Control.Reference.Representation

This module declares the representation and basic classes of references.

Documentation

data Reference wm rm s t a b

A reference is an accessor to a part or different view of some data. The reference, unlike the lens has a separate getter, setter and updater.

Reference laws

As the references are generalizations of lenses, they should conform to the lens laws:

1) You get back what you put in:

lensSet l a s >>= lensGet l ≡ a

2) Putting back what you got doesn't change anything:

lensGet l a >>= b -> lensSet l b s ≡ s

3) Setting twice is the same as setting once:

lensSet l a s >>= lensSet l b ≡ lensSet l b s

But because they are more powerful than lenses, they should be more responsible.

4) Updating something is the same as getting and then setting:

lensGet l a >>= f >>= b -> lensSet l b s ≡ lensUpdate b s

Type arguments

wm

Writer monad, controls how the value can be reassembled when the part is changed. Usually Identity.

rm

Reader monad. Controls how part of the value can be accessed. See Lens, LensPart and Traversal

s

The original context.

t

The context after replacing the accessed part to something of type b.

a

The accessed part.

b

The accessed part can be changed to this.

Constructors

Reference

Fields

lensGet :: s -> rm a

Getter for the lens

lensSet :: b -> s -> wm t

Setter for the lens

lensUpdate :: (a -> wm b) -> s -> wm t

Updater for the lens. Handles monadic update functions.

type Simple t s a = t s s a a

A monomorph Lens, Traversal, LensPart, etc... Setting or updating does not change the type of the base.

type Simple' w t s a = t w s s a a

A monomorph Lens', Traversal', LensPart', etc... Setting or updating does not change the type of the base. Needs LiberalTypeSynonyms language extension

type SimpleRef wm rm s a = Reference wm rm s s a a

type Lens = Reference Identity Identity

The Lens is a reference that represents an 1 to 1 relationship.

type Lens' w = Reference w Identity

type Traversal = Reference Identity []

The Traversal is a reference that represents an 1 to any relationship.

type Traversal' w = Reference w []

type LensPart = Reference Identity Maybe

The parital lens is a reference that represents an 1 to 0..1 relationship.

type LensPart' w = Reference w Maybe

class Monad (ResultMonad m1 m2) => MonadCompose m1 m2 where

Combines the functionality of two monads into one. Has two functions that lift a monadic action into the result monad.

Associated Types

type ResultMonad m1 m2 :: * -> *

The type of the result monad

data ComposePhantom m1 m2 :: *

A phantom type to help coercions. Coercions are often needed when only one of the lifting functions are used.

Methods

newComposePhantom :: ComposePhantom m1 m2

Creates a new phantom variable to state that two liftings result in the same type.

liftMC1 :: ComposePhantom m1 m2 -> m1 a -> ResultMonad m1 m2 a

Lifts the first monad into the result monad.

liftMC2 :: ComposePhantom m1 m2 -> m2 a -> ResultMonad m1 m2 a

Lifts the second monad into the result monad.

Instances

MonadCompose [] []

MonadCompose [] IO

MonadCompose [] Maybe

MonadCompose [] Identity

MonadCompose IO []

MonadCompose IO IO

MonadCompose IO Maybe

MonadCompose IO Identity

MonadCompose Maybe []

MonadCompose Maybe IO

MonadCompose Maybe Maybe

MonadCompose Maybe Identity

MonadCompose Identity []

MonadCompose Identity IO

MonadCompose Identity Maybe

MonadCompose Identity Identity

MonadCompose [] (ListT IO)

MonadCompose [] (MaybeT IO)

MonadCompose IO (ListT IO)

MonadCompose IO (MaybeT IO)

MonadCompose Maybe (ListT IO)

MonadCompose Maybe (MaybeT IO)

MonadCompose Identity (ListT IO)

MonadCompose Identity (MaybeT IO)

MonadCompose (ListT IO) []

MonadCompose (ListT IO) IO

MonadCompose (ListT IO) Maybe

MonadCompose (ListT IO) Identity

MonadCompose (MaybeT IO) []

MonadCompose (MaybeT IO) IO

MonadCompose (MaybeT IO) Maybe

MonadCompose (MaybeT IO) Identity

MonadCompose (ListT IO) (ListT IO)

MonadCompose (ListT IO) (MaybeT IO)

MonadCompose (MaybeT IO) (ListT IO)

MonadCompose (MaybeT IO) (MaybeT IO)

class MonadSubsume m1 m2 where

States that m1 can be represented with m2

Methods

liftMS :: m1 a -> m2 a

Lifts the first monad into the second.

Instances

MonadSubsume [] []

MonadSubsume IO IO

MonadSubsume Maybe []

MonadSubsume Maybe Maybe

MonadSubsume Identity []

MonadSubsume Identity IO

MonadSubsume Identity Maybe

MonadSubsume Identity Identity

MonadSubsume [] (ListT IO)

MonadSubsume IO (ListT IO)

MonadSubsume IO (MaybeT IO)

MonadSubsume Maybe (ListT IO)

MonadSubsume Maybe (MaybeT IO)

MonadSubsume Identity (ListT IO)

MonadSubsume Identity (MaybeT IO)

MonadSubsume (ListT IO) (ListT IO)

MonadSubsume (MaybeT IO) (ListT IO)

MonadSubsume (MaybeT IO) (MaybeT IO)