lens-4.15.3: Lenses, Folds and Traversals

Copyright | (C) 2012-2016 Edward Kmett
License | BSD-style (see the file LICENSE)
Maintainer | Edward Kmett <ekmett@gmail.com>
Stability | experimental
Portability | non-portable
Safe Haskell | None
Language | Haskell98

Control.Lens.Internal.Indexed

Contents

- An Indexed Profunctor
- Classes
- Indexing
- 64-bit Indexing
- Converting to Folds

Description

Internal implementation details for `Indexed` lens-likes

Synopsis

- newtype Indexed i a b = Indexed {
  - runIndexed :: i -> a -> b
  }
- class (Choice p, Corepresentable p, Comonad (Corep p), Traversable (Corep p), Strong p, Representable p, Monad (Rep p), MonadFix (Rep p), Distributive (Rep p), Costrong p, ArrowLoop p, ArrowApply p, ArrowChoice p, Closed p) => Conjoined p where
- class Conjoined p => Indexable i p where
- newtype Indexing f a = Indexing {
  - runIndexing :: Int -> (Int, f a)
  }
- indexing :: Indexable Int p => ((a -> Indexing f b) -> s -> Indexing f t) -> p a (f b) -> s -> f t
- newtype Indexing64 f a = Indexing64 {
  - runIndexing64 :: Int64 -> (Int64, f a)
  }
- indexing64 :: Indexable Int64 p => ((a -> Indexing64 f b) -> s -> Indexing64 f t) -> p a (f b) -> s -> f t
- withIndex :: (Indexable i p, Functor f) => p (i, s) (f (j, t)) -> Indexed i s (f t)
- asIndex :: (Indexable i p, Contravariant f, Functor f) => p i (f i) -> Indexed i s (f s)

# An Indexed Profunctor

newtype Indexed i a b #

A function with access to a index. This constructor may be useful when you need to store an `Indexable` in a container to avoid `ImpredicativeTypes`.

    index :: Indexed i a b -> i -> a -> b

Constructors

Indexed |
Fields runIndexed :: i -> a -> b

Instances

(~) * i j => Indexable i (Indexed j) # |
Methods indexed :: Indexed j a b -> i -> a -> b #
Arrow (Indexed i) # |
Methods arr :: (b -> c) -> Indexed i b c # first :: Indexed i b c -> Indexed i (b, d) (c, d) # second :: Indexed i b c -> Indexed i (d, b) (d, c) # (***) :: Indexed i b c -> Indexed i b' c' -> Indexed i (b, b') (c, c') # (&&&) :: Indexed i b c -> Indexed i b c' -> Indexed i b (c, c') #
ArrowChoice (Indexed i) # |
Methods left :: Indexed i b c -> Indexed i (Either b d) (Either c d) # right :: Indexed i b c -> Indexed i (Either d b) (Either d c) # (+++) :: Indexed i b c -> Indexed i b' c' -> Indexed i (Either b b') (Either c c') # (|||) :: Indexed i b d -> Indexed i c d -> Indexed i (Either b c) d #
ArrowApply (Indexed i) # |
Methods app :: Indexed i (Indexed i b c, b) c #
ArrowLoop (Indexed i) # |
Methods loop :: Indexed i (b, d) (c, d) -> Indexed i b c #
Representable (Indexed i) # |
Associated Types type Rep (Indexed i :: * -> * -> *) :: * -> * # Methods tabulate :: (d -> Rep (Indexed i) c) -> Indexed i d c #
Corepresentable (Indexed i) # |
Associated Types type Corep (Indexed i :: * -> * -> *) :: * -> * # Methods cotabulate :: (Corep (Indexed i) d -> c) -> Indexed i d c #
Closed (Indexed i) # |
Methods closed :: Indexed i a b -> Indexed i (x -> a) (x -> b) #
Choice (Indexed i) # |
Methods left' :: Indexed i a b -> Indexed i (Either a c) (Either b c) # right' :: Indexed i a b -> Indexed i (Either c a) (Either c b) #
Strong (Indexed i) # |
Methods first' :: Indexed i a b -> Indexed i (a, c) (b, c) # second' :: Indexed i a b -> Indexed i (c, a) (c, b) #
Costrong (Indexed i) # |
Methods unfirst :: Indexed i (a, d) (b, d) -> Indexed i a b # unsecond :: Indexed i (d, a) (d, b) -> Indexed i a b #
Profunctor (Indexed i) # |
Methods dimap :: (a -> b) -> (c -> d) -> Indexed i b c -> Indexed i a d # lmap :: (a -> b) -> Indexed i b c -> Indexed i a c # rmap :: (b -> c) -> Indexed i a b -> Indexed i a c # (#.) :: Coercible * c b => (b -> c) -> Indexed i a b -> Indexed i a c # (.#) :: Coercible * b a => Indexed i b c -> (a -> b) -> Indexed i a c #
Conjoined (Indexed i) # |
Methods distrib :: Functor f => Indexed i a b -> Indexed i (f a) (f b) # conjoined :: (((* -> * -> *) ~ Indexed i) (->) -> q (a -> b) r) -> q (Indexed i a b) r -> q (Indexed i a b) r #
Bizarre (Indexed Int) Mafic # |
Methods bazaar :: Applicative f => Indexed Int a (f b) -> Mafic a b t -> f t #
Category * (Indexed i) # |
Methods id :: cat a a # (.) :: cat b c -> cat a b -> cat a c #
Sieve (Indexed i) ((->) i) # |
Methods sieve :: Indexed i a b -> a -> i -> b #
Cosieve (Indexed i) ((,) i) # |
Methods cosieve :: Indexed i a b -> (i, a) -> b #
Sellable (Indexed i) (Molten i) # |
Methods sell :: Indexed i a (Molten i a b b) #
Bizarre (Indexed i) (Molten i) # |
Methods bazaar :: Applicative f => Indexed i a (f b) -> Molten i a b t -> f t #
Monad (Indexed i a) # |
Methods (>>=) :: Indexed i a a -> (a -> Indexed i a b) -> Indexed i a b # (>>) :: Indexed i a a -> Indexed i a b -> Indexed i a b # return :: a -> Indexed i a a # fail :: String -> Indexed i a a #
Functor (Indexed i a) # |
Methods fmap :: (a -> b) -> Indexed i a a -> Indexed i a b # (<$) :: a -> Indexed i a b -> Indexed i a a #
MonadFix (Indexed i a) # |
Methods mfix :: (a -> Indexed i a a) -> Indexed i a a #
Applicative (Indexed i a) # |
Methods pure :: a -> Indexed i a a # (<*>) :: Indexed i a (a -> b) -> Indexed i a a -> Indexed i a b # (*>) :: Indexed i a a -> Indexed i a b -> Indexed i a b # (<*) :: Indexed i a a -> Indexed i a b -> Indexed i a a #
Apply (Indexed i a) # |
Methods (<.>) :: Indexed i a (a -> b) -> Indexed i a a -> Indexed i a b # (.>) :: Indexed i a a -> Indexed i a b -> Indexed i a b # (<.) :: Indexed i a a -> Indexed i a b -> Indexed i a a #
Bind (Indexed i a) # |
Methods (>>-) :: Indexed i a a -> (a -> Indexed i a b) -> Indexed i a b # join :: Indexed i a (Indexed i a a) -> Indexed i a a #
type Rep (Indexed i) # |
type Rep (Indexed i) = (->) i
type Corep (Indexed i) # |
type Corep (Indexed i) = (,) i

# Classes

class (Choice p, Corepresentable p, Comonad (Corep p), Traversable (Corep p), Strong p, Representable p, Monad (Rep p), MonadFix (Rep p), Distributive (Rep p), Costrong p, ArrowLoop p, ArrowApply p, ArrowChoice p, Closed p) => Conjoined p where #

This is a `Profunctor` that is both `Corepresentable` by `f` and `Representable` by `g` such that `f` is left adjoint to `g`. From this you can derive a lot of structure due to the preservation of limits and colimits.

Methods

distrib :: Functor f => p a b -> p (f a) (f b) #

`Conjoined` is strong enough to let us distribute every `Conjoined` `Profunctor` over every Haskell `Functor`. This is effectively a generalization of `fmap`.

conjoined :: (p ~ (->) => q (a -> b) r) -> q (p a b) r -> q (p a b) r #

This permits us to make a decision at an outermost point about whether or not we use an index.

Ideally any use of this function should be done in such a way so that you compute the same answer, but this cannot be enforced at the type level.

Instances

Conjoined (->) # |
Methods distrib :: Functor f => (a -> b) -> f a -> f b # conjoined :: (((* -> * -> *) ~ (->)) (->) -> q (a -> b) r) -> q (a -> b) r -> q (a -> b) r #
Conjoined ReifiedGetter # |
Methods distrib :: Functor f => ReifiedGetter a b -> ReifiedGetter (f a) (f b) # conjoined :: (((* -> * -> *) ~ ReifiedGetter) (->) -> q (a -> b) r) -> q (ReifiedGetter a b) r -> q (ReifiedGetter a b) r #
Conjoined (Indexed i) # |
Methods distrib :: Functor f => Indexed i a b -> Indexed i (f a) (f b) # conjoined :: (((* -> * -> *) ~ Indexed i) (->) -> q (a -> b) r) -> q (Indexed i a b) r -> q (Indexed i a b) r #

class Conjoined p => Indexable i p where #

This class permits overloading of function application for things that also admit a notion of a key or index.

Minimal complete definition

indexed

Methods

indexed :: p a b -> i -> a -> b #

Build a function from an `indexed` function.

Instances

Indexable i (->) # |
Methods indexed :: (a -> b) -> i -> a -> b #
(~) * i j => Indexable i (Indexed j) # |
Methods indexed :: Indexed j a b -> i -> a -> b #

# Indexing

newtype Indexing f a #

`Applicative` composition of ``State` `Int`` with a `Functor`, used by `indexed`.

Constructors

Indexing |
Fields runIndexing :: Int -> (Int, f a)

Instances

Functor f => Functor (Indexing f) # |
Methods fmap :: (a -> b) -> Indexing f a -> Indexing f b # (<$) :: a -> Indexing f b -> Indexing f a #
Applicative f => Applicative (Indexing f) # |
Methods pure :: a -> Indexing f a # (<*>) :: Indexing f (a -> b) -> Indexing f a -> Indexing f b # (*>) :: Indexing f a -> Indexing f b -> Indexing f b # (<*) :: Indexing f a -> Indexing f b -> Indexing f a #
Contravariant f => Contravariant (Indexing f) # |
Methods contramap :: (a -> b) -> Indexing f b -> Indexing f a # (>$) :: b -> Indexing f b -> Indexing f a #
Apply f => Apply (Indexing f) # |
Methods (<.>) :: Indexing f (a -> b) -> Indexing f a -> Indexing f b # (.>) :: Indexing f a -> Indexing f b -> Indexing f b # (<.) :: Indexing f a -> Indexing f b -> Indexing f a #

indexing :: Indexable Int p => ((a -> Indexing f b) -> s -> Indexing f t) -> p a (f b) -> s -> f t #

Transform a `Traversal` into an `IndexedTraversal` or a `Fold` into an `IndexedFold`, etc.

    indexing :: Traversal s t a b -> IndexedTraversal Int s t a b
    indexing :: Prism s t a b     -> IndexedTraversal Int s t a b
    indexing :: Lens s t a b      -> IndexedLens Int  s t a b
    indexing :: Iso s t a b       -> IndexedLens Int s t a b
    indexing :: Fold s a          -> IndexedFold Int s a
    indexing :: Getter s a        -> IndexedGetter Int s a

    indexing :: Indexable Int p => LensLike (Indexing f) s t a b -> Over p f s t a b

# 64-bit Indexing

newtype Indexing64 f a #

`Applicative` composition of ``State` `Int64`` with a `Functor`, used by `indexed64`.

Constructors

Indexing64 |
Fields runIndexing64 :: Int64 -> (Int64, f a)

Instances

Functor f => Functor (Indexing64 f) # |
Methods fmap :: (a -> b) -> Indexing64 f a -> Indexing64 f b # (<$) :: a -> Indexing64 f b -> Indexing64 f a #
Applicative f => Applicative (Indexing64 f) # |
Methods pure :: a -> Indexing64 f a # (<*>) :: Indexing64 f (a -> b) -> Indexing64 f a -> Indexing64 f b # (*>) :: Indexing64 f a -> Indexing64 f b -> Indexing64 f b # (<*) :: Indexing64 f a -> Indexing64 f b -> Indexing64 f a #
Contravariant f => Contravariant (Indexing64 f) # |
Methods contramap :: (a -> b) -> Indexing64 f b -> Indexing64 f a # (>$) :: b -> Indexing64 f b -> Indexing64 f a #
Apply f => Apply (Indexing64 f) # |
Methods (<.>) :: Indexing64 f (a -> b) -> Indexing64 f a -> Indexing64 f b # (.>) :: Indexing64 f a -> Indexing64 f b -> Indexing64 f b # (<.) :: Indexing64 f a -> Indexing64 f b -> Indexing64 f a #

indexing64 :: Indexable Int64 p => ((a -> Indexing64 f b) -> s -> Indexing64 f t) -> p a (f b) -> s -> f t #

Transform a `Traversal` into an `IndexedTraversal` or a `Fold` into an `IndexedFold`, etc.

This combinator is like `indexing` except that it handles large traversals and folds gracefully.

    indexing64 :: Traversal s t a b -> IndexedTraversal Int64 s t a b
    indexing64 :: Prism s t a b     -> IndexedTraversal Int64 s t a b
    indexing64 :: Lens s t a b      -> IndexedLens Int64 s t a b
    indexing64 :: Iso s t a b       -> IndexedLens Int64 s t a b
    indexing64 :: Fold s a          -> IndexedFold Int64 s a
    indexing64 :: Getter s a        -> IndexedGetter Int64 s a

    indexing64 :: Indexable Int64 p => LensLike (Indexing64 f) s t a b -> Over p f s t a b

# Converting to Folds

withIndex :: (Indexable i p, Functor f) => p (i, s) (f (j, t)) -> Indexed i s (f t) #

Fold a container with indices returning both the indices and the values.

The result is only valid to compose in a `Traversal`, if you don't edit the index as edits to the index have no effect.

    >>> [10, 20, 30] ^.. ifolded . withIndex
    [(0,10),(1,20),(2,30)]

    >>> [10, 20, 30] ^.. ifolded . withIndex . alongside negated (re _Show)
    [(0,"10"),(-1,"20"),(-2,"30")]

asIndex :: (Indexable i p, Contravariant f, Functor f) => p i (f i) -> Indexed i s (f s) #

When composed with an `IndexedFold` or `IndexedTraversal` this yields an (`Indexed`) `Fold` of the indices.