name: lens
category: Data, Lenses
version: 1.4.1
license: BSD3
cabal-version: >= 1.6
license-file: LICENSE
author: Edward A. Kmett
maintainer: Edward A. Kmett
stability: provisional
homepage: http://github.com/ekmett/lens/
bug-reports: http://github.com/ekmett/lens/issues
copyright: Copyright (C) 2012 Edward A. Kmett
synopsis: Lenses, Folds and Traversals
description:
The combinators in @Control.Lens@ provide a highly generic toolbox for composing
families of getters, folds, traversals, setters and lenses.
.
/Getter/
.
A @'Getter' a c@ is just any function @(a -> c)@, which we've flipped into continuation
passing style, @(c -> r) -> a -> r@ and decorated with 'Const' to obtain
.
> type Getting r a b c d = (c -> Const r d) -> a -> Const r b
.
If we restrict access to knowledge about the type 'r' and can work for any d and b, we get:
.
> type Getter a c = forall r b d. Getting r a b c d
.
Everything you can do with a function, you can do with a 'Getter', but note that because of the
continuation passing style (.) composes them in the opposite order.
.
Since it is only a function, every 'Getter' obviously only retrieves a single value for a given
input.
.
/Fold/
.
A @'Fold' a c@ is a generalization of something 'Foldable'. It allows you to
extract multiple results from a container. A 'Foldable' container can be
characterized by the behavior of @foldMap :: (Foldable t, Monoid m) => (c -> m) -> t c -> m@.
Since we want to be able to work with monomorphic containers, we generalize this signature to
@forall m. 'Monoid' m => (c -> m) -> a -> m@, and then decorate it with 'Const' to obtain
.
> type Fold a c = forall m b d. Monoid m => Getting m a b c d
.
Every 'Getter' is a valid 'Fold' that simply doesn't use the 'Monoid' it is passed.
.
Everything you can do with a 'Foldable' container, you can with with a 'Fold' and there are
combinators that generalize the usual 'Foldable' operations in @Control.Lens@.
.
/Traversal/
.
A @'Traversal' a b c d@ is a generalization of 'traverse' from 'Traversable'. It allows
you to traverse over a structure and change out its contents with monadic or
applicative side-effects. Starting from
@'traverse' :: ('Traversable' t, 'Applicative' f) => (c -> f d) -> t c -> f (t d)@,
we monomorphize the contents and result to obtain
.
> type Traversal a b c d = forall f. Applicative f => (c -> f d) -> a -> f b
.
While a 'Traversal' isn't quite a 'Fold', it _can_ be used for 'Getting' like a 'Fold', because
given a 'Monoid' @m@, we have an 'Applicative' for @('Const' m)@.
.
Everything you can do with a 'Traversable' container, you can with with a 'Traversal', and there
are combinators that generalize the usual 'Traversable' operations in @Control.Lens@.
.
/Setter/
.
A @'Setter' a b c d@ is a generalization of 'fmap' from 'Functor'. It allows you to map into a
structure and change out the contents, but it isn't strong enough to allow you to
enumerate those contents. Starting with @fmap :: 'Functor' f => (c -> d) -> f c -> f d@
we monomorphize the type to obtain @(c -> d) -> a -> b@ and then decorate it with 'Identity' to obtain
.
> type Setter a b c d = (c -> Identity d) -> a -> Identity b
.
Every 'Traversal' is a valid 'Setter', since 'Identity' is 'Applicative'.
.
Everything you can do with a 'Functor', you can do with a 'Setter', and there are combinators that
generalize the usual 'Functor' operations in @Control.Lens@.
.
/Lens/
.
A @'Lens' a b c d@ is a purely functional reference.
.
While a 'Traversal' could be used for 'Getting' like a valid 'Fold', it wasn't a valid 'Getter'.
To make the 'Applicative' for 'Const' it required a 'Monoid' for the argument we passed it, which
a 'Getter' doesn't recieve.
.
However, the instance of 'Functor' for 'Const' requires no such thing. If we weaken the type
requirement from 'Applicative' to 'Functor' for 'Traversal', we obtain
.
> type Lens a b c d = forall f. Functor f => (c -> f d) -> a -> f b
.
Every 'Lens' is a valid 'Setter', choosing @f@ = 'Identity'.
.
Every 'Lens' can be used for 'Getting' like a 'Fold' that doesn't use the 'Monoid' it is passed.
.
Every 'Lens' is a valid 'Traversal' that only uses the 'Functor' part of the 'Applicative' it is supplied.
.
Every 'Lens' can be used for 'Getting' like a valid 'Getter', choosing @f@ = 'Const' @r@ for an appropriate @r@
.
Since every 'Lens' can be used for 'Getting' like a valid 'Getter' it follows that it must view exactly one
element in the structure.
.
The lens laws follow from this property and the desire for it to act like a 'Functor' when used as a 'Setter'.
.
/Isomorphisms and Iso/
.
Control.Isomorphic provides easy overloading of function application for isomorphisms and @Iso a b c d@ uses it
to form isomorphism families that can be composed with other isomorphisms and with lenses, setters, folds,
traversals and getters.
.
> type Iso a b c d = forall k f. (Isomorphic k, Functor f) => k (c -> f d) (a -> f b)
.
/Composition/
.
Note that all of these types are type aliases, and you can compose these lenses with mere function compositon.
.
This is a generalization of the well-known trick for @(.).(.)@ or @fmap.fmap@, and their less well-known cousins
@foldMap.foldMap@ @traverse.traverse@. It follows because each one is a function between values of type @(x -> f y)@
and the composition takes the intersection of supplied functionality for you automatically!
.
/Lens Families/
.
For a longer description of why you should care about lenses, and an overview of why we use 4
parameters a, b, c, and d instead of just 2, see .
.
Sometimes you won't need the flexibility those extra parameters afford you and you can use
.
> type Simple f a b = f a a b b
.
to describe a 'Simple' 'Setter', 'Simple' 'Traversal', 'Simple' 'Lens' or 'Simple' 'Iso'.
.
/Avoiding Dependencies/
.
Note: If you merely want your library to /provide/ lenses you may not
have to actually import /any/ lens library at all. For, say, a
@'Simple' 'Lens' Bar Foo@, just export a function with the signature:
.
> foo :: Functor f => (Foo -> f Foo) -> Bar -> f Bar
.
and then you can compose it with other lenses using nothing more than @(.)@ from the Prelude.
.
/Deriving Lenses/
.
You can derive lenses automatically for many data types using 'Control.Lens.TH', and if a
container is fully characterized by its lenses, you can use 'Control.Lens.Representable' to
automatically derive 'Functor', 'Applicative', 'Monad', and 'Derivable'.
build-type: Simple
tested-with: GHC == 7.4.1
extra-source-files: .travis.yml examples/Pong.hs examples/Test.hs examples/Pong2.hs
source-repository head
type: git
location: git://github.com/ekmett/lens.git
library
build-depends:
base >= 4.3 && < 5,
containers >= 0.4.2 && < 0.6,
mtl >= 2.0.1 && < 2.2,
transformers >= 0.2.2 && < 0.4
exposed-modules: Control.Indexed
Control.Isomorphic
Control.Lens
Control.Lens.Internal
Control.Lens.Representable
-- base
exposed-modules: Control.Exception.Lens
Data.Bits.Lens
Data.Complex.Lens
Data.Dynamic.Lens
Data.Either.Lens
Data.List.Lens
Data.Pair.Lens
-- containers
exposed-modules: Data.IntMap.Lens
Data.IntSet.Lens
Data.Map.Lens
Data.Sequence.Lens
Data.Set.Lens
Data.Tree.Lens
build-depends: template-haskell >= 2.4 && < 2.8
exposed-modules: Language.Haskell.TH.Lens
Control.Lens.TH
-- platform
build-depends: array >= 0.3.0.2 && < 0.5
exposed-modules: Data.Array.Lens
build-depends: bytestring >= 0.9.1.10 && < 0.10
exposed-modules: Data.ByteString.Lens Data.ByteString.Lazy.Lens
build-depends: text >= 0.11.1.5 && < 0.12
exposed-modules: Data.Text.Lens Data.Text.Lazy.Lens
build-depends: parallel >= 3.1.0.1 && < 3.3
exposed-modules: Control.Parallel.Strategies.Lens Control.Seq.Lens
other-extensions:
CPP
DeriveDataTypeable
FlexibleContexts
FlexibleInstances
LiberalTypeSynonyms
MultiParamTypeClasses
Rank2Types
RankNTypes
TemplateHaskell
TypeFamilies
TypeOperators
if (impl(ghc>=7.4))
other-extensions: Trustworthy
build-depends: ghc-prim
exposed-modules: GHC.Generics.Lens
ghc-options: -Wall -fwarn-tabs -O2 -fdicts-cheap -funbox-strict-fields
hs-source-dirs: src