Portability  Haskell98 (+CPP) 

Stability  stable 
Maintainer  wren@community.haskell.org 
Safe Haskell  SafeInferred 
This module provides the Prelude but removing all the list
functions. This is helpful for modules that overload those
function names to work for other types. Note that on GHC 7.6 and
above catch
is no longer exported from the Prelude, and also
not reexported from here; whereas, on earlier versions of GHC
(and nonGHC compilers) we still reexport it.
Be sure to disable the implicit importing of the prelude when
you import this one (by passing fnoimplicitprelude
for GHC,
or by explicitly importing the prelude with an empty import list
for most implementations).
 ($!) :: (a > b) > a > b
 ($) :: (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 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 Monad m where
 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 :: [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
 gcd :: Integral a => a > a > 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
 maybe :: b > (a > b) > Maybe a > b
 not :: Bool > Bool
 odd :: Integral a => a > Bool
 otherwise :: Bool
 print :: Show a => a > IO ()
 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
 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
 uncurry :: (a > b > c) > (a, b) > c
 undefined :: a
 until :: (a > Bool) > (a > a) > a > a
 userError :: String > IOError
 writeFile :: FilePath > String > IO ()
 () :: Bool > Bool > Bool
Documentation
($) :: (a > b) > a > b
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
(.) :: (b > c) > (a > b) > a > c
Function composition.
class Bounded a where
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
.
data Char
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 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
).
data Double
Doubleprecision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE doubleprecision type.
data Either a b
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").
class Enum a where
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
succ :: a > a
the successor of a value. For numeric types, succ
adds 1.
pred :: a > a
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
.
enumFrom :: a > [a]
Used in Haskell's translation of [n..]
.
enumFromThen :: a > a > [a]
Used in Haskell's translation of [n,n'..]
.
enumFromTo :: a > a > [a]
Used in Haskell's translation of [n..m]
.
enumFromThenTo :: a > a > a > [a]
Used in Haskell's translation of [n,n'..m]
.
class Eq a where
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
.
Eq Bool  
Eq Char  
Eq Double  
Eq Float  
Eq Int  
Eq Integer  
Eq Ordering  
Eq Word  
Eq ()  
Eq AsyncException  
Eq ArrayException  
Eq ExitCode  
Eq IOErrorType  
Eq MaskingState  
Eq IOException  
Eq a => Eq [a]  
Eq a => Eq (Ratio a)  
Eq a => Eq (Maybe a)  
(Eq a, Eq b) => Eq (Either a b)  
(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.
data Float
Singleprecision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE singleprecision type.
class Fractional a => Floating a where
Trigonometric and hyperbolic functions and related functions.
Minimal complete definition:
pi
, exp
, log
, sin
, cos
, sinh
, cosh
,
asin
, acos
, atan
, asinh
, acosh
and atanh
class Num a => Fractional a where
Fractional numbers, supporting real division.
Minimal complete definition: fromRational
and (recip
or (
)
/
)
(/) :: a > a > a
fractional division
recip :: a > a
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
Fractional Double  
Fractional Float  
(Num (Ratio a), Integral a) => Fractional (Ratio a) 
class Functor f 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.
fmap :: (a > b) > f a > f b
data IO a
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 98 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 Control.Exception.Exception.
In Haskell 98, this is an opaque type.
data Int
data Integer
Arbitraryprecision integers.
class (Real a, Enum a) => Integral a where
quot :: a > a > a
integer division truncated toward zero
rem :: a > a > a
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
div :: a > a > a
integer division truncated toward negative infinity
mod :: a > a > a
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
quotRem :: a > a > (a, a)
divMod :: a > a > (a, a)
conversion to Integer
data Maybe a
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.
class Monad m 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.
Minimal complete definition: >>=
and return
.
Instances of Monad
should satisfy the following laws:
return a >>= k == k a m >>= return == m m >>= (\x > k x >>= h) == (m >>= k) >>= h
Instances of both Monad
and Functor
should additionally satisfy the law:
fmap f xs == xs >>= return . f
The instances of Monad
for lists, Maybe
and IO
defined in the Prelude satisfy these laws.
(>>=) :: m a > (a > m b) > m b
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
(>>) :: m a > m b > m b
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
Inject a value into the monadic type.
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.
class Num a where
Basic numeric class.
Minimal complete definition: all except negate
or ()
(+) :: a > a > a
(*) :: a > a > a
() :: a > a > a
negate :: a > a
Unary negation.
abs :: a > a
Absolute value.
signum :: a > a
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.
Minimal complete definition: either compare
or <=
.
Using compare
can be more efficient for complex types.
Ord Bool  
Ord Char  
Ord Double  
Ord Float  
Ord Int  
Ord Integer  
Ord Ordering  
Ord Word  
Ord ()  
Ord AsyncException  
Ord ArrayException  
Ord ExitCode  
(Eq [a], Ord a) => Ord [a]  
(Eq (Ratio a), Integral a) => Ord (Ratio a)  
(Eq (Maybe a), Ord a) => Ord (Maybe a)  
(Eq (Either a b), Ord a, Ord b) => Ord (Either a b)  
(Eq (a, b), Ord a, Ord b) => Ord (a, b)  
(Eq (a, b, c), Ord a, Ord b, Ord c) => Ord (a, b, c)  
(Eq (a, b, c, d), Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d)  
(Eq (a, b, c, d, e), Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e)  
(Eq (a, b, c, d, e, f), Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f)  
(Eq (a, b, c, d, e, f, g), Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g)  
(Eq (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 (a, b, c, d, e, f, g, h)  
(Eq (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 (a, b, c, d, e, f, g, h, i)  
(Eq (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 (a, b, c, d, e, f, g, h, i, j)  
(Eq (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 (a, b, c, d, e, f, g, h, i, j, k)  
(Eq (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 (a, b, c, d, e, f, g, h, i, j, k, l)  
(Eq (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 (a, b, c, d, e, f, g, h, i, j, k, l, m)  
(Eq (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 (a, b, c, d, e, f, g, h, i, j, k, l, m, n)  
(Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o), 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) 
data Ordering
class Read a where
Parsing of String
s, producing values.
Minimal complete definition: readsPrec
(or, for GHC only, readPrec
)
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 98 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
:: 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.
Read Bool  
Read Char  
Read Double  
Read Float  
Read Int  
Read Integer  
Read Ordering  
Read Word  
Read ()  
Read ExitCode  
Read Lexeme  
Read a => Read [a]  
(Integral a, Read a) => Read (Ratio a)  
Read a => Read (Maybe a)  
(Read a, Read b) => Read (Either a b)  
(Read a, Read b) => Read (a, b)  
(Ix a, Read a, Read b) => Read (Array a b)  
(Read a, Read b, Read c) => Read (a, b, c)  
(Read a, Read b, Read c, Read d) => Read (a, b, c, d)  
(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e)  
(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f)  
(Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g)  
(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)  
(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)  
(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)  
(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)  
(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)  
(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)  
(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)  
(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) 
class (Num a, Ord a) => Real a where
toRational :: a > Rational
the rational equivalent of its real argument with full precision
class (RealFrac a, Floating a) => RealFloat a where
Efficient, machineindependent access to the components of a floatingpoint number.
Minimal complete definition:
all except exponent
, significand
, scaleFloat
and atan2
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
atan2 :: a > a > a
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.
class (Real a, Fractional a) => RealFrac a where
Extracting components of fractions.
Minimal complete definition: properFraction
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
; and 
f
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
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
returns the greatest integer not greater than floor
xx
class Show a where
Conversion of values to readable String
s.
Minimal complete definition: showsPrec
or show
.
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.
Show Bool  
Show Char  
Show Double  
Show Float  
Show Int  
Show Integer  
Show Ordering  
Show Word  
Show ()  
Show BlockedIndefinitelyOnMVar  
Show BlockedIndefinitelyOnSTM  
Show Deadlock  
Show AssertionFailed  
Show AsyncException  
Show ArrayException  
Show ExitCode  
Show IOErrorType  
Show MaskingState  
Show IOException  
Show a => Show [a]  
(Integral a, Show a) => Show (Ratio a)  
Show a => Show (Maybe a)  
(Show a, Show b) => Show (Either a b)  
(Show a, Show b) => Show (a, b)  
(Show a, Show b, Show c) => Show (a, b, c)  
(Show a, Show b, Show c, Show d) => Show (a, b, c, d)  
(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e)  
(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f)  
(Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g)  
(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)  
(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)  
(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)  
(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)  
(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)  
(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)  
(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)  
(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) 
(^^) :: (Fractional a, Integral b) => a > b > a
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]])
asTypeOf :: a > a > a
const :: a > b > a
Constant function.
flip :: (a > b > c) > b > a > c
takes its (first) two arguments in the reverse order of flip
ff
.
fromIntegral :: (Integral a, Num b) => a > b
general coercion from integral types
fst :: (a, b) > a
Extract the first component of a pair.
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
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
).
id :: a > a
Identity function.
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.
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
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]])
The read
function reads input from a string, which must be
completely consumed by the input process.
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
seq :: a > b > b
Evaluates its first argument to head normal form, and then returns its second argument as the result.
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.
snd :: (a, b) > b
Extract the second component of a pair.
undefined :: a