| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Prelate.Prelude
Description
A Polysemy Prelude with some basic libraries
Synopsis
- module Incipit
- type (@@) a b = Tagged b a
- module Prelate.Atomic
- module Prelate.App
- module Prelate.Control.Applicative
- module Prelate.Control.Monad
- module Prelate.Data.List
- module Prelate.Data.Maybe
- module Prelate.Json
- class ToJSON a
- class FromJSON a
- (&) :: a -> (a -> b) -> b
- (<&>) :: Functor f => f a -> (a -> b) -> f b
- _Nothing :: Traversal' (Maybe a) ()
- _Just :: Traversal (Maybe a) (Maybe a') a a'
- _Right :: Traversal (Either a b) (Either a b') b b'
- _Left :: Traversal (Either a b) (Either a' b) a a'
- mapAccumLOf :: LensLike (State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
- _last :: Snoc s s a a => Traversal' s a
- _init :: Snoc s s a a => Traversal' s s
- _tail :: Cons s s a a => Traversal' s s
- _head :: Cons s s a a => Traversal' s a
- both :: Traversal (a, a) (b, b) a b
- filtered :: (a -> Bool) -> Traversal' a a
- failing :: Traversal s t a b -> Traversal s t a b -> Traversal s t a b
- singular :: HasCallStack => Traversal s t a a -> Lens s t a a
- forOf :: LensLike f s t a b -> s -> (a -> f b) -> f t
- traverseOf :: LensLike f s t a b -> (a -> f b) -> s -> f t
- non :: Eq a => a -> Lens' (Maybe a) a
- folding :: Foldable f => (s -> f a) -> SimpleFold s a
- has :: Getting Any s a -> s -> Bool
- forOf_ :: Functor f => Getting (Traversed r f) s a -> s -> (a -> f r) -> f ()
- traverseOf_ :: Functor f => Getting (Traversed r f) s a -> (a -> f r) -> s -> f ()
- (^?!) :: HasCallStack => s -> Getting (Endo a) s a -> a
- (^?) :: s -> Getting (First a) s a -> Maybe a
- toListOf :: Getting (Endo [a]) s a -> s -> [a]
- (^..) :: s -> Getting (Endo [a]) s a -> [a]
- to :: (s -> a) -> SimpleGetter s a
- (^.) :: s -> Getting a s a -> a
- transformOf :: ASetter a b a b -> (b -> b) -> a -> b
- rewriteOf :: ASetter a b a b -> (b -> Maybe a) -> a -> b
- (<<.~) :: LensLike ((,) a) s t a b -> b -> s -> (a, t)
- (<<%~) :: LensLike ((,) a) s t a b -> (a -> b) -> s -> (a, t)
- (<%~) :: LensLike ((,) b) s t a b -> (a -> b) -> s -> (b, t)
- mapped :: Functor f => ASetter (f a) (f b) a b
- (?~) :: ASetter s t a (Maybe b) -> b -> s -> t
- set :: ASetter s t a b -> b -> s -> t
- (.~) :: ASetter s t a b -> b -> s -> t
- (<>~) :: Monoid a => ASetter s t a a -> a -> s -> t
- (-~) :: Num a => ASetter s t a a -> a -> s -> t
- (+~) :: Num a => ASetter s t a a -> a -> s -> t
- over :: ASetter s t a b -> (a -> b) -> s -> t
- (%~) :: ASetter s t a b -> (a -> b) -> s -> t
- sets :: ((a -> b) -> s -> t) -> ASetter s t a b
- folded :: forall (f :: TYPE LiftedRep -> Type) a. Foldable f => SimpleFold (f a) a
- traversed :: forall (f :: Type -> Type) a b. Traversable f => Traversal (f a) (f b) a b
- each :: Each s t a b => Traversal s t a b
- ix :: Ixed m => Index m -> Traversal' m (IxValue m)
- at :: At m => Index m -> Lens' m (Maybe (IxValue m))
- _1 :: Field1 s t a b => Lens s t a b
- _2 :: Field2 s t a b => Lens s t a b
- _3 :: Field3 s t a b => Lens s t a b
- _4 :: Field4 s t a b => Lens s t a b
- _5 :: Field5 s t a b => Lens s t a b
- strict :: Strict lazy strict => Lens' lazy strict
- lazy :: Strict lazy strict => Lens' strict lazy
- type ASetter s t a b = (a -> Identity b) -> s -> Identity t
- type ASetter' s a = ASetter s s a a
- type SimpleGetter s a = forall r. Getting r s a
- type Getting r s a = (a -> Const r a) -> s -> Const r s
- type SimpleFold s a = forall r. Monoid r => Getting r s a
- type Lens s t a b = forall (f :: Type -> Type). Functor f => (a -> f b) -> s -> f t
- type Lens' s a = Lens s s a a
- type Traversal s t a b = forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t
- type Traversal' s a = Traversal s s a a
- type LensLike (f :: Type -> Type) s t a b = (a -> f b) -> s -> f t
- type LensLike' (f :: Type -> Type) s a = LensLike f s s a a
- at :: At m => Index m -> Lens' m (Maybe (IxValue m))
Documentation
module Incipit
module Prelate.Atomic
module Prelate.App
module Prelate.Control.Applicative
module Prelate.Control.Monad
module Prelate.Data.List
module Prelate.Data.Maybe
module Prelate.Json
A type that can be converted to JSON.
Instances in general must specify toJSON and should (but don't need
to) specify toEncoding.
An example type and instance:
-- Allow ourselves to writeTextliterals. {-# LANGUAGE OverloadedStrings #-} data Coord = Coord { x :: Double, y :: Double } instanceToJSONCoord wheretoJSON(Coord x y) =object["x".=x, "y".=y]toEncoding(Coord x y) =pairs("x".=x<>"y".=y)
Instead of manually writing your ToJSON instance, there are two options
to do it automatically:
- Data.Aeson.TH provides Template Haskell functions which will derive an instance at compile time. The generated instance is optimized for your type so it will probably be more efficient than the following option.
- The compiler can provide a default generic implementation for
toJSON.
To use the second, simply add a deriving clause to your
datatype and declare a GenericToJSON instance. If you require nothing other than
defaultOptions, it is sufficient to write (and this is the only
alternative where the default toJSON implementation is sufficient):
{-# LANGUAGE DeriveGeneric #-}
import GHC.Generics
data Coord = Coord { x :: Double, y :: Double } deriving Generic
instance ToJSON Coord where
toEncoding = genericToEncoding defaultOptions
If on the other hand you wish to customize the generic decoding, you have to implement both methods:
customOptions =defaultOptions{fieldLabelModifier=maptoUpper} instanceToJSONCoord wheretoJSON=genericToJSONcustomOptionstoEncoding=genericToEncodingcustomOptions
Previous versions of this library only had the toJSON method. Adding
toEncoding had two reasons:
- toEncoding is more efficient for the common case that the output of
toJSONis directly serialized to aByteString. Further, expressing either method in terms of the other would be non-optimal. - The choice of defaults allows a smooth transition for existing users:
Existing instances that do not define
toEncodingstill compile and have the correct semantics. This is ensured by making the default implementation oftoEncodingusetoJSON. This produces correct results, but since it performs an intermediate conversion to aValue, it will be less efficient than directly emitting anEncoding. (this also means that specifying nothing more thaninstance ToJSON Coordwould be sufficient as a generically decoding instance, but there probably exists no good reason to not specifytoEncodingin new instances.)
Instances
A type that can be converted from JSON, with the possibility of failure.
In many cases, you can get the compiler to generate parsing code for you (see below). To begin, let's cover writing an instance by hand.
There are various reasons a conversion could fail. For example, an
Object could be missing a required key, an Array could be of
the wrong size, or a value could be of an incompatible type.
The basic ways to signal a failed conversion are as follows:
failyields a custom error message: it is the recommended way of reporting a failure;empty(ormzero) is uninformative: use it when the error is meant to be caught by some(;<|>)typeMismatchcan be used to report a failure when the encountered value is not of the expected JSON type;unexpectedis an appropriate alternative when more than one type may be expected, or to keep the expected type implicit.
prependFailure (or modifyFailure) add more information to a parser's
error messages.
An example type and instance using typeMismatch and prependFailure:
-- Allow ourselves to writeTextliterals. {-# LANGUAGE OverloadedStrings #-} data Coord = Coord { x :: Double, y :: Double } instanceFromJSONCoord whereparseJSON(Objectv) = Coord<$>v.:"x"<*>v.:"y" -- We do not expect a non-Objectvalue here. -- We could useemptyto fail, buttypeMismatch-- gives a much more informative error message.parseJSONinvalid =prependFailure"parsing Coord failed, " (typeMismatch"Object" invalid)
For this common case of only being concerned with a single
type of JSON value, the functions withObject, withScientific, etc.
are provided. Their use is to be preferred when possible, since
they are more terse. Using withObject, we can rewrite the above instance
(assuming the same language extension and data type) as:
instanceFromJSONCoord whereparseJSON=withObject"Coord" $ \v -> Coord<$>v.:"x"<*>v.:"y"
Instead of manually writing your FromJSON instance, there are two options
to do it automatically:
- Data.Aeson.TH provides Template Haskell functions which will derive an instance at compile time. The generated instance is optimized for your type so it will probably be more efficient than the following option.
- The compiler can provide a default generic implementation for
parseJSON.
To use the second, simply add a deriving clause to your
datatype and declare a GenericFromJSON instance for your datatype without giving
a definition for parseJSON.
For example, the previous example can be simplified to just:
{-# LANGUAGE DeriveGeneric #-}
import GHC.Generics
data Coord = Coord { x :: Double, y :: Double } deriving Generic
instance FromJSON Coord
The default implementation will be equivalent to
parseJSON = ; if you need different
options, you can customize the generic decoding by defining:genericParseJSON defaultOptions
customOptions =defaultOptions{fieldLabelModifier=maptoUpper} instanceFromJSONCoord whereparseJSON=genericParseJSONcustomOptions
Instances
_Nothing :: Traversal' (Maybe a) () #
_Nothing targets a () if the Maybe is a Nothing, and doesn't target anything otherwise:
>>>Just 1 ^.. _Nothing[]
>>>Nothing ^.. _Nothing[()]
It's not particularly useful (unless you want to use has _NothingisNothing), and provided mainly for consistency.
Implementation:
_Nothingf Nothing =constNothing<$>f ()_Nothing_ j =purej
_Just :: Traversal (Maybe a) (Maybe a') a a' #
_Just targets the value contained in a Maybe, provided it's a Just.
See documentation for _Left (as these 2 are pretty similar). In particular, it can be used to write these:
- Unsafely extracting a value from a
Just:
fromJust= (^?!_Just)
- Checking whether a value is a
Just:
isJust=has_Just
- Converting a
Maybeto a list (empty or consisting of a single element):
maybeToList= (^.._Just)
- Gathering all
Justs in a list:
catMaybes= (^..each._Just)
_Left :: Traversal (Either a b) (Either a' b) a a' #
_Left targets the value contained in an Either, provided it's a Left.
Gathering all Lefts in a structure (like the lefts function, but not necessarily just for lists):
>>>[Left 1, Right 'c', Left 3] ^.. each._Left[1,3]
Checking whether an Either is a Left (like isLeft):
>>>has _Left (Left 1)True
>>>has _Left (Right 1)False
Extracting a value (if you're sure it's a Left):
>>>Left 1 ^?! _Left1
Mapping over all Lefts:
>>>(each._Left %~ map toUpper) [Left "foo", Right "bar"][Left "FOO",Right "bar"]
Implementation:
_Leftf (Left a) =Left<$>f a_Left_ (Right b) =pure(Rightb)
mapAccumLOf :: LensLike (State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t) #
This generalizes mapAccumL to an arbitrary Traversal. (Note that it doesn't work on folds, only traversals.)
mapAccumL≡mapAccumLOftraverse
_last :: Snoc s s a a => Traversal' s a #
_init :: Snoc s s a a => Traversal' s s #
_tail :: Cons s s a a => Traversal' s s #
_tail gives you access to the tail of a list (or Seq, etc):
>>>[1..5] ^? _tailJust [2,3,4,5]
You can modify the tail as well:
>>>[4,1,2,3] & _tail %~ reverse[4,3,2,1]
Since lists are monoids, you can use _tail with plain (^.) (and then it'll return an empty list if you give it an empty list):
>>>[1..5] ^. _tail[2,3,4,5]
>>>[] ^. _tail[]
If you want to traverse each element of the tail, use _tail with each:
>>>"I HATE CAPS." & _tail.each %~ toLower"I hate caps."
This package only lets you use _tail on lists, but if you use microlens-ghc you get instances for ByteString and Seq, and if you use microlens-platform you additionally get instances for Text and Vector.
_head :: Cons s s a a => Traversal' s a #
_head traverses the 1st element of something (usually a list, but can also be a Seq, etc):
>>>[1..5] ^? _headJust 1
It can be used to modify too, as in this example where the 1st letter of a sentence is capitalised:
>>>"mary had a little lamb." & _head %~ toTitle"Mary had a little lamb."
The reason it's a traversal and not a lens is that there's nothing to traverse when the list is empty:
>>>[] ^? _headNothing
This package only lets you use _head on lists, but if you use microlens-ghc you get instances for ByteString and Seq, and if you use microlens-platform you additionally get instances for Text and Vector.
filtered :: (a -> Bool) -> Traversal' a a #
filtered is a traversal that filters elements “passing” through it:
>>>(1,2,3,4) ^.. each[1,2,3,4]
>>>(1,2,3,4) ^.. each . filtered even[2,4]
It also can be used to modify elements selectively:
>>>(1,2,3,4) & each . filtered even %~ (*100)(1,200,3,400)
The implementation of filtered is very simple. Consider this traversal, which always “traverses” just the value it's given:
id :: Traversal' a a
id f s = f s
And this traversal, which traverses nothing (in other words, doesn't traverse the value it's given):
ignored ::Traversal'a a ignored f s =pures
And now combine them into a traversal that conditionally traverses the value it's given, and you get filtered:
filtered :: (a -> Bool) ->Traversal'a a filtered p f s = if p s then f s elsepures
By the way, note that filtered can generate illegal traversals – sometimes this can bite you. In particular, an optimisation that should be safe becomes unsafe. (To the best of my knowledge, this optimisation never happens automatically. If you just use filtered to modify/view something, you're safe. If you don't define any traversals that use filtered, you're safe too.)
Let's use evens as an example:
evens =filteredeven
If evens was a legal traversal, you'd be able to fuse several applications of evens like this:
overevens f.overevens g =overevens (f.g)
Unfortunately, in case of evens this isn't a correct optimisation:
- the left-side variant applies
gto all even numbers, and then appliesfto all even numbers that are left afterf(becausefmight've turned some even numbers into odd ones) - the right-side variant applies
fandgto all even numbers
Of course, when you are careful and know what you're doing, you won't try to make such an optimisation. However, if you export an illegal traversal created with filtered and someone tries to use it, they might mistakenly assume that it's legal, do the optimisation, and silently get an incorrect result.
If you are using filtered with some another traversal that doesn't overlap with -whatever the predicate checks-, the resulting traversal will be legal. For instance, here the predicate looks at the 1st element of a tuple, but the resulting traversal only gives you access to the 2nd:
pairedWithEvens ::Traversal[(Int, a)] [(Int, b)] a b pairedWithEvens =each.filtered(even.fst)._2
Since you can't do anything with the 1st components through this traversal, the following holds for any f and g:
overpairedWithEvens f.overpairedWithEvens g =overpairedWithEvens (f.g)
failing :: Traversal s t a b -> Traversal s t a b -> Traversal s t a b infixl 5 #
failing lets you chain traversals together; if the 1st traversal fails, the 2nd traversal will be used.
>>>([1,2],[3]) & failing (_1.each) (_2.each) .~ 0([0,0],[3])
>>>([],[3]) & failing (_1.each) (_2.each) .~ 0([],[0])
Note that the resulting traversal won't be valid unless either both traversals don't touch each others' elements, or both traversals return exactly the same results. To see an example of how failing can generate invalid traversals, see this Stackoverflow question.
singular :: HasCallStack => Traversal s t a a -> Lens s t a a #
singular turns a traversal into a lens that behaves like a single-element traversal:
>>>[1,2,3] ^. singular each1
>>>[1,2,3] & singular each %~ negate[-1,2,3]
If there is nothing to return, it'll throw an error:
>>>[] ^. singular each*** Exception: Lens.Micro.singular: empty traversal
However, it won't fail if you are merely setting the value:
>>>[] & singular each %~ negate
forOf :: LensLike f s t a b -> s -> (a -> f b) -> f t #
traverseOf with flipped arguments. Useful if the “loop body” is a lambda or
a do block.
traverseOf :: LensLike f s t a b -> (a -> f b) -> s -> f t #
Apply an action to all targets (like mapM or traverse):
>>>traverseOf both readFile ("file1", "file2")(<contents of file1>, <contents of file2>)
>>>traverseOf _1 id (Just 1, 2)Just (1, 2)>>>traverseOf _1 id (Nothing, 2)Nothing
You can also just apply the lens/traversal directly (but traverseOf might be more readable):
>>>both readFile ("file1", "file2")(<contents of file1>, <contents of file2>)
If you don't need the result, use traverseOf_.
non :: Eq a => a -> Lens' (Maybe a) a #
non lets you “relabel” a Maybe by equating Nothing to an arbitrary value (which you can choose):
>>>Just 1 ^. non 01
>>>Nothing ^. non 00
The most useful thing about non is that relabeling also works in other direction. If you try to set the “forbidden” value, it'll be turned to Nothing:
>>>Just 1 & non 0 .~ 0Nothing
Setting anything else works just fine:
>>>Just 1 & non 0 .~ 5Just 5
Same happens if you try to modify a value:
>>>Just 1 & non 0 %~ subtract 1Nothing
>>>Just 1 & non 0 %~ (+ 1)Just 2
non is often useful when combined with at. For instance, if you have a map of songs and their playcounts, it makes sense not to store songs with 0 plays in the map; non can act as a filter that wouldn't pass such entries.
Decrease playcount of a song to 0, and it'll be gone:
>>>fromList [("Soon",1),("Yesterday",3)] & at "Soon" . non 0 %~ subtract 1fromList [("Yesterday",3)]
Try to add a song with 0 plays, and it won't be added:
>>>fromList [("Yesterday",3)] & at "Soon" . non 0 .~ 0fromList [("Yesterday",3)]
But it will be added if you set any other number:
>>>fromList [("Yesterday",3)] & at "Soon" . non 0 .~ 1fromList [("Soon",1),("Yesterday",3)]
non is also useful when working with nested maps. Here a nested map is created when it's missing:
>>>Map.empty & at "Dez Mona" . non Map.empty . at "Soon" .~ Just 1fromList [("Dez Mona",fromList [("Soon",1)])]
and here it is deleted when its last entry is deleted (notice that non is used twice here):
>>>fromList [("Dez Mona",fromList [("Soon",1)])] & at "Dez Mona" . non Map.empty . at "Soon" . non 0 %~ subtract 1fromList []
To understand the last example better, observe the flow of values in it:
- the map goes into
at "Dez Mona" - the nested map (wrapped into
Just) goes intonon Map.empty Justis unwrapped and the nested map goes intoat "Soon"Just 1is unwrapped bynon 0
Then the final value – i.e. 1 – is modified by subtract 1 and the result (which is 0) starts flowing backwards:
non 0sees the 0 and produces aNothingat "Soon"seesNothingand deletes the corresponding value from the map- the resulting empty map is passed to
non Map.empty, which sees that it's empty and thus producesNothing at "Dez Mona"seesNothingand removes the key from the map
folding :: Foldable f => (s -> f a) -> SimpleFold s a #
has :: Getting Any s a -> s -> Bool #
has checks whether a getter (any getter, including lenses, traversals, and folds) returns at least 1 value.
Checking whether a list is non-empty:
>>>has each []False
You can also use it with e.g. _Left (and other 0-or-1 traversals) as a replacement for isNothing, isJust and other isConstructorName functions:
>>>has _Left (Left 1)True
forOf_ :: Functor f => Getting (Traversed r f) s a -> s -> (a -> f r) -> f () #
traverseOf_ with flipped arguments. Useful if the “loop body” is a lambda
or a do block, or in some other cases – for instance, you can avoid
accidentally using for_ on a tuple or Either by switching
to forOf_ each
forOf_both(a, b) $ \x -> ...forOf_each[1..10] $ \x -> ...forOf_(each._Right) $ \x -> ...
traverseOf_ :: Functor f => Getting (Traversed r f) s a -> (a -> f r) -> s -> f () #
Apply an action to all targets and discard the result (like mapM_ or traverse_):
>>>traverseOf_ both putStrLn ("hello", "world")hello world
Works with anything that allows getting, including lenses and getters (so, anything except for ASetter). Should be faster than traverseOf when you don't need the result.
(^?!) :: HasCallStack => s -> Getting (Endo a) s a -> a infixl 8 #
(^?) :: s -> Getting (First a) s a -> Maybe a infixl 8 #
s ^? t returns the 1st element t returns, or Nothing if t doesn't return anything. It's trivially implemented by passing the First monoid to the getter.
Safe head:
>>>[] ^? eachNothing
>>>[1..3] ^? eachJust 1
>>>Left 1 ^? _RightNothing
>>>Right 1 ^? _RightJust 1
A non-operator version of (^?) is called preview, and – like view – it's a bit more general than (^?) (it works in MonadReader). If you need the general version, you can get it from microlens-mtl; otherwise there's preview available in Lens.Micro.Extras.
(^..) :: s -> Getting (Endo [a]) s a -> [a] infixl 8 #
s ^.. t returns the list of all values that t gets from s.
A Maybe contains either 0 or 1 values:
>>>Just 3 ^.. _Just[3]
Gathering all values in a list of tuples:
>>>[(1,2),(3,4)] ^.. each.each[1,2,3,4]
to :: (s -> a) -> SimpleGetter s a #
to creates a getter from any function:
a^.tof = f a
It's most useful in chains, because it lets you mix lenses and ordinary functions. Suppose you have a record which comes from some third-party library and doesn't have any lens accessors. You want to do something like this:
value ^. _1 . field . at 2
However, field isn't a getter, and you have to do this instead:
field (value ^. _1) ^. at 2
but now value is in the middle and it's hard to read the resulting code. A variant with to is prettier and more readable:
value ^. _1 . to field . at 2
(^.) :: s -> Getting a s a -> a infixl 8 #
(^.) applies a getter to a value; in other words, it gets a value out of a structure using a getter (which can be a lens, traversal, fold, etc.).
Getting 1st field of a tuple:
(^._1) :: (a, b) -> a (^._1) =fst
When (^.) is used with a traversal, it combines all results using the Monoid instance for the resulting type. For instance, for lists it would be simple concatenation:
>>>("str","ing") ^. each"string"
The reason for this is that traversals use Applicative, and the Applicative instance for Const uses monoid concatenation to combine “effects” of Const.
A non-operator version of (^.) is called view, and it's a bit more general than (^.) (it works in MonadReader). If you need the general version, you can get it from microlens-mtl; otherwise there's view available in Lens.Micro.Extras.
transformOf :: ASetter a b a b -> (b -> b) -> a -> b #
Transform every element by recursively applying a given ASetter in a bottom-up manner.
Since: microlens-0.4.11
rewriteOf :: ASetter a b a b -> (b -> Maybe a) -> a -> b #
→ See an example on GitHub.
Rewrite by applying a rule everywhere you can. Ensures that the rule cannot be applied anywhere in the result.
Usually transformOf is more appropriate, but rewriteOf can give better compositionality. Given two single transformations f and g, you can construct \a -> f a which performs both rewrites until a fixed point.<|> g a
Since: microlens-0.4.11
(<%~) :: LensLike ((,) b) s t a b -> (a -> b) -> s -> (b, t) infixr 4 #
This is a version of (%~) which modifies the structure and returns it along with the new value:
>>>(1, 2) & _1 <%~ negate(-1, (-1, 2))
Simpler type signatures:
(<%~) ::Lenss t a b -> (a -> b) -> s -> (b, t) (<%~) ::Monoidb =>Traversals t a b -> (a -> b) -> s -> (b, t)
Since it does getting in addition to setting, you can't use it with ASetter (but you can use it with lens and traversals).
mapped :: Functor f => ASetter (f a) (f b) a b #
mapped is a setter for everything contained in a functor. You can use it to map over lists, Maybe, or even IO (which is something you can't do with traversed or each).
Here mapped is used to turn a value to all non-Nothing values in a list:
>>>[Just 3,Nothing,Just 5] & mapped.mapped .~ 0[Just 0,Nothing,Just 0]
Keep in mind that while mapped is a more powerful setter than each, it can't be used as a getter! This won't work (and will fail with a type error):
[(1,2),(3,4),(5,6)]^..mapped.both
(<>~) :: Monoid a => ASetter s t a a -> a -> s -> t infixr 4 #
(<>~) appends a value monoidally to the target.
>>>("hello", "goodbye") & both <>~ " world!"("hello world!", "goodbye world!")
Since: microlens-0.4.9
(-~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4 #
Decrement the target(s) of a numerically valued Lens, or Traversal.
>>>(a,b) & _1 -~ c(a - c,b)
>>>(a,b) & both -~ c(a - c,b - c)
>>>_1 -~ 2 $ (1,2)(-1,2)
>>>mapped.mapped -~ 1 $ [[4,5],[6,7]][[3,4],[5,6]]
(-~) ::Numa =>Lens's a -> a -> s -> s (-~) ::Numa =>Traversal's a -> a -> s -> s
Since: microlens-0.4.10
(+~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4 #
Increment the target(s) of a numerically valued Lens or Traversal.
>>>(a,b) & _1 +~ c(a + c,b)
>>>(a,b) & both +~ c(a + c,b + c)
>>>(1,2) & _2 +~ 1(1,3)
>>>[(a,b),(c,d)] & traverse.both +~ e[(a + e,b + e),(c + e,d + e)]
(+~) ::Numa =>Lens's a -> a -> s -> s (+~) ::Numa =>Traversal's a -> a -> s -> s
Since: microlens-0.4.10
over :: ASetter s t a b -> (a -> b) -> s -> t #
Getting fmap in a roundabout way:
overmapped::Functorf => (a -> b) -> f a -> f bovermapped=fmap
Applying a function to both components of a pair:
overboth:: (a -> b) -> (a, a) -> (b, b)overboth= \f t -> (f (fst t), f (snd t))
Using over _2second:
>>>over _2 show (10,20)(10,"20")
(%~) :: ASetter s t a b -> (a -> b) -> s -> t infixr 4 #
(%~) applies a function to the target; an alternative explanation is that it is an inverse of sets, which turns a setter into an ordinary function. mapped %~ reversefmap reverse
See over if you want a non-operator synonym.
Negating the 1st element of a pair:
>>>(1,2) & _1 %~ negate(-1,2)
Turning all Lefts in a list to upper case:
>>>(mapped._Left.mapped %~ toUpper) [Left "foo", Right "bar"][Left "FOO",Right "bar"]
traversed :: forall (f :: Type -> Type) a b. Traversable f => Traversal (f a) (f b) a b #
traversed traverses any Traversable container (list, vector, Map, Maybe, you name it):
>>>Just 1 ^.. traversed[1]
traversed is the same as traverse, but can be faster thanks to magic rewrite rules.
each :: Each s t a b => Traversal s t a b #
each tries to be a universal Traversal – it behaves like traversed in most situations, but also adds support for e.g. tuples with same-typed values:
>>>(1,2) & each %~ succ(2,3)
>>>["x", "y", "z"] ^. each"xyz"
However, note that each doesn't work on every instance of Traversable. If you have a Traversable which isn't supported by each, you can use traversed instead. Personally, I like using each instead of traversed whenever possible – it's shorter and more descriptive.
You can use each with these things:
each::Traversal[a] [b] a beach::Traversal(Maybea) (Maybeb) a beach::Traversal(Eithera a) (Eitherb b) a b -- since 0.4.11each::Traversal(a,a) (b,b) a beach::Traversal(a,a,a) (b,b,b) a beach::Traversal(a,a,a,a) (b,b,b,b) a beach::Traversal(a,a,a,a,a) (b,b,b,b,b) a beach:: (RealFloata,RealFloatb) =>Traversal(Complexa) (Complexb) a b
You can also use each with types from array, bytestring, and containers by using microlens-ghc, or additionally with types from vector, text, and unordered-containers by using microlens-platform.
ix :: Ixed m => Index m -> Traversal' m (IxValue m) #
This traversal lets you access (and update) an arbitrary element in a list, array, Map, etc. (If you want to insert or delete elements as well, look at at.)
An example for lists:
>>>[0..5] & ix 3 .~ 10[0,1,2,10,4,5]
You can use it for getting, too:
>>>[0..5] ^? ix 3Just 3
Of course, the element may not be present (which means that you can use ix as a safe variant of (!!)):
>>>[0..5] ^? ix 10Nothing
Another useful instance is the one for functions – it lets you modify their outputs for specific inputs. For instance, here's maximum that returns 0 when the list is empty (instead of throwing an exception):
maximum0 =maximum&ix[].~0
The following instances are provided in this package:
ix::Int->Traversal'[a] aix::Int->Traversal'(NonEmpty a) aix:: (Eqe) => e ->Traversal'(e -> a) a
You can also use ix with types from array, bytestring, and containers by using microlens-ghc, or additionally with types from vector, text, and unordered-containers by using microlens-platform.
at :: At m => Index m -> Lens' m (Maybe (IxValue m)) #
This lens lets you read, write, or delete elements in Map-like structures. It returns Nothing when the value isn't found, just like lookup:
Data.Map.lookup k m = m ^. at k
However, it also lets you insert and delete values by setting the value to Just valueNothing:
Data.Map.insert k a m = m&at k.~Just a Data.Map.delete k m = m&at k.~Nothing
Or you could use (?~) instead of (.~):
Data.Map.insert k a m = m&at k?~a
Note that at doesn't work for arrays or lists. You can't delete an arbitrary element from an array (what would be left in its place?), and you can't set an arbitrary element in a list because if the index is out of list's bounds, you'd have to somehow fill the stretch between the last element and the element you just inserted (i.e. [1,2,3] & at 10 .~ 5 is undefined). If you want to modify an already existing value in an array or list, you should use ix instead.
at is often used with non. See the documentation of non for examples.
Note that at isn't strict for Map, even if you're using Data.Map.Strict:
>>>Data.Map.Strict.size (Data.Map.Strict.empty & at 1 .~ Just undefined)1
The reason for such behavior is that there's actually no “strict Map” type; Data.Map.Strict just provides some strict functions for ordinary Maps.
This package doesn't actually provide any instances for at, but there are instances for Map and IntMap in microlens-ghc and an instance for HashMap in microlens-platform.
_1 :: Field1 s t a b => Lens s t a b #
Gives access to the 1st field of a tuple (up to 5-tuples).
Getting the 1st component:
>>>(1,2,3,4,5) ^. _11
Setting the 1st component:
>>>(1,2,3) & _1 .~ 10(10,2,3)
Note that this lens is lazy, and can set fields even of undefined:
>>>set _1 10 undefined :: (Int, Int)(10,*** Exception: Prelude.undefined
This is done to avoid violating a lens law stating that you can get back what you put:
>>>view _1 . set _1 10 $ (undefined :: (Int, Int))10
The implementation (for 2-tuples) is:
_1f t = (,)<$>f (fstt)<*>pure(sndt)
or, alternatively,
_1f ~(a,b) = (\a' -> (a',b))<$>f a
(where ~ means a lazy pattern).
strict :: Strict lazy strict => Lens' lazy strict #
strict lets you convert between strict and lazy versions of a datatype:
>>>let someText = "hello" :: Lazy.Text>>>someText ^. strict"hello" :: Strict.Text
It can also be useful if you have a function that works on a strict type but your type is lazy:
stripDiacritics :: Strict.Text -> Strict.Text stripDiacritics = ...
>>>let someText = "Paul Erdős" :: Lazy.Text>>>someText & strict %~ stripDiacritics"Paul Erdos" :: Lazy.Text
strict works on ByteString and StateT/WriterT/RWST if you use microlens-ghc, and additionally on Text if you use microlens-platform.
type ASetter s t a b = (a -> Identity b) -> s -> Identity t #
ASetter s t a b is something that turns a function modifying a value into a function modifying a structure. If you ignore Identity (as Identity a is the same thing as a), the type is:
type ASetter s t a b = (a -> b) -> s -> t
The reason Identity is used here is for ASetter to be composable with other types, such as Lens.
Technically, if you're writing a library, you shouldn't use this type for setters you are exporting from your library; the right type to use is Setter, but it is not provided by this package (because then it'd have to depend on distributive). It's completely alright, however, to export functions which take an ASetter as an argument.
type SimpleGetter s a = forall r. Getting r s a #
A SimpleGetter s a extracts a from s; so, it's the same thing as (s -> a), but you can use it in lens chains because its type looks like this:
type SimpleGetter s a = forall r. (a -> Const r a) -> s -> Const r s
Since Const r is a functor, SimpleGetter has the same shape as other lens types and can be composed with them. To get (s -> a) out of a SimpleGetter, choose r ~ a and feed Const :: a -> Const a a to the getter:
-- the actual signature is more permissive: --view::Gettinga s a -> s -> aview::SimpleGetters a -> s -> aviewgetter =getConst. getterConst
The actual Getter from lens is more general:
type Getter s a = forall f. (Contravariant f, Functor f) => (a -> f a) -> s -> f s
I'm not currently aware of any functions that take lens's Getter but won't accept SimpleGetter, but you should try to avoid exporting SimpleGetters anyway to minimise confusion. Alternatively, look at microlens-contra, which provides a fully lens-compatible Getter.
Lens users: you can convert a SimpleGetter to Getter by applying to . view to it.
type Getting r s a = (a -> Const r a) -> s -> Const r s #
Functions that operate on getters and folds – such as (^.), (^..), (^?) – use Getter r s a (with different values of r) to describe what kind of result they need. For instance, (^.) needs the getter to be able to return a single value, and so it accepts a getter of type Getting a s a. (^..) wants the getter to gather values together, so it uses Getting (Endo [a]) s a (it could've used Getting [a] s a instead, but it's faster with Endo). The choice of r depends on what you want to do with elements you're extracting from s.
type SimpleFold s a = forall r. Monoid r => Getting r s a #
A SimpleFold s a extracts several as from s; so, it's pretty much the same thing as (s -> [a]), but you can use it with lens operators.
The actual Fold from lens is more general:
type Fold s a = forall f. (Contravariant f, Applicative f) => (a -> f a) -> s -> f s
There are several functions in lens that accept lens's Fold but won't accept SimpleFold; I'm aware of
takingWhile,
droppingWhile,
backwards,
foldByOf,
foldMapByOf.
For this reason, try not to export SimpleFolds if at all possible. microlens-contra provides a fully lens-compatible Fold.
Lens users: you can convert a SimpleFold to Fold by applying folded . toListOf to it.
type Lens s t a b = forall (f :: Type -> Type). Functor f => (a -> f b) -> s -> f t #
Lens s t a b is the lowest common denominator of a setter and a getter, something that has the power of both; it has a Functor constraint, and since both Const and Identity are functors, it can be used whenever a getter or a setter is needed.
ais the type of the value inside of structurebis the type of the replaced valuesis the type of the whole structuretis the type of the structure after replacingain it withb
type Lens' s a = Lens s s a a #
This is a type alias for monomorphic lenses which don't change the type of the container (or of the value inside).
type Traversal s t a b = forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t #
Traversal s t a b is a generalisation of Lens which allows many targets (possibly 0). It's achieved by changing the constraint to Applicative instead of Functor – indeed, the point of Applicative is that you can combine effects, which is just what we need to have many targets.
Ultimately, traversals should follow 2 laws:
t pure ≡ pure fmap (t f) . t g ≡ getCompose . t (Compose . fmap f . g)
The 1st law states that you can't change the shape of the structure or do anything funny with elements (traverse elements which aren't in the structure, create new elements out of thin air, etc.). The 2nd law states that you should be able to fuse 2 identical traversals into one. For a more detailed explanation of the laws, see this blog post (if you prefer rambling blog posts), or The Essence Of The Iterator Pattern (if you prefer papers).
Traversing any value twice is a violation of traversal laws. You can, however, traverse values in any order.
type Traversal' s a = Traversal s s a a #
This is a type alias for monomorphic traversals which don't change the type of the container (or of the values inside).
type LensLike (f :: Type -> Type) s t a b = (a -> f b) -> s -> f t #
LensLike is a type that is often used to make combinators as general as possible. For instance, take (<<%~), which only requires the passed lens to be able to work with the (,) a functor (lenses and traversals can do that). The fully expanded type is as follows:
(<<%~) :: ((a -> (a, b)) -> s -> (a, t)) -> (a -> b) -> s -> (a, t)
With LensLike, the intent to use the (,) a functor can be made a bit clearer:
(<<%~) :: LensLike ((,) a) s t a b -> (a -> b) -> s -> (a, t)
type LensLike' (f :: Type -> Type) s a = LensLike f s s a a #
A type alias for monomorphic LensLikes.
at :: At m => Index m -> Lens' m (Maybe (IxValue m)) #
This lens lets you read, write, or delete elements in Map-like structures. It returns Nothing when the value isn't found, just like lookup:
Data.Map.lookup k m = m ^. at k
However, it also lets you insert and delete values by setting the value to Just valueNothing:
Data.Map.insert k a m = m&at k.~Just a Data.Map.delete k m = m&at k.~Nothing
Or you could use (?~) instead of (.~):
Data.Map.insert k a m = m&at k?~a
Note that at doesn't work for arrays or lists. You can't delete an arbitrary element from an array (what would be left in its place?), and you can't set an arbitrary element in a list because if the index is out of list's bounds, you'd have to somehow fill the stretch between the last element and the element you just inserted (i.e. [1,2,3] & at 10 .~ 5 is undefined). If you want to modify an already existing value in an array or list, you should use ix instead.
at is often used with non. See the documentation of non for examples.
Note that at isn't strict for Map, even if you're using Data.Map.Strict:
>>>Data.Map.Strict.size (Data.Map.Strict.empty & at 1 .~ Just undefined)1
The reason for such behavior is that there's actually no “strict Map” type; Data.Map.Strict just provides some strict functions for ordinary Maps.
This package doesn't actually provide any instances for at, but there are instances for Map and IntMap in microlens-ghc and an instance for HashMap in microlens-platform.