # b ≡ a
relike a # b ≡ from (const a) # b

Combine two Views into a View to a product.

toProduct :: View s a1 -> View s a2 -> View s (a1 , a2)

Combine two Reviews into a Review from a sum.

fromSum :: Review t b1 -> Review t b2 -> Review t (b1 + b2)

View the focus of an optic.

Fixity and semantics are such that subsequent field accesses can be performed with (.).

>>> ("hello","world") ^. second'
"world"

>>> 5 ^. to succ
6

>>> import Data.Complex
>>> ((0, 1 :+ 2), 3) ^. first' . second' . to magnitude
2.23606797749979

A prefix alias for ^..

view . to ≡ id

>>> view second' (1, "hello")
"hello"

>>> view (to succ) 5
6

>>> view (second' . first') ("hello",("world","!!!"))
"world"

Map each part of a structure viewed to a semantic editor combinator.

'views o f ≡ withFold o f'
foldMap = views folding'

>>> views both id (["foo"], ["bar", "baz"])
["foo","bar","baz"]

TODO: Document

Use the target of a Lens, Iso or View in the current state, or use a summary of a Fold or Traversal that points to a monoidal value.

>>> evalState (uses first' length) ("hello","world!")
5

A prefix alias of .^.

review ≡ view . re
review . from ≡ id

>>> review left' 4
Left 4
>>> review (from succ) 5
6

Turn an optic around and look through the other end, applying a function.

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

>>> reviews left' isRight "mustard"
False

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

Turn an optic around and use a value (or the current environment) through it the other way.

reuse ≡ use . re
reuse . from ≡ gets

>>> evalState (reuse left') 5
Left 5

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

Turn an optic around and use the current state through it the other way, applying a function.

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

>>> evalState (reuses left' isLeft) (5 :: Int)
True