Safe Haskell  Safe 

Language  Haskell98 
Synopsis
 ($!) :: (a > b) > a > b
 catch :: IO a > (IOError > IO a) > IO a
 gcd :: Integral a => a > a > a
 ($) :: (a > b) > a > b
 (&&) :: Bool > Bool > Bool
 (.) :: (b > c) > (a > b) > a > c
 (=<<) :: Monad m => (a > m b) > m a > m b
 data Bool
 class Bounded a where
 data Char
 data Double
 data Either a b
 class Enum a where
 succ :: a > a
 pred :: a > a
 toEnum :: Int > a
 fromEnum :: a > Int
 enumFrom :: a > [a]
 enumFromThen :: a > a > [a]
 enumFromTo :: a > a > [a]
 enumFromThenTo :: a > a > a > [a]
 class Eq a where
 type FilePath = String
 data Float
 class Fractional a => Floating a where
 class Num a => Fractional a where
 (/) :: a > a > a
 recip :: a > a
 fromRational :: Rational > a
 class Functor (f :: Type > Type) where
 fmap :: (a > b) > f a > f b
 data IO a
 type IOError = IOException
 data Int
 data Integer
 class (Real a, Enum a) => Integral a where
 data Maybe a
 class Applicative m => Monad (m :: Type > Type) where
 fail :: Monad m => String > m a
 class Num a where
 class Eq a => Ord a where
 data Ordering
 type Rational = Ratio Integer
 class Read a where
 type ReadS a = String > [(a, String)]
 class (Num a, Ord a) => Real a where
 toRational :: a > Rational
 class (RealFrac a, Floating a) => RealFloat a where
 floatRadix :: a > Integer
 floatDigits :: a > Int
 floatRange :: a > (Int, Int)
 decodeFloat :: a > (Integer, Int)
 encodeFloat :: Integer > Int > a
 exponent :: a > Int
 significand :: a > a
 scaleFloat :: Int > a > a
 isNaN :: a > Bool
 isInfinite :: a > Bool
 isDenormalized :: a > Bool
 isNegativeZero :: a > Bool
 isIEEE :: a > Bool
 atan2 :: a > a > a
 class (Real a, Fractional a) => RealFrac a where
 class Show a where
 type ShowS = String > String
 type String = [Char]
 (^) :: (Num a, Integral b) => a > b > a
 (^^) :: (Fractional a, Integral b) => a > b > a
 appendFile :: FilePath > String > IO ()
 asTypeOf :: a > a > a
 const :: a > b > a
 curry :: ((a, b) > c) > a > b > c
 either :: (a > c) > (b > c) > Either a b > c
 error :: HasCallStack => [Char] > a
 even :: Integral a => a > Bool
 flip :: (a > b > c) > b > a > c
 fromIntegral :: (Integral a, Num b) => a > b
 fst :: (a, b) > a
 getChar :: IO Char
 getContents :: IO String
 getLine :: IO String
 id :: a > a
 interact :: (String > String) > IO ()
 ioError :: IOError > IO a
 lcm :: Integral a => a > a > a
 lex :: ReadS String
 lines :: String > [String]
 mapM :: (Traversable t, Monad m) => (a > m b) > t a > m (t b)
 mapM_ :: (Foldable t, Monad m) => (a > m b) > t a > m ()
 maximum :: (Foldable t, Ord a) => t a > a
 maybe :: b > (a > b) > Maybe a > b
 minimum :: (Foldable t, Ord a) => t a > a
 not :: Bool > Bool
 odd :: Integral a => a > Bool
 otherwise :: Bool
 print :: Show a => a > IO ()
 product :: (Foldable t, Num a) => t a > a
 putChar :: Char > IO ()
 putStr :: String > IO ()
 putStrLn :: String > IO ()
 read :: Read a => String > a
 readFile :: FilePath > IO String
 readIO :: Read a => String > IO a
 readLn :: Read a => IO a
 readParen :: Bool > ReadS a > ReadS a
 reads :: Read a => ReadS a
 realToFrac :: (Real a, Fractional b) => a > b
 seq :: a > b > b
 sequence :: (Traversable t, Monad m) => t (m a) > m (t a)
 sequence_ :: (Foldable t, Monad m) => t (m a) > m ()
 showChar :: Char > ShowS
 showParen :: Bool > ShowS > ShowS
 showString :: String > ShowS
 shows :: Show a => a > ShowS
 snd :: (a, b) > b
 subtract :: Num a => a > a > a
 sum :: (Foldable t, Num a) => t a > a
 uncurry :: (a > b > c) > (a, b) > c
 undefined :: HasCallStack => a
 unlines :: [String] > String
 until :: (a > Bool) > (a > a) > a > a
 userError :: String > IOError
 writeFile :: FilePath > String > IO ()
 () :: Bool > Bool > Bool
 (!!) :: [a] > Int > a
 (++) :: [a] > [a] > [a]
 all :: (a > Bool) > [a] > Bool
 and :: [Bool] > Bool
 any :: (a > Bool) > [a] > Bool
 break :: (a > Bool) > [a] > ([a], [a])
 concat :: [[a]] > [a]
 concatMap :: (a > [b]) > [a] > [b]
 cycle :: [a] > [a]
 drop :: Int > [a] > [a]
 dropWhile :: (a > Bool) > [a] > [a]
 elem :: Eq a => a > [a] > Bool
 filter :: (a > Bool) > [a] > [a]
 foldl :: (a > b > a) > a > [b] > a
 foldl1 :: (a > a > a) > [a] > a
 foldr :: (a > b > b) > b > [a] > b
 foldr1 :: (a > a > a) > [a] > a
 head :: [a] > a
 init :: [a] > [a]
 iterate :: (a > a) > a > [a]
 last :: [a] > a
 length :: [a] > Int
 lookup :: Eq a => a > [(a, b)] > Maybe b
 map :: (a > b) > [a] > [b]
 notElem :: Eq a => a > [a] > Bool
 null :: [a] > Bool
 or :: [Bool] > Bool
 repeat :: a > [a]
 replicate :: Int > a > [a]
 reverse :: [a] > [a]
 scanl :: (a > b > a) > a > [b] > [a]
 scanl1 :: (a > a > a) > [a] > [a]
 scanr :: (a > b > b) > b > [a] > [b]
 scanr1 :: (a > a > a) > [a] > [a]
 span :: (a > Bool) > [a] > ([a], [a])
 splitAt :: Int > [a] > ([a], [a])
 tail :: [a] > [a]
 take :: Int > [a] > [a]
 takeWhile :: (a > Bool) > [a] > [a]
 unwords :: [String] > String
 unzip :: [(a, b)] > ([a], [b])
 unzip3 :: [(a, b, c)] > ([a], [b], [c])
 words :: String > [String]
 zip :: [a] > [b] > [(a, b)]
 zip3 :: [a] > [b] > [c] > [(a, b, c)]
 zipWith :: (a > b > c) > [a] > [b] > [c]
 zipWith3 :: (a > b > c > d) > [a] > [b] > [c] > [d]
Documentation
($!) :: (a > b) > a > b infixr 0 #
Strict (callbyvalue) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.
gcd :: Integral a => a > a > a #
is the nonnegative factor of both gcd
x yx
and y
of which
every common factor of x
and y
is also a factor; for example
, gcd
4 2 = 2
, gcd
(4) 6 = 2
= gcd
0 44
.
= gcd
0 00
.
(That is, the common divisor that is "greatest" in the divisibility
preordering.)
Note: Since for signed fixedwidth integer types,
,
the result may be negative if one of the arguments is abs
minBound
< 0
(and
necessarily is if the other is minBound
0
or
) for such types.minBound
($) :: (a > b) > a > b infixr 0 #
Application operator. This operator is redundant, since ordinary
application (f x)
means the same as (f
. However, $
x)$
has
low, rightassociative 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 higherorder situations, such as
,
or map
($
0) xs
.zipWith
($
) fs xs
Note that ($)
is levitypolymorphic in its result type, so that
foo $ True where foo :: Bool > Int#
is welltyped
(=<<) :: Monad m => (a > m b) > m a > m b infixr 1 #
Same as >>=
, but with the arguments interchanged.
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 singleconstructor datatypes whose
constituent types are in Bounded
.
Instances
Bounded Bool  Since: base2.1 
Bounded Char  Since: base2.1 
Bounded Int  Since: base2.1 
Bounded Ordering  Since: base2.1 
Bounded Word  Since: base2.1 
Bounded VecCount  Since: base4.10.0.0 
Bounded VecElem  Since: base4.10.0.0 
Bounded ()  Since: base2.1 
(Bounded a, Bounded b) => Bounded (a, b)  Since: base2.1 
(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c)  Since: base2.1 
(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d)  Since: base2.1 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e)  Since: base2.1 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f)  Since: base2.1 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g)  Since: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
The character type Char
is an enumeration whose values represent
Unicode (or equivalently ISO/IEC 10646) code points (i.e. characters, see
http://www.unicode.org/ for details). This set extends the ISO 88591
(Latin1) 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: base2.1 
Enum Char  Since: base2.1 
Eq Char  
Ord Char  
Read Char  Since: base2.1 
Show Char  Since: base2.1 
Foldable (URec Char :: Type > Type)  Since: base4.9.0.0 
Defined in Data.Foldable fold :: Monoid m => URec Char m > m # foldMap :: Monoid m => (a > m) > URec Char a > m # foldr :: (a > b > b) > b > URec Char a > b # foldr' :: (a > b > b) > b > URec Char a > b # foldl :: (b > a > b) > b > URec Char a > b # foldl' :: (b > a > b) > b > URec Char a > b # foldr1 :: (a > a > a) > URec Char a > a # foldl1 :: (a > a > a) > URec Char a > a # toList :: URec Char a > [a] # length :: URec Char a > Int # elem :: Eq a => a > URec Char a > Bool # maximum :: Ord a => URec Char a > a # minimum :: Ord a => URec Char a > a #  
Traversable (URec Char :: Type > Type)  Since: base4.9.0.0 
Doubleprecision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE doubleprecision type.
Instances
Eq Double  Note that due to the presence of
Also note that

Floating Double  Since: base2.1 
Ord Double  Note that due to the presence of
Also note that, due to the same,

Read Double  Since: base2.1 
RealFloat Double  Since: base2.1 
Defined in GHC.Float floatRadix :: Double > Integer # floatDigits :: Double > Int # floatRange :: Double > (Int, Int) # decodeFloat :: Double > (Integer, Int) # encodeFloat :: Integer > Int > Double # significand :: Double > Double # scaleFloat :: Int > Double > Double # isInfinite :: Double > Bool # isDenormalized :: Double > Bool # isNegativeZero :: Double > Bool #  
Foldable (URec Double :: Type > Type)  Since: base4.9.0.0 
Defined in Data.Foldable fold :: Monoid m => URec Double m > m # foldMap :: Monoid m => (a > m) > URec Double a > m # foldr :: (a > b > b) > b > URec Double a > b # foldr' :: (a > b > b) > b > URec Double a > b # foldl :: (b > a > b) > b > URec Double a > b # foldl' :: (b > a > b) > b > URec Double a > b # foldr1 :: (a > a > a) > URec Double a > a # foldl1 :: (a > a > a) > URec Double a > a # toList :: URec Double a > [a] # null :: URec Double a > Bool # length :: URec Double a > Int # elem :: Eq a => a > URec Double a > Bool # maximum :: Ord a => URec Double a > a # minimum :: Ord a => URec Double a > a #  
Traversable (URec Double :: Type > Type)  Since: base4.9.0.0 
Defined in Data.Traversable 
The Either
type represents values with two possibilities: a value of
type
is either Either
a b
or Left
a
.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
is the type of values which can be either
a Either
String
Int
String
or an Int
. The Left
constructor can be used only on
String
s, and the Right
constructor can be used only on Int
s:
>>>
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 Int
s.
>>>
:{
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"
Instances
Monad (Either e)  Since: base4.4.0.0 
Functor (Either a)  Since: base3.0 
Applicative (Either e)  Since: base3.0 
Foldable (Either a)  Since: base4.7.0.0 
Defined in Data.Foldable fold :: Monoid m => Either a m > m # foldMap :: Monoid m => (a0 > m) > Either a a0 > m # foldr :: (a0 > b > b) > b > Either a a0 > b # foldr' :: (a0 > b > b) > b > Either a a0 > b # foldl :: (b > a0 > b) > b > Either a a0 > b # foldl' :: (b > a0 > b) > b > Either a a0 > b # foldr1 :: (a0 > a0 > a0) > Either a a0 > a0 # foldl1 :: (a0 > a0 > a0) > Either a a0 > a0 # toList :: Either a a0 > [a0] # length :: Either a a0 > Int # elem :: Eq a0 => a0 > Either a a0 > Bool # maximum :: Ord a0 => Either a a0 > a0 # minimum :: Ord a0 => Either a a0 > a0 #  
Traversable (Either a)  Since: base4.7.0.0 
(Eq a, Eq b) => Eq (Either a b)  Since: base2.1 
(Ord a, Ord b) => Ord (Either a b)  Since: base2.1 
(Read a, Read b) => Read (Either a b)  Since: base3.0 
(Show a, Show b) => Show (Either a b)  Since: base3.0 
Semigroup (Either a b)  Since: base4.9.0.0 
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 lefttoright by fromEnum
from 0
through n1
.
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:
 The calls
andsucc
maxBound
should result in a runtime error.pred
minBound
fromEnum
andtoEnum
should give a runtime error if the result value is not representable in the result type. For example,
is an error.toEnum
7 ::Bool
enumFrom
andenumFromThen
should be defined with an implicit bound, thus:
enumFrom x = enumFromTo x maxBound enumFromThen x y = enumFromThenTo x y bound where bound  fromEnum y >= fromEnum x = maxBound  otherwise = minBound
the successor of a value. For numeric types, succ
adds 1.
the predecessor of a value. For numeric types, pred
subtracts 1.
Convert from an Int
.
Convert to an Int
.
It is implementationdependent what fromEnum
returns when
applied to a value that is too large to fit in an Int
.
Used in Haskell's translation of [n..]
with [n..] = enumFrom n
,
a possible implementation being enumFrom n = n : enumFrom (succ n)
.
For example:
enumFrom 4 :: [Integer] = [4,5,6,7,...]
enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]
enumFromThen :: a > a > [a] #
Used in Haskell's translation of [n,n'..]
with [n,n'..] = enumFromThen n n'
, a possible implementation being
enumFromThen n n' = n : n' : worker (f x) (f x n')
,
worker s v = v : worker s (s v)
, x = fromEnum n'  fromEnum n
and
f n y
 n > 0 = f (n  1) (succ y)
 n < 0 = f (n + 1) (pred y)
 otherwise = y
For example:
enumFromThen 4 6 :: [Integer] = [4,6,8,10...]
enumFromThen 6 2 :: [Int] = [6,2,2,6,...,minBound :: Int]
enumFromTo :: a > a > [a] #
Used in Haskell's translation of [n..m]
with
[n..m] = enumFromTo n m
, a possible implementation being
enumFromTo n m
 n <= m = n : enumFromTo (succ n) m
 otherwise = []
.
For example:
enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
enumFromTo 42 1 :: [Integer] = []
enumFromThenTo :: a > a > a > [a] #
Used in Haskell's translation of [n,n'..m]
with
[n,n'..m] = enumFromThenTo n n' m
, a possible implementation
being enumFromThenTo n n' m = worker (f x) (c x) n m
,
x = fromEnum n'  fromEnum n
, c x = bool (>=) ((x 0)
f n y
 n > 0 = f (n  1) (succ y)
 n < 0 = f (n + 1) (pred y)
 otherwise = y
and
worker s c v m
 c v m = v : worker s c (s v) m
 otherwise = []
For example:
enumFromThenTo 4 2 6 :: [Integer] = [4,2,0,2,4,6]
enumFromThenTo 6 8 2 :: [Int] = []
Instances
Enum Bool  Since: base2.1 
Enum Char  Since: base2.1 
Enum Int  Since: base2.1 
Enum Integer  Since: base2.1 
Enum Natural  Since: base4.8.0.0 
Enum Ordering  Since: base2.1 
Enum Word  Since: base2.1 
Enum VecCount  Since: base4.10.0.0 
Enum VecElem  Since: base4.10.0.0 
Enum ()  Since: base2.1 
Integral a => Enum (Ratio a)  Since: base2.0.1 
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
.
The Haskell Report defines no laws for Eq
. However, ==
is customarily
expected to implement an equivalence relationship where two values comparing
equal are indistinguishable by "public" functions, with a "public" function
being one not allowing to see implementation details. For example, for a
type representing nonnormalised natural numbers modulo 100, a "public"
function doesn't make the difference between 1 and 201. It is expected to
have the following properties:
Instances
Eq Bool  
Eq Char  
Eq Double  Note that due to the presence of
Also note that

Eq Float  Note that due to the presence of
Also note that

Eq Int  
Eq Integer  
Eq Natural  Since: base4.8.0.0 
Eq Ordering  
Eq Word  
Eq ()  
Eq TyCon  
Eq Module  
Eq TrName  
Eq BigNat  
Eq AsyncException  Since: base4.2.0.0 
Defined in GHC.IO.Exception (==) :: AsyncException > AsyncException > Bool # (/=) :: AsyncException > AsyncException > Bool #  
Eq ArrayException  Since: base4.2.0.0 
Defined in GHC.IO.Exception (==) :: ArrayException > ArrayException > Bool # (/=) :: ArrayException > ArrayException > Bool #  
Eq ExitCode  
Eq IOErrorType  Since: base4.1.0.0 
Defined in GHC.IO.Exception (==) :: IOErrorType > IOErrorType > Bool # (/=) :: IOErrorType > IOErrorType > Bool #  
Eq MaskingState  Since: base4.3.0.0 
Defined in GHC.IO (==) :: MaskingState > MaskingState > Bool # (/=) :: MaskingState > MaskingState > Bool #  
Eq IOException  Since: base4.1.0.0 
Defined in GHC.IO.Exception (==) :: IOException > IOException > Bool # (/=) :: IOException > IOException > Bool #  
Eq SrcLoc  Since: base4.9.0.0 
Eq a => Eq [a]  
Eq a => Eq (Maybe a)  Since: base2.1 
Eq a => Eq (Ratio a)  Since: base2.1 
Eq a => Eq (NonEmpty a)  Since: base4.9.0.0 
(Eq a, Eq b) => Eq (Either a b)  Since: base2.1 
(Eq a, Eq b) => Eq (a, b)  
(Eq a, Eq b, Eq c) => Eq (a, b, c)  
(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d)  
(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e)  
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f)  
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g)  
(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)  
(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)  
(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)  
(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)  
(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)  
(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)  
(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)  
(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)  
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.
Singleprecision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE singleprecision type.
Instances
Eq Float  Note that due to the presence of
Also note that

Floating Float  Since: base2.1 
Ord Float  Note that due to the presence of
Also note that, due to the same,

Read Float  Since: base2.1 
RealFloat Float  Since: base2.1 
Defined in GHC.Float floatRadix :: Float > Integer # floatDigits :: Float > Int # floatRange :: Float > (Int, Int) # decodeFloat :: Float > (Integer, Int) # encodeFloat :: Integer > Int > Float # significand :: Float > Float # scaleFloat :: Int > Float > Float # isInfinite :: Float > Bool # isDenormalized :: Float > Bool # isNegativeZero :: Float > Bool #  
Foldable (URec Float :: Type > Type)  Since: base4.9.0.0 
Defined in Data.Foldable fold :: Monoid m => URec Float m > m # foldMap :: Monoid m => (a > m) > URec Float a > m # foldr :: (a > b > b) > b > URec Float a > b # foldr' :: (a > b > b) > b > URec Float a > b # foldl :: (b > a > b) > b > URec Float a > b # foldl' :: (b > a > b) > b > URec Float a > b # foldr1 :: (a > a > a) > URec Float a > a # foldl1 :: (a > a > a) > URec Float a > a # toList :: URec Float a > [a] # null :: URec Float a > Bool # length :: URec Float a > Int # elem :: Eq a => a > URec Float a > Bool # maximum :: Ord a => URec Float a > a # minimum :: Ord a => URec Float a > a #  
Traversable (URec Float :: Type > Type)  Since: base4.9.0.0 
Defined in Data.Traversable 
class Fractional a => Floating a where #
Trigonometric and hyperbolic functions and related functions.
The Haskell Report defines no laws for Floating
. However, '(+)', '(*)'
and exp
are customarily expected to define an exponential field and have
the following properties:
exp (a + b)
= @exp a * exp bexp (fromInteger 0)
=fromInteger 1
class Num a => Fractional a where #
Fractional numbers, supporting real division.
The Haskell Report defines no laws for Fractional
. However, '(+)' and
'(*)' are customarily expected to define a division ring and have the
following properties:
recip
gives the multiplicative inversex * recip x
=recip x * x
=fromInteger 1
Note that it isn't customarily expected that a type instance of
Fractional
implement a field. However, all instances in base
do.
fromRational, (recip  (/))
fractional division
reciprocal fraction
fromRational :: Rational > a #
Conversion from a Rational
(that is
).
A floating literal stands for an application of Ratio
Integer
fromRational
to a value of type Rational
, so such literals have type
(
.Fractional
a) => a
class Functor (f :: Type > Type) where #
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.
Instances
Functor []  Since: base2.1 
Functor Maybe  Since: base2.1 
Functor IO  Since: base2.1 
Functor ReadP  Since: base2.1 
Functor NonEmpty  Since: base4.9.0.0 
Functor P  Since: base4.8.0.0 
Defined in Text.ParserCombinators.ReadP  
Functor (Either a)  Since: base3.0 
Functor ((,) a)  Since: base2.1 
Functor ((>) r :: Type > Type)  Since: base2.1 
A value of type
is a computation which, when performed,
does some I/O before returning a value of type IO
aa
.
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 donotation
or the >>
and >>=
operations from the Monad
class.
type IOError = IOException #
The Haskell 2010 type for exceptions in the IO
monad.
Any I/O operation may raise an IOException
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.
A fixedprecision integer type with at least the range [2^29 .. 2^291]
.
The exact range for a given implementation can be determined by using
minBound
and maxBound
from the Bounded
class.
Instances
Bounded Int  Since: base2.1 
Enum Int  Since: base2.1 
Eq Int  
Integral Int  Since: base2.0.1 
Num Int  Since: base2.1 
Ord Int  
Read Int  Since: base2.1 
Real Int  Since: base2.0.1 
Defined in GHC.Real toRational :: Int > Rational #  
Show Int  Since: base2.1 
Foldable (URec Int :: Type > Type)  Since: base4.9.0.0 
Defined in Data.Foldable fold :: Monoid m => URec Int m > m # foldMap :: Monoid m => (a > m) > URec Int a > m # foldr :: (a > b > b) > b > URec Int a > b # foldr' :: (a > b > b) > b > URec Int a > b # foldl :: (b > a > b) > b > URec Int a > b # foldl' :: (b > a > b) > b > URec Int a > b # foldr1 :: (a > a > a) > URec Int a > a # foldl1 :: (a > a > a) > URec Int a > a # elem :: Eq a => a > URec Int a > Bool # maximum :: Ord a => URec Int a > a # minimum :: Ord a => URec Int a > a #  
Traversable (URec Int :: Type > Type)  Since: base4.9.0.0 
Invariant: Jn#
and Jp#
are used iff value doesn't fit in S#
Useful properties resulting from the invariants:
Instances
Enum Integer  Since: base2.1 
Eq Integer  
Integral Integer  Since: base2.0.1 
Defined in GHC.Real  
Num Integer  Since: base2.1 
Ord Integer  
Read Integer  Since: base2.1 
Real Integer  Since: base2.0.1 
Defined in GHC.Real toRational :: Integer > Rational #  
Show Integer  Since: base2.1 
class (Real a, Enum a) => Integral a where #
Integral numbers, supporting integer division.
The Haskell Report defines no laws for Integral
. However, Integral
instances are customarily expected to define a Euclidean domain and have the
following properties for the 'div'/'mod' and 'quot'/'rem' pairs, given
suitable Euclidean functions f
and g
:
x
=y * quot x y + rem x y
withrem x y
=fromInteger 0
org (rem x y)
<g y
x
=y * div x y + mod x y
withmod x y
=fromInteger 0
orf (mod x y)
<f y
An example of a suitable Euclidean function, for Integer
's instance, is
abs
.
quot :: a > a > a infixl 7 #
integer division truncated toward zero
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
integer division truncated toward negative infinity
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
conversion to Integer
The Maybe
type encapsulates an optional value. A value of type
either contains a value of type Maybe
aa
(represented as
),
or it is empty (represented as Just
aNothing
). 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.
Instances
Monad Maybe  Since: base2.1 
Functor Maybe  Since: base2.1 
Applicative Maybe  Since: base2.1 
Foldable Maybe  Since: base2.1 
Defined in Data.Foldable fold :: Monoid m => Maybe m > m # foldMap :: Monoid m => (a > m) > Maybe a > m # foldr :: (a > b > b) > b > Maybe a > b # foldr' :: (a > b > b) > b > Maybe a > b # foldl :: (b > a > b) > b > Maybe a > b # foldl' :: (b > a > b) > b > Maybe a > b # foldr1 :: (a > a > a) > Maybe a > a # foldl1 :: (a > a > a) > Maybe a > a # elem :: Eq a => a > Maybe a > Bool # maximum :: Ord a => Maybe a > a # minimum :: Ord a => Maybe a > a #  
Traversable Maybe  Since: base2.1 
Alternative Maybe  Since: base2.1 
MonadPlus Maybe  Since: base2.1 
Eq a => Eq (Maybe a)  Since: base2.1 
Ord a => Ord (Maybe a)  Since: base2.1 
Read a => Read (Maybe a)  Since: base2.1 
Show a => Show (Maybe a)  Since: base2.1 
Semigroup a => Semigroup (Maybe a)  Since: base4.9.0.0 
Semigroup a => Monoid (Maybe a)  Lift a semigroup into Since 4.11.0: constraint on inner Since: base2.1 
class Applicative m => Monad (m :: Type > Type) where #
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.
(>>=) :: m a > (a > m b) > m b infixl 1 #
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
(>>) :: m a > m b > m b infixl 1 #
Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.
Inject a value into the monadic type.
fail :: Monad m => String > m a #
Fail with a message. This operation is not part of the
mathematical definition of a monad, but is invoked on patternmatch
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.
Basic numeric class.
The Haskell Report defines no laws for Num
. However, '(+)' and '(*)' are
customarily expected to define a ring and have the following properties:
 Associativity of (+)
(x + y) + z
=x + (y + z)
 Commutativity of (+)
x + y
=y + x
fromInteger 0
is the additive identityx + fromInteger 0
=x
negate
gives the additive inversex + negate x
=fromInteger 0
 Associativity of (*)
(x * y) * z
=x * (y * z)
fromInteger 1
is the multiplicative identityx * fromInteger 1
=x
andfromInteger 1 * x
=x
 Distributivity of (*) with respect to (+)
a * (b + c)
=(a * b) + (a * c)
and(b + c) * a
=(b * a) + (c * a)
Note that it isn't customarily expected that a type instance of both Num
and Ord
implement an ordered ring. Indeed, in base
only Integer
and
Rational
do.
Unary negation.
Absolute value.
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 #
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
The Ord
class is used for totally ordered datatypes.
Instances of Ord
can be derived for any userdefined 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.
The Haskell Report defines no laws for Ord
. However, <=
is customarily
expected to implement a nonstrict partial order and have the following
properties:
 Transitivity
 if
x <= y && y <= z
=True
, thenx <= z
=True
 Reflexivity
x <= x
=True
 Antisymmetry
 if
x <= y && y <= x
=True
, thenx == y
=True
Note that the following operator interactions are expected to hold:
x >= y
=y <= x
x < y
=x <= y && x /= y
x > y
=y < x
x < y
=compare x y == LT
x > y
=compare x y == GT
x == y
=compare x y == EQ
min x y == if x <= y then x else y
=True
max x y == if x >= y then x else y
=True
Minimal complete definition: either compare
or <=
.
Using compare
can be more efficient for complex types.
compare :: a > a > Ordering #
(<) :: a > a > Bool infix 4 #
(<=) :: a > a > Bool infix 4 #
(>) :: a > a > Bool infix 4 #
Instances
Ord Bool  
Ord Char  
Ord Double  Note that due to the presence of
Also note that, due to the same,

Ord Float  Note that due to the presence of
Also note that, due to the same,

Ord Int  
Ord Integer  
Ord Natural  Since: base4.8.0.0 
Ord Ordering  
Defined in GHC.Classes  
Ord Word  
Ord ()  
Ord TyCon  
Ord BigNat  
Ord AsyncException  Since: base4.2.0.0 
Defined in GHC.IO.Exception compare :: AsyncException > AsyncException > Ordering # (<) :: AsyncException > AsyncException > Bool # (<=) :: AsyncException > AsyncException > Bool # (>) :: AsyncException > AsyncException > Bool # (>=) :: AsyncException > AsyncException > Bool # max :: AsyncException > AsyncException > AsyncException # min :: AsyncException > AsyncException > AsyncException #  
Ord ArrayException  Since: base4.2.0.0 
Defined in GHC.IO.Exception compare :: ArrayException > ArrayException > Ordering # (<) :: ArrayException > ArrayException > Bool # (<=) :: ArrayException > ArrayException > Bool # (>) :: ArrayException > ArrayException > Bool # (>=) :: ArrayException > ArrayException > Bool # max :: ArrayException > ArrayException > ArrayException # min :: ArrayException > ArrayException > ArrayException #  
Ord ExitCode  
Defined in GHC.IO.Exception  
Ord a => Ord [a]  
Ord a => Ord (Maybe a)  Since: base2.1 
Integral a => Ord (Ratio a)  Since: base2.0.1 
Ord a => Ord (NonEmpty a)  Since: base4.9.0.0 
(Ord a, Ord b) => Ord (Either a b)  Since: base2.1 
(Ord a, Ord b) => Ord (a, b)  
(Ord a, Ord b, Ord c) => Ord (a, b, c)  
Defined in GHC.Classes  
(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d)  
Defined in GHC.Classes  
(Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e)  
Defined in GHC.Classes compare :: (a, b, c, d, e) > (a, b, c, d, e) > Ordering # (<) :: (a, b, c, d, e) > (a, b, c, d, e) > Bool # (<=) :: (a, b, c, d, e) > (a, b, c, d, e) > Bool # (>) :: (a, b, c, d, e) > (a, b, c, d, e) > Bool # (>=) :: (a, b, c, d, e) > (a, b, c, d, e) > Bool # max :: (a, b, c, d, e) > (a, b, c, d, e) > (a, b, c, d, e) # min :: (a, b, c, d, e) > (a, b, c, d, e) > (a, b, c, d, e) #  
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f)  
Defined in GHC.Classes compare :: (a, b, c, d, e, f) > (a, b, c, d, e, f) > Ordering # (<) :: (a, b, c, d, e, f) > (a, b, c, d, e, f) > Bool # (<=) :: (a, b, c, d, e, f) > (a, b, c, d, e, f) > Bool # (>) :: (a, b, c, d, e, f) > (a, b, c, d, e, f) > Bool # (>=) :: (a, b, c, d, e, f) > (a, b, c, d, e, f) > Bool # max :: (a, b, c, d, e, f) > (a, b, c, d, e, f) > (a, b, c, d, e, f) # min :: (a, b, c, d, e, f) > (a, b, c, d, e, f) > (a, b, c, d, e, f) #  
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g)  
Defined in GHC.Classes compare :: (a, b, c, d, e, f, g) > (a, b, c, d, e, f, g) > Ordering # (<) :: (a, b, c, d, e, f, g) > (a, b, c, d, e, f, g) > Bool # (<=) :: (a, b, c, d, e, f, g) > (a, b, c, d, e, f, g) > Bool # (>) :: (a, b, c, d, e, f, g) > (a, b, c, d, e, f, g) > Bool # (>=) :: (a, b, c, d, e, f, g) > (a, b, c, d, e, f, g) > Bool # max :: (a, b, c, d, e, f, g) > (a, b, c, d, e, f, g) > (a, b, c, d, e, f, g) # min :: (a, b, c, d, e, f, g) > (a, b, c, d, e, f, g) > (a, b, c, d, e, f, g) #  
(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)  
Defined in GHC.Classes compare :: (a, b, c, d, e, f, g, h) > (a, b, c, d, e, f, g, h) > Ordering # (<) :: (a, b, c, d, e, f, g, h) > (a, b, c, d, e, f, g, h) > Bool # (<=) :: (a, b, c, d, e, f, g, h) > (a, b, c, d, e, f, g, h) > Bool # (>) :: (a, b, c, d, e, f, g, h) > (a, b, c, d, e, f, g, h) > Bool # (>=) :: (a, b, c, d, e, f, g, h) > (a, b, c, d, e, f, g, h) > Bool # 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) # 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) #  
(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)  
Defined in GHC.Classes compare :: (a, b, c, d, e, f, g, h, i) > (a, b, c, d, e, f, g, h, i) > Ordering # (<) :: (a, b, c, d, e, f, g, h, i) > (a, b, c, d, e, f, g, h, i) > Bool # (<=) :: (a, b, c, d, e, f, g, h, i) > (a, b, c, d, e, f, g, h, i) > Bool # (>) :: (a, b, c, d, e, f, g, h, i) > (a, b, c, d, e, f, g, h, i) > Bool # (>=) :: (a, b, c, d, e, f, g, h, i) > (a, b, c, d, e, f, g, h, i) > Bool # 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) # 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) #  
(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)  
Defined in GHC.Classes compare :: (a, b, c, d, e, f, g, h, i, j) > (a, b, c, d, e, f, g, h, i, j) > Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j) > (a, b, c, d, e, f, g, h, i, j) > Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j) > (a, b, c, d, e, f, g, h, i, j) > Bool # (>) :: (a, b, c, d, e, f, g, h, i, j) > (a, b, c, d, e, f, g, h, i, j) > Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j) > (a, b, c, d, e, f, g, h, i, j) > Bool # 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) # 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) #  
(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)  
Defined in GHC.Classes compare :: (a, b, c, d, e, f, g, h, i, j, k) > (a, b, c, d, e, f, g, h, i, j, k) > Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k) > (a, b, c, d, e, f, g, h, i, j, k) > Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k) > (a, b, c, d, e, f, g, h, i, j, k) > Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k) > (a, b, c, d, e, f, g, h, i, j, k) > Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k) > (a, b, c, d, e, f, g, h, i, j, k) > Bool # 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) # 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) #  
(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)  
Defined in GHC.Classes 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 # (<) :: (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 # (<=) :: (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 # (>) :: (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 # (>=) :: (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 # 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) # 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) #  
(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)  
Defined in GHC.Classes 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 # (<) :: (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 # (<=) :: (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 # (>) :: (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 # (>=) :: (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 # 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) # 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) #  
(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)  
Defined in GHC.Classes 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 # (<) :: (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 # (<=) :: (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 # (>) :: (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 # (>=) :: (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 # 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) # 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) #  
(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)  
Defined in GHC.Classes 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 # (<) :: (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 # (<=) :: (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 # (>) :: (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 # (>=) :: (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 # 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) # 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) # 
Instances
Bounded Ordering  Since: base2.1 
Enum Ordering  Since: base2.1 
Eq Ordering  
Ord Ordering  
Defined in GHC.Classes  
Read Ordering  Since: base2.1 
Show Ordering  Since: base2.1 
Semigroup Ordering  Since: base4.9.0.0 
Monoid Ordering  Since: base2.1 
Parsing of String
s, 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 recordsyntax 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 rightassociativity 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 "newstyle parsers"), but its definition relies on the use
of the RankNTypes
language extension. Therefore, readPrec
(and its
cousin, readListPrec
) are marked as GHConly. 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:
instanceRead
T wherereadPrec
= ...readListPrec
=readListPrecDefault
:: Int  the operator precedence of the enclosing
context (a number from 
> 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.
Instances
Read Bool  Since: base2.1 
Read Char  Since: base2.1 
Read Double  Since: base2.1 
Read Float  Since: base2.1 
Read Int  Since: base2.1 
Read Integer  Since: base2.1 
Read Natural  Since: base4.8.0.0 
Read Ordering  Since: base2.1 
Read Word  Since: base4.5.0.0 
Read Word8  Since: base2.1 
Read Word16  Since: base2.1 
Read Word32  Since: base2.1 
Read Word64  Since: base2.1 
Read ()  Since: base2.1 
Read ExitCode  
Read Lexeme  Since: base2.1 
Read GeneralCategory  Since: base2.1 
Defined in GHC.Read  
Read a => Read [a]  Since: base2.1 
Read a => Read (Maybe a)  Since: base2.1 
(Integral a, Read a) => Read (Ratio a)  Since: base2.1 
Read a => Read (NonEmpty a)  Since: base4.11.0.0 
(Read a, Read b) => Read (Either a b)  Since: base3.0 
(Read a, Read b) => Read (a, b)  Since: base2.1 
(Ix a, Read a, Read b) => Read (Array a b)  Since: base2.1 
(Read a, Read b, Read c) => Read (a, b, c)  Since: base2.1 
(Read a, Read b, Read c, Read d) => Read (a, b, c, d)  Since: base2.1 
(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e)  Since: base2.1 
(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f)  Since: base2.1 
(Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g)  Since: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
Defined in GHC.Read 
class (Num a, Ord a) => Real a where #
toRational :: a > Rational #
the rational equivalent of its real argument with full precision
Instances
Real Int  Since: base2.0.1 
Defined in GHC.Real toRational :: Int > Rational #  
Real Integer  Since: base2.0.1 
Defined in GHC.Real toRational :: Integer > Rational #  
Real Natural  Since: base4.8.0.0 
Defined in GHC.Real toRational :: Natural > Rational #  
Real Word  Since: base2.1 
Defined in GHC.Real toRational :: Word > Rational #  
Integral a => Real (Ratio a)  Since: base2.0.1 
Defined in GHC.Real toRational :: Ratio a > Rational # 
class (RealFrac a, Floating a) => RealFloat a where #
Efficient, machineindependent access to the components of a floatingpoint number.
floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE
floatRadix :: a > Integer #
a constant function, returning the radix of the representation
(often 2
)
floatDigits :: a > Int #
a constant function, returning the number of digits of
floatRadix
in the significand
floatRange :: a > (Int, Int) #
a constant function, returning the lowest and highest values the exponent may assume
decodeFloat :: a > (Integer, Int) #
The function decodeFloat
applied to a real floatingpoint
number returns the significand expressed as an Integer
and an
appropriately scaled exponent (an Int
). If
yields decodeFloat
x(m,n)
, then x
is equal in value to m*b^^n
, where b
is the floatingpoint radix, and furthermore, either m
and n
are both zero or else b^(d1) <=
, where abs
m < b^dd
is
the value of
.
In particular, floatDigits
x
. If the type
contains a negative zero, also decodeFloat
0 = (0,0)
.
The result of decodeFloat
(0.0) = (0,0)
is unspecified if either of
decodeFloat
x
or isNaN
x
is isInfinite
xTrue
.
encodeFloat :: Integer > Int > a #
encodeFloat
performs the inverse of decodeFloat
in the
sense that for finite x
with the exception of 0.0
,
.
uncurry
encodeFloat
(decodeFloat
x) = x
is one of the two closest representable
floatingpoint numbers to encodeFloat
m nm*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
corresponds to the second component of decodeFloat
.
and for finite nonzero exponent
0 = 0x
,
.
If exponent
x = snd (decodeFloat
x) + floatDigits
xx
is a finite floatingpoint number, it is equal in value to
, where significand
x * b ^^ exponent
xb
is the
floatingpoint radix.
The behaviour is unspecified on infinite or NaN
values.
significand :: a > a #
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 floatingpoint radix.
The behaviour is unspecified on infinite or NaN
values.
scaleFloat :: Int > a > a #
multiplies a floatingpoint number by an integer power of the radix
True
if the argument is an IEEE "notanumber" (NaN) value
isInfinite :: a > Bool #
True
if the argument is an IEEE infinity or negative infinity
isDenormalized :: a > Bool #
True
if the argument is too small to be represented in
normalized format
isNegativeZero :: a > Bool #
True
if the argument is an IEEE negative zero
True
if the argument is an IEEE floating point number
a version of arctangent taking two real floatingpoint arguments.
For real floating x
and y
,
computes the angle
(from the positive xaxis) of the vector from the origin to the
point atan2
y x(x,y)
.
returns a value in the range [atan2
y xpi
,
pi
]. It follows the Common Lisp semantics for the origin when
signed zeroes are supported.
, with atan2
y 1y
in a type
that is RealFloat
, should return the same value as
.
A default definition of atan
yatan2
is provided, but implementors
can provide a more accurate implementation.
Instances
RealFloat Double  Since: base2.1 
Defined in GHC.Float floatRadix :: Double > Integer # floatDigits :: Double > Int # floatRange :: Double > (Int, Int) # decodeFloat :: Double > (Integer, Int) # encodeFloat :: Integer > Int > Double # significand :: Double > Double # scaleFloat :: Int > Double > Double # isInfinite :: Double > Bool # isDenormalized :: Double > Bool # isNegativeZero :: Double > Bool #  
RealFloat Float  Since: base2.1 
Defined in GHC.Float floatRadix :: Float > Integer # floatDigits :: Float > Int # floatRange :: Float > (Int, Int) # decodeFloat :: Float > (Integer, Int) # encodeFloat :: Integer > Int > Float # significand :: Float > Float # scaleFloat :: Int > Float > Float # isInfinite :: Float > Bool # isDenormalized :: Float > Bool # isNegativeZero :: Float > Bool # 
class (Real a, Fractional a) => RealFrac a where #
Extracting components of fractions.
properFraction :: Integral b => a > (b, a) #
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 asx
; andf
is a fraction with the same type and sign asx
, and with absolute value less than1
.
The default definitions of the ceiling
, floor
, truncate
and round
functions are in terms of properFraction
.
truncate :: Integral b => a > b #
returns the integer nearest truncate
xx
between zero and x
round :: Integral b => a > b #
returns the nearest integer to round
xx
;
the even integer if x
is equidistant between two integers
ceiling :: Integral b => a > b #
returns the least integer not less than ceiling
xx
floor :: Integral b => a > b #
returns the greatest integer not greater than floor
xx
Conversion of values to readable String
s.
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 toplevel constructor in
x
is less thand
(associativity is ignored). Thus, ifd
is0
then the result is never surrounded in parentheses; ifd
is11
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 recordsyntax 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 rightassociativity of :^:
is ignored. For example,
produces the stringshow
(Leaf 1 :^: Leaf 2 :^: Leaf 3)"Leaf 1 :^: (Leaf 2 :^: Leaf 3)"
.
:: Int  the operator precedence of the enclosing
context (a number from 
> a  the value to be converted to a 
> 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.
Instances
Show Bool  Since: base2.1 
Show Char  Since: base2.1 
Show Int  Since: base2.1 
Show Integer  Since: base2.1 
Show Natural  Since: base4.8.0.0 
Show Ordering  Since: base2.1 
Show Word  Since: base2.1 
Show RuntimeRep  Since: base4.11.0.0 
Defined in GHC.Show showsPrec :: Int > RuntimeRep > ShowS # show :: RuntimeRep > String # showList :: [RuntimeRep] > ShowS #  
Show VecCount  Since: base4.11.0.0 
Show VecElem  Since: base4.11.0.0 
Show CallStack  Since: base4.9.0.0 
Show ()  Since: base2.1 
Show TyCon  Since: base2.1 
Show Module  Since: base4.9.0.0 
Show TrName  Since: base4.9.0.0 
Show KindRep  
Show TypeLitSort  Since: base4.11.0.0 
Defined in GHC.Show showsPrec :: Int > TypeLitSort > ShowS # show :: TypeLitSort > String # showList :: [TypeLitSort] > ShowS #  
Show BlockedIndefinitelyOnMVar  Since: base4.1.0.0 
Defined in GHC.IO.Exception showsPrec :: Int > BlockedIndefinitelyOnMVar > ShowS # show :: BlockedIndefinitelyOnMVar > String # showList :: [BlockedIndefinitelyOnMVar] > ShowS #  
Show BlockedIndefinitelyOnSTM  Since: base4.1.0.0 
Defined in GHC.IO.Exception showsPrec :: Int > BlockedIndefinitelyOnSTM > ShowS # show :: BlockedIndefinitelyOnSTM > String # showList :: [BlockedIndefinitelyOnSTM] > ShowS #  
Show Deadlock  Since: base4.1.0.0 
Show AllocationLimitExceeded  Since: base4.7.1.0 
Defined in GHC.IO.Exception showsPrec :: Int > AllocationLimitExceeded > ShowS # show :: AllocationLimitExceeded > String # showList :: [AllocationLimitExceeded] > ShowS #  
Show CompactionFailed  Since: base4.10.0.0 
Defined in GHC.IO.Exception showsPrec :: Int > CompactionFailed > ShowS # show :: CompactionFailed > String # showList :: [CompactionFailed] > ShowS #  
Show AssertionFailed  Since: base4.1.0.0 
Defined in GHC.IO.Exception showsPrec :: Int > AssertionFailed > ShowS # show :: AssertionFailed > String # showList :: [AssertionFailed] > ShowS #  
Show SomeAsyncException  Since: base4.7.0.0 
Defined in GHC.IO.Exception showsPrec :: Int > SomeAsyncException > ShowS # show :: SomeAsyncException > String # showList :: [SomeAsyncException] > ShowS #  
Show AsyncException  Since: base4.1.0.0 
Defined in GHC.IO.Exception showsPrec :: Int > AsyncException > ShowS # show :: AsyncException > String # showList :: [AsyncException] > ShowS #  
Show ArrayException  Since: base4.1.0.0 
Defined in GHC.IO.Exception showsPrec :: Int > ArrayException > ShowS # show :: ArrayException > String # showList :: [ArrayException] > ShowS #  
Show FixIOException  Since: base4.11.0.0 
Defined in GHC.IO.Exception showsPrec :: Int > FixIOException > ShowS # show :: FixIOException > String # showList :: [FixIOException] > ShowS #  
Show ExitCode  
Show IOErrorType  Since: base4.1.0.0 
Defined in GHC.IO.Exception showsPrec :: Int > IOErrorType > ShowS # show :: IOErrorType > String # showList :: [IOErrorType] > ShowS #  
Show MaskingState  Since: base4.3.0.0 
Defined in GHC.IO showsPrec :: Int > MaskingState > ShowS # show :: MaskingState > String # showList :: [MaskingState] > ShowS #  
Show IOException  Since: base4.1.0.0 
Defined in GHC.IO.Exception showsPrec :: Int > IOException > ShowS # show :: IOException > String # showList :: [IOException] > ShowS #  
Show SrcLoc  Since: base4.9.0.0 
Show a => Show [a]  Since: base2.1 
Show a => Show (Maybe a)  Since: base2.1 
Show a => Show (Ratio a)  Since: base2.0.1 
Show a => Show (NonEmpty a)  Since: base4.11.0.0 
(Show a, Show b) => Show (Either a b)  Since: base3.0 
(Show a, Show b) => Show (a, b)  Since: base2.1 
(Show a, Show b, Show c) => Show (a, b, c)  Since: base2.1 
(Show a, Show b, Show c, Show d) => Show (a, b, c, d)  Since: base2.1 
(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e)  Since: base2.1 
(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f)  Since: base2.1 
(Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g)  Since: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
(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: base2.1 
(^^) :: (Fractional a, Integral b) => a > b > a infixr 8 #
raise a number to an integral power
appendFile :: FilePath > String > IO () #
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]])
const x
is a unary function which evaluates to x
for all inputs.
>>>
const 42 "hello"
42
>>>
map (const 42) [0..3]
[42,42,42,42]
either :: (a > c) > (b > c) > Either a b > c #
Case analysis for the Either
type.
If the value is
, apply the first function to Left
aa
;
if it is
, apply the second function to Right
bb
.
Examples
We create two values of type
, one using the
Either
String
Int
Left
constructor and another using the Right
constructor. Then
we apply "either" the length
function (if we have a String
)
or the "timestwo" 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
error :: HasCallStack => [Char] > a #
error
stops execution and displays an error message.
flip :: (a > b > c) > b > a > c #
takes its (first) two arguments in the reverse order of flip
ff
.
>>>
flip (++) "hello" "world"
"worldhello"
fromIntegral :: (Integral a, Num b) => a > b #
general coercion from integral types
getContents :: IO String #
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 () #
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.
lcm :: Integral a => a > a > a #
is the smallest positive integer that both lcm
x yx
and y
divide.
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
.) If there is no legal lexeme at the
beginning of the input string, lex
"" = [("","")]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
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
contains at least as many elements as newlines in lines
ss
.
mapM :: (Traversable t, Monad m) => (a > m b) > t a > m (t b) #
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_
.
maybe :: b > (a > b) > Maybe a > b #
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
""
print :: Show a => a > IO () #
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]])
product :: (Foldable t, Num a) => t a > a #
The product
function computes the product of the numbers of a
structure.
read :: Read a => String > a #
The read
function reads input from a string, which must be
completely consumed by the input process. read
fails with an error
if the
parse is unsuccessful, and it is therefore discouraged from being used in
real applications. Use readMaybe
or readEither
for safe alternatives.
>>>
read "123" :: Int
123
>>>
read "hello" :: Int
*** Exception: Prelude.read: no parse
readFile :: FilePath > IO String #
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
.
realToFrac :: (Real a, Fractional b) => a > b #
general coercion to fractional types
The value of seq a b
is bottom if a
is bottom, and
otherwise equal to b
. In other words, it evaluates the first
argument a
to weak head normal form (WHNF). 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.
sequence :: (Traversable t, Monad m) => t (m a) > m (t a) #
Evaluate each monadic action in the structure from left to
right, and collect the results. For a version that ignores the
results see sequence_
.
sequence_ :: (Foldable t, Monad m) => t (m a) > m () #
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
.
utility function converting a Char
to a show function that
simply prepends the character unchanged.
showString :: String > ShowS #
utility function converting a String
to a show function that
simply prepends the string unchanged.
sum :: (Foldable t, Num a) => t a > a #
The sum
function computes the sum of the numbers of a structure.
uncurry :: (a > b > c) > (a, b) > c #
uncurry
converts a curried function to a function on pairs.
Examples
>>>
uncurry (+) (1,2)
3
>>>
uncurry ($) (show, 1)
"1"
>>>
map (uncurry max) [(1,2), (3,4), (6,8)]
[2,4,8]
undefined :: HasCallStack => a #
until :: (a > Bool) > (a > a) > a > a #
yields the result of applying until
p ff
until p
holds.
userError :: String > IOError #
Construct an IOException
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)