base-4.10.0.0: Basic libraries

Copyright(c) The University of Glasgow 2001
LicenseBSD-style (see the file libraries/base/LICENSE)
Maintainerlibraries@haskell.org
Stabilitystable
Portabilityportable
Safe HaskellTrustworthy
LanguageHaskell2010

Prelude

Contents

Description

The Prelude: a standard module. The Prelude is imported by default into all Haskell modules unless either there is an explicit import statement for it, or the NoImplicitPrelude extension is enabled.

Synopsis

Standard types, classes and related functions

Basic data types

data Bool :: * Source #

Constructors

False 
True 

Instances

Bounded Bool #

Since: 2.1

Enum Bool #

Since: 2.1

Eq Bool 

Methods

(==) :: Bool -> Bool -> Bool Source #

(/=) :: Bool -> Bool -> Bool Source #

Data Bool #

Since: 4.0.0.0

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Bool -> c Bool Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Bool Source #

toConstr :: Bool -> Constr Source #

dataTypeOf :: Bool -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Bool) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Bool) Source #

gmapT :: (forall b. Data b => b -> b) -> Bool -> Bool Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Bool -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Bool -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Bool -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Bool -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Bool -> m Bool Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Bool -> m Bool Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Bool -> m Bool Source #

Ord Bool 
Read Bool #

Since: 2.1

Show Bool # 
Ix Bool #

Since: 2.1

Generic Bool # 

Associated Types

type Rep Bool :: * -> * Source #

Methods

from :: Bool -> Rep Bool x Source #

to :: Rep Bool x -> Bool Source #

FiniteBits Bool #

Since: 4.7.0.0

Bits Bool #

Interpret Bool as 1-bit bit-field

Since: 4.7.0.0

Storable Bool #

Since: 2.1

type Rep Bool # 
type Rep Bool = D1 * (MetaData "Bool" "GHC.Types" "ghc-prim" False) ((:+:) * (C1 * (MetaCons "False" PrefixI False) (U1 *)) (C1 * (MetaCons "True" PrefixI False) (U1 *)))
type (==) Bool a b # 
type (==) Bool a b

(&&) :: Bool -> Bool -> Bool infixr 3 Source #

Boolean "and"

(||) :: Bool -> Bool -> Bool infixr 2 Source #

Boolean "or"

not :: Bool -> Bool Source #

Boolean "not"

otherwise :: Bool Source #

otherwise is defined as the value True. It helps to make guards more readable. eg.

 f x | x < 0     = ...
     | otherwise = ...

data Maybe a Source #

The Maybe type encapsulates an optional value. A value of type Maybe a either contains a value of type a (represented as Just a), or it is empty (represented as Nothing). Using Maybe is a good way to deal with errors or exceptional cases without resorting to drastic measures such as error.

The Maybe type is also a monad. It is a simple kind of error monad, where all errors are represented by Nothing. A richer error monad can be built using the Either type.

Constructors

Nothing 
Just a 

Instances

Monad Maybe #

Since: 2.1

Methods

(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b Source #

(>>) :: Maybe a -> Maybe b -> Maybe b Source #

return :: a -> Maybe a Source #

fail :: String -> Maybe a Source #

Functor Maybe #

Since: 2.1

Methods

fmap :: (a -> b) -> Maybe a -> Maybe b Source #

(<$) :: a -> Maybe b -> Maybe a Source #

MonadFix Maybe #

Since: 2.1

Methods

mfix :: (a -> Maybe a) -> Maybe a Source #

MonadFail Maybe #

Since: 4.9.0.0

Methods

fail :: String -> Maybe a Source #

Applicative Maybe #

Since: 2.1

Methods

pure :: a -> Maybe a Source #

(<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b Source #

liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c Source #

(*>) :: Maybe a -> Maybe b -> Maybe b Source #

(<*) :: Maybe a -> Maybe b -> Maybe a Source #

Foldable Maybe #

Since: 2.1

Methods

fold :: Monoid m => Maybe m -> m Source #

foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source #

foldr :: (a -> b -> b) -> b -> Maybe a -> b Source #

foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source #

foldl :: (b -> a -> b) -> b -> Maybe a -> b Source #

foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source #

foldr1 :: (a -> a -> a) -> Maybe a -> a Source #

foldl1 :: (a -> a -> a) -> Maybe a -> a Source #

toList :: Maybe a -> [a] Source #

null :: Maybe a -> Bool Source #

length :: Maybe a -> Int Source #

elem :: Eq a => a -> Maybe a -> Bool Source #

maximum :: Ord a => Maybe a -> a Source #

minimum :: Ord a => Maybe a -> a Source #

sum :: Num a => Maybe a -> a Source #

product :: Num a => Maybe a -> a Source #

Traversable Maybe #

Since: 2.1

Methods

traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) Source #

sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) Source #

mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) Source #

sequence :: Monad m => Maybe (m a) -> m (Maybe a) Source #

MonadPlus Maybe #

Since: 2.1

Methods

mzero :: Maybe a Source #

mplus :: Maybe a -> Maybe a -> Maybe a Source #

Alternative Maybe #

Since: 2.1

Methods

empty :: Maybe a Source #

(<|>) :: Maybe a -> Maybe a -> Maybe a Source #

some :: Maybe a -> Maybe [a] Source #

many :: Maybe a -> Maybe [a] Source #

MonadZip Maybe #

Since: 4.8.0.0

Methods

mzip :: Maybe a -> Maybe b -> Maybe (a, b) Source #

mzipWith :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c Source #

munzip :: Maybe (a, b) -> (Maybe a, Maybe b) Source #

Show1 Maybe #

Since: 4.9.0.0

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Maybe a -> ShowS Source #

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Maybe a] -> ShowS Source #

Read1 Maybe #

Since: 4.9.0.0

Ord1 Maybe #

Since: 4.9.0.0

Methods

liftCompare :: (a -> b -> Ordering) -> Maybe a -> Maybe b -> Ordering Source #

Eq1 Maybe #

Since: 4.9.0.0

Methods

liftEq :: (a -> b -> Bool) -> Maybe a -> Maybe b -> Bool Source #

Eq a => Eq (Maybe a) # 

Methods

(==) :: Maybe a -> Maybe a -> Bool Source #

(/=) :: Maybe a -> Maybe a -> Bool Source #

Data a => Data (Maybe a) #

Since: 4.0.0.0

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Maybe a -> c (Maybe a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Maybe a) Source #

toConstr :: Maybe a -> Constr Source #

dataTypeOf :: Maybe a -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Maybe a)) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Maybe a)) Source #

gmapT :: (forall b. Data b => b -> b) -> Maybe a -> Maybe a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Maybe a -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Maybe a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Maybe a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Maybe a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) Source #

Ord a => Ord (Maybe a) # 

Methods

compare :: Maybe a -> Maybe a -> Ordering Source #

(<) :: Maybe a -> Maybe a -> Bool Source #

(<=) :: Maybe a -> Maybe a -> Bool Source #

(>) :: Maybe a -> Maybe a -> Bool Source #

(>=) :: Maybe a -> Maybe a -> Bool Source #

max :: Maybe a -> Maybe a -> Maybe a Source #

min :: Maybe a -> Maybe a -> Maybe a Source #

Read a => Read (Maybe a) #

Since: 2.1

Show a => Show (Maybe a) # 
Generic (Maybe a) # 

Associated Types

type Rep (Maybe a) :: * -> * Source #

Methods

from :: Maybe a -> Rep (Maybe a) x Source #

to :: Rep (Maybe a) x -> Maybe a Source #

Semigroup a => Semigroup (Maybe a) #

Since: 4.9.0.0

Methods

(<>) :: Maybe a -> Maybe a -> Maybe a Source #

sconcat :: NonEmpty (Maybe a) -> Maybe a Source #

stimes :: Integral b => b -> Maybe a -> Maybe a Source #

Monoid a => Monoid (Maybe a) #

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S." Since there used to be no "Semigroup" typeclass providing just mappend, we use Monoid instead.

Since: 2.1

Methods

mempty :: Maybe a Source #

mappend :: Maybe a -> Maybe a -> Maybe a Source #

mconcat :: [Maybe a] -> Maybe a Source #

Generic1 * Maybe # 

Associated Types

type Rep1 Maybe (f :: Maybe -> *) :: k -> * Source #

Methods

from1 :: f a -> Rep1 Maybe f a Source #

to1 :: Rep1 Maybe f a -> f a Source #

type Rep (Maybe a) # 
type Rep (Maybe a) = D1 * (MetaData "Maybe" "GHC.Base" "base" False) ((:+:) * (C1 * (MetaCons "Nothing" PrefixI False) (U1 *)) (C1 * (MetaCons "Just" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a))))
type Rep1 * Maybe # 
type (==) (Maybe k) a b # 
type (==) (Maybe k) a b

maybe :: b -> (a -> b) -> Maybe a -> b Source #

The maybe function takes a default value, a function, and a Maybe value. If the Maybe value is Nothing, the function returns the default value. Otherwise, it applies the function to the value inside the Just and returns the result.

Examples

Basic usage:

>>> maybe False odd (Just 3)
True
>>> maybe False odd Nothing
False

Read an integer from a string using readMaybe. If we succeed, return twice the integer; that is, apply (*2) to it. If instead we fail to parse an integer, return 0 by default:

>>> import Text.Read ( readMaybe )
>>> maybe 0 (*2) (readMaybe "5")
10
>>> maybe 0 (*2) (readMaybe "")
0

Apply show to a Maybe Int. If we have Just n, we want to show the underlying Int n. But if we have Nothing, we return the empty string instead of (for example) "Nothing":

>>> maybe "" show (Just 5)
"5"
>>> maybe "" show Nothing
""

data Either a b Source #

The Either type represents values with two possibilities: a value of type Either a b is either Left a or Right b.

The Either type is sometimes used to represent a value which is either correct or an error; by convention, the Left constructor is used to hold an error value and the Right constructor is used to hold a correct value (mnemonic: "right" also means "correct").

Examples

The type Either String Int is the type of values which can be either a String or an Int. The Left constructor can be used only on Strings, and the Right constructor can be used only on Ints:

>>> let s = Left "foo" :: Either String Int
>>> s
Left "foo"
>>> let n = Right 3 :: Either String Int
>>> n
Right 3
>>> :type s
s :: Either String Int
>>> :type n
n :: Either String Int

The fmap from our Functor instance will ignore Left values, but will apply the supplied function to values contained in a Right:

>>> let s = Left "foo" :: Either String Int
>>> let n = Right 3 :: Either String Int
>>> fmap (*2) s
Left "foo"
>>> fmap (*2) n
Right 6

The Monad instance for Either allows us to chain together multiple actions which may fail, and fail overall if any of the individual steps failed. First we'll write a function that can either parse an Int from a Char, or fail.

>>> import Data.Char ( digitToInt, isDigit )
>>> :{
    let parseEither :: Char -> Either String Int
        parseEither c
          | isDigit c = Right (digitToInt c)
          | otherwise = Left "parse error"
>>> :}

The following should work, since both '1' and '2' can be parsed as Ints.

>>> :{
    let parseMultiple :: Either String Int
        parseMultiple = do
          x <- parseEither '1'
          y <- parseEither '2'
          return (x + y)
>>> :}
>>> parseMultiple
Right 3

But the following should fail overall, since the first operation where we attempt to parse 'm' as an Int will fail:

>>> :{
    let parseMultiple :: Either String Int
        parseMultiple = do
          x <- parseEither 'm'
          y <- parseEither '2'
          return (x + y)
>>> :}
>>> parseMultiple
Left "parse error"

Constructors

Left a 
Right b 

Instances

Show2 Either #

Since: 4.9.0.0

Methods

liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Either a b -> ShowS Source #

liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Either a b] -> ShowS Source #

Read2 Either #

Since: 4.9.0.0

Methods

liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Either a b) Source #

liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Either a b] Source #

liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Either a b) Source #

liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Either a b] Source #

Ord2 Either #

Since: 4.9.0.0

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Either a c -> Either b d -> Ordering Source #

Eq2 Either #

Since: 4.9.0.0

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Either a c -> Either b d -> Bool Source #

Bifunctor Either #

Since: 4.8.0.0

Methods

bimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d Source #

first :: (a -> b) -> Either a c -> Either b c Source #

second :: (b -> c) -> Either a b -> Either a c Source #

Bifoldable Either #

Since: 4.10.0.0

Methods

bifold :: Monoid m => Either m m -> m Source #

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Either a b -> m Source #

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Either a b -> c Source #

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Either a b -> c Source #

Bitraversable Either #

Since: 4.10.0.0

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Either a b -> f (Either c d) Source #

Monad (Either e) #

Since: 4.4.0.0

Methods

(>>=) :: Either e a -> (a -> Either e b) -> Either e b Source #

(>>) :: Either e a -> Either e b -> Either e b Source #

return :: a -> Either e a Source #

fail :: String -> Either e a Source #

Functor (Either a) #

Since: 3.0

Methods

fmap :: (a -> b) -> Either a a -> Either a b Source #

(<$) :: a -> Either a b -> Either a a Source #

MonadFix (Either e) #

Since: 4.3.0.0

Methods

mfix :: (a -> Either e a) -> Either e a Source #

Applicative (Either e) #

Since: 3.0

Methods

pure :: a -> Either e a Source #

(<*>) :: Either e (a -> b) -> Either e a -> Either e b Source #

liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c Source #

(*>) :: Either e a -> Either e b -> Either e b Source #

(<*) :: Either e a -> Either e b -> Either e a Source #

Foldable (Either a) #

Since: 4.7.0.0

Methods

fold :: Monoid m => Either a m -> m Source #

foldMap :: Monoid m => (a -> m) -> Either a a -> m Source #

foldr :: (a -> b -> b) -> b -> Either a a -> b Source #

foldr' :: (a -> b -> b) -> b -> Either a a -> b Source #

foldl :: (b -> a -> b) -> b -> Either a a -> b Source #

foldl' :: (b -> a -> b) -> b -> Either a a -> b Source #

foldr1 :: (a -> a -> a) -> Either a a -> a Source #

foldl1 :: (a -> a -> a) -> Either a a -> a Source #

toList :: Either a a -> [a] Source #

null :: Either a a -> Bool Source #

length :: Either a a -> Int Source #

elem :: Eq a => a -> Either a a -> Bool Source #

maximum :: Ord a => Either a a -> a Source #

minimum :: Ord a => Either a a -> a Source #

sum :: Num a => Either a a -> a Source #

product :: Num a => Either a a -> a Source #

Traversable (Either a) #

Since: 4.7.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Either a a -> f (Either a b) Source #

sequenceA :: Applicative f => Either a (f a) -> f (Either a a) Source #

mapM :: Monad m => (a -> m b) -> Either a a -> m (Either a b) Source #

sequence :: Monad m => Either a (m a) -> m (Either a a) Source #

Show a => Show1 (Either a) #

Since: 4.9.0.0

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Either a a -> ShowS Source #

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Either a a] -> ShowS Source #

Read a => Read1 (Either a) #

Since: 4.9.0.0

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Either a a) Source #

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Either a a] Source #

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Either a a) Source #

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Either a a] Source #

Ord a => Ord1 (Either a) #

Since: 4.9.0.0

Methods

liftCompare :: (a -> b -> Ordering) -> Either a a -> Either a b -> Ordering Source #

Eq a => Eq1 (Either a) #

Since: 4.9.0.0

Methods

liftEq :: (a -> b -> Bool) -> Either a a -> Either a b -> Bool Source #

Generic1 * (Either a) # 

Associated Types

type Rep1 (Either a) (f :: Either a -> *) :: k -> * Source #

Methods

from1 :: f a -> Rep1 (Either a) f a Source #

to1 :: Rep1 (Either a) f a -> f a Source #

(Eq b, Eq a) => Eq (Either a b) # 

Methods

(==) :: Either a b -> Either a b -> Bool Source #

(/=) :: Either a b -> Either a b -> Bool Source #

(Data a, Data b) => Data (Either a b) #

Since: 4.0.0.0

Methods

gfoldl :: (forall d c. Data d => c (d -> c) -> d -> c c) -> (forall g. g -> c g) -> Either a b -> c (Either a b) Source #

gunfold :: (forall c r. Data c => c (c -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Either a b) Source #

toConstr :: Either a b -> Constr Source #

dataTypeOf :: Either a b -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Either a b)) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Either a b)) Source #

gmapT :: (forall c. Data c => c -> c) -> Either a b -> Either a b Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Either a b -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Either a b -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Either a b -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Either a b -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) Source #

(Ord b, Ord a) => Ord (Either a b) # 

Methods

compare :: Either a b -> Either a b -> Ordering Source #

(<) :: Either a b -> Either a b -> Bool Source #

(<=) :: Either a b -> Either a b -> Bool Source #

(>) :: Either a b -> Either a b -> Bool Source #

(>=) :: Either a b -> Either a b -> Bool Source #

max :: Either a b -> Either a b -> Either a b Source #

min :: Either a b -> Either a b -> Either a b Source #

(Read b, Read a) => Read (Either a b) # 
(Show b, Show a) => Show (Either a b) # 

Methods

showsPrec :: Int -> Either a b -> ShowS Source #

show :: Either a b -> String Source #

showList :: [Either a b] -> ShowS Source #

Generic (Either a b) # 

Associated Types

type Rep (Either a b) :: * -> * Source #

Methods

from :: Either a b -> Rep (Either a b) x Source #

to :: Rep (Either a b) x -> Either a b Source #

Semigroup (Either a b) #

Since: 4.9.0.0

Methods

(<>) :: Either a b -> Either a b -> Either a b Source #

sconcat :: NonEmpty (Either a b) -> Either a b Source #

stimes :: Integral b => b -> Either a b -> Either a b Source #

type Rep1 * (Either a) # 
type Rep (Either a b) # 
type (==) (Either k1 k2) a b # 
type (==) (Either k1 k2) a b

either :: (a -> c) -> (b -> c) -> Either a b -> c Source #

Case analysis for the Either type. If the value is Left a, apply the first function to a; if it is Right b, apply the second function to b.

Examples

We create two values of type Either String Int, one using the Left constructor and another using the Right constructor. Then we apply "either" the length function (if we have a String) or the "times-two" function (if we have an Int):

>>> let s = Left "foo" :: Either String Int
>>> let n = Right 3 :: Either String Int
>>> either length (*2) s
3
>>> either length (*2) n
6

data Ordering :: * Source #

Constructors

LT 
EQ 
GT 

Instances

Bounded Ordering #

Since: 2.1

Enum Ordering #

Since: 2.1

Eq Ordering 
Data Ordering #

Since: 4.0.0.0

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ordering -> c Ordering Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Ordering Source #

toConstr :: Ordering -> Constr Source #

dataTypeOf :: Ordering -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Ordering) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Ordering) Source #

gmapT :: (forall b. Data b => b -> b) -> Ordering -> Ordering Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ordering -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ordering -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Ordering -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Ordering -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering Source #

Ord Ordering 
Read Ordering #

Since: 2.1

Show Ordering # 
Ix Ordering #

Since: 2.1

Generic Ordering # 

Associated Types

type Rep Ordering :: * -> * Source #

Semigroup Ordering #

Since: 4.9.0.0

Monoid Ordering #

Since: 2.1

type Rep Ordering # 
type Rep Ordering = D1 * (MetaData "Ordering" "GHC.Types" "ghc-prim" False) ((:+:) * (C1 * (MetaCons "LT" PrefixI False) (U1 *)) ((:+:) * (C1 * (MetaCons "EQ" PrefixI False) (U1 *)) (C1 * (MetaCons "GT" PrefixI False) (U1 *))))
type (==) Ordering a b # 
type (==) Ordering a b

data Char :: * Source #

The character type Char is an enumeration whose values represent Unicode (or equivalently ISO/IEC 10646) characters (see http://www.unicode.org/ for details). This set extends the ISO 8859-1 (Latin-1) character set (the first 256 characters), which is itself an extension of the ASCII character set (the first 128 characters). A character literal in Haskell has type Char.

To convert a Char to or from the corresponding Int value defined by Unicode, use toEnum and fromEnum from the Enum class respectively (or equivalently ord and chr).

Instances

Bounded Char #

Since: 2.1

Enum Char #

Since: 2.1

Eq Char 

Methods

(==) :: Char -> Char -> Bool Source #

(/=) :: Char -> Char -> Bool Source #

Data Char #

Since: 4.0.0.0

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Char -> c Char Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Char Source #

toConstr :: Char -> Constr Source #

dataTypeOf :: Char -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Char) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Char) Source #

gmapT :: (forall b. Data b => b -> b) -> Char -> Char Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Char -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Char -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Char -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Char -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Char -> m Char Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Char -> m Char Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Char -> m Char Source #

Ord Char 
Read Char #

Since: 2.1

Show Char #

Since: 2.1

Ix Char #

Since: 2.1

Storable Char #

Since: 2.1

IsChar Char #

Since: 2.1

PrintfArg Char #

Since: 2.1

Generic1 k (URec k Char) # 

Associated Types

type Rep1 (URec k Char) (f :: URec k Char -> *) :: k -> * Source #

Methods

from1 :: f a -> Rep1 (URec k Char) f a Source #

to1 :: Rep1 (URec k Char) f a -> f a Source #

Functor (URec * Char) # 

Methods

fmap :: (a -> b) -> URec * Char a -> URec * Char b Source #

(<$) :: a -> URec * Char b -> URec * Char a Source #

Foldable (URec * Char) # 

Methods

fold :: Monoid m => URec * Char m -> m Source #

foldMap :: Monoid m => (a -> m) -> URec * Char a -> m Source #

foldr :: (a -> b -> b) -> b -> URec * Char a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec * Char a -> b Source #

foldl :: (b -> a -> b) -> b -> URec * Char a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec * Char a -> b Source #

foldr1 :: (a -> a -> a) -> URec * Char a -> a Source #

foldl1 :: (a -> a -> a) -> URec * Char a -> a Source #

toList :: URec * Char a -> [a] Source #

null :: URec * Char a -> Bool Source #

length :: URec * Char a -> Int Source #

elem :: Eq a => a -> URec * Char a -> Bool Source #

maximum :: Ord a => URec * Char a -> a Source #

minimum :: Ord a => URec * Char a -> a Source #

sum :: Num a => URec * Char a -> a Source #

product :: Num a => URec * Char a -> a Source #

Traversable (URec * Char) # 

Methods

traverse :: Applicative f => (a -> f b) -> URec * Char a -> f (URec * Char b) Source #

sequenceA :: Applicative f => URec * Char (f a) -> f (URec * Char a) Source #

mapM :: Monad m => (a -> m b) -> URec * Char a -> m (URec * Char b) Source #

sequence :: Monad m => URec * Char (m a) -> m (URec * Char a) Source #

Eq (URec k Char p) # 

Methods

(==) :: URec k Char p -> URec k Char p -> Bool Source #

(/=) :: URec k Char p -> URec k Char p -> Bool Source #

Ord (URec k Char p) # 

Methods

compare :: URec k Char p -> URec k Char p -> Ordering Source #

(<) :: URec k Char p -> URec k Char p -> Bool Source #

(<=) :: URec k Char p -> URec k Char p -> Bool Source #

(>) :: URec k Char p -> URec k Char p -> Bool Source #

(>=) :: URec k Char p -> URec k Char p -> Bool Source #

max :: URec k Char p -> URec k Char p -> URec k Char p Source #

min :: URec k Char p -> URec k Char p -> URec k Char p Source #

Show (URec k Char p) # 

Methods

showsPrec :: Int -> URec k Char p -> ShowS Source #

show :: URec k Char p -> String Source #

showList :: [URec k Char p] -> ShowS Source #

Generic (URec k Char p) # 

Associated Types

type Rep (URec k Char p) :: * -> * Source #

Methods

from :: URec k Char p -> Rep (URec k Char p) x Source #

to :: Rep (URec k Char p) x -> URec k Char p Source #

data URec k Char #

Used for marking occurrences of Char#

Since: 4.9.0.0

data URec k Char = UChar {}
type Rep1 k (URec k Char) # 
type Rep1 k (URec k Char) = D1 k (MetaData "URec" "GHC.Generics" "base" False) (C1 k (MetaCons "UChar" PrefixI True) (S1 k (MetaSel (Just Symbol "uChar#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UChar k)))
type Rep (URec k Char p) # 
type Rep (URec k Char p) = D1 * (MetaData "URec" "GHC.Generics" "base" False) (C1 * (MetaCons "UChar" PrefixI True) (S1 * (MetaSel (Just Symbol "uChar#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UChar *)))

type String = [Char] Source #

A String is a list of characters. String constants in Haskell are values of type String.

Tuples

fst :: (a, b) -> a Source #

Extract the first component of a pair.

snd :: (a, b) -> b Source #

Extract the second component of a pair.

curry :: ((a, b) -> c) -> a -> b -> c Source #

curry converts an uncurried function to a curried function.

uncurry :: (a -> b -> c) -> (a, b) -> c Source #

uncurry converts a curried function to a function on pairs.

Basic type classes

class Eq a where Source #

The Eq class defines equality (==) and inequality (/=). All the basic datatypes exported by the Prelude are instances of Eq, and Eq may be derived for any datatype whose constituents are also instances of Eq.

Minimal complete definition: either == or /=.

Minimal complete definition

(==) | (/=)

Methods

(==) :: a -> a -> Bool infix 4 Source #

(/=) :: a -> a -> Bool infix 4 Source #

Instances

Eq Bool 

Methods

(==) :: Bool -> Bool -> Bool Source #

(/=) :: Bool -> Bool -> Bool Source #

Eq Char 

Methods

(==) :: Char -> Char -> Bool Source #

(/=) :: Char -> Char -> Bool Source #

Eq Double 
Eq Float 

Methods

(==) :: Float -> Float -> Bool Source #

(/=) :: Float -> Float -> Bool Source #

Eq Int 

Methods

(==) :: Int -> Int -> Bool Source #

(/=) :: Int -> Int -> Bool Source #

Eq Int8 #

Since: 2.1

Methods

(==) :: Int8 -> Int8 -> Bool Source #

(/=) :: Int8 -> Int8 -> Bool Source #

Eq Int16 #

Since: 2.1

Methods

(==) :: Int16 -> Int16 -> Bool Source #

(/=) :: Int16 -> Int16 -> Bool Source #

Eq Int32 #

Since: 2.1

Methods

(==) :: Int32 -> Int32 -> Bool Source #

(/=) :: Int32 -> Int32 -> Bool Source #

Eq Int64 #

Since: 2.1

Methods

(==) :: Int64 -> Int64 -> Bool Source #

(/=) :: Int64 -> Int64 -> Bool Source #

Eq Integer 
Eq Natural # 
Eq Ordering 
Eq Word 

Methods

(==) :: Word -> Word -> Bool Source #

(/=) :: Word -> Word -> Bool Source #

Eq Word8 #

Since: 2.1

Methods

(==) :: Word8 -> Word8 -> Bool Source #

(/=) :: Word8 -> Word8 -> Bool Source #

Eq Word16 #

Since: 2.1

Eq Word32 #

Since: 2.1

Eq Word64 #

Since: 2.1

Eq SomeTypeRep # 
Eq () 

Methods

(==) :: () -> () -> Bool Source #

(/=) :: () -> () -> Bool Source #

Eq TyCon 

Methods

(==) :: TyCon -> TyCon -> Bool Source #

(/=) :: TyCon -> TyCon -> Bool Source #

Eq Module 
Eq TrName 
Eq BigNat 
Eq SrcLoc # 
Eq GeneralCategory # 
Eq Number # 
Eq Lexeme # 
Eq Fingerprint # 
Eq IOMode # 
Eq IntPtr # 
Eq WordPtr # 
Eq CUIntMax # 
Eq CIntMax # 
Eq CUIntPtr # 
Eq CIntPtr # 
Eq CSUSeconds # 
Eq CUSeconds # 
Eq CTime # 

Methods

(==) :: CTime -> CTime -> Bool Source #

(/=) :: CTime -> CTime -> Bool Source #

Eq CClock # 
Eq CSigAtomic # 
Eq CWchar # 
Eq CSize # 

Methods

(==) :: CSize -> CSize -> Bool Source #

(/=) :: CSize -> CSize -> Bool Source #

Eq CPtrdiff # 
Eq CDouble # 
Eq CFloat # 
Eq CBool # 

Methods

(==) :: CBool -> CBool -> Bool Source #

(/=) :: CBool -> CBool -> Bool Source #

Eq CULLong # 
Eq CLLong # 
Eq CULong # 
Eq CLong # 

Methods

(==) :: CLong -> CLong -> Bool Source #

(/=) :: CLong -> CLong -> Bool Source #

Eq CUInt # 

Methods

(==) :: CUInt -> CUInt -> Bool Source #

(/=) :: CUInt -> CUInt -> Bool Source #

Eq CInt # 

Methods

(==) :: CInt -> CInt -> Bool Source #

(/=) :: CInt -> CInt -> Bool Source #

Eq CUShort # 
Eq CShort # 
Eq CUChar # 
Eq CSChar # 
Eq CChar # 

Methods

(==) :: CChar -> CChar -> Bool Source #

(/=) :: CChar -> CChar -> Bool Source #

Eq SomeNat #

Since: 4.7.0.0

Eq SomeSymbol #

Since: 4.7.0.0

Eq DecidedStrictness # 
Eq SourceStrictness # 
Eq SourceUnpackedness # 
Eq Associativity # 
Eq Fixity # 
Eq Any # 

Methods

(==) :: Any -> Any -> Bool Source #

(/=) :: Any -> Any -> Bool Source #

Eq All # 

Methods

(==) :: All -> All -> Bool Source #

(/=) :: All -> All -> Bool Source #

Eq ArithException # 
Eq ErrorCall # 
Eq IOException #

Since: 4.1.0.0

Eq MaskingState # 
Eq BufferState # 
Eq CodingProgress # 
Eq SeekMode # 
Eq IODeviceType # 
Eq NewlineMode # 
Eq Newline # 
Eq BufferMode # 
Eq Handle #

Since: 4.1.0.0

Eq IOErrorType #

Since: 4.1.0.0

Eq ExitCode # 
Eq ArrayException # 
Eq AsyncException # 
Eq Errno #

Since: 2.1

Methods

(==) :: Errno -> Errno -> Bool Source #

(/=) :: Errno -> Errno -> Bool Source #

Eq Fd # 

Methods

(==) :: Fd -> Fd -> Bool Source #

(/=) :: Fd -> Fd -> Bool Source #

Eq CTimer # 
Eq CKey # 

Methods

(==) :: CKey -> CKey -> Bool Source #

(/=) :: CKey -> CKey -> Bool Source #

Eq CId # 

Methods

(==) :: CId -> CId -> Bool Source #

(/=) :: CId -> CId -> Bool Source #

Eq CFsFilCnt # 
Eq CFsBlkCnt # 
Eq CClockId # 
Eq CBlkCnt # 
Eq CBlkSize # 
Eq CRLim # 

Methods

(==) :: CRLim -> CRLim -> Bool Source #

(/=) :: CRLim -> CRLim -> Bool Source #

Eq CTcflag # 
Eq CSpeed # 
Eq CCc # 

Methods

(==) :: CCc -> CCc -> Bool Source #

(/=) :: CCc -> CCc -> Bool Source #

Eq CUid # 

Methods

(==) :: CUid -> CUid -> Bool Source #

(/=) :: CUid -> CUid -> Bool Source #

Eq CNlink # 
Eq CGid # 

Methods

(==) :: CGid -> CGid -> Bool Source #

(/=) :: CGid -> CGid -> Bool Source #

Eq CSsize # 
Eq CPid # 

Methods

(==) :: CPid -> CPid -> Bool Source #

(/=) :: CPid -> CPid -> Bool Source #

Eq COff # 

Methods

(==) :: COff -> COff -> Bool Source #

(/=) :: COff -> COff -> Bool Source #

Eq CMode # 

Methods

(==) :: CMode -> CMode -> Bool Source #

(/=) :: CMode -> CMode -> Bool Source #

Eq CIno # 

Methods

(==) :: CIno -> CIno -> Bool Source #

(/=) :: CIno -> CIno -> Bool Source #

Eq CDev # 

Methods

(==) :: CDev -> CDev -> Bool Source #

(/=) :: CDev -> CDev -> Bool Source #

Eq Lifetime # 
Eq Event # 

Methods

(==) :: Event -> Event -> Bool Source #

(/=) :: Event -> Event -> Bool Source #

Eq ThreadStatus # 
Eq BlockReason # 
Eq ThreadId #

Since: 4.2.0.0

Eq TimeoutKey # 
Eq FdKey # 

Methods

(==) :: FdKey -> FdKey -> Bool Source #

(/=) :: FdKey -> FdKey -> Bool Source #

Eq HandlePosn #

Since: 4.1.0.0

Eq Version #

Since: 2.1

Eq Unique # 
Eq Fixity # 
Eq ConstrRep # 
Eq DataRep # 
Eq Constr #

Equality of constructors

Since: 4.0.0.0

Eq SpecConstrAnnotation # 
Eq Void #

Since: 4.8.0.0

Methods

(==) :: Void -> Void -> Bool Source #

(/=) :: Void -> Void -> Bool Source #

Eq a => Eq [a] 

Methods

(==) :: [a] -> [a] -> Bool Source #

(/=) :: [a] -> [a] -> Bool Source #

Eq a => Eq (Maybe a) # 

Methods

(==) :: Maybe a -> Maybe a -> Bool Source #

(/=) :: Maybe a -> Maybe a -> Bool Source #

Eq a => Eq (Ratio a) # 

Methods

(==) :: Ratio a -> Ratio a -> Bool Source #

(/=) :: Ratio a -> Ratio a -> Bool Source #

Eq (StablePtr a) #

Since: 2.1

Eq (Ptr a) # 

Methods

(==) :: Ptr a -> Ptr a -> Bool Source #

(/=) :: Ptr a -> Ptr a -> Bool Source #

Eq (FunPtr a) # 

Methods

(==) :: FunPtr a -> FunPtr a -> Bool Source #

(/=) :: FunPtr a -> FunPtr a -> Bool Source #

Eq p => Eq (Par1 p) # 

Methods

(==) :: Par1 p -> Par1 p -> Bool Source #

(/=) :: Par1 p -> Par1 p -> Bool Source #

Eq (MVar a) #

Since: 4.1.0.0

Methods

(==) :: MVar a -> MVar a -> Bool Source #

(/=) :: MVar a -> MVar a -> Bool Source #

Eq a => Eq (Down a) # 

Methods

(==) :: Down a -> Down a -> Bool Source #

(/=) :: Down a -> Down a -> Bool Source #

Eq a => Eq (Last a) # 

Methods

(==) :: Last a -> Last a -> Bool Source #

(/=) :: Last a -> Last a -> Bool Source #

Eq a => Eq (First a) # 

Methods

(==) :: First a -> First a -> Bool Source #

(/=) :: First a -> First a -> Bool Source #

Eq a => Eq (Product a) # 

Methods

(==) :: Product a -> Product a -> Bool Source #

(/=) :: Product a -> Product a -> Bool Source #

Eq a => Eq (Sum a) # 

Methods

(==) :: Sum a -> Sum a -> Bool Source #

(/=) :: Sum a -> Sum a -> Bool Source #

Eq a => Eq (Dual a) # 

Methods

(==) :: Dual a -> Dual a -> Bool Source #

(/=) :: Dual a -> Dual a -> Bool Source #

Eq (IORef a) #

Since: 4.1.0.0

Methods

(==) :: IORef a -> IORef a -> Bool Source #

(/=) :: IORef a -> IORef a -> Bool Source #

Eq (ForeignPtr a) #

Since: 2.1

Eq (TVar a) #

Since: 4.8.0.0

Methods

(==) :: TVar a -> TVar a -> Bool Source #

(/=) :: TVar a -> TVar a -> Bool Source #

Eq a => Eq (Identity a) # 

Methods

(==) :: Identity a -> Identity a -> Bool Source #

(/=) :: Identity a -> Identity a -> Bool Source #

Eq a => Eq (ZipList a) # 

Methods

(==) :: ZipList a -> ZipList a -> Bool Source #

(/=) :: ZipList a -> ZipList a -> Bool Source #

Eq (StableName a) #

Since: 2.1

Eq (Chan a) # 

Methods

(==) :: Chan a -> Chan a -> Bool Source #

(/=) :: Chan a -> Chan a -> Bool Source #

Eq a => Eq (NonEmpty a) # 

Methods

(==) :: NonEmpty a -> NonEmpty a -> Bool Source #

(/=) :: NonEmpty a -> NonEmpty a -> Bool Source #

Eq a => Eq (Option a) # 

Methods

(==) :: Option a -> Option a -> Bool Source #

(/=) :: Option a -> Option a -> Bool Source #

Eq m => Eq (WrappedMonoid m) # 
Eq a => Eq (Last a) # 

Methods

(==) :: Last a -> Last a -> Bool Source #

(/=) :: Last a -> Last a -> Bool Source #

Eq a => Eq (First a) # 

Methods

(==) :: First a -> First a -> Bool Source #

(/=) :: First a -> First a -> Bool Source #

Eq a => Eq (Max a) # 

Methods

(==) :: Max a -> Max a -> Bool Source #

(/=) :: Max a -> Max a -> Bool Source #

Eq a => Eq (Min a) # 

Methods

(==) :: Min a -> Min a -> Bool Source #

(/=) :: Min a -> Min a -> Bool Source #

Eq (Fixed a) # 

Methods

(==) :: Fixed a -> Fixed a -> Bool Source #

(/=) :: Fixed a -> Fixed a -> Bool Source #

Eq a => Eq (Complex a) # 

Methods

(==) :: Complex a -> Complex a -> Bool Source #

(/=) :: Complex a -> Complex a -> Bool Source #

(Eq b, Eq a) => Eq (Either a b) # 

Methods

(==) :: Either a b -> Either a b -> Bool Source #

(/=) :: Either a b -> Either a b -> Bool Source #

Eq (V1 k p) # 

Methods

(==) :: V1 k p -> V1 k p -> Bool Source #

(/=) :: V1 k p -> V1 k p -> Bool Source #

Eq (U1 k p) #

Since: 4.9.0.0

Methods

(==) :: U1 k p -> U1 k p -> Bool Source #

(/=) :: U1 k p -> U1 k p -> Bool Source #

Eq (TypeRep k a) #

Since: 2.1

Methods

(==) :: TypeRep k a -> TypeRep k a -> Bool Source #

(/=) :: TypeRep k a -> TypeRep k a -> Bool Source #

(Eq a, Eq b) => Eq (a, b) 

Methods

(==) :: (a, b) -> (a, b) -> Bool Source #

(/=) :: (a, b) -> (a, b) -> Bool Source #

Eq (STRef s a) #

Since: 2.1

Methods

(==) :: STRef s a -> STRef s a -> Bool Source #

(/=) :: STRef s a -> STRef s a -> Bool Source #

Eq (Proxy k s) #

Since: 4.7.0.0

Methods

(==) :: Proxy k s -> Proxy k s -> Bool Source #

(/=) :: Proxy k s -> Proxy k s -> Bool Source #

Eq a => Eq (Arg a b) #

Since: 4.9.0.0

Methods

(==) :: Arg a b -> Arg a b -> Bool Source #

(/=) :: Arg a b -> Arg a b -> Bool Source #

Eq (f p) => Eq (Rec1 k f p) # 

Methods

(==) :: Rec1 k f p -> Rec1 k f p -> Bool Source #

(/=) :: Rec1 k f p -> Rec1 k f p -> Bool Source #

Eq (URec k Word p) # 

Methods

(==) :: URec k Word p -> URec k Word p -> Bool Source #

(/=) :: URec k Word p -> URec k Word p -> Bool Source #

Eq (URec k Int p) # 

Methods

(==) :: URec k Int p -> URec k Int p -> Bool Source #

(/=) :: URec k Int p -> URec k Int p -> Bool Source #

Eq (URec k Float p) # 

Methods

(==) :: URec k Float p -> URec k Float p -> Bool Source #

(/=) :: URec k Float p -> URec k Float p -> Bool Source #

Eq (URec k Double p) # 

Methods

(==) :: URec k Double p -> URec k Double p -> Bool Source #

(/=) :: URec k Double p -> URec k Double p -> Bool Source #

Eq (URec k Char p) # 

Methods

(==) :: URec k Char p -> URec k Char p -> Bool Source #

(/=) :: URec k Char p -> URec k Char p -> Bool Source #

Eq (URec k (Ptr ()) p) # 

Methods

(==) :: URec k (Ptr ()) p -> URec k (Ptr ()) p -> Bool Source #

(/=) :: URec k (Ptr ()) p -> URec k (Ptr ()) p -> Bool Source #

(Eq a, Eq b, Eq c) => Eq (a, b, c) 

Methods

(==) :: (a, b, c) -> (a, b, c) -> Bool Source #

(/=) :: (a, b, c) -> (a, b, c) -> Bool Source #

Eq ((:~:) k a b) # 

Methods

(==) :: (k :~: a) b -> (k :~: a) b -> Bool Source #

(/=) :: (k :~: a) b -> (k :~: a) b -> Bool Source #

Eq (Coercion k a b) # 

Methods

(==) :: Coercion k a b -> Coercion k a b -> Bool Source #

(/=) :: Coercion k a b -> Coercion k a b -> Bool Source #

Eq (f a) => Eq (Alt k f a) # 

Methods

(==) :: Alt k f a -> Alt k f a -> Bool Source #

(/=) :: Alt k f a -> Alt k f a -> Bool Source #

Eq a => Eq (Const k a b) # 

Methods

(==) :: Const k a b -> Const k a b -> Bool Source #

(/=) :: Const k a b -> Const k a b -> Bool Source #

Eq c => Eq (K1 k i c p) # 

Methods

(==) :: K1 k i c p -> K1 k i c p -> Bool Source #

(/=) :: K1 k i c p -> K1 k i c p -> Bool Source #

(Eq (g p), Eq (f p)) => Eq ((:+:) k f g p) # 

Methods

(==) :: (k :+: f) g p -> (k :+: f) g p -> Bool Source #

(/=) :: (k :+: f) g p -> (k :+: f) g p -> Bool Source #

(Eq (g p), Eq (f p)) => Eq ((:*:) k f g p) # 

Methods

(==) :: (k :*: f) g p -> (k :*: f) g p -> Bool Source #

(/=) :: (k :*: f) g p -> (k :*: f) g p -> Bool Source #

(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) 

Methods

(==) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source #

(/=) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source #

Eq ((:~~:) k1 k2 a b) #

Since: 4.10.0.0

Methods

(==) :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> Bool Source #

(/=) :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> Bool Source #

(Eq1 f, Eq1 g, Eq a) => Eq (Sum * f g a) #

Since: 4.9.0.0

Methods

(==) :: Sum * f g a -> Sum * f g a -> Bool Source #

(/=) :: Sum * f g a -> Sum * f g a -> Bool Source #

(Eq1 f, Eq1 g, Eq a) => Eq (Product * f g a) #

Since: 4.9.0.0

Methods

(==) :: Product * f g a -> Product * f g a -> Bool Source #

(/=) :: Product * f g a -> Product * f g a -> Bool Source #

Eq (f p) => Eq (M1 k i c f p) # 

Methods

(==) :: M1 k i c f p -> M1 k i c f p -> Bool Source #

(/=) :: M1 k i c f p -> M1 k i c f p -> Bool Source #

Eq (f (g p)) => Eq ((:.:) k2 k1 f g p) # 

Methods

(==) :: (k2 :.: k1) f g p -> (k2 :.: k1) f g p -> Bool Source #

(/=) :: (k2 :.: k1) f g p -> (k2 :.: k1) f g p -> Bool Source #

(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) 

Methods

(==) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source #

(/=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source #

(Eq1 f, Eq1 g, Eq a) => Eq (Compose * * f g a) #

Since: 4.9.0.0

Methods

(==) :: Compose * * f g a -> Compose * * f g a -> Bool Source #

(/=) :: Compose * * f g a -> Compose * * f g a -> Bool Source #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) 

Methods

(==) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source #

(/=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) 

Methods

(==) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source #

(/=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) 

Methods

(==) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source #

(/=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) 

Methods

(==) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source #

(/=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) 

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source #

(/=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) 

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source #

(/=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) 

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source #

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) 

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source #

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) 

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source #

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) 

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source #

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source #

class Eq a => Ord a where Source #

The Ord class is used for totally ordered datatypes.

Instances of Ord can be derived for any user-defined datatype whose constituent types are in Ord. The declared order of the constructors in the data declaration determines the ordering in derived Ord instances. The Ordering datatype allows a single comparison to determine the precise ordering of two objects.

Minimal complete definition: either compare or <=. Using compare can be more efficient for complex types.

Minimal complete definition

compare | (<=)

Methods

compare :: a -> a -> Ordering Source #

(<) :: a -> a -> Bool infix 4 Source #

(<=) :: a -> a -> Bool infix 4 Source #

(>) :: a -> a -> Bool infix 4 Source #

(>=) :: a -> a -> Bool infix 4 Source #

max :: a -> a -> a Source #

min :: a -> a -> a Source #

Instances

Ord Bool 
Ord Char 
Ord Double 
Ord Float 
Ord Int 

Methods

compare :: Int -> Int -> Ordering Source #

(<) :: Int -> Int -> Bool Source #

(<=) :: Int -> Int -> Bool Source #

(>) :: Int -> Int -> Bool Source #

(>=) :: Int -> Int -> Bool Source #

max :: Int -> Int -> Int Source #

min :: Int -> Int -> Int Source #

Ord Int8 #

Since: 2.1

Ord Int16 #

Since: 2.1

Ord Int32 #

Since: 2.1

Ord Int64 #

Since: 2.1

Ord Integer 
Ord Natural # 
Ord Ordering 
Ord Word 
Ord Word8 #

Since: 2.1

Ord Word16 #

Since: 2.1

Ord Word32 #

Since: 2.1

Ord Word64 #

Since: 2.1

Ord SomeTypeRep # 
Ord () 

Methods

compare :: () -> () -> Ordering Source #

(<) :: () -> () -> Bool Source #

(<=) :: () -> () -> Bool Source #

(>) :: () -> () -> Bool Source #

(>=) :: () -> () -> Bool Source #

max :: () -> () -> () Source #

min :: () -> () -> () Source #

Ord TyCon 
Ord BigNat 
Ord GeneralCategory # 
Ord Fingerprint # 
Ord IOMode # 
Ord IntPtr # 
Ord WordPtr # 
Ord CUIntMax # 
Ord CIntMax # 
Ord CUIntPtr # 
Ord CIntPtr # 
Ord CSUSeconds # 
Ord CUSeconds # 
Ord CTime # 
Ord CClock # 
Ord CSigAtomic # 
Ord CWchar # 
Ord CSize # 
Ord CPtrdiff # 
Ord CDouble # 
Ord CFloat # 
Ord CBool # 
Ord CULLong # 
Ord CLLong # 
Ord CULong # 
Ord CLong # 
Ord CUInt # 
Ord CInt # 
Ord CUShort # 
Ord CShort # 
Ord CUChar # 
Ord CSChar # 
Ord CChar # 
Ord SomeNat #

Since: 4.7.0.0

Ord SomeSymbol #

Since: 4.7.0.0

Ord DecidedStrictness # 
Ord SourceStrictness # 
Ord SourceUnpackedness # 
Ord Associativity # 
Ord Fixity # 
Ord Any # 

Methods

compare :: Any -> Any -> Ordering Source #

(<) :: Any -> Any -> Bool Source #

(<=) :: Any -> Any -> Bool Source #

(>) :: Any -> Any -> Bool Source #

(>=) :: Any -> Any -> Bool Source #

max :: Any -> Any -> Any Source #

min :: Any -> Any -> Any Source #

Ord All # 

Methods

compare :: All -> All -> Ordering Source #

(<) :: All -> All -> Bool Source #

(<=) :: All -> All -> Bool Source #

(>) :: All -> All -> Bool Source #

(>=) :: All -> All -> Bool Source #

max :: All -> All -> All Source #

min :: All -> All -> All Source #

Ord ArithException # 
Ord ErrorCall # 
Ord SeekMode # 
Ord NewlineMode # 
Ord Newline # 
Ord BufferMode # 
Ord ExitCode # 
Ord ArrayException # 
Ord AsyncException # 
Ord Fd # 

Methods

compare :: Fd -> Fd -> Ordering Source #

(<) :: Fd -> Fd -> Bool Source #

(<=) :: Fd -> Fd -> Bool Source #

(>) :: Fd -> Fd -> Bool Source #

(>=) :: Fd -> Fd -> Bool Source #

max :: Fd -> Fd -> Fd Source #

min :: Fd -> Fd -> Fd Source #

Ord CTimer # 
Ord CKey # 
Ord CId # 

Methods

compare :: CId -> CId -> Ordering Source #

(<) :: CId -> CId -> Bool Source #

(<=) :: CId -> CId -> Bool Source #

(>) :: CId -> CId -> Bool Source #

(>=) :: CId -> CId -> Bool Source #

max :: CId -> CId -> CId Source #

min :: CId -> CId -> CId Source #

Ord CFsFilCnt # 
Ord CFsBlkCnt # 
Ord CClockId # 
Ord CBlkCnt # 
Ord CBlkSize # 
Ord CRLim # 
Ord CTcflag # 
Ord CSpeed # 
Ord CCc # 

Methods

compare :: CCc -> CCc -> Ordering Source #

(<) :: CCc -> CCc -> Bool Source #

(<=) :: CCc -> CCc -> Bool Source #

(>) :: CCc -> CCc -> Bool Source #

(>=) :: CCc -> CCc -> Bool Source #

max :: CCc -> CCc -> CCc Source #

min :: CCc -> CCc -> CCc Source #

Ord CUid # 
Ord CNlink # 
Ord CGid # 
Ord CSsize # 
Ord CPid # 
Ord COff # 
Ord CMode # 
Ord CIno # 
Ord CDev # 
Ord ThreadStatus # 
Ord BlockReason # 
Ord ThreadId #

Since: 4.2.0.0

Ord Version #

Since: 2.1

Ord Unique # 
Ord Void #

Since: 4.8.0.0

Ord a => Ord [a] 

Methods

compare :: [a] -> [a] -> Ordering Source #

(<) :: [a] -> [a] -> Bool Source #

(<=) :: [a] -> [a] -> Bool Source #

(>) :: [a] -> [a] -> Bool Source #

(>=) :: [a] -> [a] -> Bool Source #

max :: [a] -> [a] -> [a] Source #

min :: [a] -> [a] -> [a] Source #

Ord a => Ord (Maybe a) # 

Methods

compare :: Maybe a -> Maybe a -> Ordering Source #

(<) :: Maybe a -> Maybe a -> Bool Source #

(<=) :: Maybe a -> Maybe a -> Bool Source #

(>) :: Maybe a -> Maybe a -> Bool Source #

(>=) :: Maybe a -> Maybe a -> Bool Source #

max :: Maybe a -> Maybe a -> Maybe a Source #

min :: Maybe a -> Maybe a -> Maybe a Source #

Integral a => Ord (Ratio a) #

Since: 2.0.1

Methods

compare :: Ratio a -> Ratio a -> Ordering Source #

(<) :: Ratio a -> Ratio a -> Bool Source #

(<=) :: Ratio a -> Ratio a -> Bool Source #

(>) :: Ratio a -> Ratio a -> Bool Source #

(>=) :: Ratio a -> Ratio a -> Bool Source #

max :: Ratio a -> Ratio a -> Ratio a Source #

min :: Ratio a -> Ratio a -> Ratio a Source #

Ord (Ptr a) # 

Methods

compare :: Ptr a -> Ptr a -> Ordering Source #

(<) :: Ptr a -> Ptr a -> Bool Source #

(<=) :: Ptr a -> Ptr a -> Bool Source #

(>) :: Ptr a -> Ptr a -> Bool Source #

(>=) :: Ptr a -> Ptr a -> Bool Source #

max :: Ptr a -> Ptr a -> Ptr a Source #

min :: Ptr a -> Ptr a -> Ptr a Source #

Ord (FunPtr a) # 

Methods

compare :: FunPtr a -> FunPtr a -> Ordering Source #

(<) :: FunPtr a -> FunPtr a -> Bool Source #

(<=) :: FunPtr a -> FunPtr a -> Bool Source #

(>) :: FunPtr a -> FunPtr a -> Bool Source #

(>=) :: FunPtr a -> FunPtr a -> Bool Source #

max :: FunPtr a -> FunPtr a -> FunPtr a Source #

min :: FunPtr a -> FunPtr a -> FunPtr a Source #

Ord p => Ord (Par1 p) # 

Methods

compare :: Par1 p -> Par1 p -> Ordering Source #

(<) :: Par1 p -> Par1 p -> Bool Source #

(<=) :: Par1 p -> Par1 p -> Bool Source #

(>) :: Par1 p -> Par1 p -> Bool Source #

(>=) :: Par1 p -> Par1 p -> Bool Source #

max :: Par1 p -> Par1 p -> Par1 p Source #

min :: Par1 p -> Par1 p -> Par1 p Source #

Ord a => Ord (Down a) #

Since: 4.6.0.0

Methods

compare :: Down a -> Down a -> Ordering Source #

(<) :: Down a -> Down a -> Bool Source #

(<=) :: Down a -> Down a -> Bool Source #

(>) :: Down a -> Down a -> Bool Source #

(>=) :: Down a -> Down a -> Bool Source #

max :: Down a -> Down a -> Down a Source #

min :: Down a -> Down a -> Down a Source #

Ord a => Ord (Last a) # 

Methods

compare :: Last a -> Last a -> Ordering Source #

(<) :: Last a -> Last a -> Bool Source #

(<=) :: Last a -> Last a -> Bool Source #

(>) :: Last a -> Last a -> Bool Source #

(>=) :: Last a -> Last a -> Bool Source #

max :: Last a -> Last a -> Last a Source #

min :: Last a -> Last a -> Last a Source #

Ord a => Ord (First a) # 

Methods

compare :: First a -> First a -> Ordering Source #

(<) :: First a -> First a -> Bool Source #

(<=) :: First a -> First a -> Bool Source #

(>) :: First a -> First a -> Bool Source #

(>=) :: First a -> First a -> Bool Source #

max :: First a -> First a -> First a Source #

min :: First a -> First a -> First a Source #

Ord a => Ord (Product a) # 
Ord a => Ord (Sum a) # 

Methods

compare :: Sum a -> Sum a -> Ordering Source #

(<) :: Sum a -> Sum a -> Bool Source #

(<=) :: Sum a -> Sum a -> Bool Source #

(>) :: Sum a -> Sum a -> Bool Source #

(>=) :: Sum a -> Sum a -> Bool Source #

max :: Sum a -> Sum a -> Sum a Source #

min :: Sum a -> Sum a -> Sum a Source #

Ord a => Ord (Dual a) # 

Methods

compare :: Dual a -> Dual a -> Ordering Source #

(<) :: Dual a -> Dual a -> Bool Source #

(<=) :: Dual a -> Dual a -> Bool Source #

(>) :: Dual a -> Dual a -> Bool Source #

(>=) :: Dual a -> Dual a -> Bool Source #

max :: Dual a -> Dual a -> Dual a Source #

min :: Dual a -> Dual a -> Dual a Source #

Ord (ForeignPtr a) #

Since: 2.1

Ord a => Ord (Identity a) # 
Ord a => Ord (ZipList a) # 
Ord a => Ord (NonEmpty a) # 
Ord a => Ord (Option a) # 

Methods

compare :: Option a -> Option a -> Ordering Source #

(<) :: Option a -> Option a -> Bool Source #

(<=) :: Option a -> Option a -> Bool Source #

(>) :: Option a -> Option a -> Bool Source #

(>=) :: Option a -> Option a -> Bool Source #

max :: Option a -> Option a -> Option a Source #

min :: Option a -> Option a -> Option a Source #

Ord m => Ord (WrappedMonoid m) # 
Ord a => Ord (Last a) # 

Methods

compare :: Last a -> Last a -> Ordering Source #

(<) :: Last a -> Last a -> Bool Source #

(<=) :: Last a -> Last a -> Bool Source #

(>) :: Last a -> Last a -> Bool Source #

(>=) :: Last a -> Last a -> Bool Source #

max :: Last a -> Last a -> Last a Source #

min :: Last a -> Last a -> Last a Source #

Ord a => Ord (First a) # 

Methods

compare :: First a -> First a -> Ordering Source #

(<) :: First a -> First a -> Bool Source #

(<=) :: First a -> First a -> Bool Source #

(>) :: First a -> First a -> Bool Source #

(>=) :: First a -> First a -> Bool Source #

max :: First a -> First a -> First a Source #

min :: First a -> First a -> First a Source #

Ord a => Ord (Max a) # 

Methods

compare :: Max a -> Max a -> Ordering Source #

(<) :: Max a -> Max a -> Bool Source #

(<=) :: Max a -> Max a -> Bool Source #

(>) :: Max a -> Max a -> Bool Source #

(>=) :: Max a -> Max a -> Bool Source #

max :: Max a -> Max a -> Max a Source #

min :: Max a -> Max a -> Max a Source #

Ord a => Ord (Min a) # 

Methods

compare :: Min a -> Min a -> Ordering Source #

(<) :: Min a -> Min a -> Bool Source #

(<=) :: Min a -> Min a -> Bool Source #

(>) :: Min a -> Min a -> Bool Source #

(>=) :: Min a -> Min a -> Bool Source #

max :: Min a -> Min a -> Min a Source #

min :: Min a -> Min a -> Min a Source #

Ord (Fixed a) # 

Methods

compare :: Fixed a -> Fixed a -> Ordering Source #

(<) :: Fixed a -> Fixed a -> Bool Source #

(<=) :: Fixed a -> Fixed a -> Bool Source #

(>) :: Fixed a -> Fixed a -> Bool Source #

(>=) :: Fixed a -> Fixed a -> Bool Source #

max :: Fixed a -> Fixed a -> Fixed a Source #

min :: Fixed a -> Fixed a -> Fixed a Source #

(Ord b, Ord a) => Ord (Either a b) # 

Methods

compare :: Either a b -> Either a b -> Ordering Source #

(<) :: Either a b -> Either a b -> Bool Source #

(<=) :: Either a b -> Either a b -> Bool Source #

(>) :: Either a b -> Either a b -> Bool Source #

(>=) :: Either a b -> Either a b -> Bool Source #

max :: Either a b -> Either a b -> Either a b Source #

min :: Either a b -> Either a b -> Either a b Source #

Ord (V1 k p) # 

Methods

compare :: V1 k p -> V1 k p -> Ordering Source #

(<) :: V1 k p -> V1 k p -> Bool Source #

(<=) :: V1 k p -> V1 k p -> Bool Source #

(>) :: V1 k p -> V1 k p -> Bool Source #

(>=) :: V1 k p -> V1 k p -> Bool Source #

max :: V1 k p -> V1 k p -> V1 k p Source #

min :: V1 k p -> V1 k p -> V1 k p Source #

Ord (U1 k p) #

Since: 4.9.0.0

Methods

compare :: U1 k p -> U1 k p -> Ordering Source #

(<) :: U1 k p -> U1 k p -> Bool Source #

(<=) :: U1 k p -> U1 k p -> Bool Source #

(>) :: U1 k p -> U1 k p -> Bool Source #

(>=) :: U1 k p -> U1 k p -> Bool Source #

max :: U1 k p -> U1 k p -> U1 k p Source #

min :: U1 k p -> U1 k p -> U1 k p Source #

Ord (TypeRep k a) #

Since: 4.4.0.0

Methods

compare :: TypeRep k a -> TypeRep k a -> Ordering Source #

(<) :: TypeRep k a -> TypeRep k a -> Bool Source #

(<=) :: TypeRep k a -> TypeRep k a -> Bool Source #

(>) :: TypeRep k a -> TypeRep k a -> Bool Source #

(>=) :: TypeRep k a -> TypeRep k a -> Bool Source #

max :: TypeRep k a -> TypeRep k a -> TypeRep k a Source #

min :: TypeRep k a -> TypeRep k a -> TypeRep k a Source #

(Ord a, Ord b) => Ord (a, b) 

Methods

compare :: (a, b) -> (a, b) -> Ordering Source #

(<) :: (a, b) -> (a, b) -> Bool Source #

(<=) :: (a, b) -> (a, b) -> Bool Source #

(>) :: (a, b) -> (a, b) -> Bool Source #

(>=) :: (a, b) -> (a, b) -> Bool Source #

max :: (a, b) -> (a, b) -> (a, b) Source #

min :: (a, b) -> (a, b) -> (a, b) Source #

Ord (Proxy k s) #

Since: 4.7.0.0

Methods

compare :: Proxy k s -> Proxy k s -> Ordering Source #

(<) :: Proxy k s -> Proxy k s -> Bool Source #

(<=) :: Proxy k s -> Proxy k s -> Bool Source #

(>) :: Proxy k s -> Proxy k s -> Bool Source #

(>=) :: Proxy k s -> Proxy k s -> Bool Source #

max :: Proxy k s -> Proxy k s -> Proxy k s Source #

min :: Proxy k s -> Proxy k s -> Proxy k s Source #

Ord a => Ord (Arg a b) #

Since: 4.9.0.0

Methods

compare :: Arg a b -> Arg a b -> Ordering Source #

(<) :: Arg a b -> Arg a b -> Bool Source #

(<=) :: Arg a b -> Arg a b -> Bool Source #

(>) :: Arg a b -> Arg a b -> Bool Source #

(>=) :: Arg a b -> Arg a b -> Bool Source #

max :: Arg a b -> Arg a b -> Arg a b Source #

min :: Arg a b -> Arg a b -> Arg a b Source #

Ord (f p) => Ord (Rec1 k f p) # 

Methods

compare :: Rec1 k f p -> Rec1 k f p -> Ordering Source #

(<) :: Rec1 k f p -> Rec1 k f p -> Bool Source #

(<=) :: Rec1 k f p -> Rec1 k f p -> Bool Source #

(>) :: Rec1 k f p -> Rec1 k f p -> Bool Source #

(>=) :: Rec1 k f p -> Rec1 k f p -> Bool Source #

max :: Rec1 k f p -> Rec1 k f p -> Rec1 k f p Source #

min :: Rec1 k f p -> Rec1 k f p -> Rec1 k f p Source #

Ord (URec k Word p) # 

Methods

compare :: URec k Word p -> URec k Word p -> Ordering Source #

(<) :: URec k Word p -> URec k Word p -> Bool Source #

(<=) :: URec k Word p -> URec k Word p -> Bool Source #

(>) :: URec k Word p -> URec k Word p -> Bool Source #

(>=) :: URec k Word p -> URec k Word p -> Bool Source #

max :: URec k Word p -> URec k Word p -> URec k Word p Source #

min :: URec k Word p -> URec k Word p -> URec k Word p Source #

Ord (URec k Int p) # 

Methods

compare :: URec k Int p -> URec k Int p -> Ordering Source #

(<) :: URec k Int p -> URec k Int p -> Bool Source #

(<=) :: URec k Int p -> URec k Int p -> Bool Source #

(>) :: URec k Int p -> URec k Int p -> Bool Source #

(>=) :: URec k Int p -> URec k Int p -> Bool Source #

max :: URec k Int p -> URec k Int p -> URec k Int p Source #

min :: URec k Int p -> URec k Int p -> URec k Int p Source #

Ord (URec k Float p) # 

Methods

compare :: URec k Float p -> URec k Float p -> Ordering Source #

(<) :: URec k Float p -> URec k Float p -> Bool Source #

(<=) :: URec k Float p -> URec k Float p -> Bool Source #

(>) :: URec k Float p -> URec k Float p -> Bool Source #

(>=) :: URec k Float p -> URec k Float p -> Bool Source #

max :: URec k Float p -> URec k Float p -> URec k Float p Source #

min :: URec k Float p -> URec k Float p -> URec k Float p Source #

Ord (URec k Double p) # 

Methods

compare :: URec k Double p -> URec k Double p -> Ordering Source #

(<) :: URec k Double p -> URec k Double p -> Bool Source #

(<=) :: URec k Double p -> URec k Double p -> Bool Source #

(>) :: URec k Double p -> URec k Double p -> Bool Source #

(>=) :: URec k Double p -> URec k Double p -> Bool Source #

max :: URec k Double p -> URec k Double p -> URec k Double p Source #

min :: URec k Double p -> URec k Double p -> URec k Double p Source #

Ord (URec k Char p) # 

Methods

compare :: URec k Char p -> URec k Char p -> Ordering Source #

(<) :: URec k Char p -> URec k Char p -> Bool Source #

(<=) :: URec k Char p -> URec k Char p -> Bool Source #

(>) :: URec k Char p -> URec k Char p -> Bool Source #

(>=) :: URec k Char p -> URec k Char p -> Bool Source #

max :: URec k Char p -> URec k Char p -> URec k Char p Source #

min :: URec k Char p -> URec k Char p -> URec k Char p Source #

Ord (URec k (Ptr ()) p) # 

Methods

compare :: URec k (Ptr ()) p -> URec k (Ptr ()) p -> Ordering Source #

(<) :: URec k (Ptr ()) p -> URec k (Ptr ()) p -> Bool Source #

(<=) :: URec k (Ptr ()) p -> URec k (Ptr ()) p -> Bool Source #

(>) :: URec k (Ptr ()) p -> URec k (Ptr ()) p -> Bool Source #

(>=) :: URec k (Ptr ()) p -> URec k (Ptr ()) p -> Bool Source #

max :: URec k (Ptr ()) p -> URec k (Ptr ()) p -> URec k (Ptr ()) p Source #

min :: URec k (Ptr ()) p -> URec k (Ptr ()) p -> URec k (Ptr ()) p Source #

(Ord a, Ord b, Ord c) => Ord (a, b, c) 

Methods

compare :: (a, b, c) -> (a, b, c) -> Ordering Source #

(<) :: (a, b, c) -> (a, b, c) -> Bool Source #

(<=) :: (a, b, c) -> (a, b, c) -> Bool Source #

(>) :: (a, b, c) -> (a, b, c) -> Bool Source #

(>=) :: (a, b, c) -> (a, b, c) -> Bool Source #

max :: (a, b, c) -> (a, b, c) -> (a, b, c) Source #

min :: (a, b, c) -> (a, b, c) -> (a, b, c) Source #

Ord ((:~:) k a b) # 

Methods

compare :: (k :~: a) b -> (k :~: a) b -> Ordering Source #

(<) :: (k :~: a) b -> (k :~: a) b -> Bool Source #

(<=) :: (k :~: a) b -> (k :~: a) b -> Bool Source #

(>) :: (k :~: a) b -> (k :~: a) b -> Bool Source #

(>=) :: (k :~: a) b -> (k :~: a) b -> Bool Source #

max :: (k :~: a) b -> (k :~: a) b -> (k :~: a) b Source #

min :: (k :~: a) b -> (k :~: a) b -> (k :~: a) b Source #

Ord (Coercion k a b) # 

Methods

compare :: Coercion k a b -> Coercion k a b -> Ordering Source #

(<) :: Coercion k a b -> Coercion k a b -> Bool Source #

(<=) :: Coercion k a b -> Coercion k a b -> Bool Source #

(>) :: Coercion k a b -> Coercion k a b -> Bool Source #

(>=) :: Coercion k a b -> Coercion k a b -> Bool Source #

max :: Coercion k a b -> Coercion k a b -> Coercion k a b Source #

min :: Coercion k a b -> Coercion k a b -> Coercion k a b Source #

Ord (f a) => Ord (Alt k f a) # 

Methods

compare :: Alt k f a -> Alt k f a -> Ordering Source #

(<) :: Alt k f a -> Alt k f a -> Bool Source #

(<=) :: Alt k f a -> Alt k f a -> Bool Source #

(>) :: Alt k f a -> Alt k f a -> Bool Source #

(>=) :: Alt k f a -> Alt k f a -> Bool Source #

max :: Alt k f a -> Alt k f a -> Alt k f a Source #

min :: Alt k f a -> Alt k f a -> Alt k f a Source #

Ord a => Ord (Const k a b) # 

Methods

compare :: Const k a b -> Const k a b -> Ordering Source #

(<) :: Const k a b -> Const k a b -> Bool Source #

(<=) :: Const k a b -> Const k a b -> Bool Source #

(>) :: Const k a b -> Const k a b -> Bool Source #

(>=) :: Const k a b -> Const k a b -> Bool Source #

max :: Const k a b -> Const k a b -> Const k a b Source #

min :: Const k a b -> Const k a b -> Const k a b Source #

Ord c => Ord (K1 k i c p) # 

Methods

compare :: K1 k i c p -> K1 k i c p -> Ordering Source #

(<) :: K1 k i c p -> K1 k i c p -> Bool Source #

(<=) :: K1 k i c p -> K1 k i c p -> Bool Source #

(>) :: K1 k i c p -> K1 k i c p -> Bool Source #

(>=) :: K1 k i c p -> K1 k i c p -> Bool Source #

max :: K1 k i c p -> K1 k i c p -> K1 k i c p Source #

min :: K1 k i c p -> K1 k i c p -> K1 k i c p Source #

(Ord (g p), Ord (f p)) => Ord ((:+:) k f g p) # 

Methods

compare :: (k :+: f) g p -> (k :+: f) g p -> Ordering Source #

(<) :: (k :+: f) g p -> (k :+: f) g p -> Bool Source #

(<=) :: (k :+: f) g p -> (k :+: f) g p -> Bool Source #

(>) :: (k :+: f) g p -> (k :+: f) g p -> Bool Source #

(>=) :: (k :+: f) g p -> (k :+: f) g p -> Bool Source #

max :: (k :+: f) g p -> (k :+: f) g p -> (k :+: f) g p Source #

min :: (k :+: f) g p -> (k :+: f) g p -> (k :+: f) g p Source #

(Ord (g p), Ord (f p)) => Ord ((:*:) k f g p) # 

Methods

compare :: (k :*: f) g p -> (k :*: f) g p -> Ordering Source #

(<) :: (k :*: f) g p -> (k :*: f) g p -> Bool Source #

(<=) :: (k :*: f) g p -> (k :*: f) g p -> Bool Source #

(>) :: (k :*: f) g p -> (k :*: f) g p -> Bool Source #

(>=) :: (k :*: f) g p -> (k :*: f) g p -> Bool Source #

max :: (k :*: f) g p -> (k :*: f) g p -> (k :*: f) g p Source #

min :: (k :*: f) g p -> (k :*: f) g p -> (k :*: f) g p Source #

(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) 

Methods

compare :: (a, b, c, d) -> (a, b, c, d) -> Ordering Source #

(<) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source #

(<=) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source #

(>) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source #

(>=) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source #

max :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source #

min :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source #

Ord ((:~~:) k1 k2 a b) #

Since: 4.10.0.0

Methods

compare :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> Ordering Source #

(<) :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> Bool Source #

(<=) :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> Bool Source #

(>) :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> Bool Source #

(>=) :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> Bool Source #

max :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> (k1 :~~: k2) a b Source #

min :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> (k1 :~~: k2) a b Source #

(Ord1 f, Ord1 g, Ord a) => Ord (Sum * f g a) #

Since: 4.9.0.0

Methods

compare :: Sum * f g a -> Sum * f g a -> Ordering Source #

(<) :: Sum * f g a -> Sum * f g a -> Bool Source #

(<=) :: Sum * f g a -> Sum * f g a -> Bool Source #

(>) :: Sum * f g a -> Sum * f g a -> Bool Source #

(>=) :: Sum * f g a -> Sum * f g a -> Bool Source #

max :: Sum * f g a -> Sum * f g a -> Sum * f g a Source #

min :: Sum * f g a -> Sum * f g a -> Sum * f g a Source #

(Ord1 f, Ord1 g, Ord a) => Ord (Product * f g a) #

Since: 4.9.0.0

Methods

compare :: Product * f g a -> Product * f g a -> Ordering Source #

(<) :: Product * f g a -> Product * f g a -> Bool Source #

(<=) :: Product * f g a -> Product * f g a -> Bool Source #

(>) :: Product * f g a -> Product * f g a -> Bool Source #

(>=) :: Product * f g a -> Product * f g a -> Bool Source #

max :: Product * f g a -> Product * f g a -> Product * f g a Source #

min :: Product * f g a -> Product * f g a -> Product * f g a Source #

Ord (f p) => Ord (M1 k i c f p) # 

Methods

compare :: M1 k i c f p -> M1 k i c f p -> Ordering Source #

(<) :: M1 k i c f p -> M1 k i c f p -> Bool Source #

(<=) :: M1 k i c f p -> M1 k i c f p -> Bool Source #

(>) :: M1 k i c f p -> M1 k i c f p -> Bool Source #

(>=) :: M1 k i c f p -> M1 k i c f p -> Bool Source #

max :: M1 k i c f p -> M1 k i c f p -> M1 k i c f p Source #

min :: M1 k i c f p -> M1 k i c f p -> M1 k i c f p Source #

Ord (f (g p)) => Ord ((:.:) k2 k1 f g p) # 

Methods

compare :: (k2 :.: k1) f g p -> (k2 :.: k1) f g p -> Ordering Source #

(<) :: (k2 :.: k1) f g p -> (k2 :.: k1) f g p -> Bool Source #

(<=) :: (k2 :.: k1) f g p -> (k2 :.: k1) f g p -> Bool Source #

(>) :: (k2 :.: k1) f g p -> (k2 :.: k1) f g p -> Bool Source #

(>=) :: (k2 :.: k1) f g p -> (k2 :.: k1) f g p -> Bool Source #

max :: (k2 :.: k1) f g p -> (k2 :.: k1) f g p -> (k2 :.: k1) f g p Source #

min :: (k2 :.: k1) f g p -> (k2 :.: k1) f g p -> (k2 :.: k1) f g p Source #

(Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) 

Methods

compare :: (a, b, c, d, e) -> (a, b, c, d, e) -> Ordering Source #

(<) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source #

(<=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source #

(>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source #

(>=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source #

max :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source #

min :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source #

(Ord1 f, Ord1 g, Ord a) => Ord (Compose * * f g a) #

Since: 4.9.0.0

Methods

compare :: Compose * * f g a -> Compose * * f g a -> Ordering Source #

(<) :: Compose * * f g a -> Compose * * f g a -> Bool Source #

(<=) :: Compose * * f g a -> Compose * * f g a -> Bool Source #

(>) :: Compose * * f g a -> Compose * * f g a -> Bool Source #

(>=) :: Compose * * f g a -> Compose * * f g a -> Bool Source #

max :: Compose * * f g a -> Compose * * f g a -> Compose * * f g a Source #

min :: Compose * * f g a -> Compose * * f g a -> Compose * * f g a Source #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) 

Methods

compare :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Ordering Source #

(<) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source #

(<=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source #

(>) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source #

(>=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source #

max :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source #

min :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) 

Methods

compare :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Ordering Source #

(<) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source #

(<=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source #

(>) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source #

(>=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source #

max :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source #

min :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) 

Methods

compare :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Ordering Source #

(<) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source #

(<=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source #

(>) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source #

(>=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source #

max :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) Source #

min :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) Source #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) 

Methods

compare :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Ordering Source #

(<) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source #

(<=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source #

(>) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source #

(>=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source #

max :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) Source #

min :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) Source #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) 

Methods

compare :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Ordering Source #

(<) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source #

(<=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source #

(>) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source #

(>=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source #

max :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) Source #

min :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) Source #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) 

Methods

compare :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Ordering Source #

(<) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source #

(<=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source #

(>) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source #

(>=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source #

max :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) Source #

min :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) Source #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) 

Methods

compare :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Ordering Source #

(<) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source #

(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source #

(>) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source #

(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source #

max :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) Source #

min :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) Source #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) 

Methods

compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Ordering Source #

(<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source #

(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source #

(>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source #

(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source #

max :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) Source #

min :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) Source #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) 

Methods

compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Ordering Source #

(<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source #

(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source #

(>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source #

(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source #

max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source #

min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) 

Methods

compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Ordering Source #

(<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source #

(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source #

(>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source #

(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source #

max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source #

min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source #

class Enum a where Source #

Class Enum defines operations on sequentially ordered types.

The enumFrom... methods are used in Haskell's translation of arithmetic sequences.

Instances of Enum may be derived for any enumeration type (types whose constructors have no fields). The nullary constructors are assumed to be numbered left-to-right by fromEnum from 0 through n-1. See Chapter 10 of the Haskell Report for more details.

For any type that is an instance of class Bounded as well as Enum, the following should hold:

   enumFrom     x   = enumFromTo     x maxBound
   enumFromThen x y = enumFromThenTo x y bound
     where
       bound | fromEnum y >= fromEnum x = maxBound
             | otherwise                = minBound

Minimal complete definition

toEnum, fromEnum

Methods

succ :: a -> a Source #

the successor of a value. For numeric types, succ adds 1.

pred :: a -> a Source #

the predecessor of a value. For numeric types, pred subtracts 1.

toEnum :: Int -> a Source #

Convert from an Int.

fromEnum :: a -> Int Source #

Convert to an Int. It is implementation-dependent what fromEnum returns when applied to a value that is too large to fit in an Int.

enumFrom :: a -> [a] Source #

Used in Haskell's translation of [n..].

enumFromThen :: a -> a -> [a] Source #

Used in Haskell's translation of [n,n'..].

enumFromTo :: a -> a -> [a] Source #

Used in Haskell's translation of [n..m].

enumFromThenTo :: a -> a -> a -> [a] Source #

Used in Haskell's translation of [n,n'..m].

Instances

Enum Bool #

Since: 2.1

Enum Char #

Since: 2.1

Enum Int #

Since: 2.1

Enum Int8 #

Since: 2.1

Enum Int16 #

Since: 2.1

Enum Int32 #

Since: 2.1

Enum Int64 #

Since: 2.1

Enum Integer #

Since: 2.1

Enum Natural #

Since: 4.8.0.0

Enum Ordering #

Since: 2.1

Enum Word #

Since: 2.1

Enum Word8 #

Since: 2.1

Enum Word16 #

Since: 2.1

Enum Word32 #

Since: 2.1

Enum Word64 #

Since: 2.1

Enum VecCount #

Since: 4.10.0.0

Enum VecElem #

Since: 4.10.0.0

Enum () #

Since: 2.1

Methods

succ :: () -> () Source #

pred :: () -> () Source #

toEnum :: Int -> () Source #

fromEnum :: () -> Int Source #

enumFrom :: () -> [()] Source #

enumFromThen :: () -> () -> [()] Source #

enumFromTo :: () -> () -> [()] Source #

enumFromThenTo :: () -> () -> () -> [()] Source #

Enum GeneralCategory # 
Enum IOMode # 
Enum IntPtr # 
Enum WordPtr # 
Enum CUIntMax # 
Enum CIntMax # 
Enum CUIntPtr # 
Enum CIntPtr # 
Enum CSUSeconds # 
Enum CUSeconds # 
Enum CTime # 
Enum CClock # 
Enum CSigAtomic # 
Enum CWchar # 
Enum CSize # 
Enum CPtrdiff # 
Enum CDouble # 
Enum CFloat # 
Enum CBool # 
Enum CULLong # 
Enum CLLong # 
Enum CULong # 
Enum CLong # 
Enum CUInt # 
Enum CInt # 
Enum CUShort # 
Enum CShort # 
Enum CUChar # 
Enum CSChar # 
Enum CChar # 
Enum DecidedStrictness # 
Enum SourceStrictness # 
Enum SourceUnpackedness # 
Enum Associativity # 
Enum SeekMode # 
Enum Fd # 

Methods

succ :: Fd -> Fd Source #

pred :: Fd -> Fd Source #

toEnum :: Int -> Fd Source #

fromEnum :: Fd -> Int Source #

enumFrom :: Fd -> [Fd] Source #

enumFromThen :: Fd -> Fd -> [Fd] Source #

enumFromTo :: Fd -> Fd -> [Fd] Source #

enumFromThenTo :: Fd -> Fd -> Fd -> [Fd] Source #

Enum CKey # 
Enum CId # 
Enum CFsFilCnt # 
Enum CFsBlkCnt # 
Enum CClockId # 
Enum CBlkCnt # 
Enum CBlkSize # 
Enum CRLim # 
Enum CTcflag # 
Enum CSpeed # 
Enum CCc # 
Enum CUid # 
Enum CNlink # 
Enum CGid # 
Enum CSsize # 
Enum CPid # 
Enum COff # 
Enum CMode # 
Enum CIno # 
Enum CDev # 
Enum DoTrace #

Since: 4.8.0.0

Enum DoHeapProfile #

Since: 4.8.0.0

Enum DoCostCentres #

Since: 4.8.0.0

Enum GiveGCStats #

Since: 4.8.0.0

Integral a => Enum (Ratio a) #

Since: 2.0.1

Methods

succ :: Ratio a -> Ratio a Source #

pred :: Ratio a -> Ratio a Source #

toEnum :: Int -> Ratio a Source #

fromEnum :: Ratio a -> Int Source #

enumFrom :: Ratio a -> [Ratio a] Source #

enumFromThen :: Ratio a -> Ratio a -> [Ratio a] Source #

enumFromTo :: Ratio a -> Ratio a -> [Ratio a] Source #

enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a] Source #

Enum a => Enum (Identity a) # 
Enum a => Enum (WrappedMonoid a) #

Since: 4.9.0.0

Enum a => Enum (Last a) #

Since: 4.9.0.0

Methods

succ :: Last a -> Last a Source #

pred :: Last a -> Last a Source #

toEnum :: Int -> Last a Source #

fromEnum :: Last a -> Int Source #

enumFrom :: Last a -> [Last a] Source #

enumFromThen :: Last a -> Last a -> [Last a] Source #

enumFromTo :: Last a -> Last a -> [Last a] Source #

enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] Source #

Enum a => Enum (First a) #

Since: 4.9.0.0

Methods

succ :: First a -> First a Source #

pred :: First a -> First a Source #

toEnum :: Int -> First a Source #

fromEnum :: First a -> Int Source #

enumFrom :: First a -> [First a] Source #

enumFromThen :: First a -> First a -> [First a] Source #

enumFromTo :: First a -> First a -> [First a] Source #

enumFromThenTo :: First a -> First a -> First a -> [First a] Source #

Enum a => Enum (Max a) #

Since: 4.9.0.0

Methods

succ :: Max a -> Max a Source #

pred :: Max a -> Max a Source #

toEnum :: Int -> Max a Source #

fromEnum :: Max a -> Int Source #

enumFrom :: Max a -> [Max a] Source #

enumFromThen :: Max a -> Max a -> [Max a] Source #

enumFromTo :: Max a -> Max a -> [Max a] Source #

enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] Source #

Enum a => Enum (Min a) #

Since: 4.9.0.0

Methods

succ :: Min a -> Min a Source #

pred :: Min a -> Min a Source #

toEnum :: Int -> Min a Source #

fromEnum :: Min a -> Int Source #

enumFrom :: Min a -> [Min a] Source #

enumFromThen :: Min a -> Min a -> [Min a] Source #

enumFromTo :: Min a -> Min a -> [Min a] Source #

enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] Source #

Enum (Fixed a) #

Since: 2.1

Methods

succ :: Fixed a -> Fixed a Source #

pred :: Fixed a -> Fixed a Source #

toEnum :: Int -> Fixed a Source #

fromEnum :: Fixed a -> Int Source #

enumFrom :: Fixed a -> [Fixed a] Source #

enumFromThen :: Fixed a -> Fixed a -> [Fixed a] Source #

enumFromTo :: Fixed a -> Fixed a -> [Fixed a] Source #

enumFromThenTo :: Fixed a -> Fixed a -> Fixed a -> [Fixed a] Source #

Enum (Proxy k s) #

Since: 4.7.0.0

Methods

succ :: Proxy k s -> Proxy k s Source #

pred :: Proxy k s -> Proxy k s Source #

toEnum :: Int -> Proxy k s Source #

fromEnum :: Proxy k s -> Int Source #

enumFrom :: Proxy k s -> [Proxy k s] Source #

enumFromThen :: Proxy k s -> Proxy k s -> [Proxy k s] Source #

enumFromTo :: Proxy k s -> Proxy k s -> [Proxy k s] Source #

enumFromThenTo :: Proxy k s -> Proxy k s -> Proxy k s -> [Proxy k s] Source #

(~) k a b => Enum ((:~:) k a b) #

Since: 4.7.0.0

Methods

succ :: (k :~: a) b -> (k :~: a) b Source #

pred :: (k :~: a) b -> (k :~: a) b Source #

toEnum :: Int -> (k :~: a) b Source #

fromEnum :: (k :~: a) b -> Int Source #

enumFrom :: (k :~: a) b -> [(k :~: a) b] Source #

enumFromThen :: (k :~: a) b -> (k :~: a) b -> [(k :~: a) b] Source #

enumFromTo :: (k :~: a) b -> (k :~: a) b -> [(k :~: a) b] Source #

enumFromThenTo :: (k :~: a) b -> (k :~: a) b -> (k :~: a) b -> [(k :~: a) b] Source #

Coercible k a b => Enum (Coercion k a b) #

Since: 4.7.0.0

Methods

succ :: Coercion k a b -> Coercion k a b Source #

pred :: Coercion k a b -> Coercion k a b Source #

toEnum :: Int -> Coercion k a b Source #

fromEnum :: Coercion k a b -> Int Source #

enumFrom :: Coercion k a b -> [Coercion k a b] Source #

enumFromThen :: Coercion k a b -> Coercion k a b -> [Coercion k a b] Source #

enumFromTo :: Coercion k a b -> Coercion k a b -> [Coercion k a b] Source #

enumFromThenTo :: Coercion k a b -> Coercion k a b -> Coercion k a b -> [Coercion k a b] Source #

Enum (f a) => Enum (Alt k f a) # 

Methods

succ :: Alt k f a -> Alt k f a Source #

pred :: Alt k f a -> Alt k f a Source #

toEnum :: Int -> Alt k f a Source #

fromEnum :: Alt k f a -> Int Source #

enumFrom :: Alt k f a -> [Alt k f a] Source #

enumFromThen :: Alt k f a -> Alt k f a -> [Alt k f a] Source #

enumFromTo :: Alt k f a -> Alt k f a -> [Alt k f a] Source #

enumFromThenTo :: Alt k f a -> Alt k f a -> Alt k f a -> [Alt k f a] Source #

Enum a => Enum (Const k a b) # 

Methods

succ :: Const k a b -> Const k a b Source #

pred :: Const k a b -> Const k a b Source #

toEnum :: Int -> Const k a b Source #

fromEnum :: Const k a b -> Int Source #

enumFrom :: Const k a b -> [Const k a b] Source #

enumFromThen :: Const k a b -> Const k a b -> [Const k a b] Source #

enumFromTo :: Const k a b -> Const k a b -> [Const k a b] Source #

enumFromThenTo :: Const k a b -> Const k a b -> Const k a b -> [Const k a b] Source #

(~~) k1 k2 a b => Enum ((:~~:) k1 k2 a b) #

Since: 4.10.0.0

Methods

succ :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b Source #

pred :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b Source #

toEnum :: Int -> (k1 :~~: k2) a b Source #

fromEnum :: (k1 :~~: k2) a b -> Int Source #

enumFrom :: (k1 :~~: k2) a b -> [(k1 :~~: k2) a b] Source #

enumFromThen :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> [(k1 :~~: k2) a b] Source #

enumFromTo :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> [(k1 :~~: k2) a b] Source #

enumFromThenTo :: (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> (k1 :~~: k2) a b -> [(k1 :~~: k2) a b] Source #

class Bounded a where Source #

The Bounded class is used to name the upper and lower limits of a type. Ord is not a superclass of Bounded since types that are not totally ordered may also have upper and lower bounds.

The Bounded class may be derived for any enumeration type; minBound is the first constructor listed in the data declaration and maxBound is the last. Bounded may also be derived for single-constructor datatypes whose constituent types are in Bounded.

Minimal complete definition

minBound, maxBound

Methods

minBound, maxBound :: a Source #

Instances

Bounded Bool #

Since: 2.1

Bounded Char #

Since: 2.1

Bounded Int #

Since: 2.1

Bounded Int8 #

Since: 2.1

Bounded Int16 #

Since: 2.1

Bounded Int32 #

Since: 2.1

Bounded Int64 #

Since: 2.1

Bounded Ordering #

Since: 2.1

Bounded Word #

Since: 2.1

Bounded Word8 #

Since: 2.1

Bounded Word16 #

Since: 2.1

Bounded Word32 #

Since: 2.1

Bounded Word64 #

Since: 2.1

Bounded VecCount #

Since: 4.10.0.0

Bounded VecElem #

Since: 4.10.0.0

Bounded () #

Since: 2.1

Methods

minBound :: () Source #

maxBound :: () Source #

Bounded GeneralCategory # 
Bounded IntPtr # 
Bounded WordPtr # 
Bounded CUIntMax # 
Bounded CIntMax # 
Bounded CUIntPtr # 
Bounded CIntPtr # 
Bounded CSigAtomic # 
Bounded CWchar # 
Bounded CSize # 
Bounded CPtrdiff # 
Bounded CBool # 
Bounded CULLong # 
Bounded CLLong # 
Bounded CULong # 
Bounded CLong # 
Bounded CUInt # 
Bounded CInt # 
Bounded CUShort # 
Bounded CShort # 
Bounded CUChar # 
Bounded CSChar # 
Bounded CChar # 
Bounded DecidedStrictness # 
Bounded SourceStrictness # 
Bounded SourceUnpackedness # 
Bounded Associativity # 
Bounded Any # 
Bounded All # 
Bounded Fd # 
Bounded CKey # 
Bounded CId # 
Bounded CFsFilCnt # 
Bounded CFsBlkCnt # 
Bounded CClockId # 
Bounded CBlkCnt # 
Bounded CBlkSize # 
Bounded CRLim # 
Bounded CTcflag # 
Bounded CUid # 
Bounded CNlink # 
Bounded CGid # 
Bounded CSsize # 
Bounded CPid # 
Bounded COff # 
Bounded CMode # 
Bounded CIno # 
Bounded CDev # 
Bounded a => Bounded (Product a) # 
Bounded a => Bounded (Sum a) # 
Bounded a => Bounded (Dual a) # 
Bounded a => Bounded (Identity a) # 
Bounded m => Bounded (WrappedMonoid m) # 
Bounded a => Bounded (Last a) # 
Bounded a => Bounded (First a) # 
Bounded a => Bounded (Max a) # 
Bounded a => Bounded (Min a) # 
(Bounded a, Bounded b) => Bounded (a, b) #

Since: 2.1

Methods

minBound :: (a, b) Source #

maxBound :: (a, b) Source #

Bounded (Proxy k t) # 

Methods

minBound :: Proxy k t Source #

maxBound :: Proxy k t Source #

(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) #

Since: 2.1

Methods

minBound :: (a, b, c) Source #

maxBound :: (a, b, c) Source #

(~) k a b => Bounded ((:~:) k a b) #

Since: 4.7.0.0

Methods

minBound :: (k :~: a) b Source #

maxBound :: (k :~: a) b Source #

Coercible k a b => Bounded (Coercion k a b) #

Since: 4.7.0.0

Methods

minBound :: Coercion k a b Source #

maxBound :: Coercion k a b Source #

Bounded a => Bounded (Const k a b) # 

Methods

minBound :: Const k a b Source #

maxBound :: Const k a b Source #

(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) #

Since: 2.1

Methods

minBound :: (a, b, c, d) Source #

maxBound :: (a, b, c, d) Source #

(~~) k1 k2 a b => Bounded ((:~~:) k1 k2 a b) #

Since: 4.10.0.0

Methods

minBound :: (k1 :~~: k2) a b Source #

maxBound :: (k1 :~~: k2) a b Source #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) #

Since: 2.1

Methods

minBound :: (a, b, c, d, e) Source #

maxBound :: (a, b, c, d, e) Source #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) #

Since: 2.1

Methods

minBound :: (a, b, c, d, e, f) Source #

maxBound :: (a, b, c, d, e, f) Source #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) #

Since: 2.1

Methods

minBound :: (a, b, c, d, e, f, g) Source #

maxBound :: (a, b, c, d, e, f, g) Source #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) #

Since: 2.1

Methods

minBound :: (a, b, c, d, e, f, g, h) Source #

maxBound :: (a, b, c, d, e, f, g, h) Source #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) #

Since: 2.1

Methods

minBound :: (a, b, c, d, e, f, g, h, i) Source #

maxBound :: (a, b, c, d, e, f, g, h, i) Source #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) #

Since: 2.1

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j) Source #

maxBound :: (a, b, c, d, e, f, g, h, i, j) Source #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) #

Since: 2.1

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k) Source #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k) Source #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) #

Since: 2.1

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l) Source #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l) Source #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) #

Since: 2.1

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) Source #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) Source #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #

Since: 2.1

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

Since: 2.1

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source #

Numbers

Numeric types

data Int :: * Source #

A fixed-precision integer type with at least the range [-2^29 .. 2^29-1]. The exact range for a given implementation can be determined by using minBound and maxBound from the Bounded class.

Instances

Bounded Int #

Since: 2.1

Enum Int #

Since: 2.1

Eq Int 

Methods

(==) :: Int -> Int -> Bool Source #

(/=) :: Int -> Int -> Bool Source #

Integral Int #

Since: 2.0.1

Methods

quot :: Int -> Int -> Int Source #

rem :: Int -> Int -> Int Source #

div :: Int -> Int -> Int Source #

mod :: Int -> Int -> Int Source #

quotRem :: Int -> Int -> (Int, Int) Source #

divMod :: Int -> Int -> (Int, Int) Source #

toInteger :: Int -> Integer Source #

Data Int #

Since: 4.0.0.0

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Int -> c Int Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Int Source #

toConstr :: Int -> Constr Source #

dataTypeOf :: Int -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Int) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Int) Source #

gmapT :: (forall b. Data b => b -> b) -> Int -> Int Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Int -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Int -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Int -> m Int Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int Source #

Num Int #

Since: 2.1

Ord Int 

Methods

compare :: Int -> Int -> Ordering Source #

(<) :: Int -> Int -> Bool Source #

(<=) :: Int -> Int -> Bool Source #

(>) :: Int -> Int -> Bool Source #

(>=) :: Int -> Int -> Bool Source #

max :: Int -> Int -> Int Source #

min :: Int -> Int -> Int Source #

Read Int #

Since: 2.1

Real Int #

Since: 2.0.1

Show Int #

Since: 2.1

Ix Int #

Since: 2.1

Methods

range :: (Int, Int) -> [Int] Source #

index :: (Int, Int) -> Int -> Int Source #

unsafeIndex :: (Int, Int) -> Int -> Int

inRange :: (Int, Int) -> Int -> Bool Source #

rangeSize :: (Int, Int) -> Int Source #

unsafeRangeSize :: (Int, Int) -> Int

FiniteBits Int #

Since: 4.6.0.0

Bits Int #

Since: 2.1

Storable Int #

Since: 2.1

PrintfArg Int #

Since: 2.1

Generic1 k (URec k Int) # 

Associated Types

type Rep1 (URec k Int) (f :: URec k Int -> *) :: k -> * Source #

Methods

from1 :: f a -> Rep1 (URec k Int) f a Source #

to1 :: Rep1 (URec k Int) f a -> f a Source #

Functor (URec * Int) # 

Methods

fmap :: (a -> b) -> URec * Int a -> URec * Int b Source #

(<$) :: a -> URec * Int b -> URec * Int a Source #

Foldable (URec * Int) # 

Methods

fold :: Monoid m => URec * Int m -> m Source #

foldMap :: Monoid m => (a -> m) -> URec * Int a -> m Source #

foldr :: (a -> b -> b) -> b -> URec * Int a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec * Int a -> b Source #

foldl :: (b -> a -> b) -> b -> URec * Int a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec * Int a -> b Source #

foldr1 :: (a -> a -> a) -> URec * Int a -> a Source #

foldl1 :: (a -> a -> a) -> URec * Int a -> a Source #

toList :: URec * Int a -> [a] Source #

null :: URec * Int a -> Bool Source #

length :: URec * Int a -> Int Source #

elem :: Eq a => a -> URec * Int a -> Bool Source #

maximum :: Ord a => URec * Int a -> a Source #

minimum :: Ord a => URec * Int a -> a Source #

sum :: Num a => URec * Int a -> a Source #

product :: Num a => URec * Int a -> a Source #

Traversable (URec * Int) # 

Methods

traverse :: Applicative f => (a -> f b) -> URec * Int a -> f (URec * Int b) Source #

sequenceA :: Applicative f => URec * Int (f a) -> f (URec * Int a) Source #

mapM :: Monad m => (a -> m b) -> URec * Int a -> m (URec * Int b) Source #

sequence :: Monad m => URec * Int (m a) -> m (URec * Int a) Source #

Eq (URec k Int p) # 

Methods

(==) :: URec k Int p -> URec k Int p -> Bool Source #

(/=) :: URec k Int p -> URec k Int p -> Bool Source #

Ord (URec k Int p) # 

Methods

compare :: URec k Int p -> URec k Int p -> Ordering Source #

(<) :: URec k Int p -> URec k Int p -> Bool Source #

(<=) :: URec k Int p -> URec k Int p -> Bool Source #

(>) :: URec k Int p -> URec k Int p -> Bool Source #

(>=) :: URec k Int p -> URec k Int p -> Bool Source #

max :: URec k Int p -> URec k Int p -> URec k Int p Source #

min :: URec k Int p -> URec k Int p -> URec k Int p Source #

Show (URec k Int p) # 

Methods

showsPrec :: Int -> URec k Int p -> ShowS Source #

show :: URec k Int p -> String Source #

showList :: [URec k Int p] -> ShowS Source #

Generic (URec k Int p) # 

Associated Types

type Rep (URec k Int p) :: * -> * Source #

Methods

from :: URec k Int p -> Rep (URec k Int p) x Source #

to :: Rep (URec k Int p) x -> URec k Int p Source #

data URec k Int #

Used for marking occurrences of Int#

Since: 4.9.0.0

data URec k Int = UInt {}
type Rep1 k (URec k Int) # 
type Rep1 k (URec k Int) = D1 k (MetaData "URec" "GHC.Generics" "base" False) (C1 k (MetaCons "UInt" PrefixI True) (S1 k (MetaSel (Just Symbol "uInt#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UInt k)))
type Rep (URec k Int p) # 
type Rep (URec k Int p) = D1 * (MetaData "URec" "GHC.Generics" "base" False) (C1 * (MetaCons "UInt" PrefixI True) (S1 * (MetaSel (Just Symbol "uInt#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UInt *)))

data Integer :: * Source #

Invariant: Jn# and Jp# are used iff value doesn't fit in S#

Useful properties resulting from the invariants:

Instances

Enum Integer #

Since: 2.1

Eq Integer 
Integral Integer #

Since: 2.0.1

Data Integer #

Since: 4.0.0.0

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Integer -> c Integer Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Integer Source #

toConstr :: Integer -> Constr Source #

dataTypeOf :: Integer -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Integer) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Integer) Source #

gmapT :: (forall b. Data b => b -> b) -> Integer -> Integer Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Integer -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Integer -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source #

Num Integer #

Since: 2.1

Ord Integer 
Read Integer #

Since: 2.1

Real Integer #

Since: 2.0.1

Show Integer #

Since: 2.1

Ix Integer #

Since: 2.1

Bits Integer #

Since: 2.1

PrintfArg Integer #

Since: 2.1

data Float :: * Source #

Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.

Instances

Eq Float 

Methods

(==) :: Float -> Float -> Bool Source #

(/=) :: Float -> Float -> Bool Source #

Floating Float #

Since: 2.1

Data Float #

Since: 4.0.0.0

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Float -> c Float Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Float Source #

toConstr :: Float -> Constr Source #

dataTypeOf :: Float -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Float) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Float) Source #

gmapT :: (forall b. Data b => b -> b) -> Float -> Float Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Float -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Float -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Float -> m Float Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float Source #

Ord Float 
Read Float #

Since: 2.1

RealFloat Float #

Since: 2.1

Storable Float #

Since: 2.1

PrintfArg Float #

Since: 2.1

Generic1 k (URec k Float) # 

Associated Types

type Rep1 (URec k Float) (f :: URec k Float -> *) :: k -> * Source #

Methods

from1 :: f a -> Rep1 (URec k Float) f a Source #

to1 :: Rep1 (URec k Float) f a -> f a Source #

Functor (URec * Float) # 

Methods

fmap :: (a -> b) -> URec * Float a -> URec * Float b Source #

(<$) :: a -> URec * Float b -> URec * Float a Source #

Foldable (URec * Float) # 

Methods

fold :: Monoid m => URec * Float m -> m Source #

foldMap :: Monoid m => (a -> m) -> URec * Float a -> m Source #

foldr :: (a -> b -> b) -> b -> URec * Float a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec * Float a -> b Source #

foldl :: (b -> a -> b) -> b -> URec * Float a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec * Float a -> b Source #

foldr1 :: (a -> a -> a) -> URec * Float a -> a Source #

foldl1 :: (a -> a -> a) -> URec * Float a -> a Source #

toList :: URec * Float a -> [a] Source #

null :: URec * Float a -> Bool Source #

length :: URec * Float a -> Int Source #

elem :: Eq a => a -> URec * Float a -> Bool Source #

maximum :: Ord a => URec * Float a -> a Source #

minimum :: Ord a => URec * Float a -> a Source #

sum :: Num a => URec * Float a -> a Source #

product :: Num a => URec * Float a -> a Source #

Traversable (URec * Float) # 

Methods

traverse :: Applicative f => (a -> f b) -> URec * Float a -> f (URec * Float b) Source #

sequenceA :: Applicative f => URec * Float (f a) -> f (URec * Float a) Source #

mapM :: Monad m => (a -> m b) -> URec * Float a -> m (URec * Float b) Source #

sequence :: Monad m => URec * Float (m a) -> m (URec * Float a) Source #

Eq (URec k Float p) # 

Methods

(==) :: URec k Float p -> URec k Float p -> Bool Source #

(/=) :: URec k Float p -> URec k Float p -> Bool Source #

Ord (URec k Float p) # 

Methods

compare :: URec k Float p -> URec k Float p -> Ordering Source #

(<) :: URec k Float p -> URec k Float p -> Bool Source #

(<=) :: URec k Float p -> URec k Float p -> Bool Source #

(>) :: URec k Float p -> URec k Float p -> Bool Source #

(>=) :: URec k Float p -> URec k Float p -> Bool Source #

max :: URec k Float p -> URec k Float p -> URec k Float p Source #

min :: URec k Float p -> URec k Float p -> URec k Float p Source #

Show (URec k Float p) # 
Generic (URec k Float p) # 

Associated Types

type Rep (URec k Float p) :: * -> * Source #

Methods

from :: URec k Float p -> Rep (URec k Float p) x Source #

to :: Rep (URec k Float p) x -> URec k Float p Source #

data URec k Float #

Used for marking occurrences of Float#

Since: 4.9.0.0

type Rep1 k (URec k Float) # 
type Rep1 k (URec k Float) = D1 k (MetaData "URec" "GHC.Generics" "base" False) (C1 k (MetaCons "UFloat" PrefixI True) (S1 k (MetaSel (Just Symbol "uFloat#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UFloat k)))
type Rep (URec k Float p) # 
type Rep (URec k Float p) = D1 * (MetaData "URec" "GHC.Generics" "base" False) (C1 * (MetaCons "UFloat" PrefixI True) (S1 * (MetaSel (Just Symbol "uFloat#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UFloat *)))

data Double :: * Source #

Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.

Instances

Eq Double 
Floating Double #

Since: 2.1

Data Double #

Since: 4.0.0.0

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Double -> c Double Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Double Source #

toConstr :: Double -> Constr Source #

dataTypeOf :: Double -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Double) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Double) Source #

gmapT :: (forall b. Data b => b -> b) -> Double -> Double Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Double -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Double -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Double -> m Double Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double Source #

Ord Double 
Read Double #

Since: 2.1

RealFloat Double #

Since: 2.1

Storable Double #

Since: 2.1

PrintfArg Double #

Since: 2.1

Generic1 k (URec k Double) # 

Associated Types

type Rep1 (URec k Double) (f :: URec k Double -> *) :: k -> * Source #

Methods

from1 :: f a -> Rep1 (URec k Double) f a Source #

to1 :: Rep1 (URec k Double) f a -> f a Source #

Functor (URec * Double) # 

Methods

fmap :: (a -> b) -> URec * Double a -> URec * Double b Source #

(<$) :: a -> URec * Double b -> URec * Double a Source #

Foldable (URec * Double) # 

Methods

fold :: Monoid m => URec * Double m -> m Source #

foldMap :: Monoid m => (a -> m) -> URec * Double a -> m Source #

foldr :: (a -> b -> b) -> b -> URec * Double a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec * Double a -> b Source #

foldl :: (b -> a -> b) -> b -> URec * Double a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec * Double a -> b Source #

foldr1 :: (a -> a -> a) -> URec * Double a -> a Source #

foldl1 :: (a -> a -> a) -> URec * Double a -> a Source #

toList :: URec * Double a -> [a] Source #

null :: URec * Double a -> Bool Source #

length :: URec * Double a -> Int Source #

elem :: Eq a => a -> URec * Double a -> Bool Source #

maximum :: Ord a => URec * Double a -> a Source #

minimum :: Ord a => URec * Double a -> a Source #

sum :: Num a => URec * Double a -> a Source #

product :: Num a => URec * Double a -> a Source #

Traversable (URec * Double) # 

Methods

traverse :: Applicative f => (a -> f b) -> URec * Double a -> f (URec * Double b) Source #

sequenceA :: Applicative f => URec * Double (f a) -> f (URec * Double a) Source #

mapM :: Monad m => (a -> m b) -> URec * Double a -> m (URec * Double b) Source #

sequence :: Monad m => URec * Double (m a) -> m (URec * Double a) Source #

Eq (URec k Double p) # 

Methods

(==) :: URec k Double p -> URec k Double p -> Bool Source #

(/=) :: URec k Double p -> URec k Double p -> Bool Source #

Ord (URec k Double p) # 

Methods

compare :: URec k Double p -> URec k Double p -> Ordering Source #

(<) :: URec k Double p -> URec k Double p -> Bool Source #

(<=) :: URec k Double p -> URec k Double p -> Bool Source #

(>) :: URec k Double p -> URec k Double p -> Bool Source #

(>=) :: URec k Double p -> URec k Double p -> Bool Source #

max :: URec k Double p -> URec k Double p -> URec k Double p Source #

min :: URec k Double p -> URec k Double p -> URec k Double p Source #

Show (URec k Double p) # 
Generic (URec k Double p) # 

Associated Types

type Rep (URec k Double p) :: * -> * Source #

Methods

from :: URec k Double p -> Rep (URec k Double p) x Source #

to :: Rep (URec k Double p) x -> URec k Double p Source #

data URec k Double #

Used for marking occurrences of Double#

Since: 4.9.0.0

type Rep1 k (URec k Double) # 
type Rep1 k (URec k Double) = D1 k (MetaData "URec" "GHC.Generics" "base" False) (C1 k (MetaCons "UDouble" PrefixI True) (S1 k (MetaSel (Just Symbol "uDouble#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UDouble k)))
type Rep (URec k Double p) # 
type Rep (URec k Double p) = D1 * (MetaData "URec" "GHC.Generics" "base" False) (C1 * (MetaCons "UDouble" PrefixI True) (S1 * (MetaSel (Just Symbol "uDouble#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UDouble *)))

type Rational = Ratio Integer Source #

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.

data Word :: * Source #

A Word is an unsigned integral type, with the same size as Int.

Instances

Bounded Word #

Since: 2.1

Enum Word #

Since: 2.1

Eq Word 

Methods

(==) :: Word -> Word -> Bool Source #

(/=) :: Word -> Word -> Bool Source #

Integral Word #

Since: 2.1

Data Word #

Since: 4.0.0.0

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Word -> c Word Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Word Source #

toConstr :: Word -> Constr Source #

dataTypeOf :: Word -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Word) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Word) Source #

gmapT :: (forall b. Data b => b -> b) -> Word -> Word Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Word -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Word -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Word -> m Word Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word Source #

Num Word #

Since: 2.1

Ord Word 
Read Word #

Since: 4.5.0.0

Real Word #

Since: 2.1

Show Word #

Since: 2.1

Ix Word #

Since: 4.6.0.0

FiniteBits Word #

Since: 4.6.0.0

Bits Word #

Since: 2.1

Storable Word #

Since: 2.1

PrintfArg Word #

Since: 2.1

Generic1 k (URec k Word) # 

Associated Types

type Rep1 (URec k Word) (f :: URec k Word -> *) :: k -> * Source #

Methods

from1 :: f a -> Rep1 (URec k Word) f a Source #

to1 :: Rep1 (URec k Word) f a -> f a Source #

Functor (URec * Word) # 

Methods

fmap :: (a -> b) -> URec * Word a -> URec * Word b Source #

(<$) :: a -> URec * Word b -> URec * Word a Source #

Foldable (URec * Word) # 

Methods

fold :: Monoid m => URec * Word m -> m Source #

foldMap :: Monoid m => (a -> m) -> URec * Word a -> m Source #

foldr :: (a -> b -> b) -> b -> URec * Word a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec * Word a -> b Source #

foldl :: (b -> a -> b) -> b -> URec * Word a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec * Word a -> b Source #

foldr1 :: (a -> a -> a) -> URec * Word a -> a Source #

foldl1 :: (a -> a -> a) -> URec * Word a -> a Source #

toList :: URec * Word a -> [a] Source #

null :: URec * Word a -> Bool Source #

length :: URec * Word a -> Int Source #

elem :: Eq a => a -> URec * Word a -> Bool Source #

maximum :: Ord a => URec * Word a -> a Source #

minimum :: Ord a => URec * Word a -> a Source #

sum :: Num a => URec * Word a -> a Source #

product :: Num a => URec * Word a -> a Source #

Traversable (URec * Word) # 

Methods

traverse :: Applicative f => (a -> f b) -> URec * Word a -> f (URec * Word b) Source #

sequenceA :: Applicative f => URec * Word (f a) -> f (URec * Word a) Source #

mapM :: Monad m => (a -> m b) -> URec * Word a -> m (URec * Word b) Source #

sequence :: Monad m => URec * Word (m a) -> m (URec * Word a) Source #

Eq (URec k Word p) # 

Methods

(==) :: URec k Word p -> URec k Word p -> Bool Source #

(/=) :: URec k Word p -> URec k Word p -> Bool Source #

Ord (URec k Word p) # 

Methods

compare :: URec k Word p -> URec k Word p -> Ordering Source #

(<) :: URec k Word p -> URec k Word p -> Bool Source #

(<=) :: URec k Word p -> URec k Word p -> Bool Source #

(>) :: URec k Word p -> URec k Word p -> Bool Source #

(>=) :: URec k Word p -> URec k Word p -> Bool Source #

max :: URec k Word p -> URec k Word p -> URec k Word p Source #

min :: URec k Word p -> URec k Word p -> URec k Word p Source #

Show (URec k Word p) # 

Methods

showsPrec :: Int -> URec k Word p -> ShowS Source #

show :: URec k Word p -> String Source #

showList :: [URec k Word p] -> ShowS Source #

Generic (URec k Word p) # 

Associated Types

type Rep (URec k Word p) :: * -> * Source #

Methods

from :: URec k Word p -> Rep (URec k Word p) x Source #

to :: Rep (URec k Word p) x -> URec k Word p Source #

data URec k Word #

Used for marking occurrences of Word#

Since: 4.9.0.0

data URec k Word = UWord {}
type Rep1 k (URec k Word) # 
type Rep1 k (URec k Word) = D1 k (MetaData "URec" "GHC.Generics" "base" False) (C1 k (MetaCons "UWord" PrefixI True) (S1 k (MetaSel (Just Symbol "uWord#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UWord k)))
type Rep (URec k Word p) # 
type Rep (URec k Word p) = D1 * (MetaData "URec" "GHC.Generics" "base" False) (C1 * (MetaCons "UWord" PrefixI True) (S1 * (MetaSel (Just Symbol "uWord#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UWord *)))

Numeric type classes

class Num a where Source #

Basic numeric class.

Minimal complete definition

(+), (*), abs, signum, fromInteger, (negate | (-))

Methods

(+), (-), (*) :: a -> a -> a infixl 7 *infixl 6 +, - Source #

negate :: a -> a Source #

Unary negation.

abs :: a -> a Source #

Absolute value.

signum :: a -> a Source #

Sign of a number. The functions abs and signum should satisfy the law:

abs x * signum x == x

For real numbers, the signum is either -1 (negative), 0 (zero) or 1 (positive).

fromInteger :: Integer -> a Source #

Conversion from an Integer. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer, so such literals have type (Num a) => a.

Instances

Num Int #

Since: 2.1

Num Int8 #

Since: 2.1

Num Int16 #

Since: 2.1

Num Int32 #

Since: 2.1

Num Int64 #

Since: 2.1

Num Integer #

Since: 2.1

Num Natural #

Since: 4.8.0.0

Num Word #

Since: 2.1

Num Word8 #

Since: 2.1

Num Word16 #

Since: 2.1

Num Word32 #

Since: 2.1

Num Word64 #

Since: 2.1

Num IntPtr # 
Num WordPtr # 
Num CUIntMax # 
Num CIntMax # 
Num CUIntPtr # 
Num CIntPtr # 
Num CSUSeconds # 
Num CUSeconds # 
Num CTime # 
Num CClock # 
Num CSigAtomic # 
Num CWchar # 
Num CSize # 
Num CPtrdiff # 
Num CDouble # 
Num CFloat # 
Num CBool # 
Num CULLong # 
Num CLLong # 
Num CULong # 
Num CLong # 
Num CUInt # 
Num CInt # 
Num CUShort # 
Num CShort # 
Num CUChar # 
Num CSChar # 
Num CChar # 
Num Fd # 

Methods

(+) :: Fd -> Fd -> Fd Source #

(-) :: Fd -> Fd -> Fd Source #

(*) :: Fd -> Fd -> Fd Source #

negate :: Fd -> Fd Source #

abs :: Fd -> Fd Source #

signum :: Fd -> Fd Source #

fromInteger :: Integer -> Fd Source #

Num CKey # 
Num CId # 
Num CFsFilCnt # 
Num CFsBlkCnt # 
Num CClockId # 
Num CBlkCnt # 
Num CBlkSize # 
Num CRLim # 
Num CTcflag # 
Num CSpeed # 
Num CCc # 
Num CUid # 
Num CNlink # 
Num CGid # 
Num CSsize # 
Num CPid # 
Num COff # 
Num CMode # 
Num CIno # 
Num CDev # 
Integral a => Num (Ratio a) #

Since: 2.0.1

Methods

(+) :: Ratio a -> Ratio a -> Ratio a Source #

(-) :: Ratio a -> Ratio a -> Ratio a Source #

(*) :: Ratio a -> Ratio a -> Ratio a Source #

negate :: Ratio a -> Ratio a Source #

abs :: Ratio a -> Ratio a Source #

signum :: Ratio a -> Ratio a Source #

fromInteger :: Integer -> Ratio a Source #

Num a => Num (Product a) # 
Num a => Num (Sum a) # 

Methods

(+) :: Sum a -> Sum a -> Sum a Source #

(-) :: Sum a -> Sum a -> Sum a Source #

(*) :: Sum a -> Sum a -> Sum a Source #

negate :: Sum a -> Sum a Source #

abs :: Sum a -> Sum a Source #

signum :: Sum a -> Sum a Source #

fromInteger :: Integer -> Sum a Source #

Num a => Num (Identity a) # 
Num a => Num (Max a) #

Since: 4.9.0.0

Methods

(+) :: Max a -> Max a -> Max a Source #

(-) :: Max a -> Max a -> Max a Source #

(*) :: Max a -> Max a -> Max a Source #

negate :: Max a -> Max a Source #

abs :: Max a -> Max a Source #

signum :: Max a -> Max a Source #

fromInteger :: Integer -> Max a Source #

Num a => Num (Min a) #

Since: 4.9.0.0

Methods

(+) :: Min a -> Min a -> Min a Source #

(-) :: Min a -> Min a -> Min a Source #

(*) :: Min a -> Min a -> Min a Source #

negate :: Min a -> Min a Source #

abs :: Min a -> Min a Source #

signum :: Min a -> Min a Source #

fromInteger :: Integer -> Min a Source #

HasResolution a => Num (Fixed a) #

Since: 2.1

Methods

(+) :: Fixed a -> Fixed a -> Fixed a Source #

(-) :: Fixed a -> Fixed a -> Fixed a Source #

(*) :: Fixed a -> Fixed a -> Fixed a Source #

negate :: Fixed a -> Fixed a Source #

abs :: Fixed a -> Fixed a Source #

signum :: Fixed a -> Fixed a Source #

fromInteger :: Integer -> Fixed a Source #

RealFloat a => Num (Complex a) #

Since: 2.1

Num (f a) => Num (Alt k f a) # 

Methods

(+) :: Alt k f a -> Alt k f a -> Alt k f a Source #

(-) :: Alt k f a -> Alt k f a -> Alt k f a Source #

(*) :: Alt k f a -> Alt k f a -> Alt k f a Source #

negate :: Alt k f a -> Alt k f a Source #

abs :: Alt k f a -> Alt k f a Source #

signum :: Alt k f a -> Alt k f a Source #

fromInteger :: Integer -> Alt k f a Source #

Num a => Num (Const k a b) # 

Methods

(+) :: Const k a b -> Const k a b -> Const k a b Source #

(-) :: Const k a b -> Const k a b -> Const k a b Source #

(*) :: Const k a b -> Const k a b -> Const k a b Source #

negate :: Const k a b -> Const k a b Source #

abs :: Const k a b -> Const k a b Source #

signum :: Const k a b -> Const k a b Source #

fromInteger :: Integer -> Const k a b Source #

class (Num a, Ord a) => Real a where Source #

Minimal complete definition

toRational

Methods

toRational :: a -> Rational Source #

the rational equivalent of its real argument with full precision

Instances

Real Int #

Since: 2.0.1

Real Int8 #

Since: 2.1

Real Int16 #

Since: 2.1

Real Int32 #

Since: 2.1

Real Int64 #

Since: 2.1

Real Integer #

Since: 2.0.1

Real Natural #

Since: 4.8.0.0

Real Word #

Since: 2.1

Real Word8 #

Since: 2.1

Real Word16 #

Since: 2.1

Real Word32 #

Since: 2.1

Real Word64 #

Since: 2.1

Real IntPtr # 
Real WordPtr # 
Real CUIntMax # 
Real CIntMax # 
Real CUIntPtr # 
Real CIntPtr # 
Real CSUSeconds # 
Real CUSeconds # 
Real CTime # 
Real CClock # 
Real CSigAtomic # 
Real CWchar # 
Real CSize # 
Real CPtrdiff # 
Real CDouble # 
Real CFloat # 
Real CBool # 
Real CULLong # 
Real CLLong # 
Real CULong # 
Real CLong # 
Real CUInt # 
Real CInt # 
Real CUShort # 
Real CShort # 
Real CUChar # 
Real CSChar # 
Real CChar # 
Real Fd # 
Real CKey # 
Real CId # 
Real CFsFilCnt # 
Real CFsBlkCnt # 
Real CClockId # 
Real CBlkCnt # 
Real CBlkSize # 
Real CRLim # 
Real CTcflag # 
Real CSpeed # 
Real CCc # 
Real CUid # 
Real CNlink # 
Real CGid # 
Real CSsize # 
Real CPid # 
Real COff # 
Real CMode # 
Real CIno # 
Real CDev # 
Integral a => Real (Ratio a) #

Since: 2.0.1

Real a => Real (Identity a) # 
HasResolution a => Real (Fixed a) #

Since: 2.1

Real a => Real (Const k a b) # 

Methods

toRational :: Const k a b -> Rational Source #

class (Real a, Enum a) => Integral a where Source #

Integral numbers, supporting integer division.

Minimal complete definition

quotRem, toInteger

Methods

quot :: a -> a -> a infixl 7 Source #

integer division truncated toward zero

rem :: a -> a -> a infixl 7 Source #

integer remainder, satisfying

(x `quot` y)*y + (x `rem` y) == x

div :: a -> a -> a infixl 7 Source #

integer division truncated toward negative infinity

mod :: a -> a -> a infixl 7 Source #

integer modulus, satisfying

(x `div` y)*y + (x `mod` y) == x

quotRem :: a -> a -> (a, a) Source #

simultaneous quot and rem

divMod :: a -> a -> (a, a) Source #

simultaneous div and mod

toInteger :: a -> Integer Source #

conversion to Integer

Instances

Integral Int #

Since: 2.0.1

Methods

quot :: Int -> Int -> Int Source #

rem :: Int -> Int -> Int Source #

div :: Int -> Int -> Int Source #

mod :: Int -> Int -> Int Source #

quotRem :: Int -> Int -> (Int, Int) Source #

divMod :: Int -> Int -> (Int, Int) Source #

toInteger :: Int -> Integer Source #

Integral Int8 #

Since: 2.1

Integral Int16 #

Since: 2.1

Integral Int32 #

Since: 2.1

Integral Int64 #

Since: 2.1

Integral Integer #

Since: 2.0.1

Integral Natural #

Since: 4.8.0.0

Integral Word #

Since: 2.1

Integral Word8 #

Since: 2.1

Integral Word16 #

Since: 2.1

Integral Word32 #

Since: 2.1

Integral Word64 #

Since: 2.1

Integral IntPtr # 
Integral WordPtr # 
Integral CUIntMax # 
Integral CIntMax # 
Integral CUIntPtr # 
Integral CIntPtr # 
Integral CSigAtomic # 
Integral CWchar # 
Integral CSize # 
Integral CPtrdiff # 
Integral CBool # 
Integral CULLong # 
Integral CLLong # 
Integral CULong # 
Integral CLong # 
Integral CUInt # 
Integral CInt # 
Integral CUShort # 
Integral CShort # 
Integral CUChar # 
Integral CSChar # 
Integral CChar # 
Integral Fd # 

Methods

quot :: Fd -> Fd -> Fd Source #

rem :: Fd -> Fd -> Fd Source #

div :: Fd -> Fd -> Fd Source #

mod :: Fd -> Fd -> Fd Source #

quotRem :: Fd -> Fd -> (Fd, Fd) Source #

divMod :: Fd -> Fd -> (Fd, Fd) Source #

toInteger :: Fd -> Integer Source #

Integral CKey # 
Integral CId # 

Methods

quot :: CId -> CId -> CId Source #

rem :: CId -> CId -> CId Source #

div :: CId -> CId -> CId Source #

mod :: CId -> CId -> CId Source #

quotRem :: CId -> CId -> (CId, CId) Source #

divMod :: CId -> CId -> (CId, CId) Source #

toInteger :: CId -> Integer Source #

Integral CFsFilCnt # 
Integral CFsBlkCnt # 
Integral CClockId # 
Integral CBlkCnt # 
Integral CBlkSize # 
Integral CRLim # 
Integral CTcflag # 
Integral CUid # 
Integral CNlink # 
Integral CGid # 
Integral CSsize # 
Integral CPid # 
Integral COff # 
Integral CMode # 
Integral CIno # 
Integral CDev # 
Integral a => Integral (Identity a) # 
Integral a => Integral (Const k a b) # 

Methods

quot :: Const k a b -> Const k a b -> Const k a b Source #

rem :: Const k a b -> Const k a b -> Const k a b Source #

div :: Const k a b -> Const k a b -> Const k a b Source #

mod :: Const k a b -> Const k a b -> Const k a b Source #

quotRem :: Const k a b -> Const k a b -> (Const k a b, Const k a b) Source #

divMod :: Const k a b -> Const k a b -> (Const k a b, Const k a b) Source #

toInteger :: Const k a b -> Integer Source #

class Num a => Fractional a where Source #

Fractional numbers, supporting real division.

Minimal complete definition

fromRational, (recip | (/))

Methods

(/) :: a -> a -> a infixl 7 Source #

fractional division

recip :: a -> a Source #

reciprocal fraction

fromRational :: Rational -> a Source #

Conversion from a Rational (that is Ratio Integer). A floating literal stands for an application of fromRational to a value of type Rational, so such literals have type (Fractional a) => a.

class Fractional a => Floating a where Source #

Trigonometric and hyperbolic functions and related functions.

Minimal complete definition

pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh

Methods

pi :: a Source #

exp, log, sqrt :: a -> a Source #

(**), logBase :: a -> a -> a infixr 8 Source #

sin, cos, tan :: a -> a Source #

asin, acos, atan :: a -> a Source #

sinh, cosh, tanh :: a -> a Source #

asinh, acosh, atanh :: a -> a Source #

Instances

Floating Double #

Since: 2.1

Floating Float #

Since: 2.1

Floating CDouble # 
Floating CFloat # 
Floating a => Floating (Identity a) # 
RealFloat a => Floating (Complex a) #

Since: 2.1

Floating a => Floating (Const k a b) # 

Methods

pi :: Const k a b Source #

exp :: Const k a b -> Const k a b Source #

log :: Const k a b -> Const k a b Source #

sqrt :: Const k a b -> Const k a b Source #

(**) :: Const k a b -> Const k a b -> Const k a b Source #

logBase :: Const k a b -> Const k a b -> Const k a b Source #

sin :: Const k a b -> Const k a b Source #

cos :: Const k a b -> Const k a b Source #

tan :: Const k a b -> Const k a b Source #

asin :: Const k a b -> Const k a b Source #

acos :: Const k a b -> Const k a b Source #

atan :: Const k a b -> Const k a b Source #

sinh :: Const k a b -> Const k a b Source #

cosh :: Const k a b -> Const k a b Source #

tanh :: Const k a b -> Const k a b Source #

asinh :: Const k a b -> Const k a b Source #

acosh :: Const k a b -> Const k a b Source #

atanh :: Const k a b -> Const k a b Source #

log1p :: Const k a b -> Const k a b Source #

expm1 :: Const k a b -> Const k a b Source #

log1pexp :: Const k a b -> Const k a b Source #

log1mexp :: Const k a b -> Const k a b Source #

class (Real a, Fractional a) => RealFrac a where Source #

Extracting components of fractions.

Minimal complete definition

properFraction

Methods

properFraction :: Integral b => a -> (b, a) Source #

The function properFraction takes a real fractional number x and returns a pair (n,f) such that x = n+f, and:

  • n is an integral number with the same sign as x; and
  • f is a fraction with the same type and sign as x, and with absolute value less than 1.

The default definitions of the ceiling, floor, truncate and round functions are in terms of properFraction.

truncate :: Integral b => a -> b Source #

truncate x returns the integer nearest x between zero and x

round :: Integral b => a -> b Source #

round x returns the nearest integer to x; the even integer if x is equidistant between two integers

ceiling :: Integral b => a -> b Source #

ceiling x returns the least integer not less than x

floor :: Integral b => a -> b Source #

floor x returns the greatest integer not greater than x

Instances

RealFrac CDouble # 
RealFrac CFloat # 
Integral a => RealFrac (Ratio a) #

Since: 2.0.1

Methods

properFraction :: Integral b => Ratio a -> (b, Ratio a) Source #

truncate :: Integral b => Ratio a -> b Source #

round :: Integral b => Ratio a -> b Source #

ceiling :: Integral b => Ratio a -> b Source #

floor :: Integral b => Ratio a -> b Source #

RealFrac a => RealFrac (Identity a) # 

Methods

properFraction :: Integral b => Identity a -> (b, Identity a) Source #

truncate :: Integral b => Identity a -> b Source #

round :: Integral b => Identity a -> b Source #

ceiling :: Integral b => Identity a -> b Source #

floor :: Integral b => Identity a -> b Source #

HasResolution a => RealFrac (Fixed a) #

Since: 2.1

Methods

properFraction :: Integral b => Fixed a -> (b, Fixed a) Source #

truncate :: Integral b => Fixed a -> b Source #

round :: Integral b => Fixed a -> b Source #

ceiling :: Integral b => Fixed a -> b Source #

floor :: Integral b => Fixed a -> b Source #

RealFrac a => RealFrac (Const k a b) # 

Methods

properFraction :: Integral b => Const k a b -> (b, Const k a b) Source #

truncate :: Integral b => Const k a b -> b Source #

round :: Integral b => Const k a b -> b Source #

ceiling :: Integral b => Const k a b -> b Source #

floor :: Integral b => Const k a b -> b Source #

class (RealFrac a, Floating a) => RealFloat a where Source #

Efficient, machine-independent access to the components of a floating-point number.

Methods

floatRadix :: a -> Integer Source #

a constant function, returning the radix of the representation (often 2)

floatDigits :: a -> Int Source #

a constant function, returning the number of digits of floatRadix in the significand

floatRange :: a -> (Int, Int) Source #

a constant function, returning the lowest and highest values the exponent may assume

decodeFloat :: a -> (Integer, Int) Source #

The function decodeFloat applied to a real floating-point number returns the significand expressed as an Integer and an appropriately scaled exponent (an Int). If decodeFloat x yields (m,n), then x is equal in value to m*b^^n, where b is the floating-point radix, and furthermore, either m and n are both zero or else b^(d-1) <= abs m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0). If the type contains a negative zero, also decodeFloat (-0.0) = (0,0). The result of decodeFloat x is unspecified if either of isNaN x or isInfinite x is True.

encodeFloat :: Integer -> Int -> a Source #

encodeFloat performs the inverse of decodeFloat in the sense that for finite x with the exception of -0.0, uncurry encodeFloat (decodeFloat x) = x. encodeFloat m n is one of the two closest representable floating-point numbers to m*b^^n (or ±Infinity if overflow occurs); usually the closer, but if m contains too many bits, the result may be rounded in the wrong direction.

exponent :: a -> Int Source #

exponent corresponds to the second component of decodeFloat. exponent 0 = 0 and for finite nonzero x, exponent x = snd (decodeFloat x) + floatDigits x. If x is a finite floating-point number, it is equal in value to significand x * b ^^ exponent x, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

significand :: a -> a Source #

The first component of decodeFloat, scaled to lie in the open interval (-1,1), either 0.0 or of absolute value >= 1/b, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

scaleFloat :: Int -> a -> a Source #

multiplies a floating-point number by an integer power of the radix

isNaN :: a -> Bool Source #

True if the argument is an IEEE "not-a-number" (NaN) value

isInfinite :: a -> Bool Source #

True if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool Source #

True if the argument is too small to be represented in normalized format

isNegativeZero :: a -> Bool Source #

True if the argument is an IEEE negative zero

isIEEE :: a -> Bool Source #

True if the argument is an IEEE floating point number

atan2 :: a -> a -> a Source #

a version of arctangent taking two real floating-point arguments. For real floating x and y, atan2 y x computes the angle (from the positive x-axis) of the vector from the origin to the point (x,y). atan2 y x returns a value in the range [-pi, pi]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. atan2 y 1, with y in a type that is RealFloat, should return the same value as atan y. A default definition of atan2 is provided, but implementors can provide a more accurate implementation.

Instances

RealFloat Double #

Since: 2.1

RealFloat Float #

Since: 2.1

RealFloat CDouble # 
RealFloat CFloat # 
RealFloat a => RealFloat (Identity a) # 
RealFloat a => RealFloat (Const k a b) # 

Methods

floatRadix :: Const k a b -> Integer Source #

floatDigits :: Const k a b -> Int Source #

floatRange :: Const k a b -> (Int, Int) Source #

decodeFloat :: Const k a b -> (Integer, Int) Source #

encodeFloat :: Integer -> Int -> Const k a b Source #

exponent :: Const k a b -> Int Source #

significand :: Const k a b -> Const k a b Source #

scaleFloat :: Int -> Const k a b -> Const k a b Source #

isNaN :: Const k a b -> Bool Source #

isInfinite :: Const k a b -> Bool Source #

isDenormalized :: Const k a b -> Bool Source #

isNegativeZero :: Const k a b -> Bool Source #

isIEEE :: Const k a b -> Bool Source #

atan2 :: Const k a b -> Const k a b -> Const k a b Source #

Numeric functions

subtract :: Num a => a -> a -> a Source #

the same as flip (-).

Because - is treated specially in the Haskell grammar, (- e) is not a section, but an application of prefix negation. However, (subtract exp) is equivalent to the disallowed section.

even :: Integral a => a -> Bool Source #

odd :: Integral a => a -> Bool Source #

gcd :: Integral a => a -> a -> a Source #

gcd x y is the non-negative factor of both x and y of which every common factor of x and y is also a factor; for example gcd 4 2 = 2, gcd (-4) 6 = 2, gcd 0 4 = 4. gcd 0 0 = 0. (That is, the common divisor that is "greatest" in the divisibility preordering.)

Note: Since for signed fixed-width integer types, abs minBound < 0, the result may be negative if one of the arguments is minBound (and necessarily is if the other is 0 or minBound) for such types.

lcm :: Integral a => a -> a -> a Source #

lcm x y is the smallest positive integer that both x and y divide.

(^) :: (Num a, Integral b) => a -> b -> a infixr 8 Source #

raise a number to a non-negative integral power

(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 Source #

raise a number to an integral power

fromIntegral :: (Integral a, Num b) => a -> b Source #

general coercion from integral types

realToFrac :: (Real a, Fractional b) => a -> b Source #

general coercion to fractional types

Monoids

class Monoid a where Source #

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:

  • mappend mempty x = x
  • mappend x mempty = x
  • mappend x (mappend y z) = mappend (mappend x y) z
  • mconcat = foldr mappend mempty

The method names refer to the monoid of lists under concatenation, but there are many other instances.

Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product.

Minimal complete definition

mempty, mappend

Methods

mempty :: a Source #

Identity of mappend

mappend :: a -> a -> a Source #

An associative operation

mconcat :: [a] -> a Source #

Fold a list using the monoid. For most types, the default definition for mconcat will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

Instances

Monoid Ordering #

Since: 2.1

Monoid () #

Since: 2.1

Methods

mempty :: () Source #

mappend :: () -> () -> () Source #

mconcat :: [()] -> () Source #

Monoid Any #

Since: 2.1

Monoid All #

Since: 2.1

Monoid Lifetime #

mappend takes the longer of two lifetimes.

Since: 4.8.0.0

Monoid Event #

Since: 4.3.1.0

Monoid [a] #

Since: 2.1

Methods

mempty :: [a] Source #

mappend :: [a] -> [a] -> [a] Source #

mconcat :: [[a]] -> [a] Source #

Monoid a => Monoid (Maybe a) #

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S." Since there used to be no "Semigroup" typeclass providing just mappend, we use Monoid instead.

Since: 2.1

Methods

mempty :: Maybe a Source #

mappend :: Maybe a -> Maybe a -> Maybe a Source #

mconcat :: [Maybe a] -> Maybe a Source #

Monoid a => Monoid (IO a) #

Since: 4.9.0.0

Methods

mempty :: IO a Source #

mappend :: IO a -> IO a -> IO a Source #

mconcat :: [IO a] -> IO a Source #

Monoid (Last a) #

Since: 2.1

Methods

mempty :: Last a Source #

mappend :: Last a -> Last a -> Last a Source #

mconcat :: [Last a] -> Last a Source #

Monoid (First a) #

Since: 2.1

Methods

mempty :: First a Source #

mappend :: First a -> First a -> First a Source #

mconcat :: [First a] -> First a Source #

Num a => Monoid (Product a) #

Since: 2.1

Num a => Monoid (Sum a) #

Since: 2.1

Methods

mempty :: Sum a Source #

mappend :: Sum a -> Sum a -> Sum a Source #

mconcat :: [Sum a] -> Sum a Source #

Monoid (Endo a) #

Since: 2.1

Methods

mempty :: Endo a Source #

mappend :: Endo a -> Endo a -> Endo a Source #

mconcat :: [Endo a] -> Endo a Source #

Monoid a => Monoid (Dual a) #

Since: 2.1

Methods

mempty :: Dual a Source #

mappend :: Dual a -> Dual a -> Dual a Source #

mconcat :: [Dual a] -> Dual a Source #

Monoid a => Monoid (Identity a) # 
Semigroup a => Monoid (Option a) #

Since: 4.9.0.0

Monoid m => Monoid (WrappedMonoid m) #

Since: 4.9.0.0

(Ord a, Bounded a) => Monoid (Max a) #

Since: 4.9.0.0

Methods

mempty :: Max a Source #

mappend :: Max a -> Max a -> Max a Source #

mconcat :: [Max a] -> Max a Source #

(Ord a, Bounded a) => Monoid (Min a) #

Since: 4.9.0.0

Methods

mempty :: Min a Source #

mappend :: Min a -> Min a -> Min a Source #

mconcat :: [Min a] -> Min a Source #

Monoid b => Monoid (a -> b) #

Since: 2.1

Methods

mempty :: a -> b Source #

mappend :: (a -> b) -> (a -> b) -> a -> b Source #

mconcat :: [a -> b] -> a -> b Source #

(Monoid a, Monoid b) => Monoid (a, b) #

Since: 2.1

Methods

mempty :: (a, b) Source #

mappend :: (a, b) -> (a, b) -> (a, b) Source #

mconcat :: [(a, b)] -> (a, b) Source #

Monoid (Proxy k s) #

Since: 4.7.0.0

Methods

mempty :: Proxy k s Source #

mappend :: Proxy k s -> Proxy k s -> Proxy k s Source #

mconcat :: [Proxy k s] -> Proxy k s Source #

(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) #

Since: 2.1

Methods

mempty :: (a, b, c) Source #

mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) Source #

mconcat :: [(a, b, c)] -> (a, b, c) Source #

Alternative f => Monoid (Alt * f a) #

Since: 4.8.0.0

Methods

mempty :: Alt * f a Source #

mappend :: Alt * f a -> Alt * f a -> Alt * f a Source #

mconcat :: [Alt * f a] -> Alt * f a Source #

Monoid a => Monoid (Const k a b) # 

Methods

mempty :: Const k a b Source #

mappend :: Const k a b -> Const k a b -> Const k a b Source #

mconcat :: [Const k a b] -> Const k a b Source #

(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) #

Since: 2.1

Methods

mempty :: (a, b, c, d) Source #

mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source #

mconcat :: [(a, b, c, d)] -> (a, b, c, d) Source #

(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) #

Since: 2.1

Methods

mempty :: (a, b, c, d, e) Source #

mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source #

mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) Source #

Monads and functors

class Functor f where Source #

The Functor class is used for types that can be mapped over. Instances of Functor should satisfy the following laws:

fmap id  ==  id
fmap (f . g)  ==  fmap f . fmap g

The instances of Functor for lists, Maybe and IO satisfy these laws.

Minimal complete definition

fmap

Methods

fmap :: (a -> b) -> f a -> f b Source #

(<$) :: a -> f b -> f a infixl 4 Source #

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

Instances

Functor [] #

Since: 2.1

Methods

fmap :: (a -> b) -> [a] -> [b] Source #

(<$) :: a -> [b] -> [a] Source #

Functor Maybe #

Since: 2.1

Methods

fmap :: (a -> b) -> Maybe a -> Maybe b Source #

(<$) :: a -> Maybe b -> Maybe a Source #

Functor IO #

Since: 2.1

Methods

fmap :: (a -> b) -> IO a -> IO b Source #

(<$) :: a -> IO b -> IO a Source #

Functor Par1 # 

Methods

fmap :: (a -> b) -> Par1 a -> Par1 b Source #

(<$) :: a -> Par1 b -> Par1 a Source #

Functor ReadP #

Since: 2.1

Methods

fmap :: (a -> b) -> ReadP a -> ReadP b Source #

(<$) :: a -> ReadP b -> ReadP a Source #

Functor ReadPrec #

Since: 2.1

Methods

fmap :: (a -> b) -> ReadPrec a -> ReadPrec b Source #

(<$) :: a -> ReadPrec b -> ReadPrec a Source #

Functor Last # 

Methods

fmap :: (a -> b) -> Last a -> Last b Source #

(<$) :: a -> Last b -> Last a Source #

Functor First # 

Methods

fmap :: (a -> b) -> First a -> First b Source #

(<$) :: a -> First b -> First a Source #

Functor Product #

Since: 4.8.0.0

Methods

fmap :: (a -> b) -> Product a -> Product b Source #

(<$) :: a -> Product b -> Product a Source #

Functor Sum #

Since: 4.8.0.0

Methods

fmap :: (a -> b) -> Sum a -> Sum b Source #

(<$) :: a -> Sum b -> Sum a Source #

Functor Dual #

Since: 4.8.0.0

Methods

fmap :: (a -> b) -> Dual a -> Dual b Source #

(<$) :: a -> Dual b -> Dual a Source #

Functor STM #

Since: 4.3.0.0

Methods

fmap :: (a -> b) -> STM a -> STM b Source #

(<$) :: a -> STM b -> STM a Source #

Functor Handler #

Since: 4.6.0.0

Methods

fmap :: (a -> b) -> Handler a -> Handler b Source #

(<$) :: a -> Handler b -> Handler a Source #

Functor Identity #

Since: 4.8.0.0

Methods

fmap :: (a -> b) -> Identity a -> Identity b Source #

(<$) :: a -> Identity b -> Identity a Source #

Functor ZipList # 

Methods

fmap :: (a -> b) -> ZipList a -> ZipList b Source #

(<$) :: a -> ZipList b -> ZipList a Source #

Functor ArgDescr #

Since: 4.6.0.0

Methods

fmap :: (a -> b) -> ArgDescr a -> ArgDescr b Source #

(<$) :: a -> ArgDescr b -> ArgDescr a Source #

Functor OptDescr #

Since: 4.6.0.0

Methods

fmap :: (a -> b) -> OptDescr a -> OptDescr b Source #

(<$) :: a -> OptDescr b -> OptDescr a Source #

Functor ArgOrder #

Since: 4.6.0.0

Methods

fmap :: (a -> b) -> ArgOrder a -> ArgOrder b Source #

(<$) :: a -> ArgOrder b -> ArgOrder a Source #

Functor NonEmpty #

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source #

(<$) :: a -> NonEmpty b -> NonEmpty a Source #

Functor Option #

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Option a -> Option b Source #

(<$) :: a -> Option b -> Option a Source #

Functor Last #

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Last a -> Last b Source #

(<$) :: a -> Last b -> Last a Source #

Functor First #

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> First a -> First b Source #

(<$) :: a -> First b -> First a Source #

Functor Max #

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Max a -> Max b Source #

(<$) :: a -> Max b -> Max a Source #

Functor Min #

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Min a -> Min b Source #

(<$) :: a -> Min b -> Min a Source #

Functor Complex # 

Methods

fmap :: (a -> b) -> Complex a -> Complex b Source #

(<$) :: a -> Complex b -> Complex a Source #

Functor (Either a) #

Since: 3.0

Methods

fmap :: (a -> b) -> Either a a -> Either a b Source #

(<$) :: a -> Either a b -> Either a a Source #

Functor (V1 *) # 

Methods

fmap :: (a -> b) -> V1 * a -> V1 * b Source #

(<$) :: a -> V1 * b -> V1 * a Source #

Functor (U1 *) #

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> U1 * a -> U1 * b Source #

(<$) :: a -> U1 * b -> U1 * a Source #

Functor ((,) a) #

Since: 2.1

Methods

fmap :: (a -> b) -> (a, a) -> (a, b) Source #

(<$) :: a -> (a, b) -> (a, a) Source #

Functor (ST s) #

Since: 2.1

Methods

fmap :: (a -> b) -> ST s a -> ST s b Source #

(<$) :: a -> ST s b -> ST s a Source #

Functor (Proxy *) #

Since: 4.7.0.0

Methods

fmap :: (a -> b) -> Proxy * a -> Proxy * b Source #

(<$) :: a -> Proxy * b -> Proxy * a Source #

Arrow a => Functor (ArrowMonad a) #

Since: 4.6.0.0

Methods

fmap :: (a -> b) -> ArrowMonad a a -> ArrowMonad a b Source #

(<$) :: a -> ArrowMonad a b -> ArrowMonad a a Source #

Monad m => Functor (WrappedMonad m) #

Since: 2.1

Methods

fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source #

(<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source #

Functor (ST s) #

Since: 2.1

Methods

fmap :: (a -> b) -> ST s a -> ST s b Source #

(<$) :: a -> ST s b -> ST s a Source #

Functor (Arg a) #

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Arg a a -> Arg a b Source #

(<$) :: a -> Arg a b -> Arg a a Source #

Functor f => Functor (Rec1 * f) # 

Methods

fmap :: (a -> b) -> Rec1 * f a -> Rec1 * f b Source #

(<$) :: a -> Rec1 * f b -> Rec1 * f a Source #

Functor (URec * Char) # 

Methods

fmap :: (a -> b) -> URec * Char a -> URec * Char b Source #

(<$) :: a -> URec * Char b -> URec * Char a Source #

Functor (URec * Double) # 

Methods

fmap :: (a -> b) -> URec * Double a -> URec * Double b Source #

(<$) :: a -> URec * Double b -> URec * Double a Source #

Functor (URec * Float) # 

Methods

fmap :: (a -> b) -> URec * Float a -> URec * Float b Source #

(<$) :: a -> URec * Float b -> URec * Float a Source #

Functor (URec * Int) # 

Methods

fmap :: (a -> b) -> URec * Int a -> URec * Int b Source #

(<$) :: a -> URec * Int b -> URec * Int a Source #

Functor (URec * Word) # 

Methods

fmap :: (a -> b) -> URec * Word a -> URec * Word b Source #

(<$) :: a -> URec * Word b -> URec * Word a Source #

Functor (URec * (Ptr ())) # 

Methods

fmap :: (a -> b) -> URec * (Ptr ()) a -> URec * (Ptr ()) b Source #

(<$) :: a -> URec * (Ptr ()) b -> URec * (Ptr ()) a Source #

Functor f => Functor (Alt * f) # 

Methods

fmap :: (a -> b) -> Alt * f a -> Alt * f b Source #

(<$) :: a -> Alt * f b -> Alt * f a Source #

Functor (Const * m) #

Since: 2.1

Methods

fmap :: (a -> b) -> Const * m a -> Const * m b Source #

(<$) :: a -> Const * m b -> Const * m a Source #

Arrow a => Functor (WrappedArrow a b) #

Since: 2.1

Methods

fmap :: (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b Source #

(<$) :: a -> WrappedArrow a b b -> WrappedArrow a b a Source #

Functor ((->) LiftedRep LiftedRep r) #

Since: 2.1

Methods

fmap :: (a -> b) -> (LiftedRep -> LiftedRep) r a -> (LiftedRep -> LiftedRep) r b Source #

(<$) :: a -> (LiftedRep -> LiftedRep) r b -> (LiftedRep -> LiftedRep) r a Source #

Functor (K1 * i c) # 

Methods

fmap :: (a -> b) -> K1 * i c a -> K1 * i c b Source #

(<$) :: a -> K1 * i c b -> K1 * i c a Source #

(Functor g, Functor f) => Functor ((:+:) * f g) # 

Methods

fmap :: (a -> b) -> (* :+: f) g a -> (* :+: f) g b Source #

(<$) :: a -> (* :+: f) g b -> (* :+: f) g a Source #

(Functor g, Functor f) => Functor ((:*:) * f g) # 

Methods

fmap :: (a -> b) -> (* :*: f) g a -> (* :*: f) g b Source #

(<$) :: a -> (* :*: f) g b -> (* :*: f) g a Source #

(Functor f, Functor g) => Functor (Sum * f g) #

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Sum * f g a -> Sum * f g b Source #

(<$) :: a -> Sum * f g b -> Sum * f g a Source #

(Functor f, Functor g) => Functor (Product * f g) #

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Product * f g a -> Product * f g b Source #

(<$) :: a -> Product * f g b -> Product * f g a Source #

Functor f => Functor (M1 * i c f) # 

Methods

fmap :: (a -> b) -> M1 * i c f a -> M1 * i c f b Source #

(<$) :: a -> M1 * i c f b -> M1 * i c f a Source #

(Functor g, Functor f) => Functor ((:.:) * * f g) # 

Methods

fmap :: (a -> b) -> (* :.: *) f g a -> (* :.: *) f g b Source #

(<$) :: a -> (* :.: *) f g b -> (* :.: *) f g a Source #

(Functor f, Functor g) => Functor (Compose * * f g) #

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Compose * * f g a -> Compose * * f g b Source #

(<$) :: a -> Compose * * f g b -> Compose * * f g a Source #

(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 Source #

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

Convert from a Maybe Int to a Maybe String using show:

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

Convert from an Either Int Int to an Either Int String using show:

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

Double each element of a list:

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

Apply even to the second element of a pair:

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

class Functor f => Applicative f where Source #

A functor with application, providing operations to

  • embed pure expressions (pure), and
  • sequence computations and combine their results (<*> and liftA2).

A minimal complete definition must include implementations of pure and of either <*> or liftA2. If it defines both, then they must behave the same as their default definitions:

(<*>) = liftA2 id liftA2 f x y = f <$> x <*> y

Further, any definition must satisfy the following:

identity
pure id <*> v = v
composition
pure (.) <*> u <*> v <*> w = u <*> (v <*> w)
homomorphism
pure f <*> pure x = pure (f x)
interchange
u <*> pure y = pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

As a consequence of these laws, the Functor instance for f will satisfy

It may be useful to note that supposing

forall x y. p (q x y) = f x . g y

it follows from the above that

liftA2 p (liftA2 q u v) = liftA2 f u . liftA2 g v

If f is also a Monad, it should satisfy

(which implies that pure and <*> satisfy the applicative functor laws).

Minimal complete definition

pure, ((<*>) | liftA2)

Methods

pure :: a -> f a Source #

Lift a value.

(<*>) :: f (a -> b) -> f a -> f b infixl 4 Source #

Sequential application.

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

(*>) :: f a -> f b -> f b infixl 4 Source #

Sequence actions, discarding the value of the first argument.

(<*) :: f a -> f b -> f a infixl 4 Source #

Sequence actions, discarding the value of the second argument.

Instances

Applicative [] #

Since: 2.1

Methods

pure :: a -> [a] Source #

(<*>) :: [a -> b] -> [a] -> [b] Source #

liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c] Source #

(*>) :: [a] -> [b] -> [b] Source #

(<*) :: [a] -> [b] -> [a] Source #

Applicative Maybe #

Since: 2.1

Methods

pure :: a -> Maybe a Source #

(<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b Source #

liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c Source #

(*>) :: Maybe a -> Maybe b -> Maybe b Source #

(<*) :: Maybe a -> Maybe b -> Maybe a Source #

Applicative IO #

Since: 2.1

Methods

pure :: a -> IO a Source #

(<*>) :: IO (a -> b) -> IO a -> IO b Source #

liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c Source #

(*>) :: IO a -> IO b -> IO b Source #

(<*) :: IO a -> IO b -> IO a Source #

Applicative Par1 #

Since: 4.9.0.0

Methods

pure :: a -> Par1 a Source #

(<*>) :: Par1 (a -> b) -> Par1 a -> Par1 b Source #

liftA2 :: (a -> b -> c) -> Par1 a -> Par1 b -> Par1 c Source #

(*>) :: Par1 a -> Par1 b -> Par1 b Source #

(<*) :: Par1 a -> Par1 b -> Par1 a Source #

Applicative ReadP #

Since: 4.6.0.0

Methods

pure :: a -> ReadP a Source #

(<*>) :: ReadP (a -> b) -> ReadP a -> ReadP b Source #

liftA2 :: (a -> b -> c) -> ReadP a -> ReadP b -> ReadP c Source #

(*>) :: ReadP a -> ReadP b -> ReadP b Source #

(<*) :: ReadP a -> ReadP b -> ReadP a Source #

Applicative ReadPrec #

Since: 4.6.0.0

Methods

pure :: a -> ReadPrec a Source #

(<*>) :: ReadPrec (a -> b) -> ReadPrec a -> ReadPrec b Source #

liftA2 :: (a -> b -> c) -> ReadPrec a -> ReadPrec b -> ReadPrec c Source #

(*>) :: ReadPrec a -> ReadPrec b -> ReadPrec b Source #

(<*) :: ReadPrec a -> ReadPrec b -> ReadPrec a Source #

Applicative Last # 

Methods

pure :: a -> Last a Source #

(<*>) :: Last (a -> b) -> Last a -> Last b Source #

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source #

(*>) :: Last a -> Last b -> Last b Source #

(<*) :: Last a -> Last b -> Last a Source #

Applicative First # 

Methods

pure :: a -> First a Source #

(<*>) :: First (a -> b) -> First a -> First b Source #

liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source #

(*>) :: First a -> First b -> First b Source #

(<*) :: First a -> First b -> First a Source #

Applicative Product #

Since: 4.8.0.0

Methods

pure :: a -> Product a Source #

(<*>) :: Product (a -> b) -> Product a -> Product b Source #

liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source #

(*>) :: Product a -> Product b -> Product b Source #

(<*) :: Product a -> Product b -> Product a Source #

Applicative Sum #

Since: 4.8.0.0

Methods

pure :: a -> Sum a Source #

(<*>) :: Sum (a -> b) -> Sum a -> Sum b Source #

liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source #

(*>) :: Sum a -> Sum b -> Sum b Source #

(<*) :: Sum a -> Sum b -> Sum a Source #

Applicative Dual #

Since: 4.8.0.0

Methods

pure :: a -> Dual a Source #

(<*>) :: Dual (a -> b) -> Dual a -> Dual b Source #

liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source #

(*>) :: Dual a -> Dual b -> Dual b Source #

(<*) :: Dual a -> Dual b -> Dual a Source #

Applicative STM #

Since: 4.8.0.0

Methods

pure :: a -> STM a Source #

(<*>) :: STM (a -> b) -> STM a -> STM b Source #

liftA2 :: (a -> b -> c) -> STM a -> STM b -> STM c Source #

(*>) :: STM a -> STM b -> STM b Source #

(<*) :: STM a -> STM b -> STM a Source #

Applicative Identity #

Since: 4.8.0.0

Methods

pure :: a -> Identity a Source #

(<*>) :: Identity (a -> b) -> Identity a -> Identity b Source #

liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c Source #

(*>) :: Identity a -> Identity b -> Identity b Source #

(<*) :: Identity a -> Identity b -> Identity a Source #

Applicative ZipList #
f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsN

ZipList (zipWithN f xs1 ... xsN)

where zipWithN refers to the zipWith function of the appropriate arity (zipWith, zipWith3, zipWith4, ...). For example:

(\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..]
    = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..])
    = ZipList {getZipList = ["a5","b6b6","c7c7c7"]}

Since: 2.1

Methods

pure :: a -> ZipList a Source #

(<*>) :: ZipList (a -> b) -> ZipList a -> ZipList b Source #

liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c Source #

(*>) :: ZipList a -> ZipList b -> ZipList b Source #

(<*) :: ZipList a -> ZipList b -> ZipList a Source #

Applicative NonEmpty #

Since: 4.9.0.0

Methods

pure :: a -> NonEmpty a Source #

(<*>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b Source #

liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c Source #

(*>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source #

(<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a Source #

Applicative Option #

Since: 4.9.0.0

Methods

pure :: a -> Option a Source #

(<*>) :: Option (a -> b) -> Option a -> Option b Source #

liftA2 :: (a -> b -> c) -> Option a -> Option b -> Option c Source #

(*>) :: Option a -> Option b -> Option b Source #

(<*) :: Option a -> Option b -> Option a Source #

Applicative Last #

Since: 4.9.0.0

Methods

pure :: a -> Last a Source #

(<*>) :: Last (a -> b) -> Last a -> Last b Source #

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source #

(*>) :: Last a -> Last b -> Last b Source #

(<*) :: Last a -> Last b -> Last a Source #

Applicative First #

Since: 4.9.0.0

Methods

pure :: a -> First a Source #

(<*>) :: First (a -> b) -> First a -> First b Source #

liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source #

(*>) :: First a -> First b -> First b Source #

(<*) :: First a -> First b -> First a Source #

Applicative Max #

Since: 4.9.0.0

Methods

pure :: a -> Max a Source #

(<*>) :: Max (a -> b) -> Max a -> Max b Source #

liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c Source #

(*>) :: Max a -> Max b -> Max b Source #

(<*) :: Max a -> Max b -> Max a Source #

Applicative Min #

Since: 4.9.0.0

Methods

pure :: a -> Min a Source #

(<*>) :: Min (a -> b) -> Min a -> Min b Source #

liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c Source #

(*>) :: Min a -> Min b -> Min b Source #

(<*) :: Min a -> Min b -> Min a Source #

Applicative Complex #

Since: 4.9.0.0

Methods

pure :: a -> Complex a Source #

(<*>) :: Complex (a -> b) -> Complex a -> Complex b Source #

liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c Source #

(*>) :: Complex a -> Complex b -> Complex b Source #

(<*) :: Complex a -> Complex b -> Complex a Source #

Applicative (Either e) #

Since: 3.0

Methods

pure :: a -> Either e a Source #

(<*>) :: Either e (a -> b) -> Either e a -> Either e b Source #

liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c Source #

(*>) :: Either e a -> Either e b -> Either e b Source #

(<*) :: Either e a -> Either e b -> Either e a Source #

Applicative (U1 *) #

Since: 4.9.0.0

Methods

pure :: a -> U1 * a Source #

(<*>) :: U1 * (a -> b) -> U1 * a -> U1 * b Source #

liftA2 :: (a -> b -> c) -> U1 * a -> U1 * b -> U1 * c Source #

(*>) :: U1 * a -> U1 * b -> U1 * b Source #

(<*) :: U1 * a -> U1 * b -> U1 * a Source #

Monoid a => Applicative ((,) a) #

For tuples, the Monoid constraint on a determines how the first values merge. For example, Strings concatenate:

("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)

Since: 2.1

Methods

pure :: a -> (a, a) Source #

(<*>) :: (a, a -> b) -> (a, a) -> (a, b) Source #

liftA2 :: (a -> b -> c) -> (a, a) -> (a, b) -> (a, c) Source #

(*>) :: (a, a) -> (a, b) -> (a, b) Source #

(<*) :: (a, a) -> (a, b) -> (a, a) Source #

Applicative (ST s) #

Since: 4.4.0.0

Methods

pure :: a -> ST s a Source #

(<*>) :: ST s (a -> b) -> ST s a -> ST s b Source #

liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c Source #

(*>) :: ST s a -> ST s b -> ST s b Source #

(<*) :: ST s a -> ST s b -> ST s a Source #

Applicative (Proxy *) #

Since: 4.7.0.0

Methods

pure :: a -> Proxy * a Source #

(<*>) :: Proxy * (a -> b) -> Proxy * a -> Proxy * b Source #

liftA2 :: (a -> b -> c) -> Proxy * a -> Proxy * b -> Proxy * c Source #

(*>) :: Proxy * a -> Proxy * b -> Proxy * b Source #

(<*) :: Proxy * a -> Proxy * b -> Proxy * a Source #

Arrow a => Applicative (ArrowMonad a) #

Since: 4.6.0.0

Methods

pure :: a -> ArrowMonad a a Source #

(<*>) :: ArrowMonad a (a -> b) -> ArrowMonad a a -> ArrowMonad a b Source #

liftA2 :: (a -> b -> c) -> ArrowMonad a a -> ArrowMonad a b -> ArrowMonad a c Source #

(*>) :: ArrowMonad a a -> ArrowMonad a b -> ArrowMonad a b Source #

(<*) :: ArrowMonad a a -> ArrowMonad a b -> ArrowMonad a a Source #

Monad m => Applicative (WrappedMonad m) #

Since: 2.1

Methods

pure :: a -> WrappedMonad m a Source #

(<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source #

liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c Source #

(*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source #

(<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source #

Applicative (ST s) #

Since: 2.1

Methods

pure :: a -> ST s a Source #

(<*>) :: ST s (a -> b) -> ST s a -> ST s b Source #

liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c Source #

(*>) :: ST s a -> ST s b -> ST s b Source #

(<*) :: ST s a -> ST s b -> ST s a Source #

Applicative f => Applicative (Rec1 * f) #

Since: 4.9.0.0

Methods

pure :: a -> Rec1 * f a Source #

(<*>) :: Rec1 * f (a -> b) -> Rec1 * f a -> Rec1 * f b Source #

liftA2 :: (a -> b -> c) -> Rec1 * f a -> Rec1 * f b -> Rec1 * f c Source #

(*>) :: Rec1 * f a -> Rec1 * f b -> Rec1 * f b Source #

(<*) :: Rec1 * f a -> Rec1 * f b -> Rec1 * f a Source #

Applicative f => Applicative (Alt * f) # 

Methods

pure :: a -> Alt * f a Source #

(<*>) :: Alt * f (a -> b) -> Alt * f a -> Alt * f b Source #

liftA2 :: (a -> b -> c) -> Alt * f a -> Alt * f b -> Alt * f c Source #

(*>) :: Alt * f a -> Alt * f b -> Alt * f b Source #

(<*) :: Alt * f a -> Alt * f b -> Alt * f a Source #

Monoid m => Applicative (Const * m) #

Since: 2.0.1

Methods

pure :: a -> Const * m a Source #

(<*>) :: Const * m (a -> b) -> Const * m a -> Const * m b Source #

liftA2 :: (a -> b -> c) -> Const * m a -> Const * m b -> Const * m c Source #

(*>) :: Const * m a -> Const * m b -> Const * m b Source #

(<*) :: Const * m a -> Const * m b -> Const * m a Source #

Arrow a => Applicative (WrappedArrow a b) #

Since: 2.1

Methods

pure :: a -> WrappedArrow a b a Source #

(<*>) :: WrappedArrow a b (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b Source #

liftA2 :: (a -> b -> c) -> WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b c Source #

(*>) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b b Source #

(<*) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b a Source #

Applicative ((->) LiftedRep LiftedRep a) #

Since: 2.1

Methods

pure :: a -> (LiftedRep -> LiftedRep) a a Source #

(<*>) :: (LiftedRep -> LiftedRep) a (a -> b) -> (LiftedRep -> LiftedRep) a a -> (LiftedRep -> LiftedRep) a b Source #

liftA2 :: (a -> b -> c) -> (LiftedRep -> LiftedRep) a a -> (LiftedRep -> LiftedRep) a b -> (LiftedRep -> LiftedRep) a c Source #

(*>) :: (LiftedRep -> LiftedRep) a a -> (LiftedRep -> LiftedRep) a b -> (LiftedRep -> LiftedRep) a b Source #

(<*) :: (LiftedRep -> LiftedRep) a a -> (LiftedRep -> LiftedRep) a b -> (LiftedRep -> LiftedRep) a a Source #

(Applicative f, Applicative g) => Applicative ((:*:) * f g) #

Since: 4.9.0.0

Methods

pure :: a -> (* :*: f) g a Source #

(<*>) :: (* :*: f) g (a -> b) -> (* :*: f) g a -> (* :*: f) g b Source #

liftA2 :: (a -> b -> c) -> (* :*: f) g a -> (* :*: f) g b -> (* :*: f) g c Source #

(*>) :: (* :*: f) g a -> (* :*: f) g b -> (* :*: f) g b Source #

(<*) :: (* :*: f) g a -> (* :*: f) g b -> (* :*: f) g a Source #

(Applicative f, Applicative g) => Applicative (Product * f g) #

Since: 4.9.0.0

Methods

pure :: a -> Product * f g a Source #

(<*>) :: Product * f g (a -> b) -> Product * f g a -> Product * f g b Source #

liftA2 :: (a -> b -> c) -> Product * f g a -> Product * f g b -> Product * f g c Source #

(*>) :: Product * f g a -> Product * f g b -> Product * f g b Source #

(<*) :: Product * f g a -> Product * f g b -> Product * f g a Source #

Applicative f => Applicative (M1 * i c f) #

Since: 4.9.0.0

Methods

pure :: a -> M1 * i c f a Source #

(<*>) :: M1 * i c f (a -> b) -> M1 * i c f a -> M1 * i c f b Source #

liftA2 :: (a -> b -> c) -> M1 * i c f a -> M1 * i c f b -> M1 * i c f c Source #

(*>) :: M1 * i c f a -> M1 * i c f b -> M1 * i c f b Source #

(<*) :: M1 * i c f a -> M1 * i c f b -> M1 * i c f a Source #

(Applicative f, Applicative g) => Applicative ((:.:) * * f g) #

Since: 4.9.0.0

Methods

pure :: a -> (* :.: *) f g a Source #

(<*>) :: (* :.: *) f g (a -> b) -> (* :.: *) f g a -> (* :.: *) f g b Source #

liftA2 :: (a -> b -> c) -> (* :.: *) f g a -> (* :.: *) f g b -> (* :.: *) f g c Source #

(*>) :: (* :.: *) f g a -> (* :.: *) f g b -> (* :.: *) f g b Source #

(<*) :: (* :.: *) f g a -> (* :.: *) f g b -> (* :.: *) f g a Source #

(Applicative f, Applicative g) => Applicative (Compose * * f g) #

Since: 4.9.0.0

Methods

pure :: a -> Compose * * f g a Source #

(<*>) :: Compose * * f g (a -> b) -> Compose * * f g a -> Compose * * f g b Source #

liftA2 :: (a -> b -> c) -> Compose * * f g a -> Compose * * f g b -> Compose * * f g c Source #

(*>) :: Compose * * f g a -> Compose * * f g b -> Compose * * f g b Source #

(<*) :: Compose * * f g a -> Compose * * f g b -> Compose * * f g a Source #

class Applicative m => Monad m where Source #

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Instances of Monad should satisfy the following laws:

Furthermore, the Monad and Applicative operations should relate as follows:

The above laws imply:

and that pure and (<*>) satisfy the applicative functor laws.

The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=)

Methods

(>>=) :: forall a b. m a -> (a -> m b) -> m b infixl 1 Source #

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

(>>) :: forall a b. m a -> m b -> m b infixl 1 Source #

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

return :: a -> m a Source #

Inject a value into the monadic type.

fail :: String -> m a Source #

Fail with a message. This operation is not part of the mathematical definition of a monad, but is invoked on pattern-match failure in a do expression.

As part of the MonadFail proposal (MFP), this function is moved to its own class MonadFail (see Control.Monad.Fail for more details). The definition here will be removed in a future release.

Instances

Monad [] #

Since: 2.1

Methods

(>>=) :: [a] -> (a -> [b]) -> [b] Source #

(>>) :: [a] -> [b] -> [b] Source #

return :: a -> [a] Source #

fail :: String -> [a] Source #

Monad Maybe #

Since: 2.1

Methods

(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b Source #

(>>) :: Maybe a -> Maybe b -> Maybe b Source #

return :: a -> Maybe a Source #

fail :: String -> Maybe a Source #

Monad IO #

Since: 2.1

Methods

(>>=) :: IO a -> (a -> IO b) -> IO b Source #

(>>) :: IO a -> IO b -> IO b Source #

return :: a -> IO a Source #

fail :: String -> IO a Source #

Monad Par1 #

Since: 4.9.0.0

Methods

(>>=) :: Par1 a -> (a -> Par1 b) -> Par1 b Source #

(>>) :: Par1 a -> Par1 b -> Par1 b Source #

return :: a -> Par1 a Source #

fail :: String -> Par1 a Source #

Monad ReadP #

Since: 2.1

Methods

(>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b Source #

(>>) :: ReadP a -> ReadP b -> ReadP b Source #

return :: a -> ReadP a Source #

fail :: String -> ReadP a Source #

Monad ReadPrec #

Since: 2.1

Methods

(>>=) :: ReadPrec a -> (a -> ReadPrec b) -> ReadPrec b Source #

(>>) :: ReadPrec a -> ReadPrec b -> ReadPrec b Source #

return :: a -> ReadPrec a Source #

fail :: String -> ReadPrec a Source #

Monad Last # 

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b Source #

(>>) :: Last a -> Last b -> Last b Source #

return :: a -> Last a Source #

fail :: String -> Last a Source #

Monad First # 

Methods

(>>=) :: First a -> (a -> First b) -> First b Source #

(>>) :: First a -> First b -> First b Source #

return :: a -> First a Source #

fail :: String -> First a Source #

Monad Product #

Since: 4.8.0.0

Methods

(>>=) :: Product a -> (a -> Product b) -> Product b Source #

(>>) :: Product a -> Product b -> Product b Source #

return :: a -> Product a Source #

fail :: String -> Product a Source #

Monad Sum #

Since: 4.8.0.0

Methods

(>>=) :: Sum a -> (a -> Sum b) -> Sum b Source #

(>>) :: Sum a -> Sum b -> Sum b Source #

return :: a -> Sum a Source #

fail :: String -> Sum a Source #

Monad Dual #

Since: 4.8.0.0

Methods

(>>=) :: Dual a -> (a -> Dual b) -> Dual b Source #

(>>) :: Dual a -> Dual b -> Dual b Source #

return :: a -> Dual a Source #

fail :: String -> Dual a Source #

Monad STM #

Since: 4.3.0.0

Methods

(>>=) :: STM a -> (a -> STM b) -> STM b Source #

(>>) :: STM a -> STM b -> STM b Source #

return :: a -> STM a Source #

fail :: String -> STM a Source #

Monad Identity #

Since: 4.8.0.0

Methods

(>>=) :: Identity a -> (a -> Identity b) -> Identity b Source #

(>>) :: Identity a -> Identity b -> Identity b Source #

return :: a -> Identity a Source #

fail :: String -> Identity a Source #

Monad NonEmpty #

Since: 4.9.0.0

Methods

(>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b Source #

(>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source #

return :: a -> NonEmpty a Source #

fail :: String -> NonEmpty a Source #

Monad Option #

Since: 4.9.0.0

Methods

(>>=) :: Option a -> (a -> Option b) -> Option b Source #

(>>) :: Option a -> Option b -> Option b Source #

return :: a -> Option a Source #

fail :: String -> Option a Source #

Monad Last #

Since: 4.9.0.0

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b Source #

(>>) :: Last a -> Last b -> Last b Source #

return :: a -> Last a Source #

fail :: String -> Last a Source #

Monad First #

Since: 4.9.0.0

Methods

(>>=) :: First a -> (a -> First b) -> First b Source #

(>>) :: First a -> First b -> First b Source #

return :: a -> First a Source #

fail :: String -> First a Source #

Monad Max #

Since: 4.9.0.0

Methods

(>>=) :: Max a -> (a -> Max b) -> Max b Source #

(>>) :: Max a -> Max b -> Max b Source #

return :: a -> Max a Source #

fail :: String -> Max a Source #

Monad Min #

Since: 4.9.0.0

Methods

(>>=) :: Min a -> (a -> Min b) -> Min b Source #

(>>) :: Min a -> Min b -> Min b Source #

return :: a -> Min a Source #

fail :: String -> Min a Source #

Monad Complex #

Since: 4.9.0.0

Methods

(>>=) :: Complex a -> (a -> Complex b) -> Complex b Source #

(>>) :: Complex a -> Complex b -> Complex b Source #

return :: a -> Complex a Source #

fail :: String -> Complex a Source #

Monad (Either e) #

Since: 4.4.0.0

Methods

(>>=) :: Either e a -> (a -> Either e b) -> Either e b Source #

(>>) :: Either e a -> Either e b -> Either e b Source #

return :: a -> Either e a Source #

fail :: String -> Either e a Source #

Monad (U1 *) #

Since: 4.9.0.0

Methods

(>>=) :: U1 * a -> (a -> U1 * b) -> U1 * b Source #

(>>) :: U1 * a -> U1 * b -> U1 * b Source #

return :: a -> U1 * a Source #

fail :: String -> U1 * a Source #

Monoid a => Monad ((,) a) #

Since: 4.9.0.0

Methods

(>>=) :: (a, a) -> (a -> (a, b)) -> (a, b) Source #

(>>) :: (a, a) -> (a, b) -> (a, b) Source #

return :: a -> (a, a) Source #

fail :: String -> (a, a) Source #

Monad (ST s) #

Since: 2.1

Methods

(>>=) :: ST s a -> (a -> ST s b) -> ST s b Source #

(>>) :: ST s a -> ST s b -> ST s b Source #

return :: a -> ST s a Source #

fail :: String -> ST s a Source #

Monad (Proxy *) #

Since: 4.7.0.0

Methods

(>>=) :: Proxy * a -> (a -> Proxy * b) -> Proxy * b Source #

(>>) :: Proxy * a -> Proxy * b -> Proxy * b Source #

return :: a -> Proxy * a Source #

fail :: String -> Proxy * a Source #

ArrowApply a => Monad (ArrowMonad a) #

Since: 2.1

Methods

(>>=) :: ArrowMonad a a -> (a -> ArrowMonad a b) -> ArrowMonad a b Source #

(>>) :: ArrowMonad a a -> ArrowMonad a b -> ArrowMonad a b Source #

return :: a -> ArrowMonad a a Source #

fail :: String -> ArrowMonad a a Source #

Monad m => Monad (WrappedMonad m) # 
Monad (ST s) #

Since: 2.1

Methods

(>>=) :: ST s a -> (a -> ST s b) -> ST s b Source #

(>>) :: ST s a -> ST s b -> ST s b Source #

return :: a -> ST s a Source #

fail :: String -> ST s a Source #

Monad f => Monad (Rec1 * f) #

Since: 4.9.0.0

Methods

(>>=) :: Rec1 * f a -> (a -> Rec1 * f b) -> Rec1 * f b Source #

(>>) :: Rec1 * f a -> Rec1 * f b -> Rec1 * f b Source #

return :: a -> Rec1 * f a Source #

fail :: String -> Rec1 * f a Source #

Monad f => Monad (Alt * f) # 

Methods

(>>=) :: Alt * f a -> (a -> Alt * f b) -> Alt * f b Source #

(>>) :: Alt * f a -> Alt * f b -> Alt * f b Source #

return :: a -> Alt * f a Source #

fail :: String -> Alt * f a Source #

Monad ((->) LiftedRep LiftedRep r) #

Since: 2.1

Methods

(>>=) :: (LiftedRep -> LiftedRep) r a -> (a -> (LiftedRep -> LiftedRep) r b) -> (LiftedRep -> LiftedRep) r b Source #

(>>) :: (LiftedRep -> LiftedRep) r a -> (LiftedRep -> LiftedRep) r b -> (LiftedRep -> LiftedRep) r b Source #

return :: a -> (LiftedRep -> LiftedRep) r a Source #

fail :: String -> (LiftedRep -> LiftedRep) r a Source #

(Monad f, Monad g) => Monad ((:*:) * f g) #

Since: 4.9.0.0

Methods

(>>=) :: (* :*: f) g a -> (a -> (* :*: f) g b) -> (* :*: f) g b Source #

(>>) :: (* :*: f) g a -> (* :*: f) g b -> (* :*: f) g b Source #

return :: a -> (* :*: f) g a Source #

fail :: String -> (* :*: f) g a Source #

(Monad f, Monad g) => Monad (Product * f g) #

Since: 4.9.0.0

Methods

(>>=) :: Product * f g a -> (a -> Product * f g b) -> Product * f g b Source #

(>>) :: Product * f g a -> Product * f g b -> Product * f g b Source #

return :: a -> Product * f g a Source #

fail :: String -> Product * f g a Source #

Monad f => Monad (M1 * i c f) #

Since: 4.9.0.0

Methods

(>>=) :: M1 * i c f a -> (a -> M1 * i c f b) -> M1 * i c f b Source #

(>>) :: M1 * i c f a -> M1 * i c f b -> M1 * i c f b Source #

return :: a -> M1 * i c f a Source #

fail :: String -> M1 * i c f a Source #

mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m () Source #

Map each element of a structure to a monadic action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see mapM.

As of base 4.8.0.0, mapM_ is just traverse_, specialized to Monad.

sequence_ :: (Foldable t, Monad m) => t (m a) -> m () Source #

Evaluate each monadic action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequence.

As of base 4.8.0.0, sequence_ is just sequenceA_, specialized to Monad.

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source #

Same as >>=, but with the arguments interchanged.

Folds and traversals

class Foldable t where Source #

Data structures that can be folded.

For example, given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Foldable Tree where
   foldMap f Empty = mempty
   foldMap f (Leaf x) = f x
   foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r

This is suitable even for abstract types, as the monoid is assumed to satisfy the monoid laws. Alternatively, one could define foldr:

instance Foldable Tree where
   foldr f z Empty = z
   foldr f z (Leaf x) = f x z
   foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l

Foldable instances are expected to satisfy the following laws:

foldr f z t = appEndo (foldMap (Endo . f) t ) z
foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
fold = foldMap id

sum, product, maximum, and minimum should all be essentially equivalent to foldMap forms, such as

sum = getSum . foldMap Sum

but may be less defined.

If the type is also a Functor instance, it should satisfy

foldMap f = fold . fmap f

which implies that

foldMap f . fmap g = foldMap (f . g)

Minimal complete definition

foldMap | foldr

Methods

foldMap :: Monoid m => (a -> m) -> t a -> m Source #

Map each element of the structure to a monoid, and combine the results.

foldr :: (a -> b -> b) -> b -> t a -> b Source #

Right-associative fold of a structure.

In the case of lists, foldr, when applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)

Note that, since the head of the resulting expression is produced by an application of the operator to the first element of the list, foldr can produce a terminating expression from an infinite list.

For a general Foldable structure this should be semantically identical to,

foldr f z = foldr f z . toList

foldl :: (b -> a -> b) -> b -> t a -> b Source #

Left-associative fold of a structure.

In the case of lists, foldl, when applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, reduces the list using the binary operator, from left to right:

foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn

Note that to produce the outermost application of the operator the entire input list must be traversed. This means that foldl' will diverge if given an infinite list.

Also note that if you want an efficient left-fold, you probably want to use foldl' instead of foldl. The reason for this is that latter does not force the "inner" results (e.g. z f x1 in the above example) before applying them to the operator (e.g. to (f x2)). This results in a thunk chain O(n) elements long, which then must be evaluated from the outside-in.

For a general Foldable structure this should be semantically identical to,

foldl f z = foldl f z . toList

foldr1 :: (a -> a -> a) -> t a -> a Source #

A variant of foldr that has no base case, and thus may only be applied to non-empty structures.

foldr1 f = foldr1 f . toList

foldl1 :: (a -> a -> a) -> t a -> a Source #

A variant of foldl that has no base case, and thus may only be applied to non-empty structures.

foldl1 f = foldl1 f . toList

null :: t a -> Bool Source #

Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

length :: t a -> Int Source #

Returns the size/length of a finite structure as an Int. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

elem :: Eq a => a -> t a -> Bool infix 4 Source #

Does the element occur in the structure?

maximum :: forall a. Ord a => t a -> a Source #

The largest element of a non-empty structure.

minimum :: forall a. Ord a => t a -> a Source #

The least element of a non-empty structure.

sum :: Num a => t a -> a Source #

The sum function computes the sum of the numbers of a structure.

product :: Num a => t a -> a Source #

The product function computes the product of the numbers of a structure.

Instances

Foldable [] #

Since: 2.1

Methods

fold :: Monoid m => [m] -> m Source #

foldMap :: Monoid m => (a -> m) -> [a] -> m Source #

foldr :: (a -> b -> b) -> b -> [a] -> b Source #

foldr' :: (a -> b -> b) -> b -> [a] -> b Source #

foldl :: (b -> a -> b) -> b -> [a] -> b Source #

foldl' :: (b -> a -> b) -> b -> [a] -> b Source #

foldr1 :: (a -> a -> a) -> [a] -> a Source #

foldl1 :: (a -> a -> a) -> [a] -> a Source #

toList :: [a] -> [a] Source #

null :: [a] -> Bool Source #

length :: [a] -> Int Source #

elem :: Eq a => a -> [a] -> Bool Source #

maximum :: Ord a => [a] -> a Source #

minimum :: Ord a => [a] -> a Source #

sum :: Num a => [a] -> a Source #

product :: Num a => [a] -> a Source #

Foldable Maybe #

Since: 2.1

Methods

fold :: Monoid m => Maybe m -> m Source #

foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source #

foldr :: (a -> b -> b) -> b -> Maybe a -> b Source #

foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source #

foldl :: (b -> a -> b) -> b -> Maybe a -> b Source #

foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source #

foldr1 :: (a -> a -> a) -> Maybe a -> a Source #

foldl1 :: (a -> a -> a) -> Maybe a -> a Source #

toList :: Maybe a -> [a] Source #

null :: Maybe a -> Bool Source #

length :: Maybe a -> Int Source #

elem :: Eq a => a -> Maybe a -> Bool Source #

maximum :: Ord a => Maybe a -> a Source #

minimum :: Ord a => Maybe a -> a Source #

sum :: Num a => Maybe a -> a Source #

product :: Num a => Maybe a -> a Source #

Foldable Par1 # 

Methods

fold :: Monoid m => Par1 m -> m Source #

foldMap :: Monoid m => (a -> m) -> Par1 a -> m Source #

foldr :: (a -> b -> b) -> b -> Par1 a -> b Source #

foldr' :: (a -> b -> b) -> b -> Par1 a -> b Source #

foldl :: (b -> a -> b) -> b -> Par1 a -> b Source #

foldl' :: (b -> a -> b) -> b -> Par1 a -> b Source #

foldr1 :: (a -> a -> a) -> Par1 a -> a Source #

foldl1 :: (a -> a -> a) -> Par1 a -> a Source #

toList :: Par1 a -> [a] Source #

null :: Par1 a -> Bool Source #

length :: Par1 a -> Int Source #

elem :: Eq a => a -> Par1 a -> Bool Source #

maximum :: Ord a => Par1 a -> a Source #

minimum :: Ord a => Par1 a -> a Source #

sum :: Num a => Par1 a -> a Source #

product :: Num a => Par1 a -> a Source #

Foldable Last #

Since: 4.8.0.0

Methods

fold :: Monoid m => Last m -> m Source #

foldMap :: Monoid m => (a -> m) -> Last a -> m Source #

foldr :: (a -> b -> b) -> b -> Last a -> b Source #

foldr' :: (a -> b -> b) -> b -> Last a -> b Source #

foldl :: (b -> a -> b) -> b -> Last a -> b Source #

foldl' :: (b -> a -> b) -> b -> Last a -> b Source #

foldr1 :: (a -> a -> a) -> Last a -> a Source #

foldl1 :: (a -> a -> a) -> Last a -> a Source #

toList :: Last a -> [a] Source #

null :: Last a -> Bool Source #

length :: Last a -> Int Source #

elem :: Eq a => a -> Last a -> Bool Source #

maximum :: Ord a => Last a -> a Source #

minimum :: Ord a => Last a -> a Source #

sum :: Num a => Last a -> a Source #

product :: Num a => Last a -> a Source #

Foldable First #

Since: 4.8.0.0

Methods

fold :: Monoid m => First m -> m Source #

foldMap :: Monoid m => (a -> m) -> First a -> m Source #

foldr :: (a -> b -> b) -> b -> First a -> b Source #

foldr' :: (a -> b -> b) -> b -> First a -> b Source #

foldl :: (b -> a -> b) -> b -> First a -> b Source #

foldl' :: (b -> a -> b) -> b -> First a -> b Source #

foldr1 :: (a -> a -> a) -> First a -> a Source #

foldl1 :: (a -> a -> a) -> First a -> a Source #

toList :: First a -> [a] Source #

null :: First a -> Bool Source #

length :: First a -> Int Source #

elem :: Eq a => a -> First a -> Bool Source #

maximum :: Ord a => First a -> a Source #

minimum :: Ord a => First a -> a Source #

sum :: Num a => First a -> a Source #

product :: Num a => First a -> a Source #

Foldable Product #

Since: 4.8.0.0

Methods

fold :: Monoid m => Product m -> m Source #

foldMap :: Monoid m => (a -> m) -> Product a -> m Source #

foldr :: (a -> b -> b) -> b -> Product a -> b Source #

foldr' :: (a -> b -> b) -> b -> Product a -> b Source #

foldl :: (b -> a -> b) -> b -> Product a -> b Source #

foldl' :: (b -> a -> b) -> b -> Product a -> b Source #

foldr1 :: (a -> a -> a) -> Product a -> a Source #

foldl1 :: (a -> a -> a) -> Product a -> a Source #

toList :: Product a -> [a] Source #

null :: Product a -> Bool Source #

length :: Product a -> Int Source #

elem :: Eq a => a -> Product a -> Bool Source #

maximum :: Ord a => Product a -> a Source #

minimum :: Ord a => Product a -> a Source #

sum :: Num a => Product a -> a Source #

product :: Num a => Product a -> a Source #

Foldable Sum #

Since: 4.8.0.0

Methods

fold :: Monoid m => Sum m -> m Source #

foldMap :: Monoid m => (a -> m) -> Sum a -> m Source #

foldr :: (a -> b -> b) -> b -> Sum a -> b Source #

foldr' :: (a -> b -> b) -> b -> Sum a -> b Source #

foldl :: (b -> a -> b) -> b -> Sum a -> b Source #

foldl' :: (b -> a -> b) -> b -> Sum a -> b Source #

foldr1 :: (a -> a -> a) -> Sum a -> a Source #

foldl1 :: (a -> a -> a) -> Sum a -> a Source #

toList :: Sum a -> [a] Source #

null :: Sum a -> Bool Source #

length :: Sum a -> Int Source #

elem :: Eq a => a -> Sum a -> Bool Source #

maximum :: Ord a => Sum a -> a Source #

minimum :: Ord a => Sum a -> a Source #

sum :: Num a => Sum a -> a Source #

product :: Num a => Sum a -> a Source #

Foldable Dual #

Since: 4.8.0.0

Methods

fold :: Monoid m => Dual m -> m Source #

foldMap :: Monoid m => (a -> m) -> Dual a -> m Source #

foldr :: (a -> b -> b) -> b -> Dual a -> b Source #

foldr' :: (a -> b -> b) -> b -> Dual a -> b Source #

foldl :: (b -> a -> b) -> b -> Dual a -> b Source #

foldl' :: (b -> a -> b) -> b -> Dual a -> b Source #

foldr1 :: (a -> a -> a) -> Dual a -> a Source #

foldl1 :: (a -> a -> a) -> Dual a -> a Source #

toList :: Dual a -> [a] Source #

null :: Dual a -> Bool Source #

length :: Dual a -> Int Source #

elem :: Eq a => a -> Dual a -> Bool Source #

maximum :: Ord a => Dual a -> a Source #

minimum :: Ord a => Dual a -> a Source #

sum :: Num a => Dual a -> a Source #

product :: Num a => Dual a -> a Source #

Foldable Identity #

Since: 4.8.0.0

Methods

fold :: Monoid m => Identity m -> m Source #

foldMap :: Monoid m => (a -> m) -> Identity a -> m Source #

foldr :: (a -> b -> b) -> b -> Identity a -> b Source #

foldr' :: (a -> b -> b) -> b -> Identity a -> b Source #

foldl :: (b -> a -> b) -> b -> Identity a -> b Source #

foldl' :: (b -> a -> b) -> b -> Identity a -> b Source #

foldr1 :: (a -> a -> a) -> Identity a -> a Source #

foldl1 :: (a -> a -> a) -> Identity a -> a Source #

toList :: Identity a -> [a] Source #

null :: Identity a -> Bool Source #

length :: Identity a -> Int Source #

elem :: Eq a => a -> Identity a -> Bool Source #

maximum :: Ord a => Identity a -> a Source #

minimum :: Ord a => Identity a -> a Source #

sum :: Num a => Identity a -> a Source #

product :: Num a => Identity a -> a Source #

Foldable ZipList # 

Methods

fold :: Monoid m => ZipList m -> m Source #

foldMap :: Monoid m => (a -> m) -> ZipList a -> m Source #

foldr :: (a -> b -> b) -> b -> ZipList a -> b Source #

foldr' :: (a -> b -> b) -> b -> ZipList a -> b Source #

foldl :: (b -> a -> b) -> b -> ZipList a -> b Source #

foldl' :: (b -> a -> b) -> b -> ZipList a -> b Source #

foldr1 :: (a -> a -> a) -> ZipList a -> a Source #

foldl1 :: (a -> a -> a) -> ZipList a -> a Source #

toList :: ZipList a -> [a] Source #

null :: ZipList a -> Bool Source #

length :: ZipList a -> Int Source #

elem :: Eq a => a -> ZipList a -> Bool Source #

maximum :: Ord a => ZipList a -> a Source #

minimum :: Ord a => ZipList a -> a Source #

sum :: Num a => ZipList a -> a Source #

product :: Num a => ZipList a -> a Source #

Foldable NonEmpty #

Since: 4.9.0.0

Methods

fold :: Monoid m => NonEmpty m -> m Source #

foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m Source #

foldr :: (a -> b -> b) -> b -> NonEmpty a -> b Source #

foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b Source #

foldl :: (b -> a -> b) -> b -> NonEmpty a -> b Source #

foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b Source #

foldr1 :: (a -> a -> a) -> NonEmpty a -> a Source #

foldl1 :: (a -> a -> a) -> NonEmpty a -> a Source #

toList :: NonEmpty a -> [a] Source #

null :: NonEmpty a -> Bool Source #

length :: NonEmpty a -> Int Source #

elem :: Eq a => a -> NonEmpty a -> Bool Source #

maximum :: Ord a => NonEmpty a -> a Source #

minimum :: Ord a => NonEmpty a -> a Source #

sum :: Num a => NonEmpty a -> a Source #

product :: Num a => NonEmpty a -> a Source #

Foldable Option #

Since: 4.9.0.0

Methods

fold :: Monoid m => Option m -> m Source #

foldMap :: Monoid m => (a -> m) -> Option a -> m Source #

foldr :: (a -> b -> b) -> b -> Option a -> b Source #

foldr' :: (a -> b -> b) -> b -> Option a -> b Source #

foldl :: (b -> a -> b) -> b -> Option a -> b Source #

foldl' :: (b -> a -> b) -> b -> Option a -> b Source #

foldr1 :: (a -> a -> a) -> Option a -> a Source #

foldl1 :: (a -> a -> a) -> Option a -> a Source #

toList :: Option a -> [a] Source #

null :: Option a -> Bool Source #

length :: Option a -> Int Source #

elem :: Eq a => a -> Option a -> Bool Source #

maximum :: Ord a => Option a -> a Source #

minimum :: Ord a => Option a -> a Source #

sum :: Num a => Option a -> a Source #

product :: Num a => Option a -> a Source #

Foldable Last #

Since: 4.9.0.0

Methods

fold :: Monoid m => Last m -> m Source #

foldMap :: Monoid m => (a -> m) -> Last a -> m Source #

foldr :: (a -> b -> b) -> b -> Last a -> b Source #

foldr' :: (a -> b -> b) -> b -> Last a -> b Source #

foldl :: (b -> a -> b) -> b -> Last a -> b Source #

foldl' :: (b -> a -> b) -> b -> Last a -> b Source #

foldr1 :: (a -> a -> a) -> Last a -> a Source #

foldl1 :: (a -> a -> a) -> Last a -> a Source #

toList :: Last a -> [a] Source #

null :: Last a -> Bool Source #

length :: Last a -> Int Source #

elem :: Eq a => a -> Last a -> Bool Source #

maximum :: Ord a => Last a -> a Source #

minimum :: Ord a => Last a -> a Source #

sum :: Num a => Last a -> a Source #

product :: Num a => Last a -> a Source #

Foldable First #

Since: 4.9.0.0

Methods

fold :: Monoid m => First m -> m Source #

foldMap :: Monoid m => (a -> m) -> First a -> m Source #

foldr :: (a -> b -> b) -> b -> First a -> b Source #

foldr' :: (a -> b -> b) -> b -> First a -> b Source #

foldl :: (b -> a -> b) -> b -> First a -> b Source #

foldl' :: (b -> a -> b) -> b -> First a -> b Source #

foldr1 :: (a -> a -> a) -> First a -> a Source #

foldl1 :: (a -> a -> a) -> First a -> a Source #

toList :: First a -> [a] Source #

null :: First a -> Bool Source #

length :: First a -> Int Source #

elem :: Eq a => a -> First a -> Bool Source #

maximum :: Ord a => First a -> a Source #

minimum :: Ord a => First a -> a Source #

sum :: Num a => First a -> a Source #

product :: Num a => First a -> a Source #

Foldable Max #

Since: 4.9.0.0

Methods

fold :: Monoid m => Max m -> m Source #

foldMap :: Monoid m => (a -> m) -> Max a -> m Source #

foldr :: (a -> b -> b) -> b -> Max a -> b Source #

foldr' :: (a -> b -> b) -> b -> Max a -> b Source #

foldl :: (b -> a -> b) -> b -> Max a -> b Source #

foldl' :: (b -> a -> b) -> b -> Max a -> b Source #

foldr1 :: (a -> a -> a) -> Max a -> a Source #

foldl1 :: (a -> a -> a) -> Max a -> a Source #

toList :: Max a -> [a] Source #

null :: Max a -> Bool Source #

length :: Max a -> Int Source #

elem :: Eq a => a -> Max a -> Bool Source #

maximum :: Ord a => Max a -> a Source #

minimum :: Ord a => Max a -> a Source #

sum :: Num a => Max a -> a Source #

product :: Num a => Max a -> a Source #

Foldable Min #

Since: 4.9.0.0

Methods

fold :: Monoid m => Min m -> m Source #

foldMap :: Monoid m => (a -> m) -> Min a -> m Source #

foldr :: (a -> b -> b) -> b -> Min a -> b Source #

foldr' :: (a -> b -> b) -> b -> Min a -> b Source #

foldl :: (b -> a -> b) -> b -> Min a -> b Source #

foldl' :: (b -> a -> b) -> b -> Min a -> b Source #

foldr1 :: (a -> a -> a) -> Min a -> a Source #

foldl1 :: (a -> a -> a) -> Min a -> a Source #

toList :: Min a -> [a] Source #

null :: Min a -> Bool Source #

length :: Min a -> Int Source #

elem :: Eq a => a -> Min a -> Bool Source #

maximum :: Ord a => Min a -> a Source #

minimum :: Ord a => Min a -> a Source #

sum :: Num a => Min a -> a Source #

product :: Num a => Min a -> a Source #

Foldable Complex # 

Methods

fold :: Monoid m => Complex m -> m Source #

foldMap :: Monoid m => (a -> m) -> Complex a -> m Source #

foldr :: (a -> b -> b) -> b -> Complex a -> b Source #

foldr' :: (a -> b -> b) -> b -> Complex a -> b Source #

foldl :: (b -> a -> b) -> b -> Complex a -> b Source #

foldl' :: (b -> a -> b) -> b -> Complex a -> b Source #

foldr1 :: (a -> a -> a) -> Complex a -> a Source #

foldl1 :: (a -> a -> a) -> Complex a -> a Source #

toList :: Complex a -> [a] Source #

null :: Complex a -> Bool Source #

length :: Complex a -> Int Source #

elem :: Eq a => a -> Complex a -> Bool Source #

maximum :: Ord a => Complex a -> a Source #

minimum :: Ord a => Complex a -> a Source #

sum :: Num a => Complex a -> a Source #

product :: Num a => Complex a -> a Source #

Foldable (Either a) #

Since: 4.7.0.0

Methods

fold :: Monoid m => Either a m -> m Source #

foldMap :: Monoid m => (a -> m) -> Either a a -> m Source #

foldr :: (a -> b -> b) -> b -> Either a a -> b Source #

foldr' :: (a -> b -> b) -> b -> Either a a -> b Source #

foldl :: (b -> a -> b) -> b -> Either a a -> b Source #

foldl' :: (b -> a -> b) -> b -> Either a a -> b Source #

foldr1 :: (a -> a -> a) -> Either a a -> a Source #

foldl1 :: (a -> a -> a) -> Either a a -> a Source #

toList :: Either a a -> [a] Source #

null :: Either a a -> Bool Source #

length :: Either a a -> Int Source #

elem :: Eq a => a -> Either a a -> Bool Source #

maximum :: Ord a => Either a a -> a Source #

minimum :: Ord a => Either a a -> a Source #

sum :: Num a => Either a a -> a Source #

product :: Num a => Either a a -> a Source #

Foldable (V1 *) # 

Methods

fold :: Monoid m => V1 * m -> m Source #

foldMap :: Monoid m => (a -> m) -> V1 * a -> m Source #

foldr :: (a -> b -> b) -> b -> V1 * a -> b Source #

foldr' :: (a -> b -> b) -> b -> V1 * a -> b Source #

foldl :: (b -> a -> b) -> b -> V1 * a -> b Source #

foldl' :: (b -> a -> b) -> b -> V1 * a -> b Source #

foldr1 :: (a -> a -> a) -> V1 * a -> a Source #

foldl1 :: (a -> a -> a) -> V1 * a -> a Source #

toList :: V1 * a -> [a] Source #

null :: V1 * a -> Bool Source #

length :: V1 * a -> Int Source #

elem :: Eq a => a -> V1 * a -> Bool Source #

maximum :: Ord a => V1 * a -> a Source #

minimum :: Ord a => V1 * a -> a Source #

sum :: Num a => V1 * a -> a Source #

product :: Num a => V1 * a -> a Source #

Foldable (U1 *) #

Since: 4.9.0.0

Methods

fold :: Monoid m => U1 * m -> m Source #

foldMap :: Monoid m => (a -> m) -> U1 * a -> m Source #

foldr :: (a -> b -> b) -> b -> U1 * a -> b Source #

foldr' :: (a -> b -> b) -> b -> U1 * a -> b Source #

foldl :: (b -> a -> b) -> b -> U1 * a -> b Source #

foldl' :: (b -> a -> b) -> b -> U1 * a -> b Source #

foldr1 :: (a -> a -> a) -> U1 * a -> a Source #

foldl1 :: (a -> a -> a) -> U1 * a -> a Source #

toList :: U1 * a -> [a] Source #

null :: U1 * a -> Bool Source #

length :: U1 * a -> Int Source #

elem :: Eq a => a -> U1 * a -> Bool Source #

maximum :: Ord a => U1 * a -> a Source #

minimum :: Ord a => U1 * a -> a Source #

sum :: Num a => U1 * a -> a Source #

product :: Num a => U1 * a -> a Source #

Foldable ((,) a) #

Since: 4.7.0.0

Methods

fold :: Monoid m => (a, m) -> m Source #

foldMap :: Monoid m => (a -> m) -> (a, a) -> m Source #

foldr :: (a -> b -> b) -> b -> (a, a) -> b Source #

foldr' :: (a -> b -> b) -> b -> (a, a) -> b Source #

foldl :: (b -> a -> b) -> b -> (a, a) -> b Source #

foldl' :: (b -> a -> b) -> b -> (a, a) -> b Source #

foldr1 :: (a -> a -> a) -> (a, a) -> a Source #

foldl1 :: (a -> a -> a) -> (a, a) -> a Source #

toList :: (a, a) -> [a] Source #

null :: (a, a) -> Bool Source #

length :: (a, a) -> Int Source #

elem :: Eq a => a -> (a, a) -> Bool Source #

maximum :: Ord a => (a, a) -> a Source #

minimum :: Ord a => (a, a) -> a Source #

sum :: Num a => (a, a) -> a Source #

product :: Num a => (a, a) -> a Source #

Foldable (Proxy *) #

Since: 4.7.0.0

Methods

fold :: Monoid m => Proxy * m -> m Source #

foldMap :: Monoid m => (a -> m) -> Proxy * a -> m Source #

foldr :: (a -> b -> b) -> b -> Proxy * a -> b Source #

foldr' :: (a -> b -> b) -> b -> Proxy * a -> b Source #

foldl :: (b -> a -> b) -> b -> Proxy * a -> b Source #

foldl' :: (b -> a -> b) -> b -> Proxy * a -> b Source #

foldr1 :: (a -> a -> a) -> Proxy * a -> a Source #

foldl1 :: (a -> a -> a) -> Proxy * a -> a Source #

toList :: Proxy * a -> [a] Source #

null :: Proxy * a -> Bool Source #

length :: Proxy * a -> Int Source #

elem :: Eq a => a -> Proxy * a -> Bool Source #

maximum :: Ord a => Proxy * a -> a Source #

minimum :: Ord a => Proxy * a -> a Source #

sum :: Num a => Proxy * a -> a Source #

product :: Num a => Proxy * a -> a Source #

Foldable (Arg a) #

Since: 4.9.0.0

Methods

fold :: Monoid m => Arg a m -> m Source #

foldMap :: Monoid m => (a -> m) -> Arg a a -> m Source #

foldr :: (a -> b -> b) -> b -> Arg a a -> b Source #

foldr' :: (a -> b -> b) -> b -> Arg a a -> b Source #

foldl :: (b -> a -> b) -> b -> Arg a a -> b Source #

foldl' :: (b -> a -> b) -> b -> Arg a a -> b Source #

foldr1 :: (a -> a -> a) -> Arg a a -> a Source #

foldl1 :: (a -> a -> a) -> Arg a a -> a Source #

toList :: Arg a a -> [a] Source #

null :: Arg a a -> Bool Source #

length :: Arg a a -> Int Source #

elem :: Eq a => a -> Arg a a -> Bool Source #

maximum :: Ord a => Arg a a -> a Source #

minimum :: Ord a => Arg a a -> a Source #

sum :: Num a => Arg a a -> a Source #

product :: Num a => Arg a a -> a Source #

Foldable f => Foldable (Rec1 * f) # 

Methods

fold :: Monoid m => Rec1 * f m -> m Source #

foldMap :: Monoid m => (a -> m) -> Rec1 * f a -> m Source #

foldr :: (a -> b -> b) -> b -> Rec1 * f a -> b Source #

foldr' :: (a -> b -> b) -> b -> Rec1 * f a -> b Source #

foldl :: (b -> a -> b) -> b -> Rec1 * f a -> b Source #

foldl' :: (b -> a -> b) -> b -> Rec1 * f a -> b Source #

foldr1 :: (a -> a -> a) -> Rec1 * f a -> a Source #

foldl1 :: (a -> a -> a) -> Rec1 * f a -> a Source #

toList :: Rec1 * f a -> [a] Source #

null :: Rec1 * f a -> Bool Source #

length :: Rec1 * f a -> Int Source #

elem :: Eq a => a -> Rec1 * f a -> Bool Source #

maximum :: Ord a => Rec1 * f a -> a Source #

minimum :: Ord a => Rec1 * f a -> a Source #

sum :: Num a => Rec1 * f a -> a Source #

product :: Num a => Rec1 * f a -> a Source #

Foldable (URec * Char) # 

Methods

fold :: Monoid m => URec * Char m -> m Source #

foldMap :: Monoid m => (a -> m) -> URec * Char a -> m Source #

foldr :: (a -> b -> b) -> b -> URec * Char a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec * Char a -> b Source #

foldl :: (b -> a -> b) -> b -> URec * Char a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec * Char a -> b Source #

foldr1 :: (a -> a -> a) -> URec * Char a -> a Source #

foldl1 :: (a -> a -> a) -> URec * Char a -> a Source #

toList :: URec * Char a -> [a] Source #

null :: URec * Char a -> Bool Source #

length :: URec * Char a -> Int Source #

elem :: Eq a => a -> URec * Char a -> Bool Source #

maximum :: Ord a => URec * Char a -> a Source #

minimum :: Ord a => URec * Char a -> a Source #

sum :: Num a => URec * Char a -> a Source #

product :: Num a => URec * Char a -> a Source #

Foldable (URec * Double) # 

Methods

fold :: Monoid m => URec * Double m -> m Source #

foldMap :: Monoid m => (a -> m) -> URec * Double a -> m Source #

foldr :: (a -> b -> b) -> b -> URec * Double a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec * Double a -> b Source #

foldl :: (b -> a -> b) -> b -> URec * Double a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec * Double a -> b Source #

foldr1 :: (a -> a -> a) -> URec * Double a -> a Source #

foldl1 :: (a -> a -> a) -> URec * Double a -> a Source #

toList :: URec * Double a -> [a] Source #

null :: URec * Double a -> Bool Source #

length :: URec * Double a -> Int Source #

elem :: Eq a => a -> URec * Double a -> Bool Source #

maximum :: Ord a => URec * Double a -> a Source #

minimum :: Ord a => URec * Double a -> a Source #

sum :: Num a => URec * Double a -> a Source #

product :: Num a => URec * Double a -> a Source #

Foldable (URec * Float) # 

Methods

fold :: Monoid m => URec * Float m -> m Source #

foldMap :: Monoid m => (a -> m) -> URec * Float a -> m Source #

foldr :: (a -> b -> b) -> b -> URec * Float a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec * Float a -> b Source #

foldl :: (b -> a -> b) -> b -> URec * Float a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec * Float a -> b Source #

foldr1 :: (a -> a -> a) -> URec * Float a -> a Source #

foldl1 :: (a -> a -> a) -> URec * Float a -> a Source #

toList :: URec * Float a -> [a] Source #

null :: URec * Float a -> Bool Source #

length :: URec * Float a -> Int Source #

elem :: Eq a => a -> URec * Float a -> Bool Source #

maximum :: Ord a => URec * Float a -> a Source #

minimum :: Ord a => URec * Float a -> a Source #

sum :: Num a => URec * Float a -> a Source #

product :: Num a => URec * Float a -> a Source #

Foldable (URec * Int) # 

Methods

fold :: Monoid m => URec * Int m -> m Source #

foldMap :: Monoid m => (a -> m) -> URec * Int a -> m Source #

foldr :: (a -> b -> b) -> b -> URec * Int a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec * Int a -> b Source #

foldl :: (b -> a -> b) -> b -> URec * Int a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec * Int a -> b Source #

foldr1 :: (a -> a -> a) -> URec * Int a -> a Source #

foldl1 :: (a -> a -> a) -> URec * Int a -> a Source #

toList :: URec * Int a -> [a] Source #

null :: URec * Int a -> Bool Source #

length :: URec * Int a -> Int Source #

elem :: Eq a => a -> URec * Int a -> Bool Source #

maximum :: Ord a => URec * Int a -> a Source #

minimum :: Ord a => URec * Int a -> a Source #

sum :: Num a => URec * Int a -> a Source #

product :: Num a => URec * Int a -> a Source #

Foldable (URec * Word) # 

Methods

fold :: Monoid m => URec * Word m -> m Source #

foldMap :: Monoid m => (a -> m) -> URec * Word a -> m Source #

foldr :: (a -> b -> b) -> b -> URec * Word a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec * Word a -> b Source #

foldl :: (b -> a -> b) -> b -> URec * Word a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec * Word a -> b Source #

foldr1 :: (a -> a -> a) -> URec * Word a -> a Source #

foldl1 :: (a -> a -> a) -> URec * Word a -> a Source #

toList :: URec * Word a -> [a] Source #

null :: URec * Word a -> Bool Source #

length :: URec * Word a -> Int Source #

elem :: Eq a => a -> URec * Word a -> Bool Source #

maximum :: Ord a => URec * Word a -> a Source #

minimum :: Ord a => URec * Word a -> a Source #

sum :: Num a => URec * Word a -> a Source #

product :: Num a => URec * Word a -> a Source #

Foldable (URec * (Ptr ())) # 

Methods

fold :: Monoid m => URec * (Ptr ()) m -> m Source #

foldMap :: Monoid m => (a -> m) -> URec * (Ptr ()) a -> m Source #

foldr :: (a -> b -> b) -> b -> URec * (Ptr ()) a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec * (Ptr ()) a -> b Source #

foldl :: (b -> a -> b) -> b -> URec * (Ptr ()) a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec * (Ptr ()) a -> b Source #

foldr1 :: (a -> a -> a) -> URec * (Ptr ()) a -> a Source #

foldl1 :: (a -> a -> a) -> URec * (Ptr ()) a -> a Source #

toList :: URec * (Ptr ()) a -> [a] Source #

null :: URec * (Ptr ()) a -> Bool Source #

length :: URec * (Ptr ()) a -> Int Source #

elem :: Eq a => a -> URec * (Ptr ()) a -> Bool Source #

maximum :: Ord a => URec * (Ptr ()) a -> a Source #

minimum :: Ord a => URec * (Ptr ()) a -> a Source #

sum :: Num a => URec * (Ptr ()) a -> a Source #

product :: Num a => URec * (Ptr ()) a -> a Source #

Foldable (Const * m) #

Since: 4.7.0.0

Methods

fold :: Monoid m => Const * m m -> m Source #

foldMap :: Monoid m => (a -> m) -> Const * m a -> m Source #

foldr :: (a -> b -> b) -> b -> Const * m a -> b Source #

foldr' :: (a -> b -> b) -> b -> Const * m a -> b Source #

foldl :: (b -> a -> b) -> b -> Const * m a -> b Source #

foldl' :: (b -> a -> b) -> b -> Const * m a -> b Source #

foldr1 :: (a -> a -> a) -> Const * m a -> a Source #

foldl1 :: (a -> a -> a) -> Const * m a -> a Source #

toList :: Const * m a -> [a] Source #

null :: Const * m a -> Bool Source #

length :: Const * m a -> Int Source #

elem :: Eq a => a -> Const * m a -> Bool Source #

maximum :: Ord a => Const * m a -> a Source #

minimum :: Ord a => Const * m a -> a Source #

sum :: Num a => Const * m a -> a Source #

product :: Num a => Const * m a -> a Source #

Foldable (K1 * i c) # 

Methods

fold :: Monoid m => K1 * i c m -> m Source #

foldMap :: Monoid m => (a -> m) -> K1 * i c a -> m Source #

foldr :: (a -> b -> b) -> b -> K1 * i c a -> b Source #

foldr' :: (a -> b -> b) -> b -> K1 * i c a -> b Source #

foldl :: (b -> a -> b) -> b -> K1 * i c a -> b Source #

foldl' :: (b -> a -> b) -> b -> K1 * i c a -> b Source #

foldr1 :: (a -> a -> a) -> K1 * i c a -> a Source #

foldl1 :: (a -> a -> a) -> K1 * i c a -> a Source #

toList :: K1 * i c a -> [a] Source #

null :: K1 * i c a -> Bool Source #

length :: K1 * i c a -> Int Source #

elem :: Eq a => a -> K1 * i c a -> Bool Source #

maximum :: Ord a => K1 * i c a -> a Source #

minimum :: Ord a => K1 * i c a -> a Source #

sum :: Num a => K1 * i c a -> a Source #

product :: Num a => K1 * i c a -> a Source #

(Foldable f, Foldable g) => Foldable ((:+:) * f g) # 

Methods

fold :: Monoid m => (* :+: f) g m -> m Source #

foldMap :: Monoid m => (a -> m) -> (* :+: f) g a -> m Source #

foldr :: (a -> b -> b) -> b -> (* :+: f) g a -> b Source #

foldr' :: (a -> b -> b) -> b -> (* :+: f) g a -> b Source #

foldl :: (b -> a -> b) -> b -> (* :+: f) g a -> b Source #

foldl' :: (b -> a -> b) -> b -> (* :+: f) g a -> b Source #

foldr1 :: (a -> a -> a) -> (* :+: f) g a -> a Source #

foldl1 :: (a -> a -> a) -> (* :+: f) g a -> a Source #

toList :: (* :+: f) g a -> [a] Source #

null :: (* :+: f) g a -> Bool Source #

length :: (* :+: f) g a -> Int Source #

elem :: Eq a => a -> (* :+: f) g a -> Bool Source #

maximum :: Ord a => (* :+: f) g a -> a Source #

minimum :: Ord a => (* :+: f) g a -> a Source #

sum :: Num a => (* :+: f) g a -> a Source #

product :: Num a => (* :+: f) g a -> a Source #

(Foldable f, Foldable g) => Foldable ((:*:) * f g) # 

Methods

fold :: Monoid m => (* :*: f) g m -> m Source #

foldMap :: Monoid m => (a -> m) -> (* :*: f) g a -> m Source #

foldr :: (a -> b -> b) -> b -> (* :*: f) g a -> b Source #

foldr' :: (a -> b -> b) -> b -> (* :*: f) g a -> b Source #

foldl :: (b -> a -> b) -> b -> (* :*: f) g a -> b Source #

foldl' :: (b -> a -> b) -> b -> (* :*: f) g a -> b Source #

foldr1 :: (a -> a -> a) -> (* :*: f) g a -> a Source #

foldl1 :: (a -> a -> a) -> (* :*: f) g a -> a Source #

toList :: (* :*: f) g a -> [a] Source #

null :: (* :*: f) g a -> Bool Source #

length :: (* :*: f) g a -> Int Source #

elem :: Eq a => a -> (* :*: f) g a -> Bool Source #

maximum :: Ord a => (* :*: f) g a -> a Source #

minimum :: Ord a => (* :*: f) g a -> a Source #

sum :: Num a => (* :*: f) g a -> a Source #

product :: Num a => (* :*: f) g a -> a Source #

(Foldable f, Foldable g) => Foldable (Sum * f g) #

Since: 4.9.0.0

Methods

fold :: Monoid m => Sum * f g m -> m Source #

foldMap :: Monoid m => (a -> m) -> Sum * f g a -> m Source #

foldr :: (a -> b -> b) -> b -> Sum * f g a -> b Source #

foldr' :: (a -> b -> b) -> b -> Sum * f g a -> b Source #

foldl :: (b -> a -> b) -> b -> Sum * f g a -> b Source #

foldl' :: (b -> a -> b) -> b -> Sum * f g a -> b Source #

foldr1 :: (a -> a -> a) -> Sum * f g a -> a Source #

foldl1 :: (a -> a -> a) -> Sum * f g a -> a Source #

toList :: Sum * f g a -> [a] Source #

null :: Sum * f g a -> Bool Source #

length :: Sum * f g a -> Int Source #

elem :: Eq a => a -> Sum * f g a -> Bool Source #

maximum :: Ord a => Sum * f g a -> a Source #

minimum :: Ord a => Sum * f g a -> a Source #

sum :: Num a => Sum * f g a -> a Source #

product :: Num a => Sum * f g a -> a Source #

(Foldable f, Foldable g) => Foldable (Product * f g) #

Since: 4.9.0.0

Methods

fold :: Monoid m => Product * f g m -> m Source #

foldMap :: Monoid m => (a -> m) -> Product * f g a -> m Source #

foldr :: (a -> b -> b) -> b -> Product * f g a -> b Source #

foldr' :: (a -> b -> b) -> b -> Product * f g a -> b Source #

foldl :: (b -> a -> b) -> b -> Product * f g a -> b Source #

foldl' :: (b -> a -> b) -> b -> Product * f g a -> b Source #

foldr1 :: (a -> a -> a) -> Product * f g a -> a Source #

foldl1 :: (a -> a -> a) -> Product * f g a -> a Source #

toList :: Product * f g a -> [a] Source #

null :: Product * f g a -> Bool Source #

length :: Product * f g a -> Int Source #

elem :: Eq a => a -> Product * f g a -> Bool Source #

maximum :: Ord a => Product * f g a -> a Source #

minimum :: Ord a => Product * f g a -> a Source #

sum :: Num a => Product * f g a -> a Source #

product :: Num a => Product * f g a -> a Source #

Foldable f => Foldable (M1 * i c f) # 

Methods

fold :: Monoid m => M1 * i c f m -> m Source #

foldMap :: Monoid m => (a -> m) -> M1 * i c f a -> m Source #

foldr :: (a -> b -> b) -> b -> M1 * i c f a -> b Source #

foldr' :: (a -> b -> b) -> b -> M1 * i c f a -> b Source #

foldl :: (b -> a -> b) -> b -> M1 * i c f a -> b Source #

foldl' :: (b -> a -> b) -> b -> M1 * i c f a -> b Source #

foldr1 :: (a -> a -> a) -> M1 * i c f a -> a Source #

foldl1 :: (a -> a -> a) -> M1 * i c f a -> a Source #

toList :: M1 * i c f a -> [a] Source #

null :: M1 * i c f a -> Bool Source #

length :: M1 * i c f a -> Int Source #

elem :: Eq a => a -> M1 * i c f a -> Bool Source #

maximum :: Ord a => M1 * i c f a -> a Source #

minimum :: Ord a => M1 * i c f a -> a Source #

sum :: Num a => M1 * i c f a -> a Source #

product :: Num a => M1 * i c f a -> a Source #

(Foldable f, Foldable g) => Foldable ((:.:) * * f g) # 

Methods

fold :: Monoid m => (* :.: *) f g m -> m Source #

foldMap :: Monoid m => (a -> m) -> (* :.: *) f g a -> m Source #

foldr :: (a -> b -> b) -> b -> (* :.: *) f g a -> b Source #

foldr' :: (a -> b -> b) -> b -> (* :.: *) f g a -> b Source #

foldl :: (b -> a -> b) -> b -> (* :.: *) f g a -> b Source #

foldl' :: (b -> a -> b) -> b -> (* :.: *) f g a -> b Source #

foldr1 :: (a -> a -> a) -> (* :.: *) f g a -> a Source #

foldl1 :: (a -> a -> a) -> (* :.: *) f g a -> a Source #

toList :: (* :.: *) f g a -> [a] Source #

null :: (* :.: *) f g a -> Bool Source #

length :: (* :.: *) f g a -> Int Source #

elem :: Eq a => a -> (* :.: *) f g a -> Bool Source #

maximum :: Ord a => (* :.: *) f g a -> a Source #

minimum :: Ord a => (* :.: *) f g a -> a Source #

sum :: Num a => (* :.: *) f g a -> a Source #

product :: Num a => (* :.: *) f g a -> a Source #

(Foldable f, Foldable g) => Foldable (Compose * * f g) #

Since: 4.9.0.0

Methods

fold :: Monoid m => Compose * * f g m -> m Source #

foldMap :: Monoid m => (a -> m) -> Compose * * f g a -> m Source #

foldr :: (a -> b -> b) -> b -> Compose * * f g a -> b Source #

foldr' :: (a -> b -> b) -> b -> Compose * * f g a -> b Source #

foldl :: (b -> a -> b) -> b -> Compose * * f g a -> b Source #

foldl' :: (b -> a -> b) -> b -> Compose * * f g a -> b Source #

foldr1 :: (a -> a -> a) -> Compose * * f g a -> a Source #

foldl1 :: (a -> a -> a) -> Compose * * f g a -> a Source #

toList :: Compose * * f g a -> [a] Source #

null :: Compose * * f g a -> Bool Source #

length :: Compose * * f g a -> Int Source #

elem :: Eq a => a -> Compose * * f g a -> Bool Source #

maximum :: Ord a => Compose * * f g a -> a Source #

minimum :: Ord a => Compose * * f g a -> a Source #

sum :: Num a => Compose * * f g a -> a Source #

product :: Num a => Compose * * f g a -> a Source #

class (Functor t, Foldable t) => Traversable t where Source #

Functors representing data structures that can be traversed from left to right.

A definition of traverse must satisfy the following laws:

naturality
t . traverse f = traverse (t . f) for every applicative transformation t
identity
traverse Identity = Identity
composition
traverse (Compose . fmap g . f) = Compose . fmap (traverse g) . traverse f

A definition of sequenceA must satisfy the following laws:

naturality
t . sequenceA = sequenceA . fmap t for every applicative transformation t
identity
sequenceA . fmap Identity = Identity
composition
sequenceA . fmap Compose = Compose . fmap sequenceA . sequenceA

where an applicative transformation is a function

t :: (Applicative f, Applicative g) => f a -> g a

preserving the Applicative operations, i.e.

and the identity functor Identity and composition of functors Compose are defined as

  newtype Identity a = Identity a

  instance Functor Identity where
    fmap f (Identity x) = Identity (f x)

  instance Applicative Identity where
    pure x = Identity x
    Identity f <*> Identity x = Identity (f x)

  newtype Compose f g a = Compose (f (g a))

  instance (Functor f, Functor g) => Functor (Compose f g) where
    fmap f (Compose x) = Compose (fmap (fmap f) x)

  instance (Applicative f, Applicative g) => Applicative (Compose f g) where
    pure x = Compose (pure (pure x))
    Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)

(The naturality law is implied by parametricity.)

Instances are similar to Functor, e.g. given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Traversable Tree where
   traverse f Empty = pure Empty
   traverse f (Leaf x) = Leaf <$> f x
   traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r

This is suitable even for abstract types, as the laws for <*> imply a form of associativity.

The superclass instances should satisfy the following:

Minimal complete definition

traverse | sequenceA

Methods

traverse :: Applicative f => (a -> f b) -> t a -> f (t b) Source #

Map each element of a structure to an action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see traverse_.

sequenceA :: Applicative f => t (f a) -> f (t a) Source #

Evaluate each action in the structure from left to right, and and collect the results. For a version that ignores the results see sequenceA_.

mapM :: Monad m => (a -> m b) -> t a -> m (t b) Source #

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see mapM_.

sequence :: Monad m => t (m a) -> m (t a) Source #

Evaluate each monadic action in the structure from left to right, and collect the results. For a version that ignores the results see sequence_.

Instances

Traversable [] #

Since: 2.1

Methods

traverse :: Applicative f => (a -> f b) -> [a] -> f [b] Source #

sequenceA :: Applicative f => [f a] -> f [a] Source #

mapM :: Monad m => (a -> m b) -> [a] -> m [b] Source #

sequence :: Monad m => [m a] -> m [a] Source #

Traversable Maybe #

Since: 2.1

Methods

traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) Source #

sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) Source #

mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) Source #

sequence :: Monad m => Maybe (m a) -> m (Maybe a) Source #

Traversable Par1 # 

Methods

traverse :: Applicative f => (a -> f b) -> Par1 a -> f (Par1 b) Source #

sequenceA :: Applicative f => Par1 (f a) -> f (Par1 a) Source #

mapM :: Monad m => (a -> m b) -> Par1 a -> m (Par1 b) Source #

sequence :: Monad m => Par1 (m a) -> m (Par1 a) Source #

Traversable Last #

Since: 4.8.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) Source #

sequenceA :: Applicative f => Last (f a) -> f (Last a) Source #

mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) Source #

sequence :: Monad m => Last (m a) -> m (Last a) Source #

Traversable First #

Since: 4.8.0.0

Methods

traverse :: Applicative f => (a -> f b) -> First a -> f (First b) Source #

sequenceA :: Applicative f => First (f a) -> f (First a) Source #

mapM :: Monad m => (a -> m b) -> First a -> m (First b) Source #

sequence :: Monad m => First (m a) -> m (First a) Source #

Traversable Product #

Since: 4.8.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) Source #

sequenceA :: Applicative f => Product (f a) -> f (Product a) Source #

mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) Source #

sequence :: Monad m => Product (m a) -> m (Product a) Source #

Traversable Sum #

Since: 4.8.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) Source #

sequenceA :: Applicative f => Sum (f a) -> f (Sum a) Source #

mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) Source #

sequence :: Monad m => Sum (m a) -> m (Sum a) Source #

Traversable Dual #

Since: 4.8.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) Source #

sequenceA :: Applicative f => Dual (f a) -> f (Dual a) Source #

mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) Source #

sequence :: Monad m => Dual (m a) -> m (Dual a) Source #

Traversable Identity # 

Methods

traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b) Source #

sequenceA :: Applicative f => Identity (f a) -> f (Identity a) Source #

mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b) Source #

sequence :: Monad m => Identity (m a) -> m (Identity a) Source #

Traversable ZipList #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b) Source #

sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a) Source #

mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b) Source #

sequence :: Monad m => ZipList (m a) -> m (ZipList a) Source #

Traversable NonEmpty #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) Source #

sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a) Source #

mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b) Source #

sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a) Source #

Traversable Option #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Option a -> f (Option b) Source #

sequenceA :: Applicative f => Option (f a) -> f (Option a) Source #

mapM :: Monad m => (a -> m b) -> Option a -> m (Option b) Source #

sequence :: Monad m => Option (m a) -> m (Option a) Source #

Traversable Last #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) Source #

sequenceA :: Applicative f => Last (f a) -> f (Last a) Source #

mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) Source #

sequence :: Monad m => Last (m a) -> m (Last a) Source #

Traversable First #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> First a -> f (First b) Source #

sequenceA :: Applicative f => First (f a) -> f (First a) Source #

mapM :: Monad m => (a -> m b) -> First a -> m (First b) Source #

sequence :: Monad m => First (m a) -> m (First a) Source #

Traversable Max #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) Source #

sequenceA :: Applicative f => Max (f a) -> f (Max a) Source #

mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) Source #

sequence :: Monad m => Max (m a) -> m (Max a) Source #

Traversable Min #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) Source #

sequenceA :: Applicative f => Min (f a) -> f (Min a) Source #

mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) Source #

sequence :: Monad m => Min (m a) -> m (Min a) Source #

Traversable Complex # 

Methods

traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) Source #

sequenceA :: Applicative f => Complex (f a) -> f (Complex a) Source #

mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) Source #

sequence :: Monad m => Complex (m a) -> m (Complex a) Source #

Traversable (Either a) #

Since: 4.7.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Either a a -> f (Either a b) Source #

sequenceA :: Applicative f => Either a (f a) -> f (Either a a) Source #

mapM :: Monad m => (a -> m b) -> Either a a -> m (Either a b) Source #

sequence :: Monad m => Either a (m a) -> m (Either a a) Source #

Traversable (V1 *) # 

Methods

traverse :: Applicative f => (a -> f b) -> V1 * a -> f (V1 * b) Source #

sequenceA :: Applicative f => V1 * (f a) -> f (V1 * a) Source #

mapM :: Monad m => (a -> m b) -> V1 * a -> m (V1 * b) Source #

sequence :: Monad m => V1 * (m a) -> m (V1 * a) Source #

Traversable (U1 *) #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> U1 * a -> f (U1 * b) Source #

sequenceA :: Applicative f => U1 * (f a) -> f (U1 * a) Source #

mapM :: Monad m => (a -> m b) -> U1 * a -> m (U1 * b) Source #

sequence :: Monad m => U1 * (m a) -> m (U1 * a) Source #

Traversable ((,) a) #

Since: 4.7.0.0

Methods

traverse :: Applicative f => (a -> f b) -> (a, a) -> f (a, b) Source #

sequenceA :: Applicative f => (a, f a) -> f (a, a) Source #

mapM :: Monad m => (a -> m b) -> (a, a) -> m (a, b) Source #

sequence :: Monad m => (a, m a) -> m (a, a) Source #

Traversable (Proxy *) #

Since: 4.7.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Proxy * a -> f (Proxy * b) Source #

sequenceA :: Applicative f => Proxy * (f a) -> f (Proxy * a) Source #

mapM :: Monad m => (a -> m b) -> Proxy * a -> m (Proxy * b) Source #

sequence :: Monad m => Proxy * (m a) -> m (Proxy * a) Source #

Traversable (Arg a) #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Arg a a -> f (Arg a b) Source #

sequenceA :: Applicative f => Arg a (f a) -> f (Arg a a) Source #

mapM :: Monad m => (a -> m b) -> Arg a a -> m (Arg a b) Source #

sequence :: Monad m => Arg a (m a) -> m (Arg a a) Source #

Traversable f => Traversable (Rec1 * f) # 

Methods

traverse :: Applicative f => (a -> f b) -> Rec1 * f a -> f (Rec1 * f b) Source #

sequenceA :: Applicative f => Rec1 * f (f a) -> f (Rec1 * f a) Source #

mapM :: Monad m => (a -> m b) -> Rec1 * f a -> m (Rec1 * f b) Source #

sequence :: Monad m => Rec1 * f (m a) -> m (Rec1 * f a) Source #

Traversable (URec * Char) # 

Methods

traverse :: Applicative f => (a -> f b) -> URec * Char a -> f (URec * Char b) Source #

sequenceA :: Applicative f => URec * Char (f a) -> f (URec * Char a) Source #

mapM :: Monad m => (a -> m b) -> URec * Char a -> m (URec * Char b) Source #

sequence :: Monad m => URec * Char (m a) -> m (URec * Char a) Source #

Traversable (URec * Double) # 

Methods

traverse :: Applicative f => (a -> f b) -> URec * Double a -> f (URec * Double b) Source #

sequenceA :: Applicative f => URec * Double (f a) -> f (URec * Double a) Source #

mapM :: Monad m => (a -> m b) -> URec * Double a -> m (URec * Double b) Source #

sequence :: Monad m => URec * Double (m a) -> m (URec * Double a) Source #

Traversable (URec * Float) # 

Methods

traverse :: Applicative f => (a -> f b) -> URec * Float a -> f (URec * Float b) Source #

sequenceA :: Applicative f => URec * Float (f a) -> f (URec * Float a) Source #

mapM :: Monad m => (a -> m b) -> URec * Float a -> m (URec * Float b) Source #

sequence :: Monad m => URec * Float (m a) -> m (URec * Float a) Source #

Traversable (URec * Int) # 

Methods

traverse :: Applicative f => (a -> f b) -> URec * Int a -> f (URec * Int b) Source #

sequenceA :: Applicative f => URec * Int (f a) -> f (URec * Int a) Source #

mapM :: Monad m => (a -> m b) -> URec * Int a -> m (URec * Int b) Source #

sequence :: Monad m => URec * Int (m a) -> m (URec * Int a) Source #

Traversable (URec * Word) # 

Methods

traverse :: Applicative f => (a -> f b) -> URec * Word a -> f (URec * Word b) Source #

sequenceA :: Applicative f => URec * Word (f a) -> f (URec * Word a) Source #

mapM :: Monad m => (a -> m b) -> URec * Word a -> m (URec * Word b) Source #

sequence :: Monad m => URec * Word (m a) -> m (URec * Word a) Source #

Traversable (URec * (Ptr ())) # 

Methods

traverse :: Applicative f => (a -> f b) -> URec * (Ptr ()) a -> f (URec * (Ptr ()) b) Source #

sequenceA :: Applicative f => URec * (Ptr ()) (f a) -> f (URec * (Ptr ()) a) Source #

mapM :: Monad m => (a -> m b) -> URec * (Ptr ()) a -> m (URec * (Ptr ()) b) Source #

sequence :: Monad m => URec * (Ptr ()) (m a) -> m (URec * (Ptr ()) a) Source #

Traversable (Const * m) #

Since: 4.7.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Const * m a -> f (Const * m b) Source #

sequenceA :: Applicative f => Const * m (f a) -> f (Const * m a) Source #

mapM :: Monad m => (a -> m b) -> Const * m a -> m (Const * m b) Source #

sequence :: Monad m => Const * m (m a) -> m (Const * m a) Source #

Traversable (K1 * i c) # 

Methods

traverse :: Applicative f => (a -> f b) -> K1 * i c a -> f (K1 * i c b) Source #

sequenceA :: Applicative f => K1 * i c (f a) -> f (K1 * i c a) Source #

mapM :: Monad m => (a -> m b) -> K1 * i c a -> m (K1 * i c b) Source #

sequence :: Monad m => K1 * i c (m a) -> m (K1 * i c a) Source #

(Traversable f, Traversable g) => Traversable ((:+:) * f g) # 

Methods

traverse :: Applicative f => (a -> f b) -> (* :+: f) g a -> f ((* :+: f) g b) Source #

sequenceA :: Applicative f => (* :+: f) g (f a) -> f ((* :+: f) g a) Source #

mapM :: Monad m => (a -> m b) -> (* :+: f) g a -> m ((* :+: f) g b) Source #

sequence :: Monad m => (* :+: f) g (m a) -> m ((* :+: f) g a) Source #

(Traversable f, Traversable g) => Traversable ((:*:) * f g) # 

Methods

traverse :: Applicative f => (a -> f b) -> (* :*: f) g a -> f ((* :*: f) g b) Source #

sequenceA :: Applicative f => (* :*: f) g (f a) -> f ((* :*: f) g a) Source #

mapM :: Monad m => (a -> m b) -> (* :*: f) g a -> m ((* :*: f) g b) Source #

sequence :: Monad m => (* :*: f) g (m a) -> m ((* :*: f) g a) Source #

(Traversable f, Traversable g) => Traversable (Sum * f g) #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Sum * f g a -> f (Sum * f g b) Source #

sequenceA :: Applicative f => Sum * f g (f a) -> f (Sum * f g a) Source #

mapM :: Monad m => (a -> m b) -> Sum * f g a -> m (Sum * f g b) Source #

sequence :: Monad m => Sum * f g (m a) -> m (Sum * f g a) Source #

(Traversable f, Traversable g) => Traversable (Product * f g) #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Product * f g a -> f (Product * f g b) Source #

sequenceA :: Applicative f => Product * f g (f a) -> f (Product * f g a) Source #

mapM :: Monad m => (a -> m b) -> Product * f g a -> m (Product * f g b) Source #

sequence :: Monad m => Product * f g (m a) -> m (Product * f g a) Source #

Traversable f => Traversable (M1 * i c f) # 

Methods

traverse :: Applicative f => (a -> f b) -> M1 * i c f a -> f (M1 * i c f b) Source #

sequenceA :: Applicative f => M1 * i c f (f a) -> f (M1 * i c f a) Source #

mapM :: Monad m => (a -> m b) -> M1 * i c f a -> m (M1 * i c f b) Source #

sequence :: Monad m => M1 * i c f (m a) -> m (M1 * i c f a) Source #

(Traversable f, Traversable g) => Traversable ((:.:) * * f g) # 

Methods

traverse :: Applicative f => (a -> f b) -> (* :.: *) f g a -> f ((* :.: *) f g b) Source #

sequenceA :: Applicative f => (* :.: *) f g (f a) -> f ((* :.: *) f g a) Source #

mapM :: Monad m => (a -> m b) -> (* :.: *) f g a -> m ((* :.: *) f g b) Source #

sequence :: Monad m => (* :.: *) f g (m a) -> m ((* :.: *) f g a) Source #

(Traversable f, Traversable g) => Traversable (Compose * * f g) #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Compose * * f g a -> f (Compose * * f g b) Source #

sequenceA :: Applicative f => Compose * * f g (f a) -> f (Compose * * f g a) Source #

mapM :: Monad m => (a -> m b) -> Compose * * f g a -> m (Compose * * f g b) Source #

sequence :: Monad m => Compose * * f g (m a) -> m (Compose * * f g a) Source #

Miscellaneous functions

id :: a -> a Source #

Identity function.

const :: a -> b -> a Source #

const x is a unary function which evaluates to x for all inputs.

For instance,

>>> map (const 42) [0..3]
[42,42,42,42]

(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9 Source #

Function composition.

flip :: (a -> b -> c) -> b -> a -> c Source #

flip f takes its (first) two arguments in the reverse order of f.

($) :: (a -> b) -> a -> b infixr 0 Source #

Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

    f $ g $ h x  =  f (g (h x))

It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.

until :: (a -> Bool) -> (a -> a) -> a -> a Source #

until p f yields the result of applying f until p holds.

asTypeOf :: a -> a -> a Source #

asTypeOf is a type-restricted version of const. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the second.

error :: forall (r :: RuntimeRep). forall (a :: TYPE r). HasCallStack => [Char] -> a Source #

error stops execution and displays an error message.

errorWithoutStackTrace :: forall (r :: RuntimeRep). forall (a :: TYPE r). [Char] -> a Source #

A variant of error that does not produce a stack trace.

Since: 4.9.0.0

undefined :: forall (r :: RuntimeRep). forall (a :: TYPE r). HasCallStack => a Source #

A special case of error. It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in which undefined appears.

seq :: a -> b -> b Source #

The value of seq a b is bottom if a is bottom, and otherwise equal to b. seq is usually introduced to improve performance by avoiding unneeded laziness.

A note on evaluation order: the expression seq a b does not guarantee that a will be evaluated before b. The only guarantee given by seq is that the both a and b will be evaluated before seq returns a value. In particular, this means that b may be evaluated before a. If you need to guarantee a specific order of evaluation, you must use the function pseq from the "parallel" package.

($!) :: (a -> b) -> a -> b infixr 0 Source #

Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.

List operations

map :: (a -> b) -> [a] -> [b] Source #

map f xs is the list obtained by applying f to each element of xs, i.e.,

map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
map f [x1, x2, ...] == [f x1, f x2, ...]

(++) :: [a] -> [a] -> [a] infixr 5 Source #

Append two lists, i.e.,

[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
[x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]

If the first list is not finite, the result is the first list.

filter :: (a -> Bool) -> [a] -> [a] Source #

filter, applied to a predicate and a list, returns the list of those elements that satisfy the predicate; i.e.,

filter p xs = [ x | x <- xs, p x]

head :: [a] -> a Source #

Extract the first element of a list, which must be non-empty.

last :: [a] -> a Source #

Extract the last element of a list, which must be finite and non-empty.

tail :: [a] -> [a] Source #

Extract the elements after the head of a list, which must be non-empty.

init :: [a] -> [a] Source #

Return all the elements of a list except the last one. The list must be non-empty.

null :: Foldable t => t a -> Bool Source #

Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

length :: Foldable t => t a -> Int Source #

Returns the size/length of a finite structure as an Int. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

(!!) :: [a] -> Int -> a infixl 9 Source #

List index (subscript) operator, starting from 0. It is an instance of the more general genericIndex, which takes an index of any integral type.

reverse :: [a] -> [a] Source #

reverse xs returns the elements of xs in reverse order. xs must be finite.

Special folds

and :: Foldable t => t Bool -> Bool Source #

and returns the conjunction of a container of Bools. For the result to be True, the container must be finite; False, however, results from a False value finitely far from the left end.

or :: Foldable t => t Bool -> Bool Source #

or returns the disjunction of a container of Bools. For the result to be False, the container must be finite; True, however, results from a True value finitely far from the left end.

any :: Foldable t => (a -> Bool) -> t a -> Bool Source #

Determines whether any element of the structure satisfies the predicate.

all :: Foldable t => (a -> Bool) -> t a -> Bool Source #

Determines whether all elements of the structure satisfy the predicate.

concat :: Foldable t => t [a] -> [a] Source #

The concatenation of all the elements of a container of lists.

concatMap :: Foldable t => (a -> [b]) -> t a -> [b] Source #

Map a function over all the elements of a container and concatenate the resulting lists.

Building lists

Scans

scanl :: (b -> a -> b) -> b -> [a] -> [b] Source #

scanl is similar to foldl, but returns a list of successive reduced values from the left:

scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]

Note that

last (scanl f z xs) == foldl f z xs.

scanl1 :: (a -> a -> a) -> [a] -> [a] Source #

scanl1 is a variant of scanl that has no starting value argument:

scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]

scanr :: (a -> b -> b) -> b -> [a] -> [b] Source #

scanr is the right-to-left dual of scanl. Note that

head (scanr f z xs) == foldr f z xs.

scanr1 :: (a -> a -> a) -> [a] -> [a] Source #

scanr1 is a variant of scanr that has no starting value argument.

Infinite lists

iterate :: (a -> a) -> a -> [a] Source #

iterate f x returns an infinite list of repeated applications of f to x:

iterate f x == [x, f x, f (f x), ...]

repeat :: a -> [a] Source #

repeat x is an infinite list, with x the value of every element.

replicate :: Int -> a -> [a] Source #

replicate n x is a list of length n with x the value of every element. It is an instance of the more general genericReplicate, in which n may be of any integral type.

cycle :: [a] -> [a] Source #

cycle ties a finite list into a circular one, or equivalently, the infinite repetition of the original list. It is the identity on infinite lists.

Sublists

take :: Int -> [a] -> [a] Source #

take n, applied to a list xs, returns the prefix of xs of length n, or xs itself if n > length xs:

take 5 "Hello World!" == "Hello"
take 3 [1,2,3,4,5] == [1,2,3]
take 3 [1,2] == [1,2]
take 3 [] == []
take (-1) [1,2] == []
take 0 [1,2] == []

It is an instance of the more general genericTake, in which n may be of any integral type.

drop :: Int -> [a] -> [a] Source #

drop n xs returns the suffix of xs after the first n elements, or [] if n > length xs:

drop 6 "Hello World!" == "World!"
drop 3 [1,2,3,4,5] == [4,5]
drop 3 [1,2] == []
drop 3 [] == []
drop (-1) [1,2] == [1,2]
drop 0 [1,2] == [1,2]

It is an instance of the more general genericDrop, in which n may be of any integral type.

splitAt :: Int -> [a] -> ([a], [a]) Source #

splitAt n xs returns a tuple where first element is xs prefix of length n and second element is the remainder of the list:

splitAt 6 "Hello World!" == ("Hello ","World!")
splitAt 3 [1,2,3,4,5] == ([1,2,3],[4,5])
splitAt 1 [1,2,3] == ([1],[2,3])
splitAt 3 [1,2,3] == ([1,2,3],[])
splitAt 4 [1,2,3] == ([1,2,3],[])
splitAt 0 [1,2,3] == ([],[1,2,3])
splitAt (-1) [1,2,3] == ([],[1,2,3])

It is equivalent to (take n xs, drop n xs) when n is not _|_ (splitAt _|_ xs = _|_). splitAt is an instance of the more general genericSplitAt, in which n may be of any integral type.

takeWhile :: (a -> Bool) -> [a] -> [a] Source #

takeWhile, applied to a predicate p and a list xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p:

takeWhile (< 3) [1,2,3,4,1,2,3,4] == [1,2]
takeWhile (< 9) [1,2,3] == [1,2,3]
takeWhile (< 0) [1,2,3] == []

dropWhile :: (a -> Bool) -> [a] -> [a] Source #

dropWhile p xs returns the suffix remaining after takeWhile p xs:

dropWhile (< 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3]
dropWhile (< 9) [1,2,3] == []
dropWhile (< 0) [1,2,3] == [1,2,3]

span :: (a -> Bool) -> [a] -> ([a], [a]) Source #

span, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that satisfy p and second element is the remainder of the list:

span (< 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4])
span (< 9) [1,2,3] == ([1,2,3],[])
span (< 0) [1,2,3] == ([],[1,2,3])

span p xs is equivalent to (takeWhile p xs, dropWhile p xs)

break :: (a -> Bool) -> [a] -> ([a], [a]) Source #

break, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that do not satisfy p and second element is the remainder of the list:

break (> 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4])
break (< 9) [1,2,3] == ([],[1,2,3])
break (> 9) [1,2,3] == ([1,2,3],[])

break p is equivalent to span (not . p).

Searching lists

notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 Source #

notElem is the negation of elem.

lookup :: Eq a => a -> [(a, b)] -> Maybe b Source #

lookup key assocs looks up a key in an association list.

Zipping and unzipping lists

zip :: [a] -> [b] -> [(a, b)] Source #

zip takes two lists and returns a list of corresponding pairs. If one input list is short, excess elements of the longer list are discarded.

zip is right-lazy:

zip [] _|_ = []

zip3 :: [a] -> [b] -> [c] -> [(a, b, c)] Source #

zip3 takes three lists and returns a list of triples, analogous to zip.

zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] Source #

zipWith generalises zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two lists to produce the list of corresponding sums.

zipWith is right-lazy:

zipWith f [] _|_ = []

zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] Source #

The zipWith3 function takes a function which combines three elements, as well as three lists and returns a list of their point-wise combination, analogous to zipWith.

unzip :: [(a, b)] -> ([a], [b]) Source #

unzip transforms a list of pairs into a list of first components and a list of second components.

unzip3 :: [(a, b, c)] -> ([a], [b], [c]) Source #

The unzip3 function takes a list of triples and returns three lists, analogous to unzip.

Functions on strings

lines :: String -> [String] Source #

lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.

Note that after splitting the string at newline characters, the last part of the string is considered a line even if it doesn't end with a newline. For example,

lines "" == []
lines "\n" == [""]
lines "one" == ["one"]
lines "one\n" == ["one"]
lines "one\n\n" == ["one",""]
lines "one\ntwo" == ["one","two"]
lines "one\ntwo\n" == ["one","two"]

Thus lines s contains at least as many elements as newlines in s.

words :: String -> [String] Source #

words breaks a string up into a list of words, which were delimited by white space.

unlines :: [String] -> String Source #

unlines is an inverse operation to lines. It joins lines, after appending a terminating newline to each.

unwords :: [String] -> String Source #

unwords is an inverse operation to words. It joins words with separating spaces.

Converting to and from String

Converting to String

type ShowS = String -> String Source #

The shows functions return a function that prepends the output String to an existing String. This allows constant-time concatenation of results using function composition.

class Show a where Source #

Conversion of values to readable Strings.

Derived instances of Show have the following properties, which are compatible with derived instances of Read:

  • The result of show is a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used.
  • If the constructor is defined to be an infix operator, then showsPrec will produce infix applications of the constructor.
  • the representation will be enclosed in parentheses if the precedence of the top-level constructor in x is less than d (associativity is ignored). Thus, if d is 0 then the result is never surrounded in parentheses; if d is 11 it is always surrounded in parentheses, unless it is an atomic expression.
  • If the constructor is defined using record syntax, then show will produce the record-syntax form, with the fields given in the same order as the original declaration.

For example, given the declarations

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Show is equivalent to

instance (Show a) => Show (Tree a) where

       showsPrec d (Leaf m) = showParen (d > app_prec) $
            showString "Leaf " . showsPrec (app_prec+1) m
         where app_prec = 10

       showsPrec d (u :^: v) = showParen (d > up_prec) $
            showsPrec (up_prec+1) u .
            showString " :^: "      .
            showsPrec (up_prec+1) v
         where up_prec = 5

Note that right-associativity of :^: is ignored. For example,

  • show (Leaf 1 :^: Leaf 2 :^: Leaf 3) produces the string "Leaf 1 :^: (Leaf 2 :^: Leaf 3)".

Minimal complete definition

showsPrec | show

Methods

showsPrec Source #

Arguments

:: Int

the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.

-> a

the value to be converted to a String

-> ShowS 

Convert a value to a readable String.

showsPrec should satisfy the law

showsPrec d x r ++ s  ==  showsPrec d x (r ++ s)

Derived instances of Read and Show satisfy the following:

That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

show :: a -> String Source #

A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.

showList :: [a] -> ShowS Source #

The method showList is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefined Show instance of the Char type, where values of type String should be shown in double quotes, rather than between square brackets.

Instances

Show Bool # 
Show Char #

Since: 2.1

Show Int #

Since: 2.1

Show Int8 #

Since: 2.1

Show Int16 #

Since: 2.1

Show Int32 #

Since: 2.1

Show Int64 #

Since: 2.1

Show Integer #

Since: 2.1

Show Natural #

Since: 4.8.0.0

Show Ordering # 
Show Word #

Since: 2.1

Show Word8 #

Since: 2.1

Show Word16 #

Since: 2.1

Show Word32 #

Since: 2.1

Show Word64 #

Since: 2.1

Show CallStack #

Since: 4.9.0.0

Show SomeTypeRep #

Since: 4.10.0.0

Show () # 

Methods

showsPrec :: Int -> () -> ShowS Source #

show :: () -> String Source #

showList :: [()] -> ShowS Source #

Show TyCon #

Since: 2.1

Show Module #

Since: 4.9.0.0

Show TrName #

Since: 4.9.0.0

Show SrcLoc # 
Show SomeException #

Since: 3.0

Show GeneralCategory # 
Show Number # 
Show Lexeme # 
Show Fingerprint #

Since: 4.7.0.0

Show IOMode # 
Show IntPtr # 
Show WordPtr # 
Show CUIntMax # 
Show CIntMax # 
Show CUIntPtr # 
Show CIntPtr # 
Show CSUSeconds # 
Show CUSeconds # 
Show CTime # 
Show CClock # 
Show CSigAtomic # 
Show CWchar # 
Show CSize # 
Show CPtrdiff # 
Show CDouble # 
Show CFloat # 
Show CBool # 
Show CULLong # 
Show CLLong # 
Show CULong # 
Show CLong # 
Show CUInt # 
Show CInt # 
Show CUShort # 
Show CShort # 
Show CUChar # 
Show CSChar # 
Show CChar # 
Show SomeNat #

Since: 4.7.0.0

Show SomeSymbol #

Since: 4.7.0.0

Show DecidedStrictness # 
Show SourceStrictness # 
Show SourceUnpackedness # 
Show Associativity # 
Show Fixity # 
Show Any # 
Show All # 
Show ArithException #

Since: 4.0.0.0

Show ErrorCall #

Since: 4.0.0.0

Show IOException #

Since: 4.1.0.0

Show MaskingState # 
Show CodingProgress # 
Show TextEncoding #

Since: 4.3.0.0

Show SeekMode # 
Show NewlineMode # 
Show Newline # 
Show BufferMode # 
Show Handle #

Since: 4.1.0.0

Show IOErrorType #

Since: 4.1.0.0

Show ExitCode # 
Show ArrayException #

Since: 4.1.0.0

Show AsyncException #

Since: 4.1.0.0

Show SomeAsyncException #

Since: 4.7.0.0

Show AssertionFailed #

Since: 4.1.0.0

Show CompactionFailed #

Since: 4.10.0.0

Show AllocationLimitExceeded #

Since: 4.7.1.0

Show Deadlock #

Since: 4.1.0.0

Show BlockedIndefinitelyOnSTM #

Since: 4.1.0.0

Show BlockedIndefinitelyOnMVar #

Since: 4.1.0.0

Show CodingFailureMode # 
Show Fd # 
Show CTimer # 
Show CKey # 
Show CId # 
Show CFsFilCnt # 
Show CFsBlkCnt # 
Show CClockId # 
Show CBlkCnt # 
Show CBlkSize # 
Show CRLim # 
Show CTcflag # 
Show CSpeed # 
Show CCc # 
Show CUid # 
Show CNlink # 
Show CGid # 
Show CSsize # 
Show CPid # 
Show COff # 
Show CMode # 
Show CIno # 
Show CDev # 
Show Lifetime # 
Show Event #

Since: 4.3.1.0

Show Dynamic #

Since: 2.1

Show ThreadStatus # 
Show BlockReason # 
Show ThreadId #

Since: 4.2.0.0

Show NestedAtomically #

Since: 4.0

Show NonTermination #

Since: 4.0

Show TypeError #

Since: 4.9.0.0

Show NoMethodError #

Since: 4.0

Show RecUpdError #

Since: 4.0

Show RecConError #

Since: 4.0

Show RecSelError #

Since: 4.0

Show PatternMatchFail #

Since: 4.0

Show FdKey # 
Show FileLockingNotSupported # 
Show HandlePosn #

Since: 4.1.0.0

Show Version # 
Show GCStats # 
Show GCDetails # 
Show RTSStats # 
Show RTSFlags # 
Show ParFlags # 
Show TickyFlags # 
Show TraceFlags # 
Show DoTrace # 
Show ProfFlags # 
Show DoHeapProfile # 
Show CCFlags # 
Show DoCostCentres # 
Show DebugFlags # 
Show MiscFlags # 
Show ConcFlags # 
Show GCFlags # 
Show GiveGCStats # 
Show Fixity # 
Show ConstrRep # 
Show DataRep # 
Show Constr #

Since: 4.0.0.0

Show DataType # 
Show StaticPtrInfo # 
Show Void #

Since: 4.8.0.0

Show a => Show [a] #

Since: 2.1

Methods

showsPrec :: Int -> [a] -> ShowS Source #

show :: [a] -> String Source #

showList :: [[a]] -> ShowS Source #

Show a => Show (Maybe a) # 
Show a => Show (Ratio a) #

Since: 2.0.1

Show (Ptr a) #

Since: 2.1

Methods

showsPrec :: Int -> Ptr a -> ShowS Source #

show :: Ptr a -> String Source #

showList :: [Ptr a] -> ShowS Source #

Show (FunPtr a) #

Since: 2.1

Show p => Show (Par1 p) # 

Methods

showsPrec :: Int -> Par1 p -> ShowS Source #

show :: Par1 p -> String Source #

showList :: [Par1 p] -> ShowS Source #

Show a => Show (Down a) # 

Methods

showsPrec :: Int -> Down a -> ShowS Source #

show :: Down a -> String Source #

showList :: [Down a] -> ShowS Source #

Show a => Show (Last a) # 

Methods

showsPrec :: Int -> Last a -> ShowS Source #

show :: Last a -> String Source #

showList :: [Last a] -> ShowS Source #

Show a => Show (First a) # 
Show a => Show (Product a) # 
Show a => Show (Sum a) # 

Methods

showsPrec :: Int -> Sum a -> ShowS Source #

show :: Sum a -> String Source #

showList :: [Sum a] -> ShowS Source #

Show a => Show (Dual a) # 

Methods

showsPrec :: Int -> Dual a -> ShowS Source #

show :: Dual a -> String Source #

showList :: [Dual a] -> ShowS Source #

Show (ForeignPtr a) #

Since: 2.1

Show a => Show (Identity a) #

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

Since: 4.8.0.0

Show a => Show (ZipList a) # 
Show a => Show (NonEmpty a) # 
Show a => Show (Option a) # 
Show m => Show (WrappedMonoid m) # 
Show a => Show (Last a) # 

Methods

showsPrec :: Int -> Last a -> ShowS Source #

show :: Last a -> String Source #

showList :: [Last a] -> ShowS Source #

Show a => Show (First a) # 
Show a => Show (Max a) # 

Methods

showsPrec :: Int -> Max a -> ShowS Source #

show :: Max a -> String Source #

showList :: [Max a] -> ShowS Source #

Show a => Show (Min a) # 

Methods

showsPrec :: Int -> Min a -> ShowS Source #

show :: Min a -> String Source #

showList :: [Min a] -> ShowS Source #

HasResolution a => Show (Fixed a) #

Since: 2.1

Show a => Show (Complex a) # 
(Show b, Show a) => Show (Either a b) # 

Methods

showsPrec :: Int -> Either a b -> ShowS Source #

show :: Either a b -> String Source #

showList :: [Either a b] -> ShowS Source #

Show (V1 k p) # 

Methods

showsPrec :: Int -> V1 k p -> ShowS Source #

show :: V1 k p -> String Source #

showList :: [V1 k p] -> ShowS Source #

Show (U1 k p) #

Since: 4.9.0.0

Methods

showsPrec :: Int -> U1 k p -> ShowS Source #

show :: U1 k p -> String Source #

showList :: [U1 k p] -> ShowS Source #

Show (TypeRep k a) # 

Methods

showsPrec :: Int -> TypeRep k a -> ShowS Source #

show :: TypeRep k a -> String Source #

showList :: [TypeRep k a] -> ShowS Source #

(Show a, Show b) => Show (a, b) #

Since: 2.1

Methods

showsPrec :: Int -> (a, b) -> ShowS Source #

show :: (a, b) -> String Source #

showList :: [(a, b)] -> ShowS Source #

Show (ST s a) #

Since: 2.1

Methods

showsPrec :: Int -> ST s a -> ShowS Source #

show :: ST s a -> String Source #

showList :: [ST s a] -> ShowS Source #

Show (Proxy k s) #

Since: 4.7.0.0

Methods

showsPrec :: Int -> Proxy k s -> ShowS Source #

show :: Proxy k s -> String Source #

showList :: [Proxy k s] -> ShowS Source #

(Show b, Show a) => Show (Arg a b) # 

Methods

showsPrec :: Int -> Arg a b -> ShowS Source #

show :: Arg a b -> String Source #

showList :: [Arg a b] -> ShowS Source #

Show (f p) => Show (Rec1 k f p) # 

Methods

showsPrec :: Int -> Rec1 k f p -> ShowS Source #

show :: Rec1 k f p -> String Source #

showList :: [Rec1 k f p] -> ShowS Source #

Show (URec k Word p) # 

Methods

showsPrec :: Int -> URec k Word p -> ShowS Source #

show :: URec k Word p -> String Source #

showList :: [URec k Word p] -> ShowS Source #

Show (URec k Int p) # 

Methods

showsPrec :: Int -> URec k Int p -> ShowS Source #

show :: URec k Int p -> String Source #

showList :: [URec k Int p] -> ShowS Source #

Show (URec k Float p) # 
Show (URec k Double p) # 
Show (URec k Char p) # 

Methods

showsPrec :: Int -> URec k Char p -> ShowS Source #

show :: URec k Char p -> String Source #

showList :: [URec k Char p] -> ShowS Source #

(Show a, Show b, Show c) => Show (a, b, c) #

Since: 2.1

Methods

showsPrec :: Int -> (a, b, c) -> ShowS Source #

show :: (a, b, c) -> String Source #

showList :: [(a, b, c)] -> ShowS Source #

Show ((:~:) k a b) # 

Methods

showsPrec :: Int -> (k :~: a) b -> ShowS Source #

show :: (k :~: a) b -> String Source #

showList :: [(k :~: a) b] -> ShowS Source #

Show (Coercion k a b) # 

Methods

showsPrec :: Int -> Coercion k a b -> ShowS Source #

show :: Coercion k a b -> String Source #

showList :: [Coercion k a b] -> ShowS Source #

Show (f a) => Show (Alt k f a) # 

Methods

showsPrec :: Int -> Alt k f a -> ShowS Source #

show :: Alt k f a -> String Source #

showList :: [Alt k f a] -> ShowS Source #

Show a => Show (Const k a b) #

This instance would be equivalent to the derived instances of the Const newtype if the runConst field were removed

Since: 4.8.0.0

Methods

showsPrec :: Int -> Const k a b -> ShowS Source #

show :: Const k a b -> String Source #

showList :: [Const k a b] -> ShowS Source #

Show c => Show (K1 k i c p) # 

Methods

showsPrec :: Int -> K1 k i c p -> ShowS Source #

show :: K1 k i c p -> String Source #

showList :: [K1 k i c p] -> ShowS Source #

(Show (g p), Show (f p)) => Show ((:+:) k f g p) # 

Methods

showsPrec :: Int -> (k :+: f) g p -> ShowS Source #

show :: (k :+: f) g p -> String Source #

showList :: [(k :+: f) g p] -> ShowS Source #

(Show (g p), Show (f p)) => Show ((:*:) k f g p) # 

Methods

showsPrec :: Int -> (k :*: f) g p -> ShowS Source #

show :: (k :*: f) g p -> String Source #

showList :: [(k :*: f) g p] -> ShowS Source #

(Show a, Show b, Show c, Show d) => Show (a, b, c, d) #

Since: 2.1

Methods

showsPrec :: Int -> (a, b, c, d) -> ShowS Source #

show :: (a, b, c, d) -> String Source #

showList :: [(a, b, c, d)] -> ShowS Source #

Show ((:~~:) k1 k2 a b) #

Since: 4.10.0.0

Methods

showsPrec :: Int -> (k1 :~~: k2) a b -> ShowS Source #

show :: (k1 :~~: k2) a b -> String Source #

showList :: [(k1 :~~: k2) a b] -> ShowS Source #

(Show1 f, Show1 g, Show a) => Show (Sum * f g a) #

Since: 4.9.0.0

Methods

showsPrec :: Int -> Sum * f g a -> ShowS Source #

show :: Sum * f g a -> String Source #

showList :: [Sum * f g a] -> ShowS Source #

(Show1 f, Show1 g, Show a) => Show (Product * f g a) #

Since: 4.9.0.0

Methods

showsPrec :: Int -> Product * f g a -> ShowS Source #

show :: Product * f g a -> String Source #

showList :: [Product * f g a] -> ShowS Source #

Show (f p) => Show (M1 k i c f p) # 

Methods

showsPrec :: Int -> M1 k i c f p -> ShowS Source #

show :: M1 k i c f p -> String Source #

showList :: [M1 k i c f p] -> ShowS Source #

Show (f (g p)) => Show ((:.:) k2 k1 f g p) # 

Methods

showsPrec :: Int -> (k2 :.: k1) f g p -> ShowS Source #

show :: (k2 :.: k1) f g p -> String Source #

showList :: [(k2 :.: k1) f g p] -> ShowS Source #

(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e) #

Since: 2.1

Methods

showsPrec :: Int -> (a, b, c, d, e) -> ShowS Source #

show :: (a, b, c, d, e) -> String Source #

showList :: [(a, b, c, d, e)] -> ShowS Source #

(Show1 f, Show1 g, Show a) => Show (Compose * * f g a) #

Since: 4.9.0.0

Methods

showsPrec :: Int -> Compose * * f g a -> ShowS Source #

show :: Compose * * f g a -> String Source #

showList :: [Compose * * f g a] -> ShowS Source #

(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f) #

Since: 2.1

Methods

showsPrec :: Int -> (a, b, c, d, e, f) -> ShowS Source #

show :: (a, b, c, d, e, f) -> String Source #

showList :: [(a, b, c, d, e, f)] -> ShowS Source #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g) #

Since: 2.1

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g) -> ShowS Source #

show :: (a, b, c, d, e, f, g) -> String Source #

showList :: [(a, b, c, d, e, f, g)] -> ShowS Source #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h) => Show (a, b, c, d, e, f, g, h) #

Since: 2.1

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h) -> ShowS Source #

show :: (a, b, c, d, e, f, g, h) -> String Source #

showList :: [(a, b, c, d, e, f, g, h)] -> ShowS Source #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i) => Show (a, b, c, d, e, f, g, h, i) #

Since: 2.1

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i) -> ShowS Source #

show :: (a, b, c, d, e, f, g, h, i) -> String Source #

showList :: [(a, b, c, d, e, f, g, h, i)] -> ShowS Source #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j) => Show (a, b, c, d, e, f, g, h, i, j) #

Since: 2.1

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j) -> ShowS Source #

show :: (a, b, c, d, e, f, g, h, i, j) -> String Source #

showList :: [(a, b, c, d, e, f, g, h, i, j)] -> ShowS Source #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k) => Show (a, b, c, d, e, f, g, h, i, j, k) #

Since: 2.1

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k) -> ShowS Source #

show :: (a, b, c, d, e, f, g, h, i, j, k) -> String Source #

showList :: [(a, b, c, d, e, f, g, h, i, j, k)] -> ShowS Source #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l) => Show (a, b, c, d, e, f, g, h, i, j, k, l) #

Since: 2.1

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l) -> ShowS Source #

show :: (a, b, c, d, e, f, g, h, i, j, k, l) -> String Source #

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l)] -> ShowS Source #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m) #

Since: 2.1

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> ShowS Source #

show :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> String Source #

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m)] -> ShowS Source #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #

Since: 2.1

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> ShowS Source #

show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> String Source #

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] -> ShowS Source #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n, Show o) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

Since: 2.1

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> ShowS Source #

show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> String Source #

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] -> ShowS Source #

shows :: Show a => a -> ShowS Source #

equivalent to showsPrec with a precedence of 0.

showChar :: Char -> ShowS Source #

utility function converting a Char to a show function that simply prepends the character unchanged.

showString :: String -> ShowS Source #

utility function converting a String to a show function that simply prepends the string unchanged.

showParen :: Bool -> ShowS -> ShowS Source #

utility function that surrounds the inner show function with parentheses when the Bool parameter is True.

Converting from String

type ReadS a = String -> [(a, String)] Source #

A parser for a type a, represented as a function that takes a String and returns a list of possible parses as (a,String) pairs.

Note that this kind of backtracking parser is very inefficient; reading a large structure may be quite slow (cf ReadP).

class Read a where Source #

Parsing of Strings, producing values.

Derived instances of Read make the following assumptions, which derived instances of Show obey:

  • If the constructor is defined to be an infix operator, then the derived Read instance will parse only infix applications of the constructor (not the prefix form).
  • Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
  • If the constructor is defined using record syntax, the derived Read will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration.
  • The derived Read instance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.

For example, given the declarations

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Read in Haskell 2010 is equivalent to

instance (Read a) => Read (Tree a) where

        readsPrec d r =  readParen (d > app_prec)
                         (\r -> [(Leaf m,t) |
                                 ("Leaf",s) <- lex r,
                                 (m,t) <- readsPrec (app_prec+1) s]) r

                      ++ readParen (d > up_prec)
                         (\r -> [(u:^:v,w) |
                                 (u,s) <- readsPrec (up_prec+1) r,
                                 (":^:",t) <- lex s,
                                 (v,w) <- readsPrec (up_prec+1) t]) r

          where app_prec = 10
                up_prec = 5

Note that right-associativity of :^: is unused.

The derived instance in GHC is equivalent to

instance (Read a) => Read (Tree a) where

        readPrec = parens $ (prec app_prec $ do
                                 Ident "Leaf" <- lexP
                                 m <- step readPrec
                                 return (Leaf m))

                     +++ (prec up_prec $ do
                                 u <- step readPrec
                                 Symbol ":^:" <- lexP
                                 v <- step readPrec
                                 return (u :^: v))

          where app_prec = 10
                up_prec = 5

        readListPrec = readListPrecDefault

Why do both readsPrec and readPrec exist, and why does GHC opt to implement readPrec in derived Read instances instead of readsPrec? The reason is that readsPrec is based on the ReadS type, and although ReadS is mentioned in the Haskell 2010 Report, it is not a very efficient parser data structure.

readPrec, on the other hand, is based on a much more efficient ReadPrec datatype (a.k.a "new-style parsers"), but its definition relies on the use of the RankNTypes language extension. Therefore, readPrec (and its cousin, readListPrec) are marked as GHC-only. Nevertheless, it is recommended to use readPrec instead of readsPrec whenever possible for the efficiency improvements it brings.

As mentioned above, derived Read instances in GHC will implement readPrec instead of readsPrec. The default implementations of readsPrec (and its cousin, readList) will simply use readPrec under the hood. If you are writing a Read instance by hand, it is recommended to write it like so:

instance Read T where
  readPrec     = ...
  readListPrec = readListPrecDefault

Minimal complete definition

readsPrec | readPrec

Methods

readsPrec Source #

Arguments

:: Int

the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.

-> ReadS a 

attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.

Derived instances of Read and Show satisfy the following:

That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

readList :: ReadS [a] Source #

The method readList is provided to allow the programmer to give a specialised way of parsing lists of values. For example, this is used by the predefined Read instance of the Char type, where values of type String should be are expected to use double quotes, rather than square brackets.

Instances

Read Bool #

Since: 2.1

Read Char #

Since: 2.1

Read Double #

Since: 2.1

Read Float #

Since: 2.1

Read Int #

Since: 2.1

Read Int8 #

Since: 2.1

Read Int16 #

Since: 2.1

Read Int32 #

Since: 2.1

Read Int64 #

Since: 2.1

Read Integer #

Since: 2.1

Read Natural #

Since: 4.8.0.0

Read Ordering #

Since: 2.1

Read Word #

Since: 4.5.0.0

Read Word8 #

Since: 2.1

Read Word16 #

Since: 2.1

Read Word32 #

Since: 2.1

Read Word64 #

Since: 2.1

Read () #

Since: 2.1

Read GeneralCategory # 
Read Lexeme #

Since: 2.1

Read IOMode # 
Read IntPtr # 
Read WordPtr # 
Read CUIntMax # 
Read CIntMax # 
Read CUIntPtr # 
Read CIntPtr # 
Read CSUSeconds # 
Read CUSeconds # 
Read CTime # 
Read CClock # 
Read CSigAtomic # 
Read CWchar # 
Read CSize # 
Read CPtrdiff # 
Read CDouble # 
Read CFloat # 
Read CBool # 
Read CULLong # 
Read CLLong # 
Read CULong # 
Read CLong # 
Read CUInt # 
Read CInt # 
Read CUShort # 
Read CShort # 
Read CUChar # 
Read CSChar # 
Read CChar # 
Read SomeNat #

Since: 4.7.0.0

Read SomeSymbol #

Since: 4.7.0.0

Read DecidedStrictness # 
Read SourceStrictness # 
Read SourceUnpackedness # 
Read Associativity # 
Read Fixity # 
Read Any # 
Read All # 
Read SeekMode # 
Read NewlineMode # 
Read Newline # 
Read BufferMode # 
Read ExitCode # 
Read Fd # 
Read CKey # 
Read CId # 
Read CFsFilCnt # 
Read CFsBlkCnt # 
Read CClockId # 
Read CBlkCnt # 
Read CBlkSize # 
Read CRLim # 
Read CTcflag # 
Read CSpeed # 
Read CCc # 
Read CUid # 
Read CNlink # 
Read CGid # 
Read CSsize # 
Read CPid # 
Read COff # 
Read CMode # 
Read CIno # 
Read CDev # 
Read Version # 
Read GCStats # 
Read GCDetails # 
Read RTSStats # 
Read Void #

Reading a Void value is always a parse error, considering Void as a data type with no constructors. | @since 4.8.0.0

Read a => Read [a] #

Since: 2.1

Read a => Read (Maybe a) #

Since: 2.1

(Integral a, Read a) => Read (Ratio a) #

Since: 2.1

Read p => Read (Par1 p) # 
Read a => Read (Down a) # 
Read a => Read (Last a) # 
Read a => Read (First a) # 
Read a => Read (Product a) # 
Read a => Read (Sum a) # 
Read a => Read (Dual a) # 
Read a => Read (Identity a) #

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

Since: 4.8.0.0

Read a => Read (ZipList a) # 
Read a => Read (NonEmpty a) # 
Read a => Read (Option a) # 
Read m => Read (WrappedMonoid m) # 
Read a => Read (Last a) # 
Read a => Read (First a) # 
Read a => Read (Max a) # 
Read a => Read (Min a) # 
HasResolution a => Read (Fixed a) #

Since: 4.3.0.0

Read a => Read (Complex a) # 
(Read b, Read a) => Read (Either a b) # 
Read (V1 k p) # 
Read (U1 k p) #

Since: 4.9.0.0

(Read a, Read b) => Read (a, b) #

Since: 2.1

Methods

readsPrec :: Int -> ReadS (a, b) Source #

readList :: ReadS [(a, b)] Source #

readPrec :: ReadPrec (a, b) Source #

readListPrec :: ReadPrec [(a, b)] Source #

Read (Proxy k s) #

Since: 4.7.0.0

(Read b, Read a) => Read (Arg a b) # 
Read (f p) => Read (Rec1 k f p) # 
(Read a, Read b, Read c) => Read (a, b, c) #

Since: 2.1

Methods

readsPrec :: Int -> ReadS (a, b, c) Source #

readList :: ReadS [(a, b, c)] Source #

readPrec :: ReadPrec (a, b, c) Source #

readListPrec :: ReadPrec [(a, b, c)] Source #

(~) k a b => Read ((:~:) k a b) #

Since: 4.7.0.0

Methods

readsPrec :: Int -> ReadS ((k :~: a) b) Source #

readList :: ReadS [(k :~: a) b] Source #

readPrec :: ReadPrec ((k :~: a) b) Source #

readListPrec :: ReadPrec [(k :~: a) b] Source #

Coercible k a b => Read (Coercion k a b) #

Since: 4.7.0.0

Read (f a) => Read (Alt k f a) # 

Methods

readsPrec :: Int -> ReadS (Alt k f a) Source #

readList :: ReadS [Alt k f a] Source #

readPrec :: ReadPrec (Alt k f a) Source #

readListPrec :: ReadPrec [Alt k f a] Source #

Read a => Read (Const k a b) #

This instance would be equivalent to the derived instances of the Const newtype if the runConst field were removed

Since: 4.8.0.0

Read c => Read (K1 k i c p) # 

Methods

readsPrec :: Int -> ReadS (K1 k i c p) Source #

readList :: ReadS [K1 k i c p] Source #

readPrec :: ReadPrec (K1 k i c p) Source #

readListPrec :: ReadPrec [K1 k i c p] Source #

(Read (g p), Read (f p)) => Read ((:+:) k f g p) # 

Methods

readsPrec :: Int -> ReadS ((k :+: f) g p) Source #

readList :: ReadS [(k :+: f) g p] Source #

readPrec :: ReadPrec ((k :+: f) g p) Source #

readListPrec :: ReadPrec [(k :+: f) g p] Source #

(Read (g p), Read (f p)) => Read ((:*:) k f g p) # 

Methods

readsPrec :: Int -> ReadS ((k :*: f) g p) Source #

readList :: ReadS [(k :*: f) g p] Source #

readPrec :: ReadPrec ((k :*: f) g p) Source #

readListPrec :: ReadPrec [(k :*: f) g p] Source #

(Read a, Read b, Read c, Read d) => Read (a, b, c, d) #

Since: 2.1

Methods

readsPrec :: Int -> ReadS (a, b, c, d) Source #

readList :: ReadS [(a, b, c, d)] Source #

readPrec :: ReadPrec (a, b, c, d) Source #

readListPrec :: ReadPrec [(a, b, c, d)] Source #

(~~) k1 k2 a b => Read ((:~~:) k1 k2 a b) #

Since: 4.10.0.0

Methods

readsPrec :: Int -> ReadS ((k1 :~~: k2) a b) Source #

readList :: ReadS [(k1 :~~: k2) a b] Source #

readPrec :: ReadPrec ((k1 :~~: k2) a b) Source #

readListPrec :: ReadPrec [(k1 :~~: k2) a b] Source #

(Read1 f, Read1 g, Read a) => Read (Sum * f g a) #

Since: 4.9.0.0

Methods

readsPrec :: Int -> ReadS (Sum * f g a) Source #

readList :: ReadS [Sum * f g a] Source #

readPrec :: ReadPrec (Sum * f g a) Source #

readListPrec :: ReadPrec [Sum * f g a] Source #

(Read1 f, Read1 g, Read a) => Read (Product * f g a) #

Since: 4.9.0.0

Read (f p) => Read (M1 k i c f p) # 

Methods

readsPrec :: Int -> ReadS (M1 k i c f p) Source #

readList :: ReadS [M1 k i c f p] Source #

readPrec :: ReadPrec (M1 k i c f p) Source #

readListPrec :: ReadPrec [M1 k i c f p] Source #

Read (f (g p)) => Read ((:.:) k2 k1 f g p) # 

Methods

readsPrec :: Int -> ReadS ((k2 :.: k1) f g p) Source #

readList :: ReadS [(k2 :.: k1) f g p] Source #

readPrec :: ReadPrec ((k2 :.: k1) f g p) Source #

readListPrec :: ReadPrec [(k2 :.: k1) f g p] Source #

(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) #

Since: 2.1

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e) Source #

readList :: ReadS [(a, b, c, d, e)] Source #

readPrec :: ReadPrec (a, b, c, d, e) Source #

readListPrec :: ReadPrec [(a, b, c, d, e)] Source #

(Read1 f, Read1 g, Read a) => Read (Compose * * f g a) #

Since: 4.9.0.0

(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) #

Since: 2.1

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f) Source #

readList :: ReadS [(a, b, c, d, e, f)] Source #

readPrec :: ReadPrec (a, b, c, d, e, f) Source #

readListPrec :: ReadPrec [(a, b, c, d, e, f)] Source #

(Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) #

Since: 2.1

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g) Source #

readList :: ReadS [(a, b, c, d, e, f, g)] Source #

readPrec :: ReadPrec (a, b, c, d, e, f, g) Source #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g)] Source #

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) #

Since: 2.1

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h) Source #

readList :: ReadS [(a, b, c, d, e, f, g, h)] Source #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h) Source #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h)] Source #

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) #

Since: 2.1

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i) Source #

readList :: ReadS [(a, b, c, d, e, f, g, h, i)] Source #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i) Source #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i)] Source #

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) #

Since: 2.1

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j) Source #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j)] Source #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j) Source #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j)] Source #

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) #

Since: 2.1

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k) Source #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k)] Source #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k) Source #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k)] Source #

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) #

Since: 2.1

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l) Source #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l)] Source #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l) Source #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l)] Source #

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) #

Since: 2.1

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m) Source #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m)] Source #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m) Source #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m)] Source #

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #

Since: 2.1

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] Source #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] Source #

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

Since: 2.1

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] Source #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] Source #

reads :: Read a => ReadS a Source #

equivalent to readsPrec with a precedence of 0.

readParen :: Bool -> ReadS a -> ReadS a Source #

readParen True p parses what p parses, but surrounded with parentheses.

readParen False p parses what p parses, but optionally surrounded with parentheses.

read :: Read a => String -> a Source #

The read function reads input from a string, which must be completely consumed by the input process.

lex :: ReadS String Source #

The lex function reads a single lexeme from the input, discarding initial white space, and returning the characters that constitute the lexeme. If the input string contains only white space, lex returns a single successful `lexeme' consisting of the empty string. (Thus lex "" = [("","")].) If there is no legal lexeme at the beginning of the input string, lex fails (i.e. returns []).

This lexer is not completely faithful to the Haskell lexical syntax in the following respects:

  • Qualified names are not handled properly
  • Octal and hexadecimal numerics are not recognized as a single token
  • Comments are not treated properly

Basic Input and output

data IO a :: * -> * Source #

A value of type IO a is a computation which, when performed, does some I/O before returning a value of type a.

There is really only one way to "perform" an I/O action: bind it to Main.main in your program. When your program is run, the I/O will be performed. It isn't possible to perform I/O from an arbitrary function, unless that function is itself in the IO monad and called at some point, directly or indirectly, from Main.main.

IO is a monad, so IO actions can be combined using either the do-notation or the >> and >>= operations from the Monad class.

Instances

Monad IO #

Since: 2.1

Methods

(>>=) :: IO a -> (a -> IO b) -> IO b Source #

(>>) :: IO a -> IO b -> IO b Source #

return :: a -> IO a Source #

fail :: String -> IO a Source #

Functor IO #

Since: 2.1

Methods

fmap :: (a -> b) -> IO a -> IO b Source #

(<$) :: a -> IO b -> IO a Source #

MonadFix IO #

Since: 2.1

Methods

mfix :: (a -> IO a) -> IO a Source #

MonadFail IO #

Since: 4.9.0.0

Methods

fail :: String -> IO a Source #

Applicative IO #

Since: 2.1

Methods

pure :: a -> IO a Source #

(<*>) :: IO (a -> b) -> IO a -> IO b Source #

liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c Source #

(*>) :: IO a -> IO b -> IO b Source #

(<*) :: IO a -> IO b -> IO a Source #

MonadPlus IO #

Since: 4.9.0.0

Methods

mzero :: IO a Source #

mplus :: IO a -> IO a -> IO a Source #

Alternative IO #

Since: 4.9.0.0

Methods

empty :: IO a Source #

(<|>) :: IO a -> IO a -> IO a Source #

some :: IO a -> IO [a] Source #

many :: IO a -> IO [a] Source #

MonadIO IO #

Since: 4.9.0.0

Methods

liftIO :: IO a -> IO a Source #

Semigroup a => Semigroup (IO a) #

Since: 4.10.0.0

Methods

(<>) :: IO a -> IO a -> IO a Source #

sconcat :: NonEmpty (IO a) -> IO a Source #

stimes :: Integral b => b -> IO a -> IO a Source #

Monoid a => Monoid (IO a) #

Since: 4.9.0.0

Methods

mempty :: IO a Source #

mappend :: IO a -> IO a -> IO a Source #

mconcat :: [IO a] -> IO a Source #

(~) * a () => HPrintfType (IO a) #

Since: 4.7.0.0

Methods

hspr :: Handle -> String -> [UPrintf] -> IO a

(~) * a () => PrintfType (IO a) #

Since: 4.7.0.0

Methods

spr :: String -> [UPrintf] -> IO a

Simple I/O operations

Output functions

putChar :: Char -> IO () Source #

Write a character to the standard output device (same as hPutChar stdout).

putStr :: String -> IO () Source #

Write a string to the standard output device (same as hPutStr stdout).

putStrLn :: String -> IO () Source #

The same as putStr, but adds a newline character.

print :: Show a => a -> IO () Source #

The print function outputs a value of any printable type to the standard output device. Printable types are those that are instances of class Show; print converts values to strings for output using the show operation and adds a newline.

For example, a program to print the first 20 integers and their powers of 2 could be written as:

main = print ([(n, 2^n) | n <- [0..19]])

Input functions

getChar :: IO Char Source #

Read a character from the standard input device (same as hGetChar stdin).

getLine :: IO String Source #

Read a line from the standard input device (same as hGetLine stdin).

getContents :: IO String Source #

The getContents operation returns all user input as a single string, which is read lazily as it is needed (same as hGetContents stdin).

interact :: (String -> String) -> IO () Source #

The interact function takes a function of type String->String as its argument. The entire input from the standard input device is passed to this function as its argument, and the resulting string is output on the standard output device.

Files

type FilePath = String Source #

File and directory names are values of type String, whose precise meaning is operating system dependent. Files can be opened, yielding a handle which can then be used to operate on the contents of that file.

readFile :: FilePath -> IO String Source #

The readFile function reads a file and returns the contents of the file as a string. The file is read lazily, on demand, as with getContents.

writeFile :: FilePath -> String -> IO () Source #

The computation writeFile file str function writes the string str, to the file file.

appendFile :: FilePath -> String -> IO () Source #

The computation appendFile file str function appends the string str, to the file file.

Note that writeFile and appendFile write a literal string to a file. To write a value of any printable type, as with print, use the show function to convert the value to a string first.

main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])

readIO :: Read a => String -> IO a Source #

The readIO function is similar to read except that it signals parse failure to the IO monad instead of terminating the program.

readLn :: Read a => IO a Source #

The readLn function combines getLine and readIO.

Exception handling in the I/O monad

type IOError = IOException Source #

The Haskell 2010 type for exceptions in the IO monad. Any I/O operation may raise an IOError instead of returning a result. For a more general type of exception, including also those that arise in pure code, see Exception.

In Haskell 2010, this is an opaque type.

ioError :: IOError -> IO a Source #

Raise an IOError in the IO monad.

userError :: String -> IOError Source #

Construct an IOError value with a string describing the error. The fail method of the IO instance of the Monad class raises a userError, thus:

instance Monad IO where
  ...
  fail s = ioError (userError s)