Safe Haskell | Safe-Inferred |
---|---|
Language | Haskell98 |
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- and :: Foldable t => t Bool -> Bool
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- concat :: Foldable t => t [a] -> [a]
- concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
- mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
- notElem :: (Foldable t, Eq a) => a -> t a -> Bool
- or :: Foldable t => t Bool -> Bool
- sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- maybe :: b -> (a -> b) -> Maybe a -> b
- lines :: String -> [String]
- unlines :: [String] -> String
- unwords :: [String] -> String
- words :: String -> [String]
- curry :: ((a, b) -> c) -> a -> b -> c
- fst :: (a, b) -> a
- snd :: (a, b) -> b
- uncurry :: (a -> b -> c) -> (a, b) -> c
- ($!) :: (a -> b) -> a -> b
- (++) :: [a] -> [a] -> [a]
- (.) :: (b -> c) -> (a -> b) -> a -> c
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- asTypeOf :: a -> a -> a
- const :: a -> b -> a
- flip :: (a -> b -> c) -> b -> a -> c
- id :: a -> a
- map :: (a -> b) -> [a] -> [b]
- otherwise :: Bool
- until :: (a -> Bool) -> (a -> a) -> a -> a
- ioError :: IOError -> IO a
- userError :: String -> IOError
- (!!) :: [a] -> Int -> a
- break :: (a -> Bool) -> [a] -> ([a], [a])
- cycle :: [a] -> [a]
- drop :: Int -> [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- filter :: (a -> Bool) -> [a] -> [a]
- head :: [a] -> a
- init :: [a] -> [a]
- iterate :: (a -> a) -> a -> [a]
- last :: [a] -> a
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- repeat :: a -> [a]
- replicate :: Int -> a -> [a]
- reverse :: [a] -> [a]
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- 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]
- unzip :: [(a, b)] -> ([a], [b])
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- 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]
- subtract :: Num a => a -> a -> a
- lex :: ReadS String
- readParen :: Bool -> ReadS a -> ReadS a
- (^) :: (Num a, Integral b) => a -> b -> a
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- even :: Integral a => a -> Bool
- fromIntegral :: (Integral a, Num b) => a -> b
- gcd :: Integral a => a -> a -> a
- lcm :: Integral a => a -> a -> a
- odd :: Integral a => a -> Bool
- realToFrac :: (Real a, Fractional b) => a -> b
- showChar :: Char -> ShowS
- showParen :: Bool -> ShowS -> ShowS
- showString :: String -> ShowS
- shows :: Show a => a -> ShowS
- appendFile :: FilePath -> String -> IO ()
- getChar :: IO Char
- getContents :: IO String
- getLine :: IO String
- interact :: (String -> String) -> IO ()
- print :: Show a => a -> IO ()
- putChar :: Char -> IO ()
- putStr :: String -> IO ()
- putStrLn :: String -> IO ()
- readFile :: FilePath -> IO String
- readIO :: Read a => String -> IO a
- readLn :: Read a => IO a
- writeFile :: FilePath -> String -> IO ()
- read :: Read a => String -> a
- reads :: Read a => ReadS a
- (&&) :: Bool -> Bool -> Bool
- not :: Bool -> Bool
- (||) :: Bool -> Bool -> Bool
- ($) :: (a -> b) -> a -> b
- error :: [Char] -> a
- undefined :: a
- seq :: a -> b -> b
- elem :: (Foldable t, Eq a) => a -> t a -> Bool
- foldMap :: Foldable t => forall a m. Monoid m => (a -> m) -> t a -> m
- foldl :: Foldable t => forall b a. (b -> a -> b) -> b -> t a -> b
- foldl1 :: Foldable t => forall a. (a -> a -> a) -> t a -> a
- foldr :: Foldable t => forall a b. (a -> b -> b) -> b -> t a -> b
- foldr1 :: Foldable t => forall a. (a -> a -> a) -> t a -> a
- length :: Foldable t => t a -> Int
- maximum :: (Foldable t, Ord a) => t a -> a
- minimum :: (Foldable t, Ord a) => t a -> a
- null :: Foldable t => t a -> Bool
- product :: (Foldable t, Num a) => t a -> a
- sum :: (Foldable t, Num a) => t a -> a
- mapM :: Traversable t => forall a m b. Monad m => (a -> m b) -> t a -> m (t b)
- sequence :: Traversable t => forall m a. Monad m => t (m a) -> m (t a)
- sequenceA :: Traversable t => forall f a. Applicative f => t (f a) -> f (t a)
- traverse :: Traversable t => forall a f b. Applicative f => (a -> f b) -> t a -> f (t b)
- (*>) :: Applicative f => forall a b. f a -> f b -> f b
- (<*) :: Applicative f => forall a b. f a -> f b -> f a
- (<*>) :: Applicative f => forall a b. f (a -> b) -> f a -> f b
- pure :: Applicative f => forall a. a -> f a
- (<$) :: Functor f => forall a b. a -> f b -> f a
- fmap :: Functor f => forall a b. (a -> b) -> f a -> f b
- (>>) :: Monad m => forall a b. m a -> m b -> m b
- (>>=) :: Monad m => forall a b. m a -> (a -> m b) -> m b
- fail :: Monad m => forall a. String -> m a
- return :: Monad m => forall a. a -> m a
- mappend :: Monoid a => a -> a -> a
- mconcat :: Monoid a => [a] -> a
- mempty :: Monoid a => a
- maxBound :: Bounded a => a
- minBound :: Bounded a => a
- enumFrom :: Enum a => a -> [a]
- enumFromThen :: Enum a => a -> a -> [a]
- enumFromThenTo :: Enum a => a -> a -> a -> [a]
- enumFromTo :: Enum a => a -> a -> [a]
- fromEnum :: Enum a => a -> Int
- pred :: Enum a => a -> a
- succ :: Enum a => a -> a
- toEnum :: Enum a => Int -> a
- (**) :: Floating a => a -> a -> a
- acos :: Floating a => a -> a
- acosh :: Floating a => a -> a
- asin :: Floating a => a -> a
- asinh :: Floating a => a -> a
- atan :: Floating a => a -> a
- atanh :: Floating a => a -> a
- cos :: Floating a => a -> a
- cosh :: Floating a => a -> a
- exp :: Floating a => a -> a
- log :: Floating a => a -> a
- logBase :: Floating a => a -> a -> a
- pi :: Floating a => a
- sin :: Floating a => a -> a
- sinh :: Floating a => a -> a
- sqrt :: Floating a => a -> a
- tan :: Floating a => a -> a
- tanh :: Floating a => a -> a
- atan2 :: RealFloat a => a -> a -> a
- decodeFloat :: RealFloat a => a -> (Integer, Int)
- encodeFloat :: RealFloat a => Integer -> Int -> a
- exponent :: RealFloat a => a -> Int
- floatDigits :: RealFloat a => a -> Int
- floatRadix :: RealFloat a => a -> Integer
- floatRange :: RealFloat a => a -> (Int, Int)
- isDenormalized :: RealFloat a => a -> Bool
- isIEEE :: RealFloat a => a -> Bool
- isInfinite :: RealFloat a => a -> Bool
- isNaN :: RealFloat a => a -> Bool
- isNegativeZero :: RealFloat a => a -> Bool
- scaleFloat :: RealFloat a => Int -> a -> a
- significand :: RealFloat a => a -> a
- (*) :: Num a => a -> a -> a
- (+) :: Num a => a -> a -> a
- (-) :: Num a => a -> a -> a
- abs :: Num a => a -> a
- negate :: Num a => a -> a
- signum :: Num a => a -> a
- readList :: Read a => ReadS [a]
- readsPrec :: Read a => Int -> ReadS a
- (/) :: Fractional a => a -> a -> a
- fromRational :: Fractional a => Rational -> a
- recip :: Fractional a => a -> a
- div :: Integral a => a -> a -> a
- divMod :: Integral a => a -> a -> (a, a)
- mod :: Integral a => a -> a -> a
- quot :: Integral a => a -> a -> a
- quotRem :: Integral a => a -> a -> (a, a)
- rem :: Integral a => a -> a -> a
- toInteger :: Integral a => a -> Integer
- toRational :: Real a => a -> Rational
- ceiling :: RealFrac a => forall b. Integral b => a -> b
- floor :: RealFrac a => forall b. Integral b => a -> b
- properFraction :: RealFrac a => forall b. Integral b => a -> (b, a)
- round :: RealFrac a => forall b. Integral b => a -> b
- truncate :: RealFrac a => forall b. Integral b => a -> b
- show :: Show a => a -> String
- showList :: Show a => [a] -> ShowS
- showsPrec :: Show a => Int -> a -> ShowS
- (/=) :: Eq a => a -> a -> Bool
- (==) :: Eq a => a -> a -> Bool
- (<) :: Ord a => a -> a -> Bool
- (<=) :: Ord a => a -> a -> Bool
- (>) :: Ord a => a -> a -> Bool
- (>=) :: Ord a => a -> a -> Bool
- compare :: Ord a => a -> a -> Ordering
- max :: Ord a => a -> a -> a
- min :: Ord a => a -> a -> a
- class Functor f => Applicative f where
- class Bounded a where
- 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
- class Fractional a => Floating a where
- class Foldable t where
- class Num a => Fractional a where
- (/) :: a -> a -> a
- recip :: a -> a
- fromRational :: Rational -> a
- class Functor f where
- class (Real a, Enum a) => Integral a where
- class Monad m where
- class Monoid a where
- class Num a where
- class Eq a => Ord a where
- class Read a where
- 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
- class (Functor t, Foldable t) => Traversable t where
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
- sequenceA :: Applicative f => t (f a) -> f (t a)
- mapM :: Monad m => (a -> m b) -> t a -> m (t b)
- sequence :: Monad m => t (m a) -> m (t a)
- data IO a :: * -> *
- data Char :: *
- data Double :: *
- data Float :: *
- data Int :: *
- data Integer :: *
- data Word :: *
- data Bool :: *
- data Either a b :: * -> * -> *
- data Maybe a :: * -> *
- data Ordering :: *
- type FilePath = String
- type IOError = IOException
- type Rational = Ratio Integer
- type ReadS a = String -> [(a, String)]
- type ShowS = String -> String
- type String = [Char]
Documentation
all :: Foldable t => (a -> Bool) -> t a -> Bool
Determines whether all elements of the structure satisfy the predicate.
any :: Foldable t => (a -> Bool) -> t a -> Bool
Determines whether any element of the structure satisfies the predicate.
concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
Map a function over all the elements of a container and concatenate the resulting lists.
mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
Map each element of a structure to a monadic action, evaluate these actions from left to right, and ignore the results.
sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
Evaluate each monadic action in the structure from left to right, and ignore the results.
lines
breaks a string up into a list of strings at newline
characters. The resulting strings do not contain newlines.
words
breaks a string up into a list of words, which were delimited
by white space.
fst :: (a, b) -> a
Extract the first component of a pair.
snd :: (a, b) -> b
Extract the second component of a pair.
(++) :: [a] -> [a] -> [a] infixr 5
Append two lists, i.e.,
[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn] [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
If the first list is not finite, the result is the first list.
(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9
Function composition.
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1
Same as >>=
, but with the arguments interchanged.
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
.
id :: a -> a
Identity function.
map :: (a -> b) -> [a] -> [b]
map
f xs
is the list obtained by applying f
to each element
of xs
, i.e.,
map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] map f [x1, x2, ...] == [f x1, f x2, ...]
(!!) :: [a] -> Int -> a infixl 9
List index (subscript) operator, starting from 0.
It is an instance of the more general genericIndex
,
which takes an index of any integral type.
break :: (a -> Bool) -> [a] -> ([a], [a])
break
, applied to a predicate p
and a list xs
, returns a tuple where
first element is longest prefix (possibly empty) of xs
of elements that
do not satisfy p
and second element is the remainder of the list:
break (> 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4]) break (< 9) [1,2,3] == ([],[1,2,3]) break (> 9) [1,2,3] == ([1,2,3],[])
cycle :: [a] -> [a]
cycle
ties a finite list into a circular one, or equivalently,
the infinite repetition of the original list. It is the identity
on infinite lists.
drop
n xs
returns the suffix of xs
after the first n
elements, or []
if n >
:length
xs
drop 6 "Hello World!" == "World!" drop 3 [1,2,3,4,5] == [4,5] drop 3 [1,2] == [] drop 3 [] == [] drop (-1) [1,2] == [1,2] drop 0 [1,2] == [1,2]
It is an instance of the more general genericDrop
,
in which n
may be of any integral type.
filter :: (a -> Bool) -> [a] -> [a]
filter
, applied to a predicate and a list, returns the list of
those elements that satisfy the predicate; i.e.,
filter p xs = [ x | x <- xs, p x]
head :: [a] -> a
Extract the first element of a list, which must be non-empty.
init :: [a] -> [a]
Return all the elements of a list except the last one. The list must be non-empty.
iterate :: (a -> a) -> a -> [a]
iterate
f x
returns an infinite list of repeated applications
of f
to x
:
iterate f x == [x, f x, f (f x), ...]
last :: [a] -> a
Extract the last element of a list, which must be finite and non-empty.
replicate
n x
is a list of length n
with x
the value of
every element.
It is an instance of the more general genericReplicate
,
in which n
may be of any integral type.
scanl :: (b -> a -> b) -> b -> [a] -> [b]
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])
span
, applied to a predicate p
and a list xs
, returns a tuple where
first element is longest prefix (possibly empty) of xs
of elements that
satisfy p
and second element is the remainder of the list:
span (< 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4]) span (< 9) [1,2,3] == ([1,2,3],[]) span (< 0) [1,2,3] == ([],[1,2,3])
splitAt :: Int -> [a] -> ([a], [a])
splitAt
n xs
returns a tuple where first element is xs
prefix of
length n
and second element is the remainder of the list:
splitAt 6 "Hello World!" == ("Hello ","World!") splitAt 3 [1,2,3,4,5] == ([1,2,3],[4,5]) splitAt 1 [1,2,3] == ([1],[2,3]) splitAt 3 [1,2,3] == ([1,2,3],[]) splitAt 4 [1,2,3] == ([1,2,3],[]) splitAt 0 [1,2,3] == ([],[1,2,3]) splitAt (-1) [1,2,3] == ([],[1,2,3])
It is equivalent to (
when take
n xs, drop
n xs)n
is not _|_
(splitAt _|_ xs = _|_
).
splitAt
is an instance of the more general genericSplitAt
,
in which n
may be of any integral type.
tail :: [a] -> [a]
Extract the elements after the head of a list, which must be non-empty.
take
n
, applied to a list xs
, returns the prefix of xs
of length n
, or xs
itself if n >
:length
xs
take 5 "Hello World!" == "Hello" take 3 [1,2,3,4,5] == [1,2,3] take 3 [1,2] == [1,2] take 3 [] == [] take (-1) [1,2] == [] take 0 [1,2] == []
It is an instance of the more general genericTake
,
in which n
may be of any integral type.
takeWhile :: (a -> Bool) -> [a] -> [a]
takeWhile
, applied to a predicate p
and a list xs
, returns the
longest prefix (possibly empty) of xs
of elements that satisfy p
:
takeWhile (< 3) [1,2,3,4,1,2,3,4] == [1,2] takeWhile (< 9) [1,2,3] == [1,2,3] takeWhile (< 0) [1,2,3] == []
unzip :: [(a, b)] -> ([a], [b])
unzip
transforms a list of pairs into a list of first components
and a list of second components.
unzip3 :: [(a, b, c)] -> ([a], [b], [c])
zip :: [a] -> [b] -> [(a, b)]
zip
takes two lists and returns a list of corresponding pairs.
If one input list is short, excess elements of the longer list are
discarded.
zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
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
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8
raise a number to an integral power
fromIntegral :: (Integral a, Num b) => a -> b
general coercion from integral types
gcd :: Integral a => a -> a -> a
is the non-negative 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 fixed-width 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
realToFrac :: (Real a, Fractional b) => a -> b
general coercion to fractional types
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.
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]])
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.
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]])
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
.
writeFile :: FilePath -> String -> IO ()
The computation writeFile
file str
function writes the string str
,
to the file file
.
The read
function reads input from a string, which must be
completely consumed by the input process.
($) :: (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, right-associative binding precedence, so it sometimes allows
parentheses to be omitted; for example:
f $ g $ h x = f (g (h x))
It is also useful in higher-order situations, such as
,
or map
($
0) xs
.zipWith
($
) fs xs
undefined :: a
seq :: a -> b -> b
Evaluates its first argument to head normal form, and then returns its second argument as the result.
foldMap :: Foldable t => forall a m. Monoid m => (a -> m) -> t a -> m
Map each element of the structure to a monoid, and combine the results.
length :: Foldable t => t a -> Int Source
Returns the size/length of a finite structure as an Int
. The
default implementation is optimized for structures that are similar to
cons-lists, because there is no general way to do better.
null :: Foldable t => t a -> Bool Source
Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.
product :: (Foldable t, Num a) => t a -> a
The product
function computes the product of the numbers of a structure.
sum :: (Foldable t, Num a) => t a -> a
The sum
function computes the sum of the numbers of a structure.
mapM :: Traversable t => forall a m b. 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.
sequence :: Traversable t => forall m a. Monad m => t (m a) -> m (t a)
Evaluate each monadic action in the structure from left to right, and collect the results.
sequenceA :: Traversable t => forall f a. Applicative f => t (f a) -> f (t a)
Evaluate each action in the structure from left to right, and collect the results.
traverse :: Traversable t => forall a f b. Applicative f => (a -> f b) -> t a -> f (t b)
Map each element of a structure to an action, evaluate these actions from left to right, and collect the results.
(*>) :: Applicative f => forall a b. f a -> f b -> f b
Sequence actions, discarding the value of the first argument.
(<*) :: Applicative f => forall a b. f a -> f b -> f a
Sequence actions, discarding the value of the second argument.
(<*>) :: Applicative f => forall a b. f (a -> b) -> f a -> f b
Sequential application.
pure :: Applicative f => forall a. a -> f a
Lift a value.
(>>) :: Monad m => forall a b. 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.
(>>=) :: Monad m => forall a b. m a -> (a -> m b) -> m b
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
fail :: Monad m => forall a. String -> m a
Fail with a message. This operation is not part of the
mathematical definition of a monad, but is invoked on pattern-match
failure in a do
expression.
mconcat :: Monoid a => [a] -> a
Fold a list using the monoid.
For most types, the default definition for mconcat
will be
used, but the function is included in the class definition so
that an optimized version can be provided for specific types.
enumFromThen :: Enum a => a -> a -> [a]
Used in Haskell's translation of [n,n'..]
.
enumFromThenTo :: Enum a => a -> a -> a -> [a]
Used in Haskell's translation of [n,n'..m]
.
enumFromTo :: Enum a => a -> a -> [a]
Used in Haskell's translation of [n..m]
.
atan2 :: RealFloat a => a -> a -> a
a version of arctangent taking two real floating-point arguments.
For real floating x
and y
,
computes the angle
(from the positive x-axis) of the vector from the origin to the
point atan2
y x(x,y)
.
returns a value in the range [atan2
y x-pi
,
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.
decodeFloat :: RealFloat a => a -> (Integer, Int)
The function decodeFloat
applied to a real floating-point
number returns the significand expressed as an Integer
and an
appropriately scaled exponent (an Int
). If
yields decodeFloat
x(m,n)
, then x
is equal in value to m*b^^n
, where b
is the floating-point radix, and furthermore, either m
and n
are both zero or else b^(d-1) <=
, 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 :: RealFloat a => 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
floating-point 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 :: RealFloat a => a -> Int
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 floating-point number, it is equal in value to
, where significand
x * b ^^ exponent
xb
is the
floating-point radix.
The behaviour is unspecified on infinite or NaN
values.
floatDigits :: RealFloat a => a -> Int
a constant function, returning the number of digits of
floatRadix
in the significand
floatRadix :: RealFloat a => a -> Integer
a constant function, returning the radix of the representation
(often 2
)
floatRange :: RealFloat a => a -> (Int, Int)
a constant function, returning the lowest and highest values the exponent may assume
isDenormalized :: RealFloat a => a -> Bool
True
if the argument is too small to be represented in
normalized format
isInfinite :: RealFloat a => a -> Bool
True
if the argument is an IEEE infinity or negative infinity
isNegativeZero :: RealFloat a => a -> Bool
True
if the argument is an IEEE negative zero
scaleFloat :: RealFloat a => Int -> a -> a
multiplies a floating-point number by an integer power of the radix
significand :: RealFloat a => 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 floating-point radix.
The behaviour is unspecified on infinite or NaN
values.
:: Read a | |
=> 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.
(/) :: Fractional a => a -> a -> a
fractional division
fromRational :: Fractional a => 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
recip :: Fractional a => a -> a
reciprocal fraction
toRational :: Real a => a -> Rational
the rational equivalent of its real argument with full precision
ceiling :: RealFrac a => forall b. Integral b => a -> b
returns the least integer not less than ceiling
xx
floor :: RealFrac a => forall b. Integral b => a -> b
returns the greatest integer not greater than floor
xx
properFraction :: RealFrac a => forall b. 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
.
round :: RealFrac a => forall b. Integral b => a -> b
returns the nearest integer to round
xx
;
the even integer if x
is equidistant between two integers
truncate :: RealFrac a => forall b. Integral b => a -> b
returns the integer nearest truncate
xx
between zero and x
:: Show a | |
=> Int | the operator precedence of the enclosing
context (a number from |
-> a | the value to be converted to a |
-> ShowS |
class Functor f => Applicative f where
A functor with application, providing operations to
A minimal complete definition must include implementations of these functions satisfying the following laws:
- identity
pure
id
<*>
v = v- composition
pure
(.)<*>
u<*>
v<*>
w = u<*>
(v<*>
w)- homomorphism
pure
f<*>
pure
x =pure
(f x)- interchange
u
<*>
pure
y =pure
($
y)<*>
u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor
instance for f
will satisfy
If f
is also a Monad
, it should satisfy
(which implies that pure
and <*>
satisfy the applicative functor laws).
pure :: a -> f a
Lift a value.
(<*>) :: f (a -> b) -> f a -> f b infixl 4
Sequential application.
(*>) :: f a -> f b -> f b infixl 4
Sequence actions, discarding the value of the first argument.
(<*) :: f a -> f b -> f a infixl 4
Sequence actions, discarding the value of the second argument.
Applicative [] | |
Applicative IO | |
Applicative Id | |
Applicative ZipList | |
Applicative STM | |
Applicative ReadPrec | |
Applicative ReadP | |
Applicative Maybe | |
Applicative ((->) a) | |
Applicative (Either e) | |
Monoid a => Applicative ((,) a) | |
Applicative (ST s) | |
Applicative (StateL s) | |
Applicative (StateR s) | |
Monoid m => Applicative (Const m) | |
Monad m => Applicative (WrappedMonad m) | |
Applicative (ST s) | |
Arrow a => Applicative (ArrowMonad a) | |
Applicative (Proxy *) | |
Arrow a => Applicative (WrappedArrow a b) | |
Typeable ((* -> *) -> Constraint) Applicative |
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 single-constructor datatypes whose
constituent types are in Bounded
.
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 left-to-right by fromEnum
from 0
through n-1
.
See Chapter 10 of the Haskell Report for more details.
For any type that is an instance of class Bounded
as well as Enum
,
the following should hold:
- 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 implementation-dependent 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]
.
Enum Bool | |
Enum Char | |
Enum Double | |
Enum Float | |
Enum Int | |
Enum Integer | |
Enum Ordering | |
Enum Word | |
Enum Word8 | |
Enum Word16 | |
Enum Word32 | |
Enum Word64 | |
Enum () | |
Enum WordPtr | |
Enum IntPtr | |
Enum CChar | |
Enum CSChar | |
Enum CUChar | |
Enum CShort | |
Enum CUShort | |
Enum CInt | |
Enum CUInt | |
Enum CLong | |
Enum CULong | |
Enum CLLong | |
Enum CULLong | |
Enum CFloat | |
Enum CDouble | |
Enum CPtrdiff | |
Enum CSize | |
Enum CWchar | |
Enum CSigAtomic | |
Enum CClock | |
Enum CTime | |
Enum CUSeconds | |
Enum CSUSeconds | |
Enum CIntPtr | |
Enum CUIntPtr | |
Enum CIntMax | |
Enum CUIntMax | |
Integral a => Enum (Ratio a) | |
(~) k a b => Enum ((:~:) k a b) |
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 Word8 | |
Eq Word16 | |
Eq Word32 | |
Eq Word64 | |
Eq () | |
Eq Handle | |
Eq Version | |
Eq AsyncException | |
Eq ArrayException | |
Eq ExitCode | |
Eq IOErrorType | |
Eq BufferMode | |
Eq Newline | |
Eq NewlineMode | |
Eq WordPtr | |
Eq IntPtr | |
Eq CChar | |
Eq CSChar | |
Eq CUChar | |
Eq CShort | |
Eq CUShort | |
Eq CInt | |
Eq CUInt | |
Eq CLong | |
Eq CULong | |
Eq CLLong | |
Eq CULLong | |
Eq CFloat | |
Eq CDouble | |
Eq CPtrdiff | |
Eq CSize | |
Eq CWchar | |
Eq CSigAtomic | |
Eq CClock | |
Eq CTime | |
Eq CUSeconds | |
Eq CSUSeconds | |
Eq CIntPtr | |
Eq CUIntPtr | |
Eq CIntMax | |
Eq CUIntMax | |
Eq MaskingState | |
Eq IOException | |
Eq All | |
Eq Any | |
Eq Arity | |
Eq Fixity | |
Eq Associativity | |
Eq Lexeme | |
Eq Number | |
Eq a => Eq [a] | |
Eq a => Eq (Ratio a) | |
Eq (Ptr a) | |
Eq (FunPtr a) | |
Eq (U1 p) | |
Eq p => Eq (Par1 p) | |
Eq a => Eq (ZipList a) | |
Eq (MVar a) | |
Eq a => Eq (Dual a) | |
Eq a => Eq (Sum a) | |
Eq a => Eq (Product a) | |
Eq a => Eq (First a) | |
Eq a => Eq (Last a) | |
Eq a => Eq (Down a) | |
Eq a => Eq (Maybe a) | |
(Eq a, Eq b) => Eq (Either a b) | |
Eq (f p) => Eq (Rec1 f p) | |
(Eq a, Eq b) => Eq (a, b) | |
Eq c => Eq (K1 i c p) | |
(Eq (f p), Eq (g p)) => Eq ((:+:) f g p) | |
(Eq (f p), Eq (g p)) => Eq ((:*:) f g p) | |
Eq (f (g p)) => Eq ((:.:) f g p) | |
(Eq a, Eq b, Eq c) => Eq (a, b, c) | |
Eq ((:~:) k a b) | |
Eq (f p) => Eq (M1 i c f p) | |
(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) |
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 Foldable t where
Data structures that can be folded.
Minimal complete definition: foldMap
or foldr
.
For example, given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Foldable Tree where foldMap f Empty = mempty foldMap f (Leaf x) = f x foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r
This is suitable even for abstract types, as the monoid is assumed
to satisfy the monoid laws. Alternatively, one could define foldr
:
instance Foldable Tree where foldr f z Empty = z foldr f z (Leaf x) = f x z foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l
foldMap :: Monoid m => (a -> m) -> t a -> m
Map each element of the structure to a monoid, and combine the results.
foldr :: (a -> b -> b) -> b -> t a -> b
foldl :: (b -> a -> b) -> b -> t a -> b
foldr1 :: (a -> a -> a) -> t a -> a
A variant of foldr
that has no base case,
and thus may only be applied to non-empty structures.
foldr1
f =foldr1
f .toList
foldl1 :: (a -> a -> a) -> t a -> a
class Num a => Fractional a where
Fractional numbers, supporting real division.
Minimal complete definition: fromRational
and (recip
or (
)/
)
fromRational, (recip | (/))
(/) :: a -> a -> a infixl 7
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
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.
class (Real a, Enum a) => Integral a where
quot :: a -> a -> a infixl 7
integer division truncated toward zero
rem :: a -> a -> a infixl 7
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
div :: a -> a -> a infixl 7
integer division truncated toward negative infinity
mod :: a -> a -> a infixl 7
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
quotRem :: a -> a -> (a, a)
divMod :: a -> a -> (a, a)
conversion to Integer
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 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.
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 pattern-match
failure in a do
expression.
class Monoid a where
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:
mappend mempty x = x
mappend x mempty = x
mappend x (mappend y z) = mappend (mappend x y) z
mconcat =
foldr
mappend mempty
The method names refer to the monoid of lists under concatenation, but there are many other instances.
Minimal complete definition: mempty
and mappend
.
Some types can be viewed as a monoid in more than one way,
e.g. both addition and multiplication on numbers.
In such cases we often define newtype
s and make those instances
of Monoid
, e.g. Sum
and Product
.
mempty :: a
Identity of mappend
mappend :: a -> a -> a
An associative operation
mconcat :: [a] -> a
Fold a list using the monoid.
For most types, the default definition for mconcat
will be
used, but the function is included in the class definition so
that an optimized version can be provided for specific types.
Monoid Ordering | |
Monoid () | |
Monoid All | |
Monoid Any | |
Monoid [a] | |
Monoid a => Monoid (Dual a) | |
Monoid (Endo a) | |
Num a => Monoid (Sum a) | |
Num a => Monoid (Product a) | |
Monoid (First a) | |
Monoid (Last a) | |
Monoid a => Monoid (Maybe a) | Lift a semigroup into |
Monoid b => Monoid (a -> b) | |
(Monoid a, Monoid b) => Monoid (a, b) | |
Monoid a => Monoid (Const a b) | |
Monoid (Proxy * s) | |
Typeable (* -> Constraint) Monoid | |
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | |
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | |
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) |
class Num a where
Basic numeric class.
Minimal complete definition: all except negate
or (-)
(+) :: a -> a -> a infixl 6
(*) :: a -> a -> a infixl 7
(-) :: a -> a -> a infixl 6
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
Num Double | |
Num Float | |
Num Int | |
Num Integer | |
Num Word | |
Num Word8 | |
Num Word16 | |
Num Word32 | |
Num Word64 | |
Num WordPtr | |
Num IntPtr | |
Num CChar | |
Num CSChar | |
Num CUChar | |
Num CShort | |
Num CUShort | |
Num CInt | |
Num CUInt | |
Num CLong | |
Num CULong | |
Num CLLong | |
Num CULLong | |
Num CFloat | |
Num CDouble | |
Num CPtrdiff | |
Num CSize | |
Num CWchar | |
Num CSigAtomic | |
Num CClock | |
Num CTime | |
Num CUSeconds | |
Num CSUSeconds | |
Num CIntPtr | |
Num CUIntPtr | |
Num CIntMax | |
Num CUIntMax | |
Integral a => Num (Ratio a) | |
Num a => Num (Sum a) | |
Num a => Num (Product a) |
The Ord
class is used for totally ordered datatypes.
Instances of Ord
can be derived for any user-defined
datatype whose constituent types are in Ord
. The declared order
of the constructors in the data declaration determines the ordering
in derived Ord
instances. The Ordering
datatype allows a single
comparison to determine the precise ordering of two objects.
Minimal complete definition: either compare
or <=
.
Using compare
can be more efficient for complex types.
Ord Bool | |
Ord Char | |
Ord Double | |
Ord Float | |
Ord Int | |
Ord Integer | |
Ord Ordering | |
Ord Word | |
Ord Word8 | |
Ord Word16 | |
Ord Word32 | |
Ord Word64 | |
Ord () | |
Ord Version | |
Ord AsyncException | |
Ord ArrayException | |
Ord ExitCode | |
Ord BufferMode | |
Ord Newline | |
Ord NewlineMode | |
Ord WordPtr | |
Ord IntPtr | |
Ord CChar | |
Ord CSChar | |
Ord CUChar | |
Ord CShort | |
Ord CUShort | |
Ord CInt | |
Ord CUInt | |
Ord CLong | |
Ord CULong | |
Ord CLLong | |
Ord CULLong | |
Ord CFloat | |
Ord CDouble | |
Ord CPtrdiff | |
Ord CSize | |
Ord CWchar | |
Ord CSigAtomic | |
Ord CClock | |
Ord CTime | |
Ord CUSeconds | |
Ord CSUSeconds | |
Ord CIntPtr | |
Ord CUIntPtr | |
Ord CIntMax | |
Ord CUIntMax | |
Ord All | |
Ord Any | |
Ord Arity | |
Ord Fixity | |
Ord Associativity | |
Ord a => Ord [a] | |
Integral a => Ord (Ratio a) | |
Ord (Ptr a) | |
Ord (FunPtr a) | |
Ord (U1 p) | |
Ord p => Ord (Par1 p) | |
Ord a => Ord (ZipList a) | |
Ord a => Ord (Dual a) | |
Ord a => Ord (Sum a) | |
Ord a => Ord (Product a) | |
Ord a => Ord (First a) | |
Ord a => Ord (Last a) | |
Ord a => Ord (Down a) | |
Ord a => Ord (Maybe a) | |
(Ord a, Ord b) => Ord (Either a b) | |
Ord (f p) => Ord (Rec1 f p) | |
(Ord a, Ord b) => Ord (a, b) | |
Ord c => Ord (K1 i c p) | |
(Ord (f p), Ord (g p)) => Ord ((:+:) f g p) | |
(Ord (f p), Ord (g p)) => Ord ((:*:) f g p) | |
Ord (f (g p)) => Ord ((:.:) f g p) | |
(Ord a, Ord b, Ord c) => Ord (a, b, c) | |
Ord ((:~:) k a b) | |
Ord (f p) => Ord (M1 i c f p) | |
(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) | |
(Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (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) | |
(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) | |
(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) | |
(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) | |
(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) | |
(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) | |
(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) | |
(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) | |
(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) |
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 record-syntax form, and furthermore, the fields must be given in the same order as the original declaration. - The derived
Read
instance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Read
in Haskell 2010 is equivalent to
instance (Read a) => Read (Tree a) where readsPrec d r = readParen (d > app_prec) (\r -> [(Leaf m,t) | ("Leaf",s) <- lex r, (m,t) <- readsPrec (app_prec+1) s]) r ++ readParen (d > up_prec) (\r -> [(u:^:v,w) | (u,s) <- readsPrec (up_prec+1) r, (":^:",t) <- lex s, (v,w) <- readsPrec (up_prec+1) t]) r where app_prec = 10 up_prec = 5
Note that right-associativity of :^:
is unused.
The derived instance in GHC is equivalent to
instance (Read a) => Read (Tree a) where readPrec = parens $ (prec app_prec $ do Ident "Leaf" <- lexP m <- step readPrec return (Leaf m)) +++ (prec up_prec $ do u <- step readPrec Symbol ":^:" <- lexP v <- step readPrec return (u :^: v)) where app_prec = 10 up_prec = 5 readListPrec = readListPrecDefault
:: 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 Word8 | |
Read Word16 | |
Read Word32 | |
Read Word64 | |
Read () | |
Read Version | |
Read ExitCode | |
Read BufferMode | |
Read Newline | |
Read NewlineMode | |
Read WordPtr | |
Read IntPtr | |
Read CChar | |
Read CSChar | |
Read CUChar | |
Read CShort | |
Read CUShort | |
Read CInt | |
Read CUInt | |
Read CLong | |
Read CULong | |
Read CLLong | |
Read CULLong | |
Read CFloat | |
Read CDouble | |
Read CPtrdiff | |
Read CSize | |
Read CWchar | |
Read CSigAtomic | |
Read CClock | |
Read CTime | |
Read CUSeconds | |
Read CSUSeconds | |
Read CIntPtr | |
Read CUIntPtr | |
Read CIntMax | |
Read CUIntMax | |
Read All | |
Read Any | |
Read Arity | |
Read Fixity | |
Read Associativity | |
Read Lexeme | |
Read a => Read [a] | |
(Integral a, Read a) => Read (Ratio a) | |
Read (U1 p) | |
Read p => Read (Par1 p) | |
Read a => Read (ZipList a) | |
Read a => Read (Dual a) | |
Read a => Read (Sum a) | |
Read a => Read (Product a) | |
Read a => Read (First a) | |
Read a => Read (Last a) | |
Read a => Read (Down a) | |
Read a => Read (Maybe a) | |
(Read a, Read b) => Read (Either a b) | |
Read (f p) => Read (Rec1 f p) | |
(Read a, Read b) => Read (a, b) | |
(Ix a, Read a, Read b) => Read (Array a b) | |
Read c => Read (K1 i c p) | |
(Read (f p), Read (g p)) => Read ((:+:) f g p) | |
(Read (f p), Read (g p)) => Read ((:*:) f g p) | |
Read (f (g p)) => Read ((:.:) f g p) | |
(Read a, Read b, Read c) => Read (a, b, c) | |
(~) k a b => Read ((:~:) k a b) | |
Read (f p) => Read (M1 i c f p) | |
(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, machine-independent access to the components of a floating-point number.
Minimal complete definition:
all except exponent
, significand
, scaleFloat
and atan2
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 floating-point
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 floating-point radix, and furthermore, either m
and n
are both zero or else b^(d-1) <=
, 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
floating-point 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 floating-point number, it is equal in value to
, where significand
x * b ^^ exponent
xb
is the
floating-point 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 floating-point radix.
The behaviour is unspecified on infinite or NaN
values.
scaleFloat :: Int -> a -> a
multiplies a floating-point number by an integer power of the radix
True
if the argument is an IEEE "not-a-number" (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 floating-point arguments.
For real floating x
and y
,
computes the angle
(from the positive x-axis) of the vector from the origin to the
point atan2
y x(x,y)
.
returns a value in the range [atan2
y x-pi
,
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
; 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
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 top-level 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 record-syntax form, with the fields given in the same order as the original declaration.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Show
is equivalent to
instance (Show a) => Show (Tree a) where showsPrec d (Leaf m) = showParen (d > app_prec) $ showString "Leaf " . showsPrec (app_prec+1) m where app_prec = 10 showsPrec d (u :^: v) = showParen (d > up_prec) $ showsPrec (up_prec+1) u . showString " :^: " . showsPrec (up_prec+1) v where up_prec = 5
Note that right-associativity of :^:
is ignored. For example,
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.
class (Functor t, Foldable t) => Traversable t where
Functors representing data structures that can be traversed from left to right.
Minimal complete definition: traverse
or sequenceA
.
A definition of traverse
must satisfy the following laws:
- naturality
t .
for every applicative transformationtraverse
f =traverse
(t . f)t
- identity
traverse
Identity = Identity- composition
traverse
(Compose .fmap
g . f) = Compose .fmap
(traverse
g) .traverse
f
A definition of sequenceA
must satisfy the following laws:
- naturality
t .
for every applicative transformationsequenceA
=sequenceA
.fmap
tt
- identity
sequenceA
.fmap
Identity = Identity- composition
sequenceA
.fmap
Compose = Compose .fmap
sequenceA
.sequenceA
where an applicative transformation is a function
t :: (Applicative f, Applicative g) => f a -> g a
preserving the Applicative
operations, i.e.
and the identity functor Identity
and composition of functors Compose
are defined as
newtype Identity a = Identity a instance Functor Identity where fmap f (Identity x) = Identity (f x) instance Applicative Indentity where pure x = Identity x Identity f <*> Identity x = Identity (f x) newtype Compose f g a = Compose (f (g a)) instance (Functor f, Functor g) => Functor (Compose f g) where fmap f (Compose x) = Compose (fmap (fmap f) x) instance (Applicative f, Applicative g) => Applicative (Compose f g) where pure x = Compose (pure (pure x)) Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)
(The naturality law is implied by parametricity.)
Instances are similar to Functor
, e.g. given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Traversable Tree where traverse f Empty = pure Empty traverse f (Leaf x) = Leaf <$> f x traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r
This is suitable even for abstract types, as the laws for <*>
imply a form of associativity.
The superclass instances should satisfy the following:
- In the
Functor
instance,fmap
should be equivalent to traversal with the identity applicative functor (fmapDefault
). - In the
Foldable
instance,foldMap
should be equivalent to traversal with a constant applicative functor (foldMapDefault
).
traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
Map each element of a structure to an action, evaluate these actions from left to right, and collect the results.
sequenceA :: Applicative f => t (f a) -> f (t a)
Evaluate each action in the structure from left to right, and collect the results.
mapM :: 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.
sequence :: Monad m => t (m a) -> m (t a)
Evaluate each monadic action in the structure from left to right, and collect the results.
Traversable [] | |
Traversable Maybe | |
Traversable (Either a) | |
Traversable ((,) a) | |
Ix i => Traversable (Array i) | |
Traversable (Const m) | |
Traversable (Proxy *) |
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 do-notation
or the >>
and >>=
operations from the Monad
class.
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 8859-1
(Latin-1) character set (the first 256 characters), which is itself an extension
of the ASCII character set (the first 128 characters). A character literal in
Haskell has type Char
.
To convert a Char
to or from the corresponding Int
value defined
by Unicode, use toEnum
and fromEnum
from the
Enum
class respectively (or equivalently ord
and chr
).
data Double :: *
Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.
data Float :: *
Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.
data Int :: *
data Integer :: *
Arbitrary-precision integers.
data Word :: *
data Bool :: *
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").
Monad (Either e) | |
Functor (Either a) | |
Applicative (Either e) | |
Foldable (Either a) | |
Traversable (Either a) | |
Generic1 (Either a) | |
(Eq a, Eq b) => Eq (Either a b) | |
(Ord a, Ord b) => Ord (Either a b) | |
(Read a, Read b) => Read (Either a b) | |
(Show a, Show b) => Show (Either a b) | |
Generic (Either a b) | |
Typeable (* -> * -> *) Either | |
type Rep1 (Either a) = D1 D1Either ((:+:) (C1 C1_0Either (S1 NoSelector (Rec0 a))) (C1 C1_1Either (S1 NoSelector Par1))) | |
type Rep (Either a b) = D1 D1Either ((:+:) (C1 C1_0Either (S1 NoSelector (Rec0 a))) (C1 C1_1Either (S1 NoSelector (Rec0 b)))) | |
type (==) (Either k k1) a b = EqEither k k1 a b |
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.
Alternative Maybe | |
Monad Maybe | |
Functor Maybe | |
MonadPlus Maybe | |
Applicative Maybe | |
Foldable Maybe | |
Traversable Maybe | |
Generic1 Maybe | |
Eq a => Eq (Maybe a) | |
Ord a => Ord (Maybe a) | |
Read a => Read (Maybe a) | |
Show a => Show (Maybe a) | |
Generic (Maybe a) | |
Monoid a => Monoid (Maybe a) | Lift a semigroup into |
type Rep1 Maybe = D1 D1Maybe ((:+:) (C1 C1_0Maybe U1) (C1 C1_1Maybe (S1 NoSelector Par1))) | |
type Rep (Maybe a) = D1 D1Maybe ((:+:) (C1 C1_0Maybe U1) (C1 C1_1Maybe (S1 NoSelector (Rec0 a)))) | |
type (==) (Maybe k) a b = EqMaybe k a b |
data Ordering :: *
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.
type IOError = IOException
The Haskell 2010 type for exceptions in the IO
monad.
Any I/O operation may raise an IOError
instead of returning a result.
For a more general type of exception, including also those that arise
in pure code, see Control.Exception.Exception.
In Haskell 2010, this is an opaque type.