Data.Accessor.Basic

This module defines the Accessor type. It should be imported with qualification.

Documentation

data T r a

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.

Instances

Category * T

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

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.

self :: T r r

Access the record itself

null :: T r ()

Access a (non-existing) element of type ()

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

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/

set :: T r a -> a -> r -> r

Set the value of a field.

(^=) :: T r a -> a -> r -> r infixr 5

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

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

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

get :: T r a -> r -> a

Get the value of a field.

(^.) :: r -> T r a -> a infixl 8

get as infix operator. This lets us write record^.field^.subfield. This imitates Modula II syntax.

modify :: T r a -> (a -> a) -> r -> r

Transform the value of a field by a function.

(^:) :: T r a -> (a -> a) -> r -> r infixr 5

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 c infixl 9

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

(<.) :: T b c -> T a b -> T a c infixr 9

Accessor composition the other direction.

(<.) = flip (.>)

You may also use the (.) operator from Category class.

($%) :: a -> (a -> b) -> b infixl 0

Flipped version of '($)'.

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

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.