Documentation

The join function is the conventional monad join operator. It is used to remove one level of monadic structure, projecting its bound argument into the outer level.

Examples

atomically :: STM a -> IO a

atomically :: STM (IO b) -> IO (IO b)
join       :: IO (IO b)  -> IO b

join . atomically :: STM (IO b) -> IO b

The find function takes a predicate and a structure and returns the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

The fromMaybe function takes a default value and and Maybe value. If the Maybe is Nothing, it returns the default values; otherwise, it returns the value contained in the Maybe.

Examples

>>> fromMaybe "" (Just "Hello, World!")
"Hello, World!"

>>> fromMaybe "" Nothing
""

>>> import Text.Read ( readMaybe )
>>> fromMaybe 0 (readMaybe "5")
5
>>> fromMaybe 0 (readMaybe "")
0

The isJust function returns True iff its argument is of the form Just _.

Examples

>>> isJust (Just 3)
True

>>> isJust (Just ())
True

>>> isJust Nothing
False

>>> isJust (Just Nothing)
True

O(n). Return all keys of the map in ascending order. Subject to list fusion.

keys (fromList [(5,"a"), (3,"b")]) == [3,5]
keys empty == []

An infix synonym for fmap.

The name of this operator is an allusion to $. Note the similarities between their types:

 ($)  ::              (a -> b) ->   a ->   b
(<$>) :: Functor f => (a -> b) -> f a -> f b

Whereas $ is function application, <$> is function application lifted over a Functor.

Examples

>>> show <$> Nothing
Nothing
>>> show <$> Just 3
Just "3"

>>> show <$> Left 17
Left 17
>>> show <$> Right 17
Right "17"

>>> (*2) <$> [1,2,3]
[2,4,6]

>>> even <$> (2,2)
(2,True)

Sequential application.

A few functors support an implementation of <*> that is more efficient than the default one.

View the value pointed to by a Getter, Iso or Lens or the result of folding over all the results of a Fold or Traversal that points at a monoidal value.

view . to ≡ id

>>> view (to f) a
f a

>>> view _2 (1,"hello")
"hello"

>>> view (to succ) 5
6

>>> view (_2._1) ("hello",("world","!!!"))
"world"

As view is commonly used to access the target of a Getter or obtain a monoidal summary of the targets of a Fold, It may be useful to think of it as having one of these more restricted signatures:

view ::             Getter s a     -> s -> a
view :: Monoid m => Fold s m       -> s -> m
view ::             Iso' s a       -> s -> a
view ::             Lens' s a      -> s -> a
view :: Monoid m => Traversal' s m -> s -> m

In a more general setting, such as when working with a Monad transformer stack you can use:

view :: MonadReader s m             => Getter s a     -> m a
view :: (MonadReader s m, Monoid a) => Fold s a       -> m a
view :: MonadReader s m             => Iso' s a       -> m a
view :: MonadReader s m             => Lens' s a      -> m a
view :: (MonadReader s m, Monoid a) => Traversal' s a -> m a

Build an (index-preserving) Getter from an arbitrary Haskell function.

to f . to g ≡ to (g . f)

a ^. to f ≡ f a

>>> a ^.to f
f a

>>> ("hello","world")^.to snd
"world"

>>> 5^.to succ
6

>>> (0, -5)^._2.to abs
5

to :: (s -> a) -> IndexPreservingGetter s a

>>> IntSet.fromList [1,2,3,4] ^. contains 3
True

>>> IntSet.fromList [1,2,3,4] ^. contains 5
False

>>> IntSet.fromList [1,2,3,4] & contains 3 .~ False
fromList [1,2,4]

View the value pointed to by a Getter or Lens or the result of folding over all the results of a Fold or Traversal that points at a monoidal values.

This is the same operation as view with the arguments flipped.

The fixity and semantics are such that subsequent field accesses can be performed with (.).

>>> (a,b)^._2
b

>>> ("hello","world")^._2
"world"

>>> import Data.Complex
>>> ((0, 1 :+ 2), 3)^._1._2.to magnitude
2.23606797749979

(^.) ::             s -> Getter s a     -> a
(^.) :: Monoid m => s -> Fold s m       -> m
(^.) ::             s -> Iso' s a       -> a
(^.) ::             s -> Lens' s a      -> a
(^.) :: Monoid m => s -> Traversal' s m -> m

Perform a safe head of a Fold or Traversal or retrieve Just the result from a Getter or Lens.

When using a Traversal as a partial Lens, or a Fold as a partial Getter this can be a convenient way to extract the optional value.

Note: if you get stack overflows due to this, you may want to use firstOf instead, which can deal more gracefully with heavily left-biased trees.

>>> Left 4 ^?_Left
Just 4

>>> Right 4 ^?_Left
Nothing

>>> "world" ^? ix 3
Just 'l'

>>> "world" ^? ix 20
Nothing

(^?) ≡ flip preview

(^?) :: s -> Getter s a     -> Maybe a
(^?) :: s -> Fold s a       -> Maybe a
(^?) :: s -> Lens' s a      -> Maybe a
(^?) :: s -> Iso' s a       -> Maybe a
(^?) :: s -> Traversal' s a -> Maybe a

Replace the target of a Lens or all of the targets of a Setter or Traversal with a constant value.

This is an infix version of set, provided for consistency with (.=).

f <$ a ≡ mapped .~ f $ a

>>> (a,b,c,d) & _4 .~ e
(a,b,c,e)

>>> (42,"world") & _1 .~ "hello"
("hello","world")

>>> (a,b) & both .~ c
(c,c)

(.~) :: Setter s t a b    -> b -> s -> t
(.~) :: Iso s t a b       -> b -> s -> t
(.~) :: Lens s t a b      -> b -> s -> t
(.~) :: Traversal s t a b -> b -> s -> t

Set the target of a Lens, Traversal or Setter to Just a value.

l ?~ t ≡ set l (Just t)

>>> Nothing & id ?~ a
Just a

>>> Map.empty & at 3 ?~ x
fromList [(3,x)]

(?~) :: Setter s t a (Maybe b)    -> b -> s -> t
(?~) :: Iso s t a (Maybe b)       -> b -> s -> t
(?~) :: Lens s t a (Maybe b)      -> b -> s -> t
(?~) :: Traversal s t a (Maybe b) -> b -> s -> t

& is a reverse application operator. This provides notational convenience. Its precedence is one higher than that of the forward application operator $, which allows & to be nested in $.

>>> 5 & (+1) & show
"6"

Since: base-4.8.0.0

Access the 1st field of a tuple (and possibly change its type).

>>> (1,2)^._1
1

>>> _1 .~ "hello" $ (1,2)
("hello",2)

>>> (1,2) & _1 .~ "hello"
("hello",2)

>>> _1 putStrLn ("hello","world")
hello
((),"world")

This can also be used on larger tuples as well:

>>> (1,2,3,4,5) & _1 +~ 41
(42,2,3,4,5)

_1 :: Lens (a,b) (a',b) a a'
_1 :: Lens (a,b,c) (a',b,c) a a'
_1 :: Lens (a,b,c,d) (a',b,c,d) a a'
...
_1 :: Lens (a,b,c,d,e,f,g,h,i) (a',b,c,d,e,f,g,h,i) a a'

Access the 2nd field of a tuple.

>>> _2 .~ "hello" $ (1,(),3,4)
(1,"hello",3,4)

>>> (1,2,3,4) & _2 *~ 3
(1,6,3,4)

>>> _2 print (1,2)
2
(1,())

anyOf _2 :: (s -> Bool) -> (a, s) -> Bool
traverse . _2 :: (Applicative f, Traversable t) => (a -> f b) -> t (s, a) -> f (t (s, b))
foldMapOf (traverse . _2) :: (Traversable t, Monoid m) => (s -> m) -> t (b, s) -> m

This Prism provides a Traversal for tweaking the Right half of an Either:

>>> over _Right (+1) (Left 2)
Left 2

>>> over _Right (+1) (Right 2)
Right 3

>>> Right "hello" ^._Right
"hello"

>>> Left "hello" ^._Right :: [Double]
[]

It also can be turned around to obtain the embedding into the Right half of an Either:

>>> _Right # 5
Right 5

>>> 5^.re _Right
Right 5

A space efficient, packed, unboxed Unicode text type.

A set of integers.

O(n*min(n,W)). Create a set from a list of integers.

O(min(n,W)). Is the value a member of the set?

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:

• empty and mzero work, but are terse and uninformative;
• fail yields a custom error message;
• typeMismatch produces an informative message for cases when the value encountered is not of the expected type.

An example type and instance using typeMismatch:

-- Allow ourselves to write Text literals.
{-# LANGUAGE OverloadedStrings #-}

data Coord = Coord { x :: Double, y :: Double }

instance FromJSON Coord where
    parseJSON (Object v) = Coord
        <$> v .: "x"
        <*> v .: "y"

    -- We do not expect a non-Object value here.
    -- We could use mzero to fail, but typeMismatch
    -- gives a much more informative error message.
    parseJSON invalid    = typeMismatch "Coord" invalid

For this common case of only being concerned with a single type of JSON value, the functions withObject, withNumber, 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:

instance FromJSON Coord where
    parseJSON = 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 Generic clause to your datatype and declare a FromJSON 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 = genericParseJSON defaultOptions; If you need different options, you can customize the generic decoding by defining:

customOptions = defaultOptions
                { fieldLabelModifier = map toUpper
                }

instance FromJSON Coord where
    parseJSON = genericParseJSON customOptions

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 write Text literals.
{-# LANGUAGE OverloadedStrings #-}

data Coord = Coord { x :: Double, y :: Double }

instance ToJSON Coord where
  toJSON (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 Generic clause to your datatype and declare a ToJSON 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 = map toUpper
                }

instance ToJSON Coord where
    toJSON     = genericToJSON customOptions
    toEncoding = genericToEncoding customOptions

Previous versions of this library only had the toJSON method. Adding toEncoding had two reasons:

1. toEncoding is more efficient for the common case that the output of toJSON is directly serialized to a ByteString. Further, expressing either method in terms of the other would be non-optimal.
2. The choice of defaults allows a smooth transition for existing users: Existing instances that do not define toEncoding still compile and have the correct semantics. This is ensured by making the default implementation of toEncoding use toJSON. This produces correct results, but since it performs an intermediate conversion to a Value, it will be less efficient than directly emitting an Encoding. (this also means that specifying nothing more than instance ToJSON Coord would be sufficient as a generically decoding instance, but there probably exists no good reason to not specify toEncoding in new instances.)