Safe Haskell | Safe-Inferred |
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The Point data type which generalizes the different lenses and forms the
basis for vertical composition using the `Applicative`

type class.

- data Point cat g i f o = Point (cat f o) (cat (cat o i, f) g)
- get :: Point cat g i f o -> cat f o
- modify :: Point cat g i f o -> cat (cat o i, f) g
- set :: Arrow arr => Point arr g i f o -> arr (i, f) g
- identity :: ArrowApply arr => Point arr f f o o
- compose :: ArrowApply cat => Point cat t i b o -> Point cat g t f b -> Point cat g i f o
- data Iso cat i o = Iso {}
- inv :: Iso cat i o -> Iso cat o i
- type Total = (->)
- type Partial = Kleisli Maybe
- type Failing e = Kleisli (Either e)
- class Arrow a => ArrowFail e a where
- failArrow :: a e c

# The point data type that generalizes lens.

Abstract Point datatype. The getter and modifier operations work in some category. The type of the value pointed to might change, thereby changing the type of the outer structure.

Point (cat f o) (cat (cat o i, f) g) |

Arrow arr => Functor (Point arr f i f) | |

Arrow arr => Applicative (Point arr f i f) | |

Alternative (Point Partial f view f) |

identity :: ArrowApply arr => Point arr f f o oSource

Identity Point. Cannot change the type.

compose :: ArrowApply cat => Point cat t i b o -> Point cat g t f b -> Point cat g i f oSource

Point composition.

# Working with isomorphisms.

An isomorphism is like a `Category`

that works in two directions.

# Specialized lens contexts.

type Failing e = Kleisli (Either e)Source

Context that represents computations that might fail with some error.