This module defines the `Accessor`

type.
It should be imported with qualification.

- data T r a
- fromSetGet :: (a -> r -> r) -> (r -> a) -> T r a
- fromLens :: (r -> (a, a -> r)) -> T r a
- fromWrapper :: (b -> a) -> (a -> b) -> T a b
- self :: T r r
- null :: T r ()
- result :: Eq a => a -> T (a -> b) b
- set :: T r a -> a -> r -> r
- (^=) :: T r a -> a -> r -> r
- compose :: [r -> r] -> r -> r
- get :: T r a -> r -> a
- (^.) :: r -> T r a -> a
- modify :: T r a -> (a -> a) -> r -> r
- (^:) :: T r a -> (a -> a) -> r -> r
- (.>) :: T a b -> T b c -> T a c
- (<.) :: T b c -> T a b -> T a c
- ($%) :: a -> (a -> b) -> b
- merge :: T a b -> T a c -> T a (b, c)

# Documentation

The accessor function we use, has a record value as first argument and returns the content of a specific record field and a function that allows to overwrite that field with a new value.

In former version of a package
we used a function that resembled the state monad.
However this required to use an `undefined`

in the implementation of the `get`

function.

fromSetGet :: (a -> r -> r) -> (r -> a) -> T r aSource

fromWrapper :: (b -> a) -> (a -> b) -> T a bSource

If an object is wrapped in a `newtype`

,
you can generate an `Accessor`

to the unwrapped data
by providing a wrapper and an unwrapper function.
The set function is simpler in this case,
since no existing data must be kept.
Since the information content of the wrapped and unwrapped data is equivalent,
you can swap wrapper and unwrapper.
This way you can construct an `Accessor`

that treats a record field containing an unwrapped object
like a field containing a wrapped object.

newtype A = A {unA :: Int} access :: Accessor.T A Int access = fromWrapper A unA

We could also have called this function `fromBijection`

,
since it must hold `wrap . unwrap = id`

and `unwrap . wrap = id`

.

result :: Eq a => a -> T (a -> b) bSource

`result a`

accesses the value of a function for argument `a`

.
It is not very efficient to build a function
from setting all of its values using this accessor,
since every access to a function adds another `if-then-else`

.

Also see semantic editor combinators, that allow to modify all function values of a function at once. Cf. http://conal.net/blog/posts/semantic-editor-combinators/

(^=) :: T r a -> a -> r -> rSource

`set`

as infix operator.
This lets us write `first ^= 2+3 $ second ^= 5+7 $ record`

.

compose :: [r -> r] -> r -> rSource

This is a general function, but it is especially useful for setting many values of different type at once.

`get`

as infix operator.
This lets us write `record^.field^.subfield`

.
This imitates Modula II syntax.

(^:) :: T r a -> (a -> a) -> r -> rSource

`modify`

as infix operator.
This lets us write
`field^:subfield^:(2*) $ record`

,
`record$%field^:subfield^:(2*)`

or `record$%field^:subfield^:(const 1)`

.

(.>) :: T a b -> T b c -> T a cSource

Accessor composition: Combine an accessor with an accessor to a sub-field. Speak "stack".

(<.) :: T b c -> T a b -> T a cSource

Accessor composition the other direction.

(<.) = flip (.>)

You may also use the `(.)`

operator from Category class.

merge :: T a b -> T a c -> T a (b, c)Source

Merge the accessors to two independent fields.

Independency means, it must hold:

set (merge accA accB) (a,b) = set (merge accB accA) (b,a)

You may construct smart accessors
by composing a merged accessor with a `fromWrapper`

accessor.

This is a special case of the more general `Point`

concept
in the package `fclabels`

.