base-compat-0.9.0: A compatibility layer for base

Safe HaskellSafe
LanguageHaskell98

Prelude.Compat

Synopsis

Documentation

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

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

Examples

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

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

all :: Foldable t => (a -> Bool) -> t a -> Bool

Determines whether all elements of the structure satisfy the predicate.

and :: Foldable t => t Bool -> Bool

and returns the conjunction of a container of Bools. For the result to be True, the container must be finite; False, however, results from a False value finitely far from the left end.

any :: Foldable t => (a -> Bool) -> t a -> Bool

Determines whether any element of the structure satisfies the predicate.

concat :: Foldable t => t [a] -> [a]

The concatenation of all the elements of a container of lists.

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. For a version that doesn't ignore the results see mapM.

As of base 4.8.0.0, mapM_ is just traverse_, specialized to Monad.

notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4

notElem is the negation of elem.

or :: Foldable t => t Bool -> Bool

or returns the disjunction of a container of Bools. For the result to be False, the container must be finite; True, however, results from a True value finitely far from the left end.

sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()

Evaluate each monadic action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequence.

As of base 4.8.0.0, sequence_ is just sequenceA_, specialized to Monad.

(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4

An infix synonym for fmap.

Examples

Convert from a Maybe Int to a Maybe String using show:

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

Convert from an Either Int Int to an Either Int String using show:

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

Double each element of a list:

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

Apply even to the second element of a pair:

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

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

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

Examples

Basic usage:

>>> maybe False odd (Just 3)
True

>>> maybe False odd Nothing
False

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

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

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

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

lines :: String -> [String]

lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.

unlines :: [String] -> String

unlines is an inverse operation to lines. It joins lines, after appending a terminating newline to each.

unwords :: [String] -> String

unwords is an inverse operation to words. It joins words with separating spaces.

words :: String -> [String]

words breaks a string up into a list of words, which were delimited by white space.

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

curry converts an uncurried function to a curried function.

fst :: (a, b) -> a

Extract the first component of a pair.

snd :: (a, b) -> b

Extract the second component of a pair.

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

uncurry converts a curried function to a function on pairs.

($!) :: (a -> b) -> a -> b infixr 0

Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.

(++) :: [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

asTypeOf is a type-restricted version of const. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the second.

const :: a -> b -> a

Constant function.

flip :: (a -> b -> c) -> b -> a -> c

flip f takes its (first) two arguments in the reverse order of f.

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, ...]

otherwise :: Bool

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

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

until :: (a -> Bool) -> (a -> a) -> a -> a

until p f yields the result of applying f until p holds.

ioError :: IOError -> IO a

Raise an IOError in the IO monad.

userError :: String -> IOError

Construct an IOError value with a string describing the error. The fail method of the IO instance of the Monad class raises a userError, thus:

instance Monad IO where
  ...
  fail s = ioError (userError s)

(!!) :: [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],[])

break p is equivalent to span (not . p).

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 :: Int -> [a] -> [a]

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.

dropWhile :: (a -> Bool) -> [a] -> [a]

dropWhile p xs returns the suffix remaining after takeWhile p xs:

dropWhile (< 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3]
dropWhile (< 9) [1,2,3] == []
dropWhile (< 0) [1,2,3] == [1,2,3]

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.

lookup :: Eq a => a -> [(a, b)] -> Maybe b

lookup key assocs looks up a key in an association list.

repeat :: a -> [a]

repeat x is an infinite list, with x the value of every element.

replicate :: Int -> a -> [a]

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.

reverse :: [a] -> [a]

reverse xs returns the elements of xs in reverse order. xs must be finite.

scanl :: (b -> a -> b) -> b -> [a] -> [b]

scanl is similar to foldl, but returns a list of successive reduced values from the left:

scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]

Note that

last (scanl f z xs) == foldl f z xs.

scanl1 :: (a -> a -> a) -> [a] -> [a]

scanl1 is a variant of scanl that has no starting value argument:

scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]

scanr :: (a -> b -> b) -> b -> [a] -> [b]

scanr is the right-to-left dual of scanl. Note that

head (scanr f z xs) == foldr f z xs.

scanr1 :: (a -> a -> a) -> [a] -> [a]

scanr1 is a variant of scanr that has no starting value argument.

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])

span p xs is equivalent to (takeWhile p xs, dropWhile p xs)

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 (take n xs, drop n xs) when n is not _|_ (splitAt _|_ xs = _|_). splitAt is an instance of the more general genericSplitAt, in which n may be of any integral type.

tail :: [a] -> [a]

Extract the elements after the head of a list, which must be non-empty.

take :: Int -> [a] -> [a]

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])

The unzip3 function takes a list of triples and returns three lists, analogous to unzip.

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.

zip is right-lazy:

zip [] _|_ = []

zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]

zip3 takes three lists and returns a list of triples, analogous to zip.

zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]

zipWith generalises zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two lists to produce the list of corresponding sums.

zipWith is right-lazy:

zipWith f [] _|_ = []

zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]

The zipWith3 function takes a function which combines three elements, as well as three lists and returns a list of their point-wise combination, analogous to zipWith.

subtract :: Num a => a -> a -> a

the same as flip (-).

Because - is treated specially in the Haskell grammar, (- e) is not a section, but an application of prefix negation. However, (subtract exp) is equivalent to the disallowed section.

lex :: ReadS String

The lex function reads a single lexeme from the input, discarding initial white space, and returning the characters that constitute the lexeme. If the input string contains only white space, lex returns a single successful `lexeme' consisting of the empty string. (Thus lex "" = [("","")].) If there is no legal lexeme at the beginning of the input string, lex fails (i.e. returns []).

This lexer is not completely faithful to the Haskell lexical syntax in the following respects:

  • Qualified names are not handled properly
  • Octal and hexadecimal numerics are not recognized as a single token
  • Comments are not treated properly

readParen :: Bool -> ReadS a -> ReadS a

readParen True p parses what p parses, but surrounded with parentheses.

readParen False p parses what p parses, but optionally surrounded with parentheses.

(^) :: (Num a, Integral b) => a -> b -> a infixr 8

raise a number to a non-negative integral power

(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8

raise a number to an integral power

even :: Integral a => a -> Bool

fromIntegral :: (Integral a, Num b) => a -> b

general coercion from integral types

gcd :: Integral a => a -> a -> a

gcd x y is the non-negative factor of both x and y of which every common factor of x and y is also a factor; for example gcd 4 2 = 2, gcd (-4) 6 = 2, gcd 0 4 = 4. gcd 0 0 = 0. (That is, the common divisor that is "greatest" in the divisibility preordering.)

Note: Since for signed fixed-width integer types, abs minBound < 0, the result may be negative if one of the arguments is minBound (and necessarily is if the other is 0 or minBound) for such types.

lcm :: Integral a => a -> a -> a

lcm x y is the smallest positive integer that both x and y divide.

odd :: Integral a => a -> Bool

realToFrac :: (Real a, Fractional b) => a -> b

general coercion to fractional types

showChar :: Char -> ShowS

utility function converting a Char to a show function that simply prepends the character unchanged.

showParen :: Bool -> ShowS -> ShowS

utility function that surrounds the inner show function with parentheses when the Bool parameter is True.

showString :: String -> ShowS

utility function converting a String to a show function that simply prepends the string unchanged.

shows :: Show a => a -> ShowS

equivalent to showsPrec with a precedence of 0.

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]])

getChar :: IO Char

Read a character from the standard input device (same as hGetChar stdin).

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).

getLine :: IO String

Read a line from the standard input device (same as hGetLine 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.

print :: Show a => a -> IO ()

The print function outputs a value of any printable type to the standard output device. Printable types are those that are instances of class Show; print converts values to strings for output using the show operation and adds a newline.

For example, a program to print the first 20 integers and their powers of 2 could be written as:

main = print ([(n, 2^n) | n <- [0..19]])

putChar :: Char -> IO ()

Write a character to the standard output device (same as hPutChar stdout).

putStr :: String -> IO ()

Write a string to the standard output device (same as hPutStr stdout).

putStrLn :: String -> IO ()

The same as putStr, but adds a newline character.

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.

readIO :: Read a => String -> IO a

The readIO function is similar to read except that it signals parse failure to the IO monad instead of terminating the program.

readLn :: Read a => IO a

The readLn function combines getLine and readIO.

writeFile :: FilePath -> String -> IO ()

The computation writeFile file str function writes the string str, to the file file.

read :: Read a => String -> a

The read function reads input from a string, which must be completely consumed by the input process.

reads :: Read a => ReadS a

equivalent to readsPrec with a precedence of 0.

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

Boolean "and"

not :: Bool -> Bool

Boolean "not"

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

Boolean "or"

($) :: (a -> b) -> a -> b infixr 0

Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

    f $ g $ h x  =  f (g (h x))

It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.

error :: [Char] -> a

error stops execution and displays an error message.

errorWithoutStackTrace :: [Char] -> a Source

A variant of error that does not produce a stack trace.

Since: 4.9.0.0

undefined :: a

A special case of error. It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in which undefined appears.

seq :: a -> b -> b

The value of seq a b is bottom if a is bottom, and otherwise equal to b. seq is usually introduced to improve performance by avoiding unneeded laziness.

A note on evaluation order: the expression seq a b does not guarantee that a will be evaluated before b. The only guarantee given by seq is that the both a and b will be evaluated before seq returns a value. In particular, this means that b may be evaluated before a. If you need to guarantee a specific order of evaluation, you must use the function pseq from the "parallel" package.

elem :: Foldable t => forall a. Eq a => a -> t a -> Bool

Does the element occur in the structure?

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.

foldl :: Foldable t => forall b a. (b -> a -> b) -> b -> t a -> b

Left-associative fold of a structure.

foldl f z = foldl f z . toList

foldl1 :: Foldable t => forall a. (a -> a -> a) -> t a -> a

A variant of foldl that has no base case, and thus may only be applied to non-empty structures.

foldl1 f = foldl1 f . toList

foldr :: Foldable t => forall a b. (a -> b -> b) -> b -> t a -> b

Right-associative fold of a structure.

foldr f z = foldr f z . toList

foldr1 :: Foldable t => forall a. (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

length :: Foldable t => forall a. t a -> Int

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.

maximum :: Foldable t => forall a. Ord a => t a -> a

The largest element of a non-empty structure.

minimum :: Foldable t => forall a. Ord a => t a -> a

The least element of a non-empty structure.

null :: Foldable t => forall a. t a -> Bool

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 => forall a. Num a => t a -> a

The product function computes the product of the numbers of a structure.

sum :: Foldable t => forall a. 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. For a version that ignores the results see mapM_.

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. For a version that ignores the results see sequence_.

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 and collect the results. For a version that ignores the results see sequenceA_.

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. For a version that ignores the results see traverse_.

(*>) :: 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.

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

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

fmap :: Functor f => forall a b. (a -> b) -> f a -> f b

(>>) :: 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.

return :: Monad m => forall a. a -> m a

Inject a value into the monadic type.

mappend :: Monoid a => a -> a -> a

An associative operation

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.

mempty :: Monoid a => a

Identity of mappend

maxBound :: Bounded a => a

minBound :: Bounded a => a

enumFrom :: Enum a => a -> [a]

Used in Haskell's translation of [n..].

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].

fromEnum :: Enum a => a -> 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.

pred :: Enum a => a -> a

the predecessor of a value. For numeric types, pred subtracts 1.

succ :: Enum a => a -> a

the successor of a value. For numeric types, succ adds 1.

toEnum :: Enum a => Int -> a

Convert from an Int.

(**) :: 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

a version of arctangent taking two real floating-point arguments. For real floating x and y, atan2 y x computes the angle (from the positive x-axis) of the vector from the origin to the point (x,y). atan2 y x returns a value in the range [-pi, pi]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. atan2 y 1, with y in a type that is RealFloat, should return the same value as atan y. A default definition of atan2 is provided, but implementors can provide a more accurate implementation.

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 decodeFloat x yields (m,n), then x is equal in value to m*b^^n, where b is the floating-point radix, and furthermore, either m and n are both zero or else b^(d-1) <= abs m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0). If the type contains a negative zero, also decodeFloat (-0.0) = (0,0). The result of decodeFloat x is unspecified if either of isNaN x or isInfinite x is True.

encodeFloat :: 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. encodeFloat m n is one of the two closest representable floating-point numbers to m*b^^n (or ±Infinity if overflow occurs); usually the closer, but if m contains too many bits, the result may be rounded in the wrong direction.

exponent :: RealFloat a => a -> Int

exponent corresponds to the second component of decodeFloat. exponent 0 = 0 and for finite nonzero x, exponent x = snd (decodeFloat x) + floatDigits x. If x is a finite floating-point number, it is equal in value to significand x * b ^^ exponent x, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

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

isIEEE :: RealFloat a => a -> Bool

True if the argument is an IEEE floating point number

isInfinite :: RealFloat a => a -> Bool

True if the argument is an IEEE infinity or negative infinity

isNaN :: RealFloat a => a -> Bool

True if the argument is an IEEE "not-a-number" (NaN) value

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.

(*) :: Num a => a -> a -> a

(+) :: Num a => a -> a -> a

(-) :: Num a => a -> a -> a

abs :: Num a => a -> a

Absolute value.

negate :: Num a => a -> a

Unary negation.

signum :: Num a => 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).

readList :: Read a => ReadS [a]

The method readList is provided to allow the programmer to give a specialised way of parsing lists of values. For example, this is used by the predefined Read instance of the Char type, where values of type String should be are expected to use double quotes, rather than square brackets.

readsPrec

Arguments

:: Read a 
=> Int

the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.

-> ReadS a 

attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.

Derived instances of Read and Show satisfy the following:

That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

(/) :: Fractional a => a -> a -> a

fractional division

fromRational :: Fractional a => Rational -> a

Conversion from a Rational (that is Ratio Integer). A floating literal stands for an application of fromRational to a value of type Rational, so such literals have type (Fractional a) => a.

recip :: Fractional a => a -> a

reciprocal fraction

div :: Integral a => a -> a -> a

integer division truncated toward negative infinity

divMod :: Integral a => a -> a -> (a, a)

simultaneous div and mod

mod :: Integral a => a -> a -> a

integer modulus, satisfying

(x `div` y)*y + (x `mod` y) == x

quot :: Integral a => a -> a -> a

integer division truncated toward zero

quotRem :: Integral a => a -> a -> (a, a)

simultaneous quot and rem

rem :: Integral a => a -> a -> a

integer remainder, satisfying

(x `quot` y)*y + (x `rem` y) == x

toInteger :: Integral a => a -> Integer

conversion to Integer

toRational :: Real a => a -> Rational

the rational equivalent of its real argument with full precision

ceiling :: RealFrac a => forall b. Integral b => a -> b

ceiling x returns the least integer not less than x

floor :: RealFrac a => forall b. Integral b => a -> b

floor x returns the greatest integer not greater than x

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 as x; and
  • f is a fraction with the same type and sign as x, and with absolute value less than 1.

The default definitions of the ceiling, floor, truncate and round functions are in terms of properFraction.

round :: RealFrac a => forall b. Integral b => a -> b

round x returns the nearest integer to x; the even integer if x is equidistant between two integers

truncate :: RealFrac a => forall b. Integral b => a -> b

truncate x returns the integer nearest x between zero and x

show :: Show a => a -> String

A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.

showList :: Show a => [a] -> ShowS

The method showList is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefined Show instance of the Char type, where values of type String should be shown in double quotes, rather than between square brackets.

showsPrec

Arguments

:: Show a 
=> Int

the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.

-> a

the value to be converted to a String

-> ShowS 

Convert a value to a readable String.

showsPrec should satisfy the law

showsPrec d x r ++ s  ==  showsPrec d x (r ++ s)

Derived instances of Read and Show satisfy the following:

That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

(/=) :: 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

A functor with application, providing operations to

  • embed pure expressions (pure), and
  • sequence computations and combine their results (<*>).

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).

Minimal complete definition

pure, (<*>)

Methods

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.

Instances

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.

Methods

minBound :: a

maxBound :: a

Instances

Bounded Bool 
Bounded Char 
Bounded Int 
Bounded Ordering 
Bounded Word 
Bounded Word8 
Bounded Word16 
Bounded Word32 
Bounded Word64 
Bounded () 
Bounded All 
Bounded Any 
Bounded a => Bounded (Dual a) 
Bounded a => Bounded (Sum a) 
Bounded a => Bounded (Product a) 
(Bounded a, Bounded b) => Bounded (a, b) 
Bounded (Proxy k s) 
(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) 
(~) k a b => Bounded ((:~:) k a b) 
(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) 
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) 

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:

   enumFrom     x   = enumFromTo     x maxBound
   enumFromThen x y = enumFromThenTo x y bound
     where
       bound | fromEnum y >= fromEnum x = maxBound
             | otherwise                = minBound

Minimal complete definition

toEnum, fromEnum

Methods

succ :: a -> a

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.

toEnum :: Int -> a

Convert from an Int.

fromEnum :: a -> 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].

Instances

Enum Bool 
Enum Char 
Enum Int 
Enum Integer 
Enum Ordering 
Enum Word 
Enum Word8 
Enum Word16 
Enum Word32 
Enum Word64 
Enum () 
Integral a => Enum (Ratio a) 
Enum (Proxy k s) 
Enum (f a) => Enum (Alt k f 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.

Minimal complete definition: either == or /=.

Minimal complete definition

(==) | (/=)

Methods

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

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

Instances

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 BigNat 
Eq Version 
Eq ThreadId 
Eq BlockReason 
Eq ThreadStatus 
Eq AsyncException 
Eq ArrayException 
Eq ExitCode 
Eq IOErrorType 
Eq MaskingState 
Eq IOException 
Eq ErrorCall 
Eq ArithException 
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 (ForeignPtr a) 
Eq a => Eq (Complex a) 
Eq a => Eq (ZipList a) 
Eq (TVar a) 
Eq (IORef 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 (Maybe a) 
(Eq a, Eq b) => Eq (Either a b) 
Eq (f p) => Eq (Rec1 f p) 
(Eq a, Eq b) => Eq (a, b) 
(Ix i, Eq e) => Eq (Array i e) 
Eq a => Eq (Const a b) 
Eq (Proxy k s) 
Eq (STRef s a) 
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 (STArray s i e) 
Eq (f a) => Eq (Alt k f a) 
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, asin, acos, atan, sinh, cosh, asinh, acosh, atanh

Methods

pi :: a

exp :: a -> a

log :: a -> a

sqrt :: a -> a

(**) :: a -> a -> a infixr 8

logBase :: a -> a -> a

sin :: a -> a

cos :: a -> a

tan :: a -> a

asin :: a -> a

acos :: a -> a

atan :: a -> a

sinh :: a -> a

cosh :: a -> a

tanh :: a -> a

asinh :: a -> a

acosh :: a -> a

atanh :: a -> a

Instances

class Foldable t where

Data structures that can be folded.

For example, given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Foldable Tree where
   foldMap f Empty = mempty
   foldMap f (Leaf x) = f x
   foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r

This is suitable even for abstract types, as the monoid is assumed to satisfy the monoid laws. Alternatively, one could define foldr:

instance Foldable Tree where
   foldr f z Empty = z
   foldr f z (Leaf x) = f x z
   foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l

Foldable instances are expected to satisfy the following laws:

foldr f z t = appEndo (foldMap (Endo . f) t ) z
foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
fold = foldMap id

sum, product, maximum, and minimum should all be essentially equivalent to foldMap forms, such as

sum = getSum . foldMap Sum

but may be less defined.

If the type is also a Functor instance, it should satisfy

foldMap f = fold . fmap f

which implies that

foldMap f . fmap g = foldMap (f . g)

Minimal complete definition

foldMap | foldr

Methods

foldMap :: Monoid m => (a -> m) -> t a -> m

Map each element of the structure to a monoid, and combine the results.

foldr :: (a -> b -> b) -> b -> t a -> b

Right-associative fold of a structure.

foldr f z = foldr f z . toList

foldl :: (b -> a -> b) -> b -> t a -> b

Left-associative fold of a structure.

foldl f z = foldl f z . toList

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

A variant of foldl that has no base case, and thus may only be applied to non-empty structures.

foldl1 f = foldl1 f . toList

null :: t a -> Bool

Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

length :: t a -> Int

Returns the size/length of a finite structure as an Int. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

elem :: Eq a => a -> t a -> Bool infix 4

Does the element occur in the structure?

maximum :: Ord a => t a -> a

The largest element of a non-empty structure.

minimum :: Ord a => t a -> a

The least element of a non-empty structure.

sum :: Num a => t a -> a

The sum function computes the sum of the numbers of a structure.

product :: Num a => t a -> a

The product function computes the product of the numbers of a structure.

Instances

class Num a => Fractional a where

Fractional numbers, supporting real division.

Minimal complete definition

fromRational, (recip | (/))

Methods

(/) :: a -> a -> a infixl 7

fractional division

recip :: a -> a

reciprocal fraction

fromRational :: Rational -> a

Conversion from a Rational (that is Ratio Integer). A floating literal stands for an application of fromRational to a value of type Rational, so such literals have type (Fractional a) => a.

Instances

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.

Minimal complete definition

fmap

Methods

fmap :: (a -> b) -> f a -> f b

(<$) :: a -> f b -> f a infixl 4

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

Instances

class (Real a, Enum a) => Integral a where

Integral numbers, supporting integer division.

Minimal complete definition

quotRem, toInteger

Methods

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)

simultaneous quot and rem

divMod :: a -> a -> (a, a)

simultaneous div and mod

toInteger :: a -> Integer

conversion to Integer

Instances

class Applicative m => 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.

Instances of Monad should satisfy the following laws:

Furthermore, the Monad and Applicative operations should relate as follows:

The above laws imply:

and that pure and (<*>) satisfy the applicative functor laws.

The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=)

Methods

(>>=) :: 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 :: 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.

Instances

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.

Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product.

Minimal complete definition

mempty, mappend

Methods

mempty :: a

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.

Instances

Monoid Ordering 
Monoid () 
Monoid All 
Monoid Any 
Monoid [a] 
Ord a => Monoid (Max a) 
Ord a => Monoid (Min 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 Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S." Since there is no "Semigroup" typeclass providing just mappend, we use Monoid instead.

Monoid b => Monoid (a -> b) 
(Monoid a, Monoid b) => Monoid (a, b) 
Monoid a => Monoid (Const a b) 
Monoid (Proxy k s) 
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) 
Alternative f => Monoid (Alt * f a) 
(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

(+), (*), abs, signum, fromInteger, (negate | (-))

Methods

(+) :: a -> a -> a infixl 6

(-) :: a -> a -> a infixl 6

(*) :: a -> a -> a infixl 7

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.

Instances

Num Int 
Num Integer 
Num Word 
Num Word8 
Num Word16 
Num Word32 
Num Word64 
Integral a => Num (Ratio a) 
RealFloat a => Num (Complex a) 
Num a => Num (Sum a) 
Num a => Num (Product a) 
Num (f a) => Num (Alt k f a) 

class Eq a => Ord a where

The Ord class is used for totally ordered datatypes.

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

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

Minimal complete definition

compare | (<=)

Methods

compare :: a -> a -> Ordering

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

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

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

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

max :: a -> a -> a

min :: a -> a -> a

Instances

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 BigNat 
Ord Version 
Ord ThreadId 
Ord BlockReason 
Ord ThreadStatus 
Ord AsyncException 
Ord ArrayException 
Ord ExitCode 
Ord ErrorCall 
Ord ArithException 
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 (ForeignPtr a) 
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 (Maybe a) 
(Ord a, Ord b) => Ord (Either a b) 
Ord (f p) => Ord (Rec1 f p) 
(Ord a, Ord b) => Ord (a, b) 
(Ix i, Ord e) => Ord (Array i e) 
Ord a => Ord (Const a b) 
Ord (Proxy k s) 
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 (f a) => Ord (Alt k f a) 
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 Strings, producing values.

Derived instances of Read make the following assumptions, which derived instances of Show obey:

  • If the constructor is defined to be an infix operator, then the derived Read instance will parse only infix applications of the constructor (not the prefix form).
  • Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
  • If the constructor is defined using record syntax, the derived Read will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration.
  • The derived Read instance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.

For example, given the declarations

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Read in Haskell 2010 is equivalent to

instance (Read a) => Read (Tree a) where

        readsPrec d r =  readParen (d > app_prec)
                         (\r -> [(Leaf m,t) |
                                 ("Leaf",s) <- lex r,
                                 (m,t) <- readsPrec (app_prec+1) s]) r

                      ++ readParen (d > up_prec)
                         (\r -> [(u:^:v,w) |
                                 (u,s) <- readsPrec (up_prec+1) r,
                                 (":^:",t) <- lex s,
                                 (v,w) <- readsPrec (up_prec+1) t]) r

          where app_prec = 10
                up_prec = 5

Note that right-associativity of :^: is unused.

The derived instance in GHC is equivalent to

instance (Read a) => Read (Tree a) where

        readPrec = parens $ (prec app_prec $ do
                                 Ident "Leaf" <- lexP
                                 m <- step readPrec
                                 return (Leaf m))

                     +++ (prec up_prec $ do
                                 u <- step readPrec
                                 Symbol ":^:" <- lexP
                                 v <- step readPrec
                                 return (u :^: v))

          where app_prec = 10
                up_prec = 5

        readListPrec = readListPrecDefault

Minimal complete definition

readsPrec | readPrec

Methods

readsPrec

Arguments

:: Int

the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.

-> ReadS a 

attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.

Derived instances of Read and Show satisfy the following:

That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

readList :: ReadS [a]

The method readList is provided to allow the programmer to give a specialised way of parsing lists of values. For example, this is used by the predefined Read instance of the Char type, where values of type String should be are expected to use double quotes, rather than square brackets.

Instances

Read Bool 
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 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 (Complex a) 
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 (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 a => Read (Const a b) 
Read (Proxy k s) 
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) 
Read (f a) => Read (Alt k f a) 
(~) 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

Methods

toRational :: a -> Rational

the rational equivalent of its real argument with full precision

Instances

class (RealFrac a, Floating a) => RealFloat a where

Efficient, machine-independent access to the components of a floating-point number.

Minimal complete definition

floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE

Methods

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 decodeFloat x yields (m,n), then x is equal in value to m*b^^n, where b is the floating-point radix, and furthermore, either m and n are both zero or else b^(d-1) <= abs m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0). If the type contains a negative zero, also decodeFloat (-0.0) = (0,0). The result of decodeFloat x is unspecified if either of isNaN x or isInfinite x is True.

encodeFloat :: Integer -> Int -> a

encodeFloat performs the inverse of decodeFloat in the sense that for finite x with the exception of -0.0, uncurry encodeFloat (decodeFloat x) = x. encodeFloat m n is one of the two closest representable floating-point numbers to m*b^^n (or ±Infinity if overflow occurs); usually the closer, but if m contains too many bits, the result may be rounded in the wrong direction.

exponent :: a -> Int

exponent corresponds to the second component of decodeFloat. exponent 0 = 0 and for finite nonzero x, exponent x = snd (decodeFloat x) + floatDigits x. If x is a finite floating-point number, it is equal in value to significand x * b ^^ exponent x, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

significand :: a -> a

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

isNaN :: a -> Bool

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

isIEEE :: a -> Bool

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, atan2 y x computes the angle (from the positive x-axis) of the vector from the origin to the point (x,y). atan2 y x returns a value in the range [-pi, pi]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. atan2 y 1, with y in a type that is RealFloat, should return the same value as atan y. A default definition of atan2 is provided, but implementors can provide a more accurate implementation.

Instances

class (Real a, Fractional a) => RealFrac a where

Extracting components of fractions.

Minimal complete definition

properFraction

Methods

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 as x; and
  • f is a fraction with the same type and sign as x, and with absolute value less than 1.

The default definitions of the ceiling, floor, truncate and round functions are in terms of properFraction.

truncate :: Integral b => a -> b

truncate x returns the integer nearest x between zero and x

round :: Integral b => a -> b

round x returns the nearest integer to x; the even integer if x is equidistant between two integers

ceiling :: Integral b => a -> b

ceiling x returns the least integer not less than x

floor :: Integral b => a -> b

floor x returns the greatest integer not greater than x

Instances

class Show a where

Conversion of values to readable Strings.

Derived instances of Show have the following properties, which are compatible with derived instances of Read:

  • The result of show is a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used.
  • If the constructor is defined to be an infix operator, then showsPrec will produce infix applications of the constructor.
  • the representation will be enclosed in parentheses if the precedence of the top-level constructor in x is less than d (associativity is ignored). Thus, if d is 0 then the result is never surrounded in parentheses; if d is 11 it is always surrounded in parentheses, unless it is an atomic expression.
  • If the constructor is defined using record syntax, then show will produce the record-syntax form, with the fields given in the same order as the original declaration.

For example, given the declarations

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Show is equivalent to

instance (Show a) => Show (Tree a) where

       showsPrec d (Leaf m) = showParen (d > app_prec) $
            showString "Leaf " . showsPrec (app_prec+1) m
         where app_prec = 10

       showsPrec d (u :^: v) = showParen (d > up_prec) $
            showsPrec (up_prec+1) u .
            showString " :^: "      .
            showsPrec (up_prec+1) v
         where up_prec = 5

Note that right-associativity of :^: is ignored. For example,

  • show (Leaf 1 :^: Leaf 2 :^: Leaf 3) produces the string "Leaf 1 :^: (Leaf 2 :^: Leaf 3)".

Minimal complete definition

showsPrec | show

Methods

showsPrec

Arguments

:: Int

the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.

-> a

the value to be converted to a String

-> ShowS 

Convert a value to a readable String.

showsPrec should satisfy the law

showsPrec d x r ++ s  ==  showsPrec d x (r ++ s)

Derived instances of Read and Show satisfy the following:

That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

show :: a -> String

A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.

showList :: [a] -> ShowS

The method showList is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefined Show instance of the Char type, where values of type String should be shown in double quotes, rather than between square brackets.

Instances

Show Bool 
Show Char 
Show Int 
Show Integer 
Show Ordering 
Show Word 
Show Word8 
Show Word16 
Show Word32 
Show Word64 
Show () 
Show Version 
Show ThreadId 
Show BlockReason 
Show ThreadStatus 
Show BlockedIndefinitelyOnMVar 
Show BlockedIndefinitelyOnSTM 
Show Deadlock 
Show AllocationLimitExceeded 
Show AssertionFailed 
Show SomeAsyncException 
Show AsyncException 
Show ArrayException 
Show ExitCode 
Show IOErrorType 
Show MaskingState 
Show IOException 
Show ErrorCall 
Show ArithException 
Show All 
Show Any 
Show Arity 
Show Fixity 
Show Associativity 
Show Lexeme 
Show Number 
Show SomeException 
Show a => Show [a] 
(Integral a, Show a) => Show (Ratio a) 
Show (Ptr a) 
Show (FunPtr a) 
Show (U1 p) 
Show p => Show (Par1 p) 
Show (ForeignPtr a) 
Show a => Show (Complex a) 
Show a => Show (ZipList a) 
Show a => Show (Dual a) 
Show a => Show (Sum a) 
Show a => Show (Product a) 
Show a => Show (First a) 
Show a => Show (Last a) 
Show a => Show (Maybe a) 
(Show a, Show b) => Show (Either a b) 
Show (f p) => Show (Rec1 f p) 
(Show a, Show b) => Show (a, b) 
Show (ST s a) 
(Ix a, Show a, Show b) => Show (Array a b) 
Show a => Show (Const a b) 
Show (Proxy k s) 
Show c => Show (K1 i c p) 
(Show (f p), Show (g p)) => Show ((:+:) f g p) 
(Show (f p), Show (g p)) => Show ((:*:) f g p) 
Show (f (g p)) => Show ((:.:) f g p) 
(Show a, Show b, Show c) => Show (a, b, c) 
Show (f a) => Show (Alt k f a) 
Show ((:~:) k a b) 
Show (f p) => Show (M1 i c f p) 
(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) 

class (Functor t, Foldable t) => Traversable t where

Functors representing data structures that can be traversed from left to right.

A definition of traverse must satisfy the following laws:

naturality
t . traverse f = traverse (t . f) for every applicative transformation t
identity
traverse Identity = Identity
composition
traverse (Compose . fmap g . f) = Compose . fmap (traverse g) . traverse f

A definition of sequenceA must satisfy the following laws:

naturality
t . sequenceA = sequenceA . fmap t for every applicative transformation t
identity
sequenceA . fmap Identity = Identity
composition
sequenceA . fmap Compose = Compose . fmap sequenceA . sequenceA

where an applicative transformation is a function

t :: (Applicative f, Applicative g) => f a -> g a

preserving the Applicative operations, i.e.

and the identity functor Identity and composition of functors Compose are defined as

  newtype Identity a = Identity a

  instance Functor Identity where
    fmap f (Identity x) = Identity (f x)

  instance Applicative 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:

Minimal complete definition

traverse | sequenceA

Methods

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. For a version that ignores the results see traverse_.

sequenceA :: Applicative f => t (f a) -> f (t a)

Evaluate each action in the structure from left to right, and and collect the results. For a version that ignores the results see sequenceA_.

mapM :: Monad m => (a -> m b) -> t a -> m (t b)

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see mapM_.

sequence :: Monad m => t (m a) -> m (t a)

Evaluate each monadic action in the structure from left to right, and collect the results. For a version that ignores the results see sequence_.

Instances

data IO a :: * -> *

A value of type IO a is a computation which, when performed, does some I/O before returning a value of type a.

There is really only one way to "perform" an I/O action: bind it to Main.main in your program. When your program is run, the I/O will be performed. It isn't possible to perform I/O from an arbitrary function, unless that function is itself in the IO monad and called at some point, directly or indirectly, from Main.main.

IO is a monad, so IO actions can be combined using either the do-notation or the >> and >>= operations from the Monad class.

Instances

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).

Instances

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.

Instances

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.

Instances

data Int :: *

A fixed-precision integer type with at least the range [-2^29 .. 2^29-1]. The exact range for a given implementation can be determined by using minBound and maxBound from the Bounded class.

Instances

data Integer :: *

Invariant: Jn# and Jp# are used iff value doesn't fit in S#

Useful properties resulting from the invariants:

Instances

data Word :: *

A Word is an unsigned integral type, with the same size as Int.

Instances

data Bool :: *

Constructors

False 
True 

Instances

Bounded Bool 
Enum Bool 
Eq Bool 
Ord Bool 
Read Bool 
Show Bool 
Ix Bool 
Generic Bool 
Storable Bool 
Bits Bool 
FiniteBits Bool 
type Rep Bool = D1 D1Bool ((:+:) (C1 C1_0Bool U1) (C1 C1_1Bool U1)) 
type (==) Bool a b = EqBool a b 

data Either a b :: * -> * -> *

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

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

Examples

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

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

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

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

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

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

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

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

>>> parseMultiple
Right 3

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

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

>>> parseMultiple
Left "parse error"

Constructors

Left a 
Right b 

Instances

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

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

Constructors

Nothing 
Just a 

Instances

Monad Maybe 
Functor Maybe 
Applicative Maybe 
Foldable Maybe 
Traversable Maybe 
Generic1 Maybe 
Alternative Maybe 
MonadPlus 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 Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S." Since there is no "Semigroup" typeclass providing just mappend, we use Monoid instead.

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 :: *

Constructors

LT 
EQ 
GT 

Instances

Bounded Ordering 
Enum Ordering 
Eq Ordering 
Ord Ordering 
Read Ordering 
Show Ordering 
Ix Ordering 
Generic Ordering 
Monoid Ordering 
type Rep Ordering = D1 D1Ordering ((:+:) (C1 C1_0Ordering U1) ((:+:) (C1 C1_1Ordering U1) (C1 C1_2Ordering U1))) 
type (==) Ordering a b = EqOrdering a b 

type FilePath = String

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.

type Rational = Ratio Integer

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.

type ReadS a = String -> [(a, String)]

A parser for a type a, represented as a function that takes a String and returns a list of possible parses as (a,String) pairs.

Note that this kind of backtracking parser is very inefficient; reading a large structure may be quite slow (cf ReadP).

type ShowS = String -> String

The shows functions return a function that prepends the output String to an existing String. This allows constant-time concatenation of results using function composition.

type String = [Char]

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