-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Compatibility with Haskell 98
--   
--   This package provides compatibility with the modules of Haskell 98 and
--   the FFI addendum, by means of wrappers around modules from the base
--   package (which in many cases have additional features). However
--   Prelude, Numeric and Foreign are provided directly by the base
--   package.
@package haskell98
@version 2.0.0.2


-- | The Haskell 98 Prelude: a standard module imported by default into all
--   Haskell modules. For more documentation, see the Haskell 98 Report
--   <a>http://www.haskell.org/onlinereport/</a>.
module Prelude
data Bool :: *
False :: Bool
True :: Bool
(&&) :: Bool -> Bool -> Bool
(||) :: Bool -> Bool -> Bool
not :: Bool -> Bool

-- | <a>otherwise</a> is defined as the value <a>True</a>. It helps to make
--   guards more readable. eg.
--   
--   <pre>
--   f x | x &lt; 0     = ...
--       | otherwise = ...
--   </pre>
otherwise :: Bool

-- | The <a>Maybe</a> type encapsulates an optional value. A value of type
--   <tt><a>Maybe</a> a</tt> either contains a value of type <tt>a</tt>
--   (represented as <tt><a>Just</a> a</tt>), or it is empty (represented
--   as <a>Nothing</a>). Using <a>Maybe</a> is a good way to deal with
--   errors or exceptional cases without resorting to drastic measures such
--   as <a>error</a>.
--   
--   The <a>Maybe</a> type is also a monad. It is a simple kind of error
--   monad, where all errors are represented by <a>Nothing</a>. A richer
--   error monad can be built using the <a>Either</a> type.
data Maybe a :: * -> *
Nothing :: Maybe a
Just :: a -> Maybe a

-- | The <a>maybe</a> function takes a default value, a function, and a
--   <a>Maybe</a> value. If the <a>Maybe</a> value is <a>Nothing</a>, the
--   function returns the default value. Otherwise, it applies the function
--   to the value inside the <a>Just</a> and returns the result.
maybe :: b -> (a -> b) -> Maybe a -> b

-- | The <a>Either</a> type represents values with two possibilities: a
--   value of type <tt><a>Either</a> a b</tt> is either <tt><a>Left</a>
--   a</tt> or <tt><a>Right</a> b</tt>.
--   
--   The <a>Either</a> type is sometimes used to represent a value which is
--   either correct or an error; by convention, the <a>Left</a> constructor
--   is used to hold an error value and the <a>Right</a> constructor is
--   used to hold a correct value (mnemonic: "right" also means "correct").
data Either a b :: * -> * -> *
Left :: a -> Either a b
Right :: b -> Either a b

-- | Case analysis for the <a>Either</a> type. If the value is
--   <tt><a>Left</a> a</tt>, apply the first function to <tt>a</tt>; if it
--   is <tt><a>Right</a> b</tt>, apply the second function to <tt>b</tt>.
either :: (a -> c) -> (b -> c) -> Either a b -> c
data Ordering :: *
LT :: Ordering
EQ :: Ordering
GT :: Ordering
data Char :: *

-- | A <a>String</a> is a list of characters. String constants in Haskell
--   are values of type <a>String</a>.
type String = [Char]

-- | Extract the first component of a pair.
fst :: (a, b) -> a

-- | Extract the second component of a pair.
snd :: (a, b) -> b

-- | <a>curry</a> converts an uncurried function to a curried function.
curry :: ((a, b) -> c) -> a -> b -> c

-- | <a>uncurry</a> converts a curried function to a function on pairs.
uncurry :: (a -> b -> c) -> (a, b) -> c
class Eq a
(==) :: Eq a => a -> a -> Bool
(/=) :: Eq a => a -> a -> Bool
class Eq a => Ord a
compare :: Ord a => a -> a -> Ordering
(<) :: Ord a => a -> a -> Bool
(>=) :: Ord a => a -> a -> Bool
(>) :: Ord a => a -> a -> Bool
(<=) :: Ord a => a -> a -> Bool
max :: Ord a => a -> a -> a
min :: Ord a => a -> a -> a

-- | Class <a>Enum</a> defines operations on sequentially ordered types.
--   
--   The <tt>enumFrom</tt>... methods are used in Haskell's translation of
--   arithmetic sequences.
--   
--   Instances of <a>Enum</a> 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 <a>fromEnum</a> from
--   <tt>0</tt> through <tt>n-1</tt>. See Chapter 10 of the <i>Haskell
--   Report</i> for more details.
--   
--   For any type that is an instance of class <a>Bounded</a> as well as
--   <a>Enum</a>, the following should hold:
--   
--   <ul>
--   <li>The calls <tt><a>succ</a> <a>maxBound</a></tt> and <tt><a>pred</a>
--   <a>minBound</a></tt> should result in a runtime error.</li>
--   <li><a>fromEnum</a> and <a>toEnum</a> should give a runtime error if
--   the result value is not representable in the result type. For example,
--   <tt><a>toEnum</a> 7 :: <a>Bool</a></tt> is an error.</li>
--   <li><a>enumFrom</a> and <a>enumFromThen</a> should be defined with an
--   implicit bound, thus:</li>
--   </ul>
--   
--   <pre>
--   enumFrom     x   = enumFromTo     x maxBound
--   enumFromThen x y = enumFromThenTo x y bound
--     where
--       bound | fromEnum y &gt;= fromEnum x = maxBound
--             | otherwise                = minBound
--   </pre>
class Enum a
succ :: Enum a => a -> a
pred :: Enum a => a -> a
toEnum :: Enum a => Int -> a
fromEnum :: Enum a => a -> Int
enumFrom :: Enum a => a -> [a]
enumFromThen :: Enum a => a -> a -> [a]
enumFromTo :: Enum a => a -> a -> [a]
enumFromThenTo :: Enum a => a -> a -> a -> [a]

-- | The <a>Bounded</a> class is used to name the upper and lower limits of
--   a type. <a>Ord</a> is not a superclass of <a>Bounded</a> since types
--   that are not totally ordered may also have upper and lower bounds.
--   
--   The <a>Bounded</a> class may be derived for any enumeration type;
--   <a>minBound</a> is the first constructor listed in the <tt>data</tt>
--   declaration and <a>maxBound</a> is the last. <a>Bounded</a> may also
--   be derived for single-constructor datatypes whose constituent types
--   are in <a>Bounded</a>.
class Bounded a
minBound :: Bounded a => a
maxBound :: Bounded a => a
data Int :: *
data Integer :: *
data Float :: *
data Double :: *

-- | Arbitrary-precision rational numbers, represented as a ratio of two
--   <a>Integer</a> values. A rational number may be constructed using the
--   <a>%</a> operator.
type Rational = Ratio Integer

-- | Basic numeric class.
--   
--   Minimal complete definition: all except <a>negate</a> or <tt>(-)</tt>
class Num a
(+) :: Num a => a -> a -> a
(*) :: Num a => a -> a -> a
(-) :: Num a => a -> a -> a
negate :: Num a => a -> a
abs :: Num a => a -> a
signum :: Num a => a -> a
fromInteger :: Num a => Integer -> a
class (Num a, Ord a) => Real a
toRational :: Real a => a -> Rational

-- | Integral numbers, supporting integer division.
--   
--   Minimal complete definition: <a>quotRem</a> and <a>toInteger</a>
class (Real a, Enum a) => Integral a
quot :: Integral a => a -> a -> a
rem :: Integral a => a -> a -> a
div :: Integral a => a -> a -> a
mod :: Integral a => a -> a -> a
quotRem :: Integral a => a -> a -> (a, a)
divMod :: Integral a => a -> a -> (a, a)
toInteger :: Integral a => a -> Integer

-- | Fractional numbers, supporting real division.
--   
--   Minimal complete definition: <a>fromRational</a> and (<a>recip</a> or
--   <tt>(<a>/</a>)</tt>)
class Num a => Fractional a
(/) :: Fractional a => a -> a -> a
recip :: Fractional a => a -> a
fromRational :: Fractional a => Rational -> a

-- | Trigonometric and hyperbolic functions and related functions.
--   
--   Minimal complete definition: <a>pi</a>, <a>exp</a>, <a>log</a>,
--   <a>sin</a>, <a>cos</a>, <a>sinh</a>, <a>cosh</a>, <a>asin</a>,
--   <a>acos</a>, <a>atan</a>, <a>asinh</a>, <a>acosh</a> and <a>atanh</a>
class Fractional a => Floating a
pi :: Floating a => a
exp :: Floating a => a -> a
sqrt :: Floating a => a -> a
log :: Floating a => a -> a
(**) :: Floating a => a -> a -> a
logBase :: Floating a => a -> a -> a
sin :: Floating a => a -> a
tan :: Floating a => a -> a
cos :: Floating a => a -> a
asin :: Floating a => a -> a
atan :: Floating a => a -> a
acos :: Floating a => a -> a
sinh :: Floating a => a -> a
tanh :: Floating a => a -> a
cosh :: Floating a => a -> a
asinh :: Floating a => a -> a
atanh :: Floating a => a -> a
acosh :: Floating a => a -> a

-- | Extracting components of fractions.
--   
--   Minimal complete definition: <a>properFraction</a>
class (Real a, Fractional a) => RealFrac a
properFraction :: (RealFrac a, Integral b) => a -> (b, a)
truncate :: (RealFrac a, Integral b) => a -> b
round :: (RealFrac a, Integral b) => a -> b
ceiling :: (RealFrac a, Integral b) => a -> b
floor :: (RealFrac a, Integral b) => a -> b

-- | Efficient, machine-independent access to the components of a
--   floating-point number.
--   
--   Minimal complete definition: all except <a>exponent</a>,
--   <a>significand</a>, <a>scaleFloat</a> and <a>atan2</a>
class (RealFrac a, Floating a) => RealFloat a
floatRadix :: RealFloat a => a -> Integer
floatDigits :: RealFloat a => a -> Int
floatRange :: RealFloat a => a -> (Int, Int)
decodeFloat :: RealFloat a => a -> (Integer, Int)
encodeFloat :: RealFloat a => Integer -> Int -> a
exponent :: RealFloat a => a -> Int
significand :: RealFloat a => a -> a
scaleFloat :: RealFloat a => Int -> a -> a
isNaN :: RealFloat a => a -> Bool
isInfinite :: RealFloat a => a -> Bool
isDenormalized :: RealFloat a => a -> Bool
isNegativeZero :: RealFloat a => a -> Bool
isIEEE :: RealFloat a => a -> Bool
atan2 :: RealFloat a => a -> a -> a

-- | the same as <tt><a>flip</a> (<a>-</a>)</tt>.
--   
--   Because <tt>-</tt> is treated specially in the Haskell grammar,
--   <tt>(-</tt> <i>e</i><tt>)</tt> is not a section, but an application of
--   prefix negation. However, <tt>(<a>subtract</a></tt>
--   <i>exp</i><tt>)</tt> is equivalent to the disallowed section.
subtract :: Num a => a -> a -> a
even :: Integral a => a -> Bool
odd :: Integral a => a -> Bool

-- | <tt><a>gcd</a> x y</tt> is the greatest (positive) integer that
--   divides both <tt>x</tt> and <tt>y</tt>; for example <tt><a>gcd</a>
--   (-3) 6</tt> = <tt>3</tt>, <tt><a>gcd</a> (-3) (-6)</tt> = <tt>3</tt>,
--   <tt><a>gcd</a> 0 4</tt> = <tt>4</tt>. <tt><a>gcd</a> 0 0</tt> raises a
--   runtime error.
gcd :: Integral a => a -> a -> a

-- | <tt><a>lcm</a> x y</tt> is the smallest positive integer that both
--   <tt>x</tt> and <tt>y</tt> divide.
lcm :: Integral a => a -> a -> a

-- | raise a number to a non-negative integral power
(^) :: (Num a, Integral b) => a -> b -> a

-- | raise a number to an integral power
(^^) :: (Fractional a, Integral b) => a -> b -> a

-- | general coercion from integral types
fromIntegral :: (Integral a, Num b) => a -> b

-- | general coercion to fractional types
realToFrac :: (Real a, Fractional b) => a -> b

-- | The <a>Monad</a> class defines the basic operations over a
--   <i>monad</i>, a concept from a branch of mathematics known as
--   <i>category theory</i>. From the perspective of a Haskell programmer,
--   however, it is best to think of a monad as an <i>abstract datatype</i>
--   of actions. Haskell's <tt>do</tt> expressions provide a convenient
--   syntax for writing monadic expressions.
--   
--   Minimal complete definition: <a>&gt;&gt;=</a> and <a>return</a>.
--   
--   Instances of <a>Monad</a> should satisfy the following laws:
--   
--   <pre>
--   return a &gt;&gt;= k  ==  k a
--   m &gt;&gt;= return  ==  m
--   m &gt;&gt;= (\x -&gt; k x &gt;&gt;= h)  ==  (m &gt;&gt;= k) &gt;&gt;= h
--   </pre>
--   
--   Instances of both <a>Monad</a> and <a>Functor</a> should additionally
--   satisfy the law:
--   
--   <pre>
--   fmap f xs  ==  xs &gt;&gt;= return . f
--   </pre>
--   
--   The instances of <a>Monad</a> for lists, <a>Maybe</a> and <a>IO</a>
--   defined in the <a>Prelude</a> satisfy these laws.
class Monad (m :: * -> *)
(>>=) :: Monad m => m a -> (a -> m b) -> m b
(>>) :: Monad m => m a -> m b -> m b
return :: Monad m => a -> m a
fail :: Monad m => String -> m a

-- | The <a>Functor</a> class is used for types that can be mapped over.
--   Instances of <a>Functor</a> should satisfy the following laws:
--   
--   <pre>
--   fmap id  ==  id
--   fmap (f . g)  ==  fmap f . fmap g
--   </pre>
--   
--   The instances of <a>Functor</a> for lists, <a>Maybe</a> and <a>IO</a>
--   satisfy these laws.
class Functor (f :: * -> *)
fmap :: Functor f => (a -> b) -> f a -> f b

-- | <tt><a>mapM</a> f</tt> is equivalent to <tt><a>sequence</a> .
--   <a>map</a> f</tt>.
mapM :: Monad m => (a -> m b) -> [a] -> m [b]

-- | <tt><a>mapM_</a> f</tt> is equivalent to <tt><a>sequence_</a> .
--   <a>map</a> f</tt>.
mapM_ :: Monad m => (a -> m b) -> [a] -> m ()

-- | Evaluate each action in the sequence from left to right, and collect
--   the results.
sequence :: Monad m => [m a] -> m [a]

-- | Evaluate each action in the sequence from left to right, and ignore
--   the results.
sequence_ :: Monad m => [m a] -> m ()

-- | Same as <a>&gt;&gt;=</a>, but with the arguments interchanged.
(=<<) :: Monad m => (a -> m b) -> m a -> m b

-- | Identity function.
id :: a -> a

-- | Constant function.
const :: a -> b -> a

-- | Function composition.
(.) :: (b -> c) -> (a -> b) -> a -> c

-- | <tt><a>flip</a> f</tt> takes its (first) two arguments in the reverse
--   order of <tt>f</tt>.
flip :: (a -> b -> c) -> b -> a -> c

-- | Application operator. This operator is redundant, since ordinary
--   application <tt>(f x)</tt> means the same as <tt>(f <a>$</a> x)</tt>.
--   However, <a>$</a> has low, right-associative binding precedence, so it
--   sometimes allows parentheses to be omitted; for example:
--   
--   <pre>
--   f $ g $ h x  =  f (g (h x))
--   </pre>
--   
--   It is also useful in higher-order situations, such as <tt><a>map</a>
--   (<a>$</a> 0) xs</tt>, or <tt><a>zipWith</a> (<a>$</a>) fs xs</tt>.
($) :: (a -> b) -> a -> b

-- | <tt><a>until</a> p f</tt> yields the result of applying <tt>f</tt>
--   until <tt>p</tt> holds.
until :: (a -> Bool) -> (a -> a) -> a -> a

-- | <a>asTypeOf</a> is a type-restricted version of <a>const</a>. 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.
asTypeOf :: a -> a -> a

-- | <a>error</a> stops execution and displays an error message.
error :: [Char] -> a

-- | A special case of <a>error</a>. It is expected that compilers will
--   recognize this and insert error messages which are more appropriate to
--   the context in which <a>undefined</a> appears.
undefined :: a
seq :: a -> b -> b

-- | Strict (call-by-value) application, defined in terms of <a>seq</a>.
($!) :: (a -> b) -> a -> b

-- | <a>map</a> <tt>f xs</tt> is the list obtained by applying <tt>f</tt>
--   to each element of <tt>xs</tt>, i.e.,
--   
--   <pre>
--   map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
--   map f [x1, x2, ...] == [f x1, f x2, ...]
--   </pre>
map :: (a -> b) -> [a] -> [b]

-- | Append two lists, i.e.,
--   
--   <pre>
--   [x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
--   [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
--   </pre>
--   
--   If the first list is not finite, the result is the first list.
(++) :: [a] -> [a] -> [a]

-- | <a>filter</a>, applied to a predicate and a list, returns the list of
--   those elements that satisfy the predicate; i.e.,
--   
--   <pre>
--   filter p xs = [ x | x &lt;- xs, p x]
--   </pre>
filter :: (a -> Bool) -> [a] -> [a]

-- | Extract the first element of a list, which must be non-empty.
head :: [a] -> a

-- | Extract the last element of a list, which must be finite and
--   non-empty.
last :: [a] -> a

-- | Extract the elements after the head of a list, which must be
--   non-empty.
tail :: [a] -> [a]

-- | Return all the elements of a list except the last one. The list must
--   be non-empty.
init :: [a] -> [a]

-- | Test whether a list is empty.
null :: [a] -> Bool

-- | <i>O(n)</i>. <a>length</a> returns the length of a finite list as an
--   <a>Int</a>. It is an instance of the more general
--   <a>genericLength</a>, the result type of which may be any kind of
--   number.
length :: [a] -> Int

-- | List index (subscript) operator, starting from 0. It is an instance of
--   the more general <a>genericIndex</a>, which takes an index of any
--   integral type.
(!!) :: [a] -> Int -> a

-- | <a>reverse</a> <tt>xs</tt> returns the elements of <tt>xs</tt> in
--   reverse order. <tt>xs</tt> must be finite.
reverse :: [a] -> [a]

-- | <a>foldl</a>, applied to a binary operator, a starting value
--   (typically the left-identity of the operator), and a list, reduces the
--   list using the binary operator, from left to right:
--   
--   <pre>
--   foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
--   </pre>
--   
--   The list must be finite.
foldl :: (a -> b -> a) -> a -> [b] -> a

-- | <a>foldl1</a> is a variant of <a>foldl</a> that has no starting value
--   argument, and thus must be applied to non-empty lists.
foldl1 :: (a -> a -> a) -> [a] -> a

-- | <a>foldr</a>, applied to a binary operator, a starting value
--   (typically the right-identity of the operator), and a list, reduces
--   the list using the binary operator, from right to left:
--   
--   <pre>
--   foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
--   </pre>
foldr :: (a -> b -> b) -> b -> [a] -> b

-- | <a>foldr1</a> is a variant of <a>foldr</a> that has no starting value
--   argument, and thus must be applied to non-empty lists.
foldr1 :: (a -> a -> a) -> [a] -> a

-- | <a>and</a> returns the conjunction of a Boolean list. For the result
--   to be <a>True</a>, the list must be finite; <a>False</a>, however,
--   results from a <a>False</a> value at a finite index of a finite or
--   infinite list.
and :: [Bool] -> Bool

-- | <a>or</a> returns the disjunction of a Boolean list. For the result to
--   be <a>False</a>, the list must be finite; <a>True</a>, however,
--   results from a <a>True</a> value at a finite index of a finite or
--   infinite list.
or :: [Bool] -> Bool

-- | Applied to a predicate and a list, <a>any</a> determines if any
--   element of the list satisfies the predicate. For the result to be
--   <a>False</a>, the list must be finite; <a>True</a>, however, results
--   from a <a>True</a> value for the predicate applied to an element at a
--   finite index of a finite or infinite list.
any :: (a -> Bool) -> [a] -> Bool

-- | Applied to a predicate and a list, <a>all</a> determines if all
--   elements of the list satisfy the predicate. For the result to be
--   <a>True</a>, the list must be finite; <a>False</a>, however, results
--   from a <a>False</a> value for the predicate applied to an element at a
--   finite index of a finite or infinite list.
all :: (a -> Bool) -> [a] -> Bool

-- | The <a>sum</a> function computes the sum of a finite list of numbers.
sum :: Num a => [a] -> a

-- | The <a>product</a> function computes the product of a finite list of
--   numbers.
product :: Num a => [a] -> a

-- | Concatenate a list of lists.
concat :: [[a]] -> [a]

-- | Map a function over a list and concatenate the results.
concatMap :: (a -> [b]) -> [a] -> [b]

-- | <a>maximum</a> returns the maximum value from a list, which must be
--   non-empty, finite, and of an ordered type. It is a special case of
--   <a>maximumBy</a>, which allows the programmer to supply their own
--   comparison function.
maximum :: Ord a => [a] -> a

-- | <a>minimum</a> returns the minimum value from a list, which must be
--   non-empty, finite, and of an ordered type. It is a special case of
--   <a>minimumBy</a>, which allows the programmer to supply their own
--   comparison function.
minimum :: Ord a => [a] -> a

-- | <a>scanl</a> is similar to <a>foldl</a>, but returns a list of
--   successive reduced values from the left:
--   
--   <pre>
--   scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
--   </pre>
--   
--   Note that
--   
--   <pre>
--   last (scanl f z xs) == foldl f z xs.
--   </pre>
scanl :: (a -> b -> a) -> a -> [b] -> [a]

-- | <a>scanl1</a> is a variant of <a>scanl</a> that has no starting value
--   argument:
--   
--   <pre>
--   scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
--   </pre>
scanl1 :: (a -> a -> a) -> [a] -> [a]

-- | <a>scanr</a> is the right-to-left dual of <a>scanl</a>. Note that
--   
--   <pre>
--   head (scanr f z xs) == foldr f z xs.
--   </pre>
scanr :: (a -> b -> b) -> b -> [a] -> [b]

-- | <a>scanr1</a> is a variant of <a>scanr</a> that has no starting value
--   argument.
scanr1 :: (a -> a -> a) -> [a] -> [a]

-- | <a>iterate</a> <tt>f x</tt> returns an infinite list of repeated
--   applications of <tt>f</tt> to <tt>x</tt>:
--   
--   <pre>
--   iterate f x == [x, f x, f (f x), ...]
--   </pre>
iterate :: (a -> a) -> a -> [a]

-- | <a>repeat</a> <tt>x</tt> is an infinite list, with <tt>x</tt> the
--   value of every element.
repeat :: a -> [a]

-- | <a>replicate</a> <tt>n x</tt> is a list of length <tt>n</tt> with
--   <tt>x</tt> the value of every element. It is an instance of the more
--   general <a>genericReplicate</a>, in which <tt>n</tt> may be of any
--   integral type.
replicate :: Int -> a -> [a]

-- | <a>cycle</a> ties a finite list into a circular one, or equivalently,
--   the infinite repetition of the original list. It is the identity on
--   infinite lists.
cycle :: [a] -> [a]

-- | <a>take</a> <tt>n</tt>, applied to a list <tt>xs</tt>, returns the
--   prefix of <tt>xs</tt> of length <tt>n</tt>, or <tt>xs</tt> itself if
--   <tt>n &gt; <a>length</a> xs</tt>:
--   
--   <pre>
--   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] == []
--   </pre>
--   
--   It is an instance of the more general <a>genericTake</a>, in which
--   <tt>n</tt> may be of any integral type.
take :: Int -> [a] -> [a]

-- | <a>drop</a> <tt>n xs</tt> returns the suffix of <tt>xs</tt> after the
--   first <tt>n</tt> elements, or <tt>[]</tt> if <tt>n &gt; <a>length</a>
--   xs</tt>:
--   
--   <pre>
--   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]
--   </pre>
--   
--   It is an instance of the more general <a>genericDrop</a>, in which
--   <tt>n</tt> may be of any integral type.
drop :: Int -> [a] -> [a]

-- | <a>splitAt</a> <tt>n xs</tt> returns a tuple where first element is
--   <tt>xs</tt> prefix of length <tt>n</tt> and second element is the
--   remainder of the list:
--   
--   <pre>
--   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])
--   </pre>
--   
--   It is equivalent to <tt>(<a>take</a> n xs, <a>drop</a> n xs)</tt>.
--   <a>splitAt</a> is an instance of the more general
--   <a>genericSplitAt</a>, in which <tt>n</tt> may be of any integral
--   type.
splitAt :: Int -> [a] -> ([a], [a])

-- | <a>takeWhile</a>, applied to a predicate <tt>p</tt> and a list
--   <tt>xs</tt>, returns the longest prefix (possibly empty) of
--   <tt>xs</tt> of elements that satisfy <tt>p</tt>:
--   
--   <pre>
--   takeWhile (&lt; 3) [1,2,3,4,1,2,3,4] == [1,2]
--   takeWhile (&lt; 9) [1,2,3] == [1,2,3]
--   takeWhile (&lt; 0) [1,2,3] == []
--   </pre>
takeWhile :: (a -> Bool) -> [a] -> [a]

-- | <a>dropWhile</a> <tt>p xs</tt> returns the suffix remaining after
--   <a>takeWhile</a> <tt>p xs</tt>:
--   
--   <pre>
--   dropWhile (&lt; 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3]
--   dropWhile (&lt; 9) [1,2,3] == []
--   dropWhile (&lt; 0) [1,2,3] == [1,2,3]
--   </pre>
dropWhile :: (a -> Bool) -> [a] -> [a]

-- | <a>span</a>, applied to a predicate <tt>p</tt> and a list <tt>xs</tt>,
--   returns a tuple where first element is longest prefix (possibly empty)
--   of <tt>xs</tt> of elements that satisfy <tt>p</tt> and second element
--   is the remainder of the list:
--   
--   <pre>
--   span (&lt; 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4])
--   span (&lt; 9) [1,2,3] == ([1,2,3],[])
--   span (&lt; 0) [1,2,3] == ([],[1,2,3])
--   </pre>
--   
--   <a>span</a> <tt>p xs</tt> is equivalent to <tt>(<a>takeWhile</a> p xs,
--   <a>dropWhile</a> p xs)</tt>
span :: (a -> Bool) -> [a] -> ([a], [a])

-- | <a>break</a>, applied to a predicate <tt>p</tt> and a list
--   <tt>xs</tt>, returns a tuple where first element is longest prefix
--   (possibly empty) of <tt>xs</tt> of elements that <i>do not satisfy</i>
--   <tt>p</tt> and second element is the remainder of the list:
--   
--   <pre>
--   break (&gt; 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4])
--   break (&lt; 9) [1,2,3] == ([],[1,2,3])
--   break (&gt; 9) [1,2,3] == ([1,2,3],[])
--   </pre>
--   
--   <a>break</a> <tt>p</tt> is equivalent to <tt><a>span</a> (<a>not</a> .
--   p)</tt>.
break :: (a -> Bool) -> [a] -> ([a], [a])

-- | <a>elem</a> is the list membership predicate, usually written in infix
--   form, e.g., <tt>x `elem` xs</tt>. For the result to be <a>False</a>,
--   the list must be finite; <a>True</a>, however, results from an element
--   equal to <tt>x</tt> found at a finite index of a finite or infinite
--   list.
elem :: Eq a => a -> [a] -> Bool

-- | <a>notElem</a> is the negation of <a>elem</a>.
notElem :: Eq a => a -> [a] -> Bool

-- | <a>lookup</a> <tt>key assocs</tt> looks up a key in an association
--   list.
lookup :: Eq a => a -> [(a, b)] -> Maybe b

-- | <a>zip</a> 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 :: [a] -> [b] -> [(a, b)]

-- | <a>zip3</a> takes three lists and returns a list of triples, analogous
--   to <a>zip</a>.
zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]

-- | <a>zipWith</a> generalises <a>zip</a> by zipping with the function
--   given as the first argument, instead of a tupling function. For
--   example, <tt><a>zipWith</a> (+)</tt> is applied to two lists to
--   produce the list of corresponding sums.
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]

-- | The <a>zipWith3</a> function takes a function which combines three
--   elements, as well as three lists and returns a list of their
--   point-wise combination, analogous to <a>zipWith</a>.
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]

-- | <a>unzip</a> transforms a list of pairs into a list of first
--   components and a list of second components.
unzip :: [(a, b)] -> ([a], [b])

-- | The <a>unzip3</a> function takes a list of triples and returns three
--   lists, analogous to <a>unzip</a>.
unzip3 :: [(a, b, c)] -> ([a], [b], [c])

-- | <a>lines</a> breaks a string up into a list of strings at newline
--   characters. The resulting strings do not contain newlines.
lines :: String -> [String]

-- | <a>words</a> breaks a string up into a list of words, which were
--   delimited by white space.
words :: String -> [String]

-- | <a>unlines</a> is an inverse operation to <a>lines</a>. It joins
--   lines, after appending a terminating newline to each.
unlines :: [String] -> String

-- | <a>unwords</a> is an inverse operation to <a>words</a>. It joins words
--   with separating spaces.
unwords :: [String] -> String

-- | The <tt>shows</tt> functions return a function that prepends the
--   output <a>String</a> to an existing <a>String</a>. This allows
--   constant-time concatenation of results using function composition.
type ShowS = String -> String

-- | Conversion of values to readable <a>String</a>s.
--   
--   Minimal complete definition: <a>showsPrec</a> or <a>show</a>.
--   
--   Derived instances of <a>Show</a> have the following properties, which
--   are compatible with derived instances of <a>Read</a>:
--   
--   <ul>
--   <li>The result of <a>show</a> 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.</li>
--   <li>If the constructor is defined to be an infix operator, then
--   <a>showsPrec</a> will produce infix applications of the
--   constructor.</li>
--   <li>the representation will be enclosed in parentheses if the
--   precedence of the top-level constructor in <tt>x</tt> is less than
--   <tt>d</tt> (associativity is ignored). Thus, if <tt>d</tt> is
--   <tt>0</tt> then the result is never surrounded in parentheses; if
--   <tt>d</tt> is <tt>11</tt> it is always surrounded in parentheses,
--   unless it is an atomic expression.</li>
--   <li>If the constructor is defined using record syntax, then
--   <a>show</a> will produce the record-syntax form, with the fields given
--   in the same order as the original declaration.</li>
--   </ul>
--   
--   For example, given the declarations
--   
--   <pre>
--   infixr 5 :^:
--   data Tree a =  Leaf a  |  Tree a :^: Tree a
--   </pre>
--   
--   the derived instance of <a>Show</a> is equivalent to
--   
--   <pre>
--   instance (Show a) =&gt; Show (Tree a) where
--   
--          showsPrec d (Leaf m) = showParen (d &gt; app_prec) $
--               showString "Leaf " . showsPrec (app_prec+1) m
--            where app_prec = 10
--   
--          showsPrec d (u :^: v) = showParen (d &gt; up_prec) $
--               showsPrec (up_prec+1) u .
--               showString " :^: "      .
--               showsPrec (up_prec+1) v
--            where up_prec = 5
--   </pre>
--   
--   Note that right-associativity of <tt>:^:</tt> is ignored. For example,
--   
--   <ul>
--   <li><tt><a>show</a> (Leaf 1 :^: Leaf 2 :^: Leaf 3)</tt> produces the
--   string <tt>"Leaf 1 :^: (Leaf 2 :^: Leaf 3)"</tt>.</li>
--   </ul>
class Show a
showsPrec :: Show a => Int -> a -> ShowS
show :: Show a => a -> String
showList :: Show a => [a] -> ShowS

-- | equivalent to <a>showsPrec</a> with a precedence of 0.
shows :: Show a => a -> ShowS

-- | utility function converting a <a>Char</a> to a show function that
--   simply prepends the character unchanged.
showChar :: Char -> ShowS

-- | utility function converting a <a>String</a> to a show function that
--   simply prepends the string unchanged.
showString :: String -> ShowS

-- | utility function that surrounds the inner show function with
--   parentheses when the <a>Bool</a> parameter is <a>True</a>.
showParen :: Bool -> ShowS -> ShowS

-- | A parser for a type <tt>a</tt>, represented as a function that takes a
--   <a>String</a> and returns a list of possible parses as
--   <tt>(a,<a>String</a>)</tt> pairs.
--   
--   Note that this kind of backtracking parser is very inefficient;
--   reading a large structure may be quite slow (cf <a>ReadP</a>).
type ReadS a = String -> [(a, String)]

-- | Parsing of <a>String</a>s, producing values.
--   
--   Minimal complete definition: <a>readsPrec</a> (or, for GHC only,
--   <a>readPrec</a>)
--   
--   Derived instances of <a>Read</a> make the following assumptions, which
--   derived instances of <a>Show</a> obey:
--   
--   <ul>
--   <li>If the constructor is defined to be an infix operator, then the
--   derived <a>Read</a> instance will parse only infix applications of the
--   constructor (not the prefix form).</li>
--   <li>Associativity is not used to reduce the occurrence of parentheses,
--   although precedence may be.</li>
--   <li>If the constructor is defined using record syntax, the derived
--   <a>Read</a> will parse only the record-syntax form, and furthermore,
--   the fields must be given in the same order as the original
--   declaration.</li>
--   <li>The derived <a>Read</a> instance allows arbitrary Haskell
--   whitespace between tokens of the input string. Extra parentheses are
--   also allowed.</li>
--   </ul>
--   
--   For example, given the declarations
--   
--   <pre>
--   infixr 5 :^:
--   data Tree a =  Leaf a  |  Tree a :^: Tree a
--   </pre>
--   
--   the derived instance of <a>Read</a> in Haskell 98 is equivalent to
--   
--   <pre>
--   instance (Read a) =&gt; Read (Tree a) where
--   
--           readsPrec d r =  readParen (d &gt; app_prec)
--                            (\r -&gt; [(Leaf m,t) |
--                                    ("Leaf",s) &lt;- lex r,
--                                    (m,t) &lt;- readsPrec (app_prec+1) s]) r
--   
--                         ++ readParen (d &gt; up_prec)
--                            (\r -&gt; [(u:^:v,w) |
--                                    (u,s) &lt;- readsPrec (up_prec+1) r,
--                                    (":^:",t) &lt;- lex s,
--                                    (v,w) &lt;- readsPrec (up_prec+1) t]) r
--   
--             where app_prec = 10
--                   up_prec = 5
--   </pre>
--   
--   Note that right-associativity of <tt>:^:</tt> is unused.
--   
--   The derived instance in GHC is equivalent to
--   
--   <pre>
--   instance (Read a) =&gt; Read (Tree a) where
--   
--           readPrec = parens $ (prec app_prec $ do
--                                    Ident "Leaf" &lt;- lexP
--                                    m &lt;- step readPrec
--                                    return (Leaf m))
--   
--                        +++ (prec up_prec $ do
--                                    u &lt;- step readPrec
--                                    Symbol ":^:" &lt;- lexP
--                                    v &lt;- step readPrec
--                                    return (u :^: v))
--   
--             where app_prec = 10
--                   up_prec = 5
--   
--           readListPrec = readListPrecDefault
--   </pre>
class Read a
readsPrec :: Read a => Int -> ReadS a
readList :: Read a => ReadS [a]

-- | equivalent to <a>readsPrec</a> with a precedence of 0.
reads :: Read a => ReadS a

-- | <tt><a>readParen</a> <a>True</a> p</tt> parses what <tt>p</tt> parses,
--   but surrounded with parentheses.
--   
--   <tt><a>readParen</a> <a>False</a> p</tt> parses what <tt>p</tt>
--   parses, but optionally surrounded with parentheses.
readParen :: Bool -> ReadS a -> ReadS a

-- | The <a>read</a> function reads input from a string, which must be
--   completely consumed by the input process.
read :: Read a => String -> a

-- | The <a>lex</a> 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,
--   <a>lex</a> returns a single successful `lexeme' consisting of the
--   empty string. (Thus <tt><a>lex</a> "" = [("","")]</tt>.) If there is
--   no legal lexeme at the beginning of the input string, <a>lex</a> fails
--   (i.e. returns <tt>[]</tt>).
--   
--   This lexer is not completely faithful to the Haskell lexical syntax in
--   the following respects:
--   
--   <ul>
--   <li>Qualified names are not handled properly</li>
--   <li>Octal and hexadecimal numerics are not recognized as a single
--   token</li>
--   <li>Comments are not treated properly</li>
--   </ul>
lex :: ReadS String
data IO a :: * -> *

-- | Write a character to the standard output device (same as
--   <a>hPutChar</a> <a>stdout</a>).
putChar :: Char -> IO ()

-- | Write a string to the standard output device (same as <a>hPutStr</a>
--   <a>stdout</a>).
putStr :: String -> IO ()

-- | The same as <a>putStr</a>, but adds a newline character.
putStrLn :: String -> IO ()

-- | The <a>print</a> function outputs a value of any printable type to the
--   standard output device. Printable types are those that are instances
--   of class <a>Show</a>; <a>print</a> converts values to strings for
--   output using the <a>show</a> operation and adds a newline.
--   
--   For example, a program to print the first 20 integers and their powers
--   of 2 could be written as:
--   
--   <pre>
--   main = print ([(n, 2^n) | n &lt;- [0..19]])
--   </pre>
print :: Show a => a -> IO ()

-- | Read a character from the standard input device (same as
--   <a>hGetChar</a> <a>stdin</a>).
getChar :: IO Char

-- | Read a line from the standard input device (same as <a>hGetLine</a>
--   <a>stdin</a>).
getLine :: IO String

-- | The <a>getContents</a> operation returns all user input as a single
--   string, which is read lazily as it is needed (same as
--   <a>hGetContents</a> <a>stdin</a>).
getContents :: IO String

-- | The <a>interact</a> function takes a function of type
--   <tt>String-&gt;String</tt> 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.
interact :: (String -> String) -> IO ()

-- | File and directory names are values of type <a>String</a>, 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 FilePath = String

-- | The <a>readFile</a> function reads a file and returns the contents of
--   the file as a string. The file is read lazily, on demand, as with
--   <a>getContents</a>.
readFile :: FilePath -> IO String

-- | The computation <a>writeFile</a> <tt>file str</tt> function writes the
--   string <tt>str</tt>, to the file <tt>file</tt>.
writeFile :: FilePath -> String -> IO ()

-- | The computation <a>appendFile</a> <tt>file str</tt> function appends
--   the string <tt>str</tt>, to the file <tt>file</tt>.
--   
--   Note that <a>writeFile</a> and <a>appendFile</a> write a literal
--   string to a file. To write a value of any printable type, as with
--   <a>print</a>, use the <a>show</a> function to convert the value to a
--   string first.
--   
--   <pre>
--   main = appendFile "squares" (show [(x,x*x) | x &lt;- [0,0.1..2]])
--   </pre>
appendFile :: FilePath -> String -> IO ()

-- | The <a>readIO</a> function is similar to <a>read</a> except that it
--   signals parse failure to the <a>IO</a> monad instead of terminating
--   the program.
readIO :: Read a => String -> IO a

-- | The <a>readLn</a> function combines <a>getLine</a> and <a>readIO</a>.
readLn :: Read a => IO a

-- | The Haskell 98 type for exceptions in the <a>IO</a> monad. Any I/O
--   operation may raise an <a>IOError</a> instead of returning a result.
--   For a more general type of exception, including also those that arise
--   in pure code, see <a>Control.Exception.Exception</a>.
--   
--   In Haskell 98, this is an opaque type.
type IOError = IOException

-- | Raise an <a>IOError</a> in the <a>IO</a> monad.
ioError :: IOError -> IO a

-- | Construct an <a>IOError</a> value with a string describing the error.
--   The <a>fail</a> method of the <a>IO</a> instance of the <a>Monad</a>
--   class raises a <a>userError</a>, thus:
--   
--   <pre>
--   instance Monad IO where 
--     ...
--     fail s = ioError (userError s)
--   </pre>
userError :: String -> IOError

-- | The <a>catch</a> function establishes a handler that receives any
--   <a>IOError</a> raised in the action protected by <a>catch</a>. An
--   <a>IOError</a> is caught by the most recent handler established by one
--   of the exception handling functions. These handlers are not selective:
--   all <a>IOError</a>s are caught. Exception propagation must be
--   explicitly provided in a handler by re-raising any unwanted
--   exceptions. For example, in
--   
--   <pre>
--   f = catch g (\e -&gt; if IO.isEOFError e then return [] else ioError e)
--   </pre>
--   
--   the function <tt>f</tt> returns <tt>[]</tt> when an end-of-file
--   exception (cf. <a>isEOFError</a>) occurs in <tt>g</tt>; otherwise, the
--   exception is propagated to the next outer handler.
--   
--   When an exception propagates outside the main program, the Haskell
--   system prints the associated <a>IOError</a> value and exits the
--   program.
--   
--   Non-I/O exceptions are not caught by this variant; to catch all
--   exceptions, use <a>catch</a> from <a>Control.Exception</a>.
catch :: IO a -> (IOError -> IO a) -> IO a

module Numeric

-- | Converts a possibly-negative <a>Real</a> value to a string.
showSigned :: Real a => (a -> ShowS) -> Int -> a -> ShowS

-- | Shows a <i>non-negative</i> <a>Integral</a> number using the base
--   specified by the first argument, and the character representation
--   specified by the second.
showIntAtBase :: (Integral a, Show a) => a -> (Int -> Char) -> a -> ShowS

-- | Show <i>non-negative</i> <a>Integral</a> numbers in base 10.
showInt :: Integral a => a -> ShowS

-- | Show <i>non-negative</i> <a>Integral</a> numbers in base 16.
showHex :: (Integral a, Show a) => a -> ShowS

-- | Show <i>non-negative</i> <a>Integral</a> numbers in base 8.
showOct :: (Integral a, Show a) => a -> ShowS

-- | Show a signed <a>RealFloat</a> value using scientific (exponential)
--   notation (e.g. <tt>2.45e2</tt>, <tt>1.5e-3</tt>).
--   
--   In the call <tt><a>showEFloat</a> digs val</tt>, if <tt>digs</tt> is
--   <a>Nothing</a>, the value is shown to full precision; if <tt>digs</tt>
--   is <tt><a>Just</a> d</tt>, then at most <tt>d</tt> digits after the
--   decimal point are shown.
showEFloat :: RealFloat a => Maybe Int -> a -> ShowS

-- | Show a signed <a>RealFloat</a> value using standard decimal notation
--   (e.g. <tt>245000</tt>, <tt>0.0015</tt>).
--   
--   In the call <tt><a>showFFloat</a> digs val</tt>, if <tt>digs</tt> is
--   <a>Nothing</a>, the value is shown to full precision; if <tt>digs</tt>
--   is <tt><a>Just</a> d</tt>, then at most <tt>d</tt> digits after the
--   decimal point are shown.
showFFloat :: RealFloat a => Maybe Int -> a -> ShowS

-- | Show a signed <a>RealFloat</a> value using standard decimal notation
--   for arguments whose absolute value lies between <tt>0.1</tt> and
--   <tt>9,999,999</tt>, and scientific notation otherwise.
--   
--   In the call <tt><a>showGFloat</a> digs val</tt>, if <tt>digs</tt> is
--   <a>Nothing</a>, the value is shown to full precision; if <tt>digs</tt>
--   is <tt><a>Just</a> d</tt>, then at most <tt>d</tt> digits after the
--   decimal point are shown.
showGFloat :: RealFloat a => Maybe Int -> a -> ShowS

-- | Show a signed <a>RealFloat</a> value to full precision using standard
--   decimal notation for arguments whose absolute value lies between
--   <tt>0.1</tt> and <tt>9,999,999</tt>, and scientific notation
--   otherwise.
showFloat :: RealFloat a => a -> ShowS

-- | <a>floatToDigits</a> takes a base and a non-negative <a>RealFloat</a>
--   number, and returns a list of digits and an exponent. In particular,
--   if <tt>x&gt;=0</tt>, and
--   
--   <pre>
--   floatToDigits base x = ([d1,d2,...,dn], e)
--   </pre>
--   
--   then
--   
--   <ol>
--   <li><pre>n &gt;= 1</pre></li>
--   <li><pre>x = 0.d1d2...dn * (base**e)</pre></li>
--   <li><pre>0 &lt;= di &lt;= base-1</pre></li>
--   </ol>
floatToDigits :: RealFloat a => Integer -> a -> ([Int], Int)

-- | Reads a <i>signed</i> <a>Real</a> value, given a reader for an
--   unsigned value.
readSigned :: Real a => ReadS a -> ReadS a

-- | Reads an <i>unsigned</i> <a>Integral</a> value in an arbitrary base.
readInt :: Num a => a -> (Char -> Bool) -> (Char -> Int) -> ReadS a

-- | Read an unsigned number in decimal notation.
readDec :: (Eq a, Num a) => ReadS a

-- | Read an unsigned number in octal notation.
readOct :: (Eq a, Num a) => ReadS a

-- | Read an unsigned number in hexadecimal notation. Both upper or lower
--   case letters are allowed.
readHex :: (Eq a, Num a) => ReadS a

-- | Reads an <i>unsigned</i> <a>RealFrac</a> value, expressed in decimal
--   scientific notation.
readFloat :: RealFrac a => ReadS a

-- | Reads a non-empty string of decimal digits.
lexDigits :: ReadS String

-- | Converts a <a>Rational</a> value into any type in class
--   <a>RealFloat</a>.
fromRat :: RealFloat a => Rational -> a

module Maybe

-- | The <a>isJust</a> function returns <a>True</a> iff its argument is of
--   the form <tt>Just _</tt>.
isJust :: Maybe a -> Bool

-- | The <a>isNothing</a> function returns <a>True</a> iff its argument is
--   <a>Nothing</a>.
isNothing :: Maybe a -> Bool

-- | The <a>fromJust</a> function extracts the element out of a <a>Just</a>
--   and throws an error if its argument is <a>Nothing</a>.
fromJust :: Maybe a -> a

-- | The <a>fromMaybe</a> function takes a default value and and
--   <a>Maybe</a> value. If the <a>Maybe</a> is <a>Nothing</a>, it returns
--   the default values; otherwise, it returns the value contained in the
--   <a>Maybe</a>.
fromMaybe :: a -> Maybe a -> a

-- | The <a>listToMaybe</a> function returns <a>Nothing</a> on an empty
--   list or <tt><a>Just</a> a</tt> where <tt>a</tt> is the first element
--   of the list.
listToMaybe :: [a] -> Maybe a

-- | The <a>maybeToList</a> function returns an empty list when given
--   <a>Nothing</a> or a singleton list when not given <a>Nothing</a>.
maybeToList :: Maybe a -> [a]

-- | The <a>catMaybes</a> function takes a list of <a>Maybe</a>s and
--   returns a list of all the <a>Just</a> values.
catMaybes :: [Maybe a] -> [a]

-- | The <a>mapMaybe</a> function is a version of <a>map</a> which can
--   throw out elements. In particular, the functional argument returns
--   something of type <tt><a>Maybe</a> b</tt>. If this is <a>Nothing</a>,
--   no element is added on to the result list. If it just <tt><a>Just</a>
--   b</tt>, then <tt>b</tt> is included in the result list.
mapMaybe :: (a -> Maybe b) -> [a] -> [b]

-- | The <a>Maybe</a> type encapsulates an optional value. A value of type
--   <tt><a>Maybe</a> a</tt> either contains a value of type <tt>a</tt>
--   (represented as <tt><a>Just</a> a</tt>), or it is empty (represented
--   as <a>Nothing</a>). Using <a>Maybe</a> is a good way to deal with
--   errors or exceptional cases without resorting to drastic measures such
--   as <a>error</a>.
--   
--   The <a>Maybe</a> type is also a monad. It is a simple kind of error
--   monad, where all errors are represented by <a>Nothing</a>. A richer
--   error monad can be built using the <a>Either</a> type.
data Maybe a :: * -> *
Nothing :: Maybe a
Just :: a -> Maybe a

-- | The <a>maybe</a> function takes a default value, a function, and a
--   <a>Maybe</a> value. If the <a>Maybe</a> value is <a>Nothing</a>, the
--   function returns the default value. Otherwise, it applies the function
--   to the value inside the <a>Just</a> and returns the result.
maybe :: b -> (a -> b) -> Maybe a -> b

module Storable

module Bits

module Directory
data Permissions
Permissions :: Bool -> Bool -> Bool -> Bool -> Permissions
readable :: Permissions -> Bool
writable :: Permissions -> Bool
executable :: Permissions -> Bool
searchable :: Permissions -> Bool

-- | <tt><a>createDirectory</a> dir</tt> creates a new directory
--   <tt>dir</tt> which is initially empty, or as near to empty as the
--   operating system allows.
--   
--   The operation may fail with:
--   
--   <ul>
--   <li><a>isPermissionError</a> / <a>PermissionDenied</a> The process has
--   insufficient privileges to perform the operation. <tt>[EROFS,
--   EACCES]</tt></li>
--   <li><a>isAlreadyExistsError</a> / <a>AlreadyExists</a> The operand
--   refers to a directory that already exists. <tt> [EEXIST]</tt></li>
--   <li><a>HardwareFault</a> A physical I/O error has occurred.
--   <tt>[EIO]</tt></li>
--   <li><a>InvalidArgument</a> The operand is not a valid directory name.
--   <tt>[ENAMETOOLONG, ELOOP]</tt></li>
--   <li><a>NoSuchThing</a> There is no path to the directory. <tt>[ENOENT,
--   ENOTDIR]</tt></li>
--   <li><a>ResourceExhausted</a> Insufficient resources (virtual memory,
--   process file descriptors, physical disk space, etc.) are available to
--   perform the operation. <tt>[EDQUOT, ENOSPC, ENOMEM, EMLINK]</tt></li>
--   <li><a>InappropriateType</a> The path refers to an existing
--   non-directory object. <tt>[EEXIST]</tt></li>
--   </ul>
createDirectory :: FilePath -> IO ()

-- | <tt><a>removeDirectory</a> dir</tt> removes an existing directory
--   <i>dir</i>. The implementation may specify additional constraints
--   which must be satisfied before a directory can be removed (e.g. the
--   directory has to be empty, or may not be in use by other processes).
--   It is not legal for an implementation to partially remove a directory
--   unless the entire directory is removed. A conformant implementation
--   need not support directory removal in all situations (e.g. removal of
--   the root directory).
--   
--   The operation may fail with:
--   
--   <ul>
--   <li><a>HardwareFault</a> A physical I/O error has occurred. EIO</li>
--   <li><a>InvalidArgument</a> The operand is not a valid directory name.
--   [ENAMETOOLONG, ELOOP]</li>
--   <li><a>isDoesNotExistError</a> / <a>NoSuchThing</a> The directory does
--   not exist. <tt>[ENOENT, ENOTDIR]</tt></li>
--   <li><a>isPermissionError</a> / <a>PermissionDenied</a> The process has
--   insufficient privileges to perform the operation. <tt>[EROFS, EACCES,
--   EPERM]</tt></li>
--   <li><a>UnsatisfiedConstraints</a> Implementation-dependent constraints
--   are not satisfied. <tt>[EBUSY, ENOTEMPTY, EEXIST]</tt></li>
--   <li><a>UnsupportedOperation</a> The implementation does not support
--   removal in this situation. <tt>[EINVAL]</tt></li>
--   <li><a>InappropriateType</a> The operand refers to an existing
--   non-directory object. <tt>[ENOTDIR]</tt></li>
--   </ul>
removeDirectory :: FilePath -> IO ()

-- | <a>removeFile</a> <i>file</i> removes the directory entry for an
--   existing file <i>file</i>, where <i>file</i> is not itself a
--   directory. The implementation may specify additional constraints which
--   must be satisfied before a file can be removed (e.g. the file may not
--   be in use by other processes).
--   
--   The operation may fail with:
--   
--   <ul>
--   <li><a>HardwareFault</a> A physical I/O error has occurred.
--   <tt>[EIO]</tt></li>
--   <li><a>InvalidArgument</a> The operand is not a valid file name.
--   <tt>[ENAMETOOLONG, ELOOP]</tt></li>
--   <li><a>isDoesNotExistError</a> / <a>NoSuchThing</a> The file does not
--   exist. <tt>[ENOENT, ENOTDIR]</tt></li>
--   <li><a>isPermissionError</a> / <a>PermissionDenied</a> The process has
--   insufficient privileges to perform the operation. <tt>[EROFS, EACCES,
--   EPERM]</tt></li>
--   <li><a>UnsatisfiedConstraints</a> Implementation-dependent constraints
--   are not satisfied. <tt>[EBUSY]</tt></li>
--   <li><a>InappropriateType</a> The operand refers to an existing
--   directory. <tt>[EPERM, EINVAL]</tt></li>
--   </ul>
removeFile :: FilePath -> IO ()

-- | <tt><a>renameDirectory</a> old new</tt> changes the name of an
--   existing directory from <i>old</i> to <i>new</i>. If the <i>new</i>
--   directory already exists, it is atomically replaced by the <i>old</i>
--   directory. If the <i>new</i> directory is neither the <i>old</i>
--   directory nor an alias of the <i>old</i> directory, it is removed as
--   if by <a>removeDirectory</a>. A conformant implementation need not
--   support renaming directories in all situations (e.g. renaming to an
--   existing directory, or across different physical devices), but the
--   constraints must be documented.
--   
--   On Win32 platforms, <tt>renameDirectory</tt> fails if the <i>new</i>
--   directory already exists.
--   
--   The operation may fail with:
--   
--   <ul>
--   <li><a>HardwareFault</a> A physical I/O error has occurred.
--   <tt>[EIO]</tt></li>
--   <li><a>InvalidArgument</a> Either operand is not a valid directory
--   name. <tt>[ENAMETOOLONG, ELOOP]</tt></li>
--   <li><a>isDoesNotExistError</a> / <a>NoSuchThing</a> The original
--   directory does not exist, or there is no path to the target.
--   <tt>[ENOENT, ENOTDIR]</tt></li>
--   <li><a>isPermissionError</a> / <a>PermissionDenied</a> The process has
--   insufficient privileges to perform the operation. <tt>[EROFS, EACCES,
--   EPERM]</tt></li>
--   <li><a>ResourceExhausted</a> Insufficient resources are available to
--   perform the operation. <tt>[EDQUOT, ENOSPC, ENOMEM, EMLINK]</tt></li>
--   <li><a>UnsatisfiedConstraints</a> Implementation-dependent constraints
--   are not satisfied. <tt>[EBUSY, ENOTEMPTY, EEXIST]</tt></li>
--   <li><a>UnsupportedOperation</a> The implementation does not support
--   renaming in this situation. <tt>[EINVAL, EXDEV]</tt></li>
--   <li><a>InappropriateType</a> Either path refers to an existing
--   non-directory object. <tt>[ENOTDIR, EISDIR]</tt></li>
--   </ul>
renameDirectory :: FilePath -> FilePath -> IO ()

-- | <tt><a>renameFile</a> old new</tt> changes the name of an existing
--   file system object from <i>old</i> to <i>new</i>. If the <i>new</i>
--   object already exists, it is atomically replaced by the <i>old</i>
--   object. Neither path may refer to an existing directory. A conformant
--   implementation need not support renaming files in all situations (e.g.
--   renaming across different physical devices), but the constraints must
--   be documented.
--   
--   The operation may fail with:
--   
--   <ul>
--   <li><a>HardwareFault</a> A physical I/O error has occurred.
--   <tt>[EIO]</tt></li>
--   <li><a>InvalidArgument</a> Either operand is not a valid file name.
--   <tt>[ENAMETOOLONG, ELOOP]</tt></li>
--   <li><a>isDoesNotExistError</a> / <a>NoSuchThing</a> The original file
--   does not exist, or there is no path to the target. <tt>[ENOENT,
--   ENOTDIR]</tt></li>
--   <li><a>isPermissionError</a> / <a>PermissionDenied</a> The process has
--   insufficient privileges to perform the operation. <tt>[EROFS, EACCES,
--   EPERM]</tt></li>
--   <li><a>ResourceExhausted</a> Insufficient resources are available to
--   perform the operation. <tt>[EDQUOT, ENOSPC, ENOMEM, EMLINK]</tt></li>
--   <li><a>UnsatisfiedConstraints</a> Implementation-dependent constraints
--   are not satisfied. <tt>[EBUSY]</tt></li>
--   <li><a>UnsupportedOperation</a> The implementation does not support
--   renaming in this situation. <tt>[EXDEV]</tt></li>
--   <li><a>InappropriateType</a> Either path refers to an existing
--   directory. <tt>[ENOTDIR, EISDIR, EINVAL, EEXIST, ENOTEMPTY]</tt></li>
--   </ul>
renameFile :: FilePath -> FilePath -> IO ()

-- | <tt><a>getDirectoryContents</a> dir</tt> returns a list of <i>all</i>
--   entries in <i>dir</i>.
--   
--   The operation may fail with:
--   
--   <ul>
--   <li><a>HardwareFault</a> A physical I/O error has occurred.
--   <tt>[EIO]</tt></li>
--   <li><a>InvalidArgument</a> The operand is not a valid directory name.
--   <tt>[ENAMETOOLONG, ELOOP]</tt></li>
--   <li><a>isDoesNotExistError</a> / <a>NoSuchThing</a> The directory does
--   not exist. <tt>[ENOENT, ENOTDIR]</tt></li>
--   <li><a>isPermissionError</a> / <a>PermissionDenied</a> The process has
--   insufficient privileges to perform the operation.
--   <tt>[EACCES]</tt></li>
--   <li><a>ResourceExhausted</a> Insufficient resources are available to
--   perform the operation. <tt>[EMFILE, ENFILE]</tt></li>
--   <li><a>InappropriateType</a> The path refers to an existing
--   non-directory object. <tt>[ENOTDIR]</tt></li>
--   </ul>
getDirectoryContents :: FilePath -> IO [FilePath]

-- | If the operating system has a notion of current directories,
--   <a>getCurrentDirectory</a> returns an absolute path to the current
--   directory of the calling process.
--   
--   The operation may fail with:
--   
--   <ul>
--   <li><a>HardwareFault</a> A physical I/O error has occurred.
--   <tt>[EIO]</tt></li>
--   <li><a>isDoesNotExistError</a> / <a>NoSuchThing</a> There is no path
--   referring to the current directory. <tt>[EPERM, ENOENT,
--   ESTALE...]</tt></li>
--   <li><a>isPermissionError</a> / <a>PermissionDenied</a> The process has
--   insufficient privileges to perform the operation.
--   <tt>[EACCES]</tt></li>
--   <li><a>ResourceExhausted</a> Insufficient resources are available to
--   perform the operation.</li>
--   <li><a>UnsupportedOperation</a> The operating system has no notion of
--   current directory.</li>
--   </ul>
--   
--   Note that in a concurrent program, the current directory is global
--   state shared between all threads of the process. When using filesystem
--   operations from multiple threads, it is therefore highly recommended
--   to use absolute rather than relative <a>FilePath</a>s.
getCurrentDirectory :: IO FilePath

-- | If the operating system has a notion of current directories,
--   <tt><a>setCurrentDirectory</a> dir</tt> changes the current directory
--   of the calling process to <i>dir</i>.
--   
--   The operation may fail with:
--   
--   <ul>
--   <li><a>HardwareFault</a> A physical I/O error has occurred.
--   <tt>[EIO]</tt></li>
--   <li><a>InvalidArgument</a> The operand is not a valid directory name.
--   <tt>[ENAMETOOLONG, ELOOP]</tt></li>
--   <li><a>isDoesNotExistError</a> / <a>NoSuchThing</a> The directory does
--   not exist. <tt>[ENOENT, ENOTDIR]</tt></li>
--   <li><a>isPermissionError</a> / <a>PermissionDenied</a> The process has
--   insufficient privileges to perform the operation.
--   <tt>[EACCES]</tt></li>
--   <li><a>UnsupportedOperation</a> The operating system has no notion of
--   current directory, or the current directory cannot be dynamically
--   changed.</li>
--   <li><a>InappropriateType</a> The path refers to an existing
--   non-directory object. <tt>[ENOTDIR]</tt></li>
--   </ul>
--   
--   Note that in a concurrent program, the current directory is global
--   state shared between all threads of the process. When using filesystem
--   operations from multiple threads, it is therefore highly recommended
--   to use absolute rather than relative <a>FilePath</a>s.
setCurrentDirectory :: FilePath -> IO ()

-- | The operation <a>doesFileExist</a> returns <a>True</a> if the argument
--   file exists and is not a directory, and <a>False</a> otherwise.
doesFileExist :: FilePath -> IO Bool

-- | The operation <a>doesDirectoryExist</a> returns <a>True</a> if the
--   argument file exists and is a directory, and <a>False</a> otherwise.
doesDirectoryExist :: FilePath -> IO Bool
getPermissions :: FilePath -> IO Permissions
setPermissions :: FilePath -> Permissions -> IO ()

-- | The <a>getModificationTime</a> operation returns the clock time at
--   which the file or directory was last modified.
--   
--   The operation may fail with:
--   
--   <ul>
--   <li><a>isPermissionError</a> if the user is not permitted to access
--   the modification time; or</li>
--   <li><a>isDoesNotExistError</a> if the file or directory does not
--   exist.</li>
--   </ul>
getModificationTime :: FilePath -> IO UTCTime
instance Eq Permissions
instance Ord Permissions
instance Read Permissions
instance Show Permissions

module CString

module Complex

-- | Complex numbers are an algebraic type.
--   
--   For a complex number <tt>z</tt>, <tt><a>abs</a> z</tt> is a number
--   with the magnitude of <tt>z</tt>, but oriented in the positive real
--   direction, whereas <tt><a>signum</a> z</tt> has the phase of
--   <tt>z</tt>, but unit magnitude.
data Complex a :: * -> *

-- | forms a complex number from its real and imaginary rectangular
--   components.
(:+) :: !a -> !a -> Complex a

-- | Extracts the real part of a complex number.
realPart :: RealFloat a => Complex a -> a

-- | Extracts the imaginary part of a complex number.
imagPart :: RealFloat a => Complex a -> a

-- | The conjugate of a complex number.
conjugate :: RealFloat a => Complex a -> Complex a

-- | Form a complex number from polar components of magnitude and phase.
mkPolar :: RealFloat a => a -> a -> Complex a

-- | <tt><a>cis</a> t</tt> is a complex value with magnitude <tt>1</tt> and
--   phase <tt>t</tt> (modulo <tt>2*<a>pi</a></tt>).
cis :: RealFloat a => a -> Complex a

-- | The function <a>polar</a> takes a complex number and returns a
--   (magnitude, phase) pair in canonical form: the magnitude is
--   nonnegative, and the phase in the range <tt>(-<a>pi</a>,
--   <a>pi</a>]</tt>; if the magnitude is zero, then so is the phase.
polar :: RealFloat a => Complex a -> (a, a)

-- | The nonnegative magnitude of a complex number.
magnitude :: RealFloat a => Complex a -> a

-- | The phase of a complex number, in the range <tt>(-<a>pi</a>,
--   <a>pi</a>]</tt>. If the magnitude is zero, then so is the phase.
phase :: RealFloat a => Complex a -> a

module System

-- | Defines the exit codes that a program can return.
data ExitCode :: *

-- | indicates successful termination;
ExitSuccess :: ExitCode

-- | indicates program failure with an exit code. The exact interpretation
--   of the code is operating-system dependent. In particular, some values
--   may be prohibited (e.g. 0 on a POSIX-compliant system).
ExitFailure :: Int -> ExitCode

-- | Computation <a>getArgs</a> returns a list of the program's command
--   line arguments (not including the program name).
getArgs :: IO [String]

-- | Computation <a>getProgName</a> returns the name of the program as it
--   was invoked.
--   
--   However, this is hard-to-impossible to implement on some non-Unix
--   OSes, so instead, for maximum portability, we just return the leafname
--   of the program as invoked. Even then there are some differences
--   between platforms: on Windows, for example, a program invoked as foo
--   is probably really <tt>FOO.EXE</tt>, and that is what
--   <a>getProgName</a> will return.
getProgName :: IO String

-- | Computation <a>getEnv</a> <tt>var</tt> returns the value of the
--   environment variable <tt>var</tt>. For the inverse, POSIX users can
--   use <a>putEnv</a>.
--   
--   This computation may fail with:
--   
--   <ul>
--   <li><a>isDoesNotExistError</a> if the environment variable does not
--   exist.</li>
--   </ul>
getEnv :: String -> IO String

-- | Computation <tt>system cmd</tt> returns the exit code produced when
--   the operating system runs the shell command <tt>cmd</tt>.
--   
--   This computation may fail with
--   
--   <ul>
--   <li><tt>PermissionDenied</tt>: The process has insufficient privileges
--   to perform the operation.</li>
--   <li><tt>ResourceExhausted</tt>: Insufficient resources are available
--   to perform the operation.</li>
--   <li><tt>UnsupportedOperation</tt>: The implementation does not support
--   system calls.</li>
--   </ul>
--   
--   On Windows, <a>system</a> passes the command to the Windows command
--   interpreter (<tt>CMD.EXE</tt> or <tt>COMMAND.COM</tt>), hence Unixy
--   shell tricks will not work.
system :: String -> IO ExitCode

-- | Computation <a>exitWith</a> <tt>code</tt> throws <a>ExitCode</a>
--   <tt>code</tt>. Normally this terminates the program, returning
--   <tt>code</tt> to the program's caller.
--   
--   On program termination, the standard <tt>Handle</tt>s <tt>stdout</tt>
--   and <tt>stderr</tt> are flushed automatically; any other buffered
--   <tt>Handle</tt>s need to be flushed manually, otherwise the buffered
--   data will be discarded.
--   
--   A program that fails in any other way is treated as if it had called
--   <a>exitFailure</a>. A program that terminates successfully without
--   calling <a>exitWith</a> explicitly is treated as it it had called
--   <a>exitWith</a> <a>ExitSuccess</a>.
--   
--   As an <a>ExitCode</a> is not an <a>IOError</a>, <a>exitWith</a>
--   bypasses the error handling in the <a>IO</a> monad and cannot be
--   intercepted by <tt>catch</tt> from the <a>Prelude</a>. However it is a
--   <tt>SomeException</tt>, and can be caught using the functions of
--   <a>Control.Exception</a>. This means that cleanup computations added
--   with <a>bracket</a> (from <a>Control.Exception</a>) are also executed
--   properly on <a>exitWith</a>.
--   
--   Note: in GHC, <a>exitWith</a> should be called from the main program
--   thread in order to exit the process. When called from another thread,
--   <a>exitWith</a> will throw an <tt>ExitException</tt> as normal, but
--   the exception will not cause the process itself to exit.
exitWith :: ExitCode -> IO a

-- | The computation <a>exitFailure</a> is equivalent to <a>exitWith</a>
--   <tt>(</tt><a>ExitFailure</a> <i>exitfail</i><tt>)</tt>, where
--   <i>exitfail</i> is implementation-dependent.
exitFailure :: IO a

module List

-- | The <a>elemIndex</a> function returns the index of the first element
--   in the given list which is equal (by <a>==</a>) to the query element,
--   or <a>Nothing</a> if there is no such element.
elemIndex :: Eq a => a -> [a] -> Maybe Int

-- | The <a>elemIndices</a> function extends <a>elemIndex</a>, by returning
--   the indices of all elements equal to the query element, in ascending
--   order.
elemIndices :: Eq a => a -> [a] -> [Int]

-- | The <a>find</a> function takes a predicate and a list and returns the
--   first element in the list matching the predicate, or <a>Nothing</a> if
--   there is no such element.
find :: (a -> Bool) -> [a] -> Maybe a

-- | The <a>findIndex</a> function takes a predicate and a list and returns
--   the index of the first element in the list satisfying the predicate,
--   or <a>Nothing</a> if there is no such element.
findIndex :: (a -> Bool) -> [a] -> Maybe Int

-- | The <a>findIndices</a> function extends <a>findIndex</a>, by returning
--   the indices of all elements satisfying the predicate, in ascending
--   order.
findIndices :: (a -> Bool) -> [a] -> [Int]

-- | <i>O(n^2)</i>. The <a>nub</a> function removes duplicate elements from
--   a list. In particular, it keeps only the first occurrence of each
--   element. (The name <a>nub</a> means `essence'.) It is a special case
--   of <a>nubBy</a>, which allows the programmer to supply their own
--   equality test.
nub :: Eq a => [a] -> [a]

-- | The <a>nubBy</a> function behaves just like <a>nub</a>, except it uses
--   a user-supplied equality predicate instead of the overloaded <a>==</a>
--   function.
nubBy :: (a -> a -> Bool) -> [a] -> [a]

-- | <a>delete</a> <tt>x</tt> removes the first occurrence of <tt>x</tt>
--   from its list argument. For example,
--   
--   <pre>
--   delete 'a' "banana" == "bnana"
--   </pre>
--   
--   It is a special case of <a>deleteBy</a>, which allows the programmer
--   to supply their own equality test.
delete :: Eq a => a -> [a] -> [a]

-- | The <a>deleteBy</a> function behaves like <a>delete</a>, but takes a
--   user-supplied equality predicate.
deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]

-- | The <a>\\</a> function is list difference (non-associative). In the
--   result of <tt>xs</tt> <a>\\</a> <tt>ys</tt>, the first occurrence of
--   each element of <tt>ys</tt> in turn (if any) has been removed from
--   <tt>xs</tt>. Thus
--   
--   <pre>
--   (xs ++ ys) \\ xs == ys.
--   </pre>
--   
--   It is a special case of <a>deleteFirstsBy</a>, which allows the
--   programmer to supply their own equality test.
(\\) :: Eq a => [a] -> [a] -> [a]

-- | The <a>deleteFirstsBy</a> function takes a predicate and two lists and
--   returns the first list with the first occurrence of each element of
--   the second list removed.
deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]

-- | The <a>union</a> function returns the list union of the two lists. For
--   example,
--   
--   <pre>
--   "dog" `union` "cow" == "dogcw"
--   </pre>
--   
--   Duplicates, and elements of the first list, are removed from the the
--   second list, but if the first list contains duplicates, so will the
--   result. It is a special case of <a>unionBy</a>, which allows the
--   programmer to supply their own equality test.
union :: Eq a => [a] -> [a] -> [a]

-- | The <a>unionBy</a> function is the non-overloaded version of
--   <a>union</a>.
unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]

-- | The <a>intersect</a> function takes the list intersection of two
--   lists. For example,
--   
--   <pre>
--   [1,2,3,4] `intersect` [2,4,6,8] == [2,4]
--   </pre>
--   
--   If the first list contains duplicates, so will the result.
--   
--   <pre>
--   [1,2,2,3,4] `intersect` [6,4,4,2] == [2,2,4]
--   </pre>
--   
--   It is a special case of <a>intersectBy</a>, which allows the
--   programmer to supply their own equality test. If the element is found
--   in both the first and the second list, the element from the first list
--   will be used.
intersect :: Eq a => [a] -> [a] -> [a]

-- | The <a>intersectBy</a> function is the non-overloaded version of
--   <a>intersect</a>.
intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]

-- | The <a>intersperse</a> function takes an element and a list and
--   `intersperses' that element between the elements of the list. For
--   example,
--   
--   <pre>
--   intersperse ',' "abcde" == "a,b,c,d,e"
--   </pre>
intersperse :: a -> [a] -> [a]

-- | The <a>transpose</a> function transposes the rows and columns of its
--   argument. For example,
--   
--   <pre>
--   transpose [[1,2,3],[4,5,6]] == [[1,4],[2,5],[3,6]]
--   </pre>
transpose :: [[a]] -> [[a]]

-- | The <a>partition</a> function takes a predicate a list and returns the
--   pair of lists of elements which do and do not satisfy the predicate,
--   respectively; i.e.,
--   
--   <pre>
--   partition p xs == (filter p xs, filter (not . p) xs)
--   </pre>
partition :: (a -> Bool) -> [a] -> ([a], [a])

-- | The <a>group</a> function takes a list and returns a list of lists
--   such that the concatenation of the result is equal to the argument.
--   Moreover, each sublist in the result contains only equal elements. For
--   example,
--   
--   <pre>
--   group "Mississippi" = ["M","i","ss","i","ss","i","pp","i"]
--   </pre>
--   
--   It is a special case of <a>groupBy</a>, which allows the programmer to
--   supply their own equality test.
group :: Eq a => [a] -> [[a]]

-- | The <a>groupBy</a> function is the non-overloaded version of
--   <a>group</a>.
groupBy :: (a -> a -> Bool) -> [a] -> [[a]]

-- | The <a>inits</a> function returns all initial segments of the
--   argument, shortest first. For example,
--   
--   <pre>
--   inits "abc" == ["","a","ab","abc"]
--   </pre>
--   
--   Note that <a>inits</a> has the following strictness property:
--   <tt>inits _|_ = [] : _|_</tt>
inits :: [a] -> [[a]]

-- | The <a>tails</a> function returns all final segments of the argument,
--   longest first. For example,
--   
--   <pre>
--   tails "abc" == ["abc", "bc", "c",""]
--   </pre>
--   
--   Note that <a>tails</a> has the following strictness property:
--   <tt>tails _|_ = _|_ : _|_</tt>
tails :: [a] -> [[a]]

-- | The <a>isPrefixOf</a> function takes two lists and returns <a>True</a>
--   iff the first list is a prefix of the second.
isPrefixOf :: Eq a => [a] -> [a] -> Bool

-- | The <a>isSuffixOf</a> function takes two lists and returns <a>True</a>
--   iff the first list is a suffix of the second. Both lists must be
--   finite.
isSuffixOf :: Eq a => [a] -> [a] -> Bool

-- | The <a>mapAccumL</a> function behaves like a combination of <a>map</a>
--   and <a>foldl</a>; it applies a function to each element of a list,
--   passing an accumulating parameter from left to right, and returning a
--   final value of this accumulator together with the new list.
mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])

-- | The <a>mapAccumR</a> function behaves like a combination of <a>map</a>
--   and <a>foldr</a>; it applies a function to each element of a list,
--   passing an accumulating parameter from right to left, and returning a
--   final value of this accumulator together with the new list.
mapAccumR :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])

-- | The <a>sort</a> function implements a stable sorting algorithm. It is
--   a special case of <a>sortBy</a>, which allows the programmer to supply
--   their own comparison function.
sort :: Ord a => [a] -> [a]

-- | The <a>sortBy</a> function is the non-overloaded version of
--   <a>sort</a>.
sortBy :: (a -> a -> Ordering) -> [a] -> [a]

-- | The <a>insert</a> function takes an element and a list and inserts the
--   element into the list at the first position where it is less than or
--   equal to the next element. In particular, if the list is sorted before
--   the call, the result will also be sorted. It is a special case of
--   <a>insertBy</a>, which allows the programmer to supply their own
--   comparison function.
insert :: Ord a => a -> [a] -> [a]

-- | The non-overloaded version of <a>insert</a>.
insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a]

-- | The <a>maximumBy</a> function takes a comparison function and a list
--   and returns the greatest element of the list by the comparison
--   function. The list must be finite and non-empty.
maximumBy :: (a -> a -> Ordering) -> [a] -> a

-- | The <a>minimumBy</a> function takes a comparison function and a list
--   and returns the least element of the list by the comparison function.
--   The list must be finite and non-empty.
minimumBy :: (a -> a -> Ordering) -> [a] -> a

-- | The <a>genericLength</a> function is an overloaded version of
--   <a>length</a>. In particular, instead of returning an <a>Int</a>, it
--   returns any type which is an instance of <a>Num</a>. It is, however,
--   less efficient than <a>length</a>.
genericLength :: Num i => [b] -> i

-- | The <a>genericTake</a> function is an overloaded version of
--   <a>take</a>, which accepts any <a>Integral</a> value as the number of
--   elements to take.
genericTake :: Integral i => i -> [a] -> [a]

-- | The <a>genericDrop</a> function is an overloaded version of
--   <a>drop</a>, which accepts any <a>Integral</a> value as the number of
--   elements to drop.
genericDrop :: Integral i => i -> [a] -> [a]

-- | The <a>genericSplitAt</a> function is an overloaded version of
--   <a>splitAt</a>, which accepts any <a>Integral</a> value as the
--   position at which to split.
genericSplitAt :: Integral i => i -> [b] -> ([b], [b])

-- | The <a>genericIndex</a> function is an overloaded version of
--   <a>!!</a>, which accepts any <a>Integral</a> value as the index.
genericIndex :: Integral a => [b] -> a -> b

-- | The <a>genericReplicate</a> function is an overloaded version of
--   <a>replicate</a>, which accepts any <a>Integral</a> value as the
--   number of repetitions to make.
genericReplicate :: Integral i => i -> a -> [a]

-- | The <a>zip4</a> function takes four lists and returns a list of
--   quadruples, analogous to <a>zip</a>.
zip4 :: [a] -> [b] -> [c] -> [d] -> [(a, b, c, d)]

-- | The <a>zip5</a> function takes five lists and returns a list of
--   five-tuples, analogous to <a>zip</a>.
zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a, b, c, d, e)]

-- | The <a>zip6</a> function takes six lists and returns a list of
--   six-tuples, analogous to <a>zip</a>.
zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [(a, b, c, d, e, f)]

-- | The <a>zip7</a> function takes seven lists and returns a list of
--   seven-tuples, analogous to <a>zip</a>.
zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [(a, b, c, d, e, f, g)]

-- | The <a>zipWith4</a> function takes a function which combines four
--   elements, as well as four lists and returns a list of their point-wise
--   combination, analogous to <a>zipWith</a>.
zipWith4 :: (a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e]

-- | The <a>zipWith5</a> function takes a function which combines five
--   elements, as well as five lists and returns a list of their point-wise
--   combination, analogous to <a>zipWith</a>.
zipWith5 :: (a -> b -> c -> d -> e -> f) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f]

-- | The <a>zipWith6</a> function takes a function which combines six
--   elements, as well as six lists and returns a list of their point-wise
--   combination, analogous to <a>zipWith</a>.
zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g]

-- | The <a>zipWith7</a> function takes a function which combines seven
--   elements, as well as seven lists and returns a list of their
--   point-wise combination, analogous to <a>zipWith</a>.
zipWith7 :: (a -> b -> c -> d -> e -> f -> g -> h) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f] -> [g] -> [h]

-- | The <a>unzip4</a> function takes a list of quadruples and returns four
--   lists, analogous to <a>unzip</a>.
unzip4 :: [(a, b, c, d)] -> ([a], [b], [c], [d])

-- | The <a>unzip5</a> function takes a list of five-tuples and returns
--   five lists, analogous to <a>unzip</a>.
unzip5 :: [(a, b, c, d, e)] -> ([a], [b], [c], [d], [e])

-- | The <a>unzip6</a> function takes a list of six-tuples and returns six
--   lists, analogous to <a>unzip</a>.
unzip6 :: [(a, b, c, d, e, f)] -> ([a], [b], [c], [d], [e], [f])

-- | The <a>unzip7</a> function takes a list of seven-tuples and returns
--   seven lists, analogous to <a>unzip</a>.
unzip7 :: [(a, b, c, d, e, f, g)] -> ([a], [b], [c], [d], [e], [f], [g])

-- | The <a>unfoldr</a> function is a `dual' to <a>foldr</a>: while
--   <a>foldr</a> reduces a list to a summary value, <a>unfoldr</a> builds
--   a list from a seed value. The function takes the element and returns
--   <a>Nothing</a> if it is done producing the list or returns <a>Just</a>
--   <tt>(a,b)</tt>, in which case, <tt>a</tt> is a prepended to the list
--   and <tt>b</tt> is used as the next element in a recursive call. For
--   example,
--   
--   <pre>
--   iterate f == unfoldr (\x -&gt; Just (x, f x))
--   </pre>
--   
--   In some cases, <a>unfoldr</a> can undo a <a>foldr</a> operation:
--   
--   <pre>
--   unfoldr f' (foldr f z xs) == xs
--   </pre>
--   
--   if the following holds:
--   
--   <pre>
--   f' (f x y) = Just (x,y)
--   f' z       = Nothing
--   </pre>
--   
--   A simple use of unfoldr:
--   
--   <pre>
--   unfoldr (\b -&gt; if b == 0 then Nothing else Just (b, b-1)) 10
--    [10,9,8,7,6,5,4,3,2,1]
--   </pre>
unfoldr :: (b -> Maybe (a, b)) -> b -> [a]

-- | <a>map</a> <tt>f xs</tt> is the list obtained by applying <tt>f</tt>
--   to each element of <tt>xs</tt>, i.e.,
--   
--   <pre>
--   map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
--   map f [x1, x2, ...] == [f x1, f x2, ...]
--   </pre>
map :: (a -> b) -> [a] -> [b]

-- | Append two lists, i.e.,
--   
--   <pre>
--   [x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
--   [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
--   </pre>
--   
--   If the first list is not finite, the result is the first list.
(++) :: [a] -> [a] -> [a]

-- | Concatenate a list of lists.
concat :: [[a]] -> [a]

-- | <a>filter</a>, applied to a predicate and a list, returns the list of
--   those elements that satisfy the predicate; i.e.,
--   
--   <pre>
--   filter p xs = [ x | x &lt;- xs, p x]
--   </pre>
filter :: (a -> Bool) -> [a] -> [a]

-- | Extract the first element of a list, which must be non-empty.
head :: [a] -> a

-- | Extract the last element of a list, which must be finite and
--   non-empty.
last :: [a] -> a

-- | Extract the elements after the head of a list, which must be
--   non-empty.
tail :: [a] -> [a]

-- | Return all the elements of a list except the last one. The list must
--   be non-empty.
init :: [a] -> [a]

-- | Test whether a list is empty.
null :: [a] -> Bool

-- | <i>O(n)</i>. <a>length</a> returns the length of a finite list as an
--   <a>Int</a>. It is an instance of the more general
--   <a>genericLength</a>, the result type of which may be any kind of
--   number.
length :: [a] -> Int

-- | List index (subscript) operator, starting from 0. It is an instance of
--   the more general <a>genericIndex</a>, which takes an index of any
--   integral type.
(!!) :: [a] -> Int -> a

-- | <a>foldl</a>, applied to a binary operator, a starting value
--   (typically the left-identity of the operator), and a list, reduces the
--   list using the binary operator, from left to right:
--   
--   <pre>
--   foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
--   </pre>
--   
--   The list must be finite.
foldl :: (a -> b -> a) -> a -> [b] -> a

-- | <a>foldl1</a> is a variant of <a>foldl</a> that has no starting value
--   argument, and thus must be applied to non-empty lists.
foldl1 :: (a -> a -> a) -> [a] -> a

-- | <a>scanl</a> is similar to <a>foldl</a>, but returns a list of
--   successive reduced values from the left:
--   
--   <pre>
--   scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
--   </pre>
--   
--   Note that
--   
--   <pre>
--   last (scanl f z xs) == foldl f z xs.
--   </pre>
scanl :: (a -> b -> a) -> a -> [b] -> [a]

-- | <a>scanl1</a> is a variant of <a>scanl</a> that has no starting value
--   argument:
--   
--   <pre>
--   scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
--   </pre>
scanl1 :: (a -> a -> a) -> [a] -> [a]

-- | <a>foldr</a>, applied to a binary operator, a starting value
--   (typically the right-identity of the operator), and a list, reduces
--   the list using the binary operator, from right to left:
--   
--   <pre>
--   foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
--   </pre>
foldr :: (a -> b -> b) -> b -> [a] -> b

-- | <a>foldr1</a> is a variant of <a>foldr</a> that has no starting value
--   argument, and thus must be applied to non-empty lists.
foldr1 :: (a -> a -> a) -> [a] -> a

-- | <a>scanr</a> is the right-to-left dual of <a>scanl</a>. Note that
--   
--   <pre>
--   head (scanr f z xs) == foldr f z xs.
--   </pre>
scanr :: (a -> b -> b) -> b -> [a] -> [b]

-- | <a>scanr1</a> is a variant of <a>scanr</a> that has no starting value
--   argument.
scanr1 :: (a -> a -> a) -> [a] -> [a]

-- | <a>iterate</a> <tt>f x</tt> returns an infinite list of repeated
--   applications of <tt>f</tt> to <tt>x</tt>:
--   
--   <pre>
--   iterate f x == [x, f x, f (f x), ...]
--   </pre>
iterate :: (a -> a) -> a -> [a]

-- | <a>repeat</a> <tt>x</tt> is an infinite list, with <tt>x</tt> the
--   value of every element.
repeat :: a -> [a]

-- | <a>replicate</a> <tt>n x</tt> is a list of length <tt>n</tt> with
--   <tt>x</tt> the value of every element. It is an instance of the more
--   general <a>genericReplicate</a>, in which <tt>n</tt> may be of any
--   integral type.
replicate :: Int -> a -> [a]

-- | <a>cycle</a> ties a finite list into a circular one, or equivalently,
--   the infinite repetition of the original list. It is the identity on
--   infinite lists.
cycle :: [a] -> [a]

-- | <a>take</a> <tt>n</tt>, applied to a list <tt>xs</tt>, returns the
--   prefix of <tt>xs</tt> of length <tt>n</tt>, or <tt>xs</tt> itself if
--   <tt>n &gt; <a>length</a> xs</tt>:
--   
--   <pre>
--   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] == []
--   </pre>
--   
--   It is an instance of the more general <a>genericTake</a>, in which
--   <tt>n</tt> may be of any integral type.
take :: Int -> [a] -> [a]

-- | <a>drop</a> <tt>n xs</tt> returns the suffix of <tt>xs</tt> after the
--   first <tt>n</tt> elements, or <tt>[]</tt> if <tt>n &gt; <a>length</a>
--   xs</tt>:
--   
--   <pre>
--   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]
--   </pre>
--   
--   It is an instance of the more general <a>genericDrop</a>, in which
--   <tt>n</tt> may be of any integral type.
drop :: Int -> [a] -> [a]

-- | <a>splitAt</a> <tt>n xs</tt> returns a tuple where first element is
--   <tt>xs</tt> prefix of length <tt>n</tt> and second element is the
--   remainder of the list:
--   
--   <pre>
--   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])
--   </pre>
--   
--   It is equivalent to <tt>(<a>take</a> n xs, <a>drop</a> n xs)</tt>.
--   <a>splitAt</a> is an instance of the more general
--   <a>genericSplitAt</a>, in which <tt>n</tt> may be of any integral
--   type.
splitAt :: Int -> [a] -> ([a], [a])

-- | <a>takeWhile</a>, applied to a predicate <tt>p</tt> and a list
--   <tt>xs</tt>, returns the longest prefix (possibly empty) of
--   <tt>xs</tt> of elements that satisfy <tt>p</tt>:
--   
--   <pre>
--   takeWhile (&lt; 3) [1,2,3,4,1,2,3,4] == [1,2]
--   takeWhile (&lt; 9) [1,2,3] == [1,2,3]
--   takeWhile (&lt; 0) [1,2,3] == []
--   </pre>
takeWhile :: (a -> Bool) -> [a] -> [a]

-- | <a>dropWhile</a> <tt>p xs</tt> returns the suffix remaining after
--   <a>takeWhile</a> <tt>p xs</tt>:
--   
--   <pre>
--   dropWhile (&lt; 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3]
--   dropWhile (&lt; 9) [1,2,3] == []
--   dropWhile (&lt; 0) [1,2,3] == [1,2,3]
--   </pre>
dropWhile :: (a -> Bool) -> [a] -> [a]

-- | <a>span</a>, applied to a predicate <tt>p</tt> and a list <tt>xs</tt>,
--   returns a tuple where first element is longest prefix (possibly empty)
--   of <tt>xs</tt> of elements that satisfy <tt>p</tt> and second element
--   is the remainder of the list:
--   
--   <pre>
--   span (&lt; 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4])
--   span (&lt; 9) [1,2,3] == ([1,2,3],[])
--   span (&lt; 0) [1,2,3] == ([],[1,2,3])
--   </pre>
--   
--   <a>span</a> <tt>p xs</tt> is equivalent to <tt>(<a>takeWhile</a> p xs,
--   <a>dropWhile</a> p xs)</tt>
span :: (a -> Bool) -> [a] -> ([a], [a])

-- | <a>break</a>, applied to a predicate <tt>p</tt> and a list
--   <tt>xs</tt>, returns a tuple where first element is longest prefix
--   (possibly empty) of <tt>xs</tt> of elements that <i>do not satisfy</i>
--   <tt>p</tt> and second element is the remainder of the list:
--   
--   <pre>
--   break (&gt; 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4])
--   break (&lt; 9) [1,2,3] == ([],[1,2,3])
--   break (&gt; 9) [1,2,3] == ([1,2,3],[])
--   </pre>
--   
--   <a>break</a> <tt>p</tt> is equivalent to <tt><a>span</a> (<a>not</a> .
--   p)</tt>.
break :: (a -> Bool) -> [a] -> ([a], [a])

-- | <a>lines</a> breaks a string up into a list of strings at newline
--   characters. The resulting strings do not contain newlines.
lines :: String -> [String]

-- | <a>words</a> breaks a string up into a list of words, which were
--   delimited by white space.
words :: String -> [String]

-- | <a>unlines</a> is an inverse operation to <a>lines</a>. It joins
--   lines, after appending a terminating newline to each.
unlines :: [String] -> String

-- | <a>unwords</a> is an inverse operation to <a>words</a>. It joins words
--   with separating spaces.
unwords :: [String] -> String

-- | <a>reverse</a> <tt>xs</tt> returns the elements of <tt>xs</tt> in
--   reverse order. <tt>xs</tt> must be finite.
reverse :: [a] -> [a]

-- | <a>and</a> returns the conjunction of a Boolean list. For the result
--   to be <a>True</a>, the list must be finite; <a>False</a>, however,
--   results from a <a>False</a> value at a finite index of a finite or
--   infinite list.
and :: [Bool] -> Bool

-- | <a>or</a> returns the disjunction of a Boolean list. For the result to
--   be <a>False</a>, the list must be finite; <a>True</a>, however,
--   results from a <a>True</a> value at a finite index of a finite or
--   infinite list.
or :: [Bool] -> Bool

-- | Applied to a predicate and a list, <a>any</a> determines if any
--   element of the list satisfies the predicate. For the result to be
--   <a>False</a>, the list must be finite; <a>True</a>, however, results
--   from a <a>True</a> value for the predicate applied to an element at a
--   finite index of a finite or infinite list.
any :: (a -> Bool) -> [a] -> Bool

-- | Applied to a predicate and a list, <a>all</a> determines if all
--   elements of the list satisfy the predicate. For the result to be
--   <a>True</a>, the list must be finite; <a>False</a>, however, results
--   from a <a>False</a> value for the predicate applied to an element at a
--   finite index of a finite or infinite list.
all :: (a -> Bool) -> [a] -> Bool

-- | <a>elem</a> is the list membership predicate, usually written in infix
--   form, e.g., <tt>x `elem` xs</tt>. For the result to be <a>False</a>,
--   the list must be finite; <a>True</a>, however, results from an element
--   equal to <tt>x</tt> found at a finite index of a finite or infinite
--   list.
elem :: Eq a => a -> [a] -> Bool

-- | <a>notElem</a> is the negation of <a>elem</a>.
notElem :: Eq a => a -> [a] -> Bool

-- | <a>lookup</a> <tt>key assocs</tt> looks up a key in an association
--   list.
lookup :: Eq a => a -> [(a, b)] -> Maybe b

-- | The <a>sum</a> function computes the sum of a finite list of numbers.
sum :: Num a => [a] -> a

-- | The <a>product</a> function computes the product of a finite list of
--   numbers.
product :: Num a => [a] -> a

-- | <a>maximum</a> returns the maximum value from a list, which must be
--   non-empty, finite, and of an ordered type. It is a special case of
--   <a>maximumBy</a>, which allows the programmer to supply their own
--   comparison function.
maximum :: Ord a => [a] -> a

-- | <a>minimum</a> returns the minimum value from a list, which must be
--   non-empty, finite, and of an ordered type. It is a special case of
--   <a>minimumBy</a>, which allows the programmer to supply their own
--   comparison function.
minimum :: Ord a => [a] -> a

-- | Map a function over a list and concatenate the results.
concatMap :: (a -> [b]) -> [a] -> [b]

-- | <a>zip</a> 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 :: [a] -> [b] -> [(a, b)]

-- | <a>zip3</a> takes three lists and returns a list of triples, analogous
--   to <a>zip</a>.
zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]

-- | <a>zipWith</a> generalises <a>zip</a> by zipping with the function
--   given as the first argument, instead of a tupling function. For
--   example, <tt><a>zipWith</a> (+)</tt> is applied to two lists to
--   produce the list of corresponding sums.
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]

-- | The <a>zipWith3</a> function takes a function which combines three
--   elements, as well as three lists and returns a list of their
--   point-wise combination, analogous to <a>zipWith</a>.
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]

-- | <a>unzip</a> transforms a list of pairs into a list of first
--   components and a list of second components.
unzip :: [(a, b)] -> ([a], [b])

-- | The <a>unzip3</a> function takes a list of triples and returns three
--   lists, analogous to <a>unzip</a>.
unzip3 :: [(a, b, c)] -> ([a], [b], [c])

module CPUTime

-- | Computation <a>getCPUTime</a> returns the number of picoseconds CPU
--   time used by the current program. The precision of this result is
--   implementation-dependent.
getCPUTime :: IO Integer

-- | The <a>cpuTimePrecision</a> constant is the smallest measurable
--   difference in CPU time that the implementation can record, and is
--   given as an integral number of picoseconds.
cpuTimePrecision :: Integer

module Locale
data TimeLocale :: *
TimeLocale :: [(String, String)] -> [(String, String)] -> [(String, String)] -> (String, String) -> String -> String -> String -> String -> TimeLocale
defaultTimeLocale :: TimeLocale

module Time

-- | A representation of the internal clock time. Clock times may be
--   compared, converted to strings, or converted to an external calendar
--   time <a>CalendarTime</a> for I/O or other manipulations.
data ClockTime :: *

-- | A month of the year.
data Month :: *
January :: Month
February :: Month
March :: Month
April :: Month
May :: Month
June :: Month
July :: Month
August :: Month
September :: Month
October :: Month
November :: Month
December :: Month

-- | A day of the week.
data Day :: *
Sunday :: Day
Monday :: Day
Tuesday :: Day
Wednesday :: Day
Thursday :: Day
Friday :: Day
Saturday :: Day

-- | <a>CalendarTime</a> is a user-readable and manipulable representation
--   of the internal <a>ClockTime</a> type.
data CalendarTime :: *
CalendarTime :: Int -> Month -> Int -> Int -> Int -> Int -> Integer -> Day -> Int -> String -> Int -> Bool -> CalendarTime

-- | Year (pre-Gregorian dates are inaccurate)
ctYear :: CalendarTime -> Int

-- | Month of the year
ctMonth :: CalendarTime -> Month

-- | Day of the month (1 to 31)
ctDay :: CalendarTime -> Int

-- | Hour of the day (0 to 23)
ctHour :: CalendarTime -> Int

-- | Minutes (0 to 59)
ctMin :: CalendarTime -> Int

-- | Seconds (0 to 61, allowing for up to two leap seconds)
ctSec :: CalendarTime -> Int

-- | Picoseconds
ctPicosec :: CalendarTime -> Integer

-- | Day of the week
ctWDay :: CalendarTime -> Day

-- | Day of the year (0 to 364, or 365 in leap years)
ctYDay :: CalendarTime -> Int

-- | Name of the time zone
ctTZName :: CalendarTime -> String

-- | Variation from UTC in seconds
ctTZ :: CalendarTime -> Int

-- | <a>True</a> if Daylight Savings Time would be in effect, and
--   <a>False</a> otherwise
ctIsDST :: CalendarTime -> Bool

-- | records the difference between two clock times in a user-readable way.
data TimeDiff :: *
TimeDiff :: Int -> Int -> Int -> Int -> Int -> Int -> Integer -> TimeDiff
tdYear :: TimeDiff -> Int
tdMonth :: TimeDiff -> Int
tdDay :: TimeDiff -> Int
tdHour :: TimeDiff -> Int
tdMin :: TimeDiff -> Int
tdSec :: TimeDiff -> Int
tdPicosec :: TimeDiff -> Integer
getClockTime :: IO ClockTime

-- | <tt><a>addToClockTime</a> d t</tt> adds a time difference <tt>d</tt>
--   and a clock time <tt>t</tt> to yield a new clock time. The difference
--   <tt>d</tt> may be either positive or negative.
addToClockTime :: TimeDiff -> ClockTime -> ClockTime

-- | <tt><a>diffClockTimes</a> t1 t2</tt> returns the difference between
--   two clock times <tt>t1</tt> and <tt>t2</tt> as a <a>TimeDiff</a>.
diffClockTimes :: ClockTime -> ClockTime -> TimeDiff

-- | converts an internal clock time to a local time, modified by the
--   timezone and daylight savings time settings in force at the time of
--   conversion. Because of this dependence on the local environment,
--   <a>toCalendarTime</a> is in the <a>IO</a> monad.
toCalendarTime :: ClockTime -> IO CalendarTime

-- | converts an internal clock time into a <a>CalendarTime</a> in standard
--   UTC format.
toUTCTime :: ClockTime -> CalendarTime

-- | converts a <a>CalendarTime</a> into the corresponding internal
--   <a>ClockTime</a>, ignoring the contents of the <a>ctWDay</a>,
--   <a>ctYDay</a>, <a>ctTZName</a> and <a>ctIsDST</a> fields.
toClockTime :: CalendarTime -> ClockTime

-- | formats calendar times using local conventions.
calendarTimeToString :: CalendarTime -> String

-- | formats calendar times using local conventions and a formatting
--   string. The formatting string is that understood by the ISO C
--   <tt>strftime()</tt> function.
formatCalendarTime :: TimeLocale -> String -> CalendarTime -> String

module CError

module CForeign

module CTypes

module MarshalAlloc

module MarshalArray

module MarshalError

-- | An abstract type that contains a value for each variant of
--   <a>IOError</a>.
data IOErrorType :: *

-- | Construct an <a>IOError</a> of the given type where the second
--   argument describes the error location and the third and fourth
--   argument contain the file handle and file path of the file involved in
--   the error if applicable.
mkIOError :: IOErrorType -> String -> Maybe Handle -> Maybe FilePath -> IOError

-- | I/O error where the operation failed because one of its arguments
--   already exists.
alreadyExistsErrorType :: IOErrorType

-- | I/O error where the operation failed because one of its arguments does
--   not exist.
doesNotExistErrorType :: IOErrorType

-- | I/O error where the operation failed because one of its arguments is a
--   single-use resource, which is already being used.
alreadyInUseErrorType :: IOErrorType

-- | I/O error where the operation failed because the device is full.
fullErrorType :: IOErrorType

-- | I/O error where the operation failed because the end of file has been
--   reached.
eofErrorType :: IOErrorType

-- | I/O error where the operation is not possible.
illegalOperationErrorType :: IOErrorType

-- | I/O error where the operation failed because the user does not have
--   sufficient operating system privilege to perform that operation.
permissionErrorType :: IOErrorType

-- | I/O error that is programmer-defined.
userErrorType :: IOErrorType

-- | Adds a location description and maybe a file path and file handle to
--   an <a>IOError</a>. If any of the file handle or file path is not given
--   the corresponding value in the <a>IOError</a> remains unaltered.
annotateIOError :: IOError -> String -> Maybe Handle -> Maybe FilePath -> IOError

module MarshalUtils

module Random

-- | The class <a>RandomGen</a> provides a common interface to random
--   number generators.
--   
--   Minimal complete definition: <a>next</a> and <a>split</a>.
class RandomGen g where genRange _ = (minBound, maxBound)
next :: RandomGen g => g -> (Int, g)
split :: RandomGen g => g -> (g, g)
genRange :: RandomGen g => g -> (Int, Int)

-- | The <a>StdGen</a> instance of <a>RandomGen</a> has a <a>genRange</a>
--   of at least 30 bits.
--   
--   The result of repeatedly using <a>next</a> should be at least as
--   statistically robust as the <i>Minimal Standard Random Number
--   Generator</i> described by [<a>Random#Park</a>, <a>Random#Carta</a>].
--   Until more is known about implementations of <a>split</a>, all we
--   require is that <a>split</a> deliver generators that are (a) not
--   identical and (b) independently robust in the sense just given.
--   
--   The <a>Show</a> and <a>Read</a> instances of <a>StdGen</a> provide a
--   primitive way to save the state of a random number generator. It is
--   required that <tt><a>read</a> (<a>show</a> g) == g</tt>.
--   
--   In addition, <a>reads</a> may be used to map an arbitrary string (not
--   necessarily one produced by <a>show</a>) onto a value of type
--   <a>StdGen</a>. In general, the <a>Read</a> instance of <a>StdGen</a>
--   has the following properties:
--   
--   <ul>
--   <li>It guarantees to succeed on any string.</li>
--   <li>It guarantees to consume only a finite portion of the string.</li>
--   <li>Different argument strings are likely to result in different
--   results.</li>
--   </ul>
data StdGen

-- | The function <a>mkStdGen</a> provides an alternative way of producing
--   an initial generator, by mapping an <a>Int</a> into a generator.
--   Again, distinct arguments should be likely to produce distinct
--   generators.
mkStdGen :: Int -> StdGen

-- | Uses the supplied function to get a value from the current global
--   random generator, and updates the global generator with the new
--   generator returned by the function. For example, <tt>rollDice</tt>
--   gets a random integer between 1 and 6:
--   
--   <pre>
--   rollDice :: IO Int
--   rollDice = getStdRandom (randomR (1,6))
--   </pre>
getStdRandom :: (StdGen -> (a, StdGen)) -> IO a

-- | Gets the global random number generator.
getStdGen :: IO StdGen

-- | Sets the global random number generator.
setStdGen :: StdGen -> IO ()

-- | Applies <a>split</a> to the current global random generator, updates
--   it with one of the results, and returns the other.
newStdGen :: IO StdGen

-- | With a source of random number supply in hand, the <a>Random</a> class
--   allows the programmer to extract random values of a variety of types.
--   
--   Minimal complete definition: <a>randomR</a> and <a>random</a>.
class Random a where randomRs ival g = x : randomRs ival g' where (x, g') = randomR ival g randoms g = (\ (x, g') -> x : randoms g') (random g) randomRIO range = getStdRandom (randomR range) randomIO = getStdRandom random
randomR :: (Random a, RandomGen g) => (a, a) -> g -> (a, g)
random :: (Random a, RandomGen g) => g -> (a, g)
randomRs :: (Random a, RandomGen g) => (a, a) -> g -> [a]
randoms :: (Random a, RandomGen g) => g -> [a]
randomRIO :: Random a => (a, a) -> IO a
randomIO :: Random a => IO a
instance Random Float
instance Random Double
instance Random Integer
instance Random Bool
instance Random Char
instance Random Int
instance Read StdGen
instance Show StdGen
instance RandomGen StdGen

module Word

module Ptr

module StablePtr

module Monad

-- | Monads that also support choice and failure.
class Monad m => MonadPlus (m :: * -> *)
mzero :: MonadPlus m => m a
mplus :: MonadPlus m => m a -> m a -> m a

-- | The <a>join</a> function is the conventional monad join operator. It
--   is used to remove one level of monadic structure, projecting its bound
--   argument into the outer level.
join :: Monad m => m (m a) -> m a

-- | <tt><a>guard</a> b</tt> is <tt><a>return</a> ()</tt> if <tt>b</tt> is
--   <a>True</a>, and <a>mzero</a> if <tt>b</tt> is <a>False</a>.
guard :: MonadPlus m => Bool -> m ()

-- | Conditional execution of monadic expressions. For example,
--   
--   <pre>
--   when debug (putStr "Debugging\n")
--   </pre>
--   
--   will output the string <tt>Debugging\n</tt> if the Boolean value
--   <tt>debug</tt> is <a>True</a>, and otherwise do nothing.
when :: Monad m => Bool -> m () -> m ()

-- | The reverse of <a>when</a>.
unless :: Monad m => Bool -> m () -> m ()

-- | In many situations, the <a>liftM</a> operations can be replaced by
--   uses of <a>ap</a>, which promotes function application.
--   
--   <pre>
--   return f `ap` x1 `ap` ... `ap` xn
--   </pre>
--   
--   is equivalent to
--   
--   <pre>
--   liftMn f x1 x2 ... xn
--   </pre>
ap :: Monad m => m (a -> b) -> m a -> m b

-- | This generalizes the list-based <a>concat</a> function.
msum :: MonadPlus m => [m a] -> m a

-- | This generalizes the list-based <a>filter</a> function.
filterM :: Monad m => (a -> m Bool) -> [a] -> m [a]

-- | The <a>mapAndUnzipM</a> function maps its first argument over a list,
--   returning the result as a pair of lists. This function is mainly used
--   with complicated data structures or a state-transforming monad.
mapAndUnzipM :: Monad m => (a -> m (b, c)) -> [a] -> m ([b], [c])

-- | The <a>zipWithM</a> function generalizes <a>zipWith</a> to arbitrary
--   monads.
zipWithM :: Monad m => (a -> b -> m c) -> [a] -> [b] -> m [c]

-- | <a>zipWithM_</a> is the extension of <a>zipWithM</a> which ignores the
--   final result.
zipWithM_ :: Monad m => (a -> b -> m c) -> [a] -> [b] -> m ()

-- | The <a>foldM</a> function is analogous to <a>foldl</a>, except that
--   its result is encapsulated in a monad. Note that <a>foldM</a> works
--   from left-to-right over the list arguments. This could be an issue
--   where <tt>(<a>&gt;&gt;</a>)</tt> and the `folded function' are not
--   commutative.
--   
--   <pre>
--   foldM f a1 [x1, x2, ..., xm]
--   </pre>
--   
--   ==
--   
--   <pre>
--   do
--     a2 &lt;- f a1 x1
--     a3 &lt;- f a2 x2
--     ...
--     f am xm
--   </pre>
--   
--   If right-to-left evaluation is required, the input list should be
--   reversed.
foldM :: Monad m => (a -> b -> m a) -> a -> [b] -> m a

-- | Promote a function to a monad.
liftM :: Monad m => (a1 -> r) -> m a1 -> m r

-- | Promote a function to a monad, scanning the monadic arguments from
--   left to right. For example,
--   
--   <pre>
--   liftM2 (+) [0,1] [0,2] = [0,2,1,3]
--   liftM2 (+) (Just 1) Nothing = Nothing
--   </pre>
liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r

-- | Promote a function to a monad, scanning the monadic arguments from
--   left to right (cf. <a>liftM2</a>).
liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r

-- | Promote a function to a monad, scanning the monadic arguments from
--   left to right (cf. <a>liftM2</a>).
liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r

-- | Promote a function to a monad, scanning the monadic arguments from
--   left to right (cf. <a>liftM2</a>).
liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r

-- | The <a>Monad</a> class defines the basic operations over a
--   <i>monad</i>, a concept from a branch of mathematics known as
--   <i>category theory</i>. From the perspective of a Haskell programmer,
--   however, it is best to think of a monad as an <i>abstract datatype</i>
--   of actions. Haskell's <tt>do</tt> expressions provide a convenient
--   syntax for writing monadic expressions.
--   
--   Minimal complete definition: <a>&gt;&gt;=</a> and <a>return</a>.
--   
--   Instances of <a>Monad</a> should satisfy the following laws:
--   
--   <pre>
--   return a &gt;&gt;= k  ==  k a
--   m &gt;&gt;= return  ==  m
--   m &gt;&gt;= (\x -&gt; k x &gt;&gt;= h)  ==  (m &gt;&gt;= k) &gt;&gt;= h
--   </pre>
--   
--   Instances of both <a>Monad</a> and <a>Functor</a> should additionally
--   satisfy the law:
--   
--   <pre>
--   fmap f xs  ==  xs &gt;&gt;= return . f
--   </pre>
--   
--   The instances of <a>Monad</a> for lists, <a>Maybe</a> and <a>IO</a>
--   defined in the <a>Prelude</a> satisfy these laws.
class Monad (m :: * -> *)
(>>=) :: Monad m => m a -> (a -> m b) -> m b
(>>) :: Monad m => m a -> m b -> m b
return :: Monad m => a -> m a
fail :: Monad m => String -> m a

-- | The <a>Functor</a> class is used for types that can be mapped over.
--   Instances of <a>Functor</a> should satisfy the following laws:
--   
--   <pre>
--   fmap id  ==  id
--   fmap (f . g)  ==  fmap f . fmap g
--   </pre>
--   
--   The instances of <a>Functor</a> for lists, <a>Maybe</a> and <a>IO</a>
--   satisfy these laws.
class Functor (f :: * -> *)
fmap :: Functor f => (a -> b) -> f a -> f b

-- | <tt><a>mapM</a> f</tt> is equivalent to <tt><a>sequence</a> .
--   <a>map</a> f</tt>.
mapM :: Monad m => (a -> m b) -> [a] -> m [b]

-- | <tt><a>mapM_</a> f</tt> is equivalent to <tt><a>sequence_</a> .
--   <a>map</a> f</tt>.
mapM_ :: Monad m => (a -> m b) -> [a] -> m ()

-- | Evaluate each action in the sequence from left to right, and collect
--   the results.
sequence :: Monad m => [m a] -> m [a]

-- | Evaluate each action in the sequence from left to right, and ignore
--   the results.
sequence_ :: Monad m => [m a] -> m ()

-- | Same as <a>&gt;&gt;=</a>, but with the arguments interchanged.
(=<<) :: Monad m => (a -> m b) -> m a -> m b

module Ratio

-- | Rational numbers, with numerator and denominator of some
--   <a>Integral</a> type.
data Ratio a :: * -> *

-- | Arbitrary-precision rational numbers, represented as a ratio of two
--   <a>Integer</a> values. A rational number may be constructed using the
--   <a>%</a> operator.
type Rational = Ratio Integer

-- | Forms the ratio of two integral numbers.
(%) :: Integral a => a -> a -> Ratio a

-- | Extract the numerator of the ratio in reduced form: the numerator and
--   denominator have no common factor and the denominator is positive.
numerator :: Integral a => Ratio a -> a

-- | Extract the denominator of the ratio in reduced form: the numerator
--   and denominator have no common factor and the denominator is positive.
denominator :: Integral a => Ratio a -> a

-- | <a>approxRational</a>, applied to two real fractional numbers
--   <tt>x</tt> and <tt>epsilon</tt>, returns the simplest rational number
--   within <tt>epsilon</tt> of <tt>x</tt>. A rational number <tt>y</tt> is
--   said to be <i>simpler</i> than another <tt>y'</tt> if
--   
--   <ul>
--   <li><tt><a>abs</a> (<a>numerator</a> y) &lt;= <a>abs</a>
--   (<a>numerator</a> y')</tt>, and</li>
--   <li><tt><a>denominator</a> y &lt;= <a>denominator</a> y'</tt>.</li>
--   </ul>
--   
--   Any real interval contains a unique simplest rational; in particular,
--   note that <tt>0/1</tt> is the simplest rational of all.
approxRational :: RealFrac a => a -> a -> Rational

module ForeignPtr

module IO

-- | Haskell defines operations to read and write characters from and to
--   files, represented by values of type <tt>Handle</tt>. Each value of
--   this type is a <i>handle</i>: a record used by the Haskell run-time
--   system to <i>manage</i> I/O with file system objects. A handle has at
--   least the following properties:
--   
--   <ul>
--   <li>whether it manages input or output or both;</li>
--   <li>whether it is <i>open</i>, <i>closed</i> or
--   <i>semi-closed</i>;</li>
--   <li>whether the object is seekable;</li>
--   <li>whether buffering is disabled, or enabled on a line or block
--   basis;</li>
--   <li>a buffer (whose length may be zero).</li>
--   </ul>
--   
--   Most handles will also have a current I/O position indicating where
--   the next input or output operation will occur. A handle is
--   <i>readable</i> if it manages only input or both input and output;
--   likewise, it is <i>writable</i> if it manages only output or both
--   input and output. A handle is <i>open</i> when first allocated. Once
--   it is closed it can no longer be used for either input or output,
--   though an implementation cannot re-use its storage while references
--   remain to it. Handles are in the <a>Show</a> and <a>Eq</a> classes.
--   The string produced by showing a handle is system dependent; it should
--   include enough information to identify the handle for debugging. A
--   handle is equal according to <a>==</a> only to itself; no attempt is
--   made to compare the internal state of different handles for equality.
data Handle :: *
data HandlePosn :: *

-- | See <a>openFile</a>
data IOMode :: *
ReadMode :: IOMode
WriteMode :: IOMode
AppendMode :: IOMode
ReadWriteMode :: IOMode

-- | Three kinds of buffering are supported: line-buffering,
--   block-buffering or no-buffering. These modes have the following
--   effects. For output, items are written out, or <i>flushed</i>, from
--   the internal buffer according to the buffer mode:
--   
--   <ul>
--   <li><i>line-buffering</i>: the entire output buffer is flushed
--   whenever a newline is output, the buffer overflows, a <a>hFlush</a> is
--   issued, or the handle is closed.</li>
--   <li><i>block-buffering</i>: the entire buffer is written out whenever
--   it overflows, a <a>hFlush</a> is issued, or the handle is closed.</li>
--   <li><i>no-buffering</i>: output is written immediately, and never
--   stored in the buffer.</li>
--   </ul>
--   
--   An implementation is free to flush the buffer more frequently, but not
--   less frequently, than specified above. The output buffer is emptied as
--   soon as it has been written out.
--   
--   Similarly, input occurs according to the buffer mode for the handle:
--   
--   <ul>
--   <li><i>line-buffering</i>: when the buffer for the handle is not
--   empty, the next item is obtained from the buffer; otherwise, when the
--   buffer is empty, characters up to and including the next newline
--   character are read into the buffer. No characters are available until
--   the newline character is available or the buffer is full.</li>
--   <li><i>block-buffering</i>: when the buffer for the handle becomes
--   empty, the next block of data is read into the buffer.</li>
--   <li><i>no-buffering</i>: the next input item is read and returned. The
--   <a>hLookAhead</a> operation implies that even a no-buffered handle may
--   require a one-character buffer.</li>
--   </ul>
--   
--   The default buffering mode when a handle is opened is
--   implementation-dependent and may depend on the file system object
--   which is attached to that handle. For most implementations, physical
--   files will normally be block-buffered and terminals will normally be
--   line-buffered.
data BufferMode :: *

-- | buffering is disabled if possible.
NoBuffering :: BufferMode

-- | line-buffering should be enabled if possible.
LineBuffering :: BufferMode

-- | block-buffering should be enabled if possible. The size of the buffer
--   is <tt>n</tt> items if the argument is <a>Just</a> <tt>n</tt> and is
--   otherwise implementation-dependent.
BlockBuffering :: Maybe Int -> BufferMode

-- | A mode that determines the effect of <tt>hSeek</tt> <tt>hdl mode
--   i</tt>.
data SeekMode :: *

-- | the position of <tt>hdl</tt> is set to <tt>i</tt>.
AbsoluteSeek :: SeekMode

-- | the position of <tt>hdl</tt> is set to offset <tt>i</tt> from the
--   current position.
RelativeSeek :: SeekMode

-- | the position of <tt>hdl</tt> is set to offset <tt>i</tt> from the end
--   of the file.
SeekFromEnd :: SeekMode

-- | A handle managing input from the Haskell program's standard input
--   channel.
stdin :: Handle

-- | A handle managing output to the Haskell program's standard output
--   channel.
stdout :: Handle

-- | A handle managing output to the Haskell program's standard error
--   channel.
stderr :: Handle

-- | Computation <a>openFile</a> <tt>file mode</tt> allocates and returns a
--   new, open handle to manage the file <tt>file</tt>. It manages input if
--   <tt>mode</tt> is <a>ReadMode</a>, output if <tt>mode</tt> is
--   <a>WriteMode</a> or <a>AppendMode</a>, and both input and output if
--   mode is <a>ReadWriteMode</a>.
--   
--   If the file does not exist and it is opened for output, it should be
--   created as a new file. If <tt>mode</tt> is <a>WriteMode</a> and the
--   file already exists, then it should be truncated to zero length. Some
--   operating systems delete empty files, so there is no guarantee that
--   the file will exist following an <a>openFile</a> with <tt>mode</tt>
--   <a>WriteMode</a> unless it is subsequently written to successfully.
--   The handle is positioned at the end of the file if <tt>mode</tt> is
--   <a>AppendMode</a>, and otherwise at the beginning (in which case its
--   internal position is 0). The initial buffer mode is
--   implementation-dependent.
--   
--   This operation may fail with:
--   
--   <ul>
--   <li><tt>isAlreadyInUseError</tt> if the file is already open and
--   cannot be reopened;</li>
--   <li><tt>isDoesNotExistError</tt> if the file does not exist; or</li>
--   <li><tt>isPermissionError</tt> if the user does not have permission to
--   open the file.</li>
--   </ul>
--   
--   Note: if you will be working with files containing binary data, you'll
--   want to be using <a>openBinaryFile</a>.
openFile :: FilePath -> IOMode -> IO Handle

-- | Computation <a>hClose</a> <tt>hdl</tt> makes handle <tt>hdl</tt>
--   closed. Before the computation finishes, if <tt>hdl</tt> is writable
--   its buffer is flushed as for <a>hFlush</a>. Performing <a>hClose</a>
--   on a handle that has already been closed has no effect; doing so is
--   not an error. All other operations on a closed handle will fail. If
--   <a>hClose</a> fails for any reason, any further operations (apart from
--   <a>hClose</a>) on the handle will still fail as if <tt>hdl</tt> had
--   been successfully closed.
hClose :: Handle -> IO ()

-- | For a handle <tt>hdl</tt> which attached to a physical file,
--   <a>hFileSize</a> <tt>hdl</tt> returns the size of that file in 8-bit
--   bytes.
hFileSize :: Handle -> IO Integer

-- | For a readable handle <tt>hdl</tt>, <a>hIsEOF</a> <tt>hdl</tt> returns
--   <a>True</a> if no further input can be taken from <tt>hdl</tt> or for
--   a physical file, if the current I/O position is equal to the length of
--   the file. Otherwise, it returns <a>False</a>.
--   
--   NOTE: <a>hIsEOF</a> may block, because it has to attempt to read from
--   the stream to determine whether there is any more data to be read.
hIsEOF :: Handle -> IO Bool

-- | The computation <a>isEOF</a> is identical to <a>hIsEOF</a>, except
--   that it works only on <a>stdin</a>.
isEOF :: IO Bool

-- | Computation <a>hSetBuffering</a> <tt>hdl mode</tt> sets the mode of
--   buffering for handle <tt>hdl</tt> on subsequent reads and writes.
--   
--   If the buffer mode is changed from <a>BlockBuffering</a> or
--   <a>LineBuffering</a> to <a>NoBuffering</a>, then
--   
--   <ul>
--   <li>if <tt>hdl</tt> is writable, the buffer is flushed as for
--   <a>hFlush</a>;</li>
--   <li>if <tt>hdl</tt> is not writable, the contents of the buffer is
--   discarded.</li>
--   </ul>
--   
--   This operation may fail with:
--   
--   <ul>
--   <li><tt>isPermissionError</tt> if the handle has already been used for
--   reading or writing and the implementation does not allow the buffering
--   mode to be changed.</li>
--   </ul>
hSetBuffering :: Handle -> BufferMode -> IO ()

-- | Computation <a>hGetBuffering</a> <tt>hdl</tt> returns the current
--   buffering mode for <tt>hdl</tt>.
hGetBuffering :: Handle -> IO BufferMode

-- | The action <a>hFlush</a> <tt>hdl</tt> causes any items buffered for
--   output in handle <tt>hdl</tt> to be sent immediately to the operating
--   system.
--   
--   This operation may fail with:
--   
--   <ul>
--   <li><tt>isFullError</tt> if the device is full;</li>
--   <li><tt>isPermissionError</tt> if a system resource limit would be
--   exceeded. It is unspecified whether the characters in the buffer are
--   discarded or retained under these circumstances.</li>
--   </ul>
hFlush :: Handle -> IO ()

-- | Computation <a>hGetPosn</a> <tt>hdl</tt> returns the current I/O
--   position of <tt>hdl</tt> as a value of the abstract type
--   <a>HandlePosn</a>.
hGetPosn :: Handle -> IO HandlePosn

-- | If a call to <a>hGetPosn</a> <tt>hdl</tt> returns a position
--   <tt>p</tt>, then computation <a>hSetPosn</a> <tt>p</tt> sets the
--   position of <tt>hdl</tt> to the position it held at the time of the
--   call to <a>hGetPosn</a>.
--   
--   This operation may fail with:
--   
--   <ul>
--   <li><tt>isPermissionError</tt> if a system resource limit would be
--   exceeded.</li>
--   </ul>
hSetPosn :: HandlePosn -> IO ()

-- | Computation <a>hSeek</a> <tt>hdl mode i</tt> sets the position of
--   handle <tt>hdl</tt> depending on <tt>mode</tt>. The offset <tt>i</tt>
--   is given in terms of 8-bit bytes.
--   
--   If <tt>hdl</tt> is block- or line-buffered, then seeking to a position
--   which is not in the current buffer will first cause any items in the
--   output buffer to be written to the device, and then cause the input
--   buffer to be discarded. Some handles may not be seekable (see
--   <a>hIsSeekable</a>), or only support a subset of the possible
--   positioning operations (for instance, it may only be possible to seek
--   to the end of a tape, or to a positive offset from the beginning or
--   current position). It is not possible to set a negative I/O position,
--   or for a physical file, an I/O position beyond the current
--   end-of-file.
--   
--   This operation may fail with:
--   
--   <ul>
--   <li><tt>isIllegalOperationError</tt> if the Handle is not seekable, or
--   does not support the requested seek mode.</li>
--   <li><tt>isPermissionError</tt> if a system resource limit would be
--   exceeded.</li>
--   </ul>
hSeek :: Handle -> SeekMode -> Integer -> IO ()

-- | Computation <a>hWaitForInput</a> <tt>hdl t</tt> waits until input is
--   available on handle <tt>hdl</tt>. It returns <a>True</a> as soon as
--   input is available on <tt>hdl</tt>, or <a>False</a> if no input is
--   available within <tt>t</tt> milliseconds. Note that
--   <a>hWaitForInput</a> waits until one or more full <i>characters</i>
--   are available, which means that it needs to do decoding, and hence may
--   fail with a decoding error.
--   
--   If <tt>t</tt> is less than zero, then <tt>hWaitForInput</tt> waits
--   indefinitely.
--   
--   This operation may fail with:
--   
--   <ul>
--   <li><a>isEOFError</a> if the end of file has been reached.</li>
--   <li>a decoding error, if the input begins with an invalid byte
--   sequence in this Handle's encoding.</li>
--   </ul>
--   
--   NOTE for GHC users: unless you use the <tt>-threaded</tt> flag,
--   <tt>hWaitForInput t</tt> where <tt>t &gt;= 0</tt> will block all other
--   Haskell threads for the duration of the call. It behaves like a
--   <tt>safe</tt> foreign call in this respect.
hWaitForInput :: Handle -> Int -> IO Bool

-- | Computation <a>hReady</a> <tt>hdl</tt> indicates whether at least one
--   item is available for input from handle <tt>hdl</tt>.
--   
--   This operation may fail with:
--   
--   <ul>
--   <li><a>isEOFError</a> if the end of file has been reached.</li>
--   </ul>
hReady :: Handle -> IO Bool

-- | Computation <a>hGetChar</a> <tt>hdl</tt> reads a character from the
--   file or channel managed by <tt>hdl</tt>, blocking until a character is
--   available.
--   
--   This operation may fail with:
--   
--   <ul>
--   <li><a>isEOFError</a> if the end of file has been reached.</li>
--   </ul>
hGetChar :: Handle -> IO Char

-- | Computation <a>hGetLine</a> <tt>hdl</tt> reads a line from the file or
--   channel managed by <tt>hdl</tt>.
--   
--   This operation may fail with:
--   
--   <ul>
--   <li><a>isEOFError</a> if the end of file is encountered when reading
--   the <i>first</i> character of the line.</li>
--   </ul>
--   
--   If <a>hGetLine</a> encounters end-of-file at any other point while
--   reading in a line, it is treated as a line terminator and the
--   (partial) line is returned.
hGetLine :: Handle -> IO String

-- | Computation <a>hLookAhead</a> returns the next character from the
--   handle without removing it from the input buffer, blocking until a
--   character is available.
--   
--   This operation may fail with:
--   
--   <ul>
--   <li><tt>isEOFError</tt> if the end of file has been reached.</li>
--   </ul>
hLookAhead :: Handle -> IO Char

-- | Computation <a>hGetContents</a> <tt>hdl</tt> returns the list of
--   characters corresponding to the unread portion of the channel or file
--   managed by <tt>hdl</tt>, which is put into an intermediate state,
--   <i>semi-closed</i>. In this state, <tt>hdl</tt> is effectively closed,
--   but items are read from <tt>hdl</tt> on demand and accumulated in a
--   special list returned by <a>hGetContents</a> <tt>hdl</tt>.
--   
--   Any operation that fails because a handle is closed, also fails if a
--   handle is semi-closed. The only exception is <tt>hClose</tt>. A
--   semi-closed handle becomes closed:
--   
--   <ul>
--   <li>if <tt>hClose</tt> is applied to it;</li>
--   <li>if an I/O error occurs when reading an item from the handle;</li>
--   <li>or once the entire contents of the handle has been read.</li>
--   </ul>
--   
--   Once a semi-closed handle becomes closed, the contents of the
--   associated list becomes fixed. The contents of this final list is only
--   partially specified: it will contain at least all the items of the
--   stream that were evaluated prior to the handle becoming closed.
--   
--   Any I/O errors encountered while a handle is semi-closed are simply
--   discarded.
--   
--   This operation may fail with:
--   
--   <ul>
--   <li><a>isEOFError</a> if the end of file has been reached.</li>
--   </ul>
hGetContents :: Handle -> IO String

-- | Computation <a>hPutChar</a> <tt>hdl ch</tt> writes the character
--   <tt>ch</tt> to the file or channel managed by <tt>hdl</tt>. Characters
--   may be buffered if buffering is enabled for <tt>hdl</tt>.
--   
--   This operation may fail with:
--   
--   <ul>
--   <li><a>isFullError</a> if the device is full; or</li>
--   <li><a>isPermissionError</a> if another system resource limit would be
--   exceeded.</li>
--   </ul>
hPutChar :: Handle -> Char -> IO ()

-- | Computation <a>hPutStr</a> <tt>hdl s</tt> writes the string <tt>s</tt>
--   to the file or channel managed by <tt>hdl</tt>.
--   
--   This operation may fail with:
--   
--   <ul>
--   <li><a>isFullError</a> if the device is full; or</li>
--   <li><a>isPermissionError</a> if another system resource limit would be
--   exceeded.</li>
--   </ul>
hPutStr :: Handle -> String -> IO ()

-- | The same as <a>hPutStr</a>, but adds a newline character.
hPutStrLn :: Handle -> String -> IO ()

-- | Computation <a>hPrint</a> <tt>hdl t</tt> writes the string
--   representation of <tt>t</tt> given by the <a>shows</a> function to the
--   file or channel managed by <tt>hdl</tt> and appends a newline.
--   
--   This operation may fail with:
--   
--   <ul>
--   <li><a>isFullError</a> if the device is full; or</li>
--   <li><a>isPermissionError</a> if another system resource limit would be
--   exceeded.</li>
--   </ul>
hPrint :: Show a => Handle -> a -> IO ()
hIsOpen :: Handle -> IO Bool
hIsClosed :: Handle -> IO Bool
hIsReadable :: Handle -> IO Bool
hIsWritable :: Handle -> IO Bool
hIsSeekable :: Handle -> IO Bool

-- | An error indicating that an <a>IO</a> operation failed because one of
--   its arguments already exists.
isAlreadyExistsError :: IOError -> Bool

-- | An error indicating that an <a>IO</a> operation failed because one of
--   its arguments does not exist.
isDoesNotExistError :: IOError -> Bool

-- | An error indicating that an <a>IO</a> operation failed because one of
--   its arguments is a single-use resource, which is already being used
--   (for example, opening the same file twice for writing might give this
--   error).
isAlreadyInUseError :: IOError -> Bool

-- | An error indicating that an <a>IO</a> operation failed because the
--   device is full.
isFullError :: IOError -> Bool

-- | An error indicating that an <a>IO</a> operation failed because the end
--   of file has been reached.
isEOFError :: IOError -> Bool

-- | An error indicating that an <a>IO</a> operation failed because the
--   operation was not possible. Any computation which returns an <a>IO</a>
--   result may fail with <a>isIllegalOperation</a>. In some cases, an
--   implementation will not be able to distinguish between the possible
--   error causes. In this case it should fail with
--   <a>isIllegalOperation</a>.
isIllegalOperation :: IOError -> Bool

-- | An error indicating that an <a>IO</a> operation failed because the
--   user does not have sufficient operating system privilege to perform
--   that operation.
isPermissionError :: IOError -> Bool

-- | A programmer-defined error value constructed using <a>userError</a>.
isUserError :: IOError -> Bool
ioeGetErrorString :: IOError -> String
ioeGetHandle :: IOError -> Maybe Handle
ioeGetFileName :: IOError -> Maybe FilePath

-- | The construct <a>try</a> <tt>comp</tt> exposes IO errors which occur
--   within a computation, and which are not fully handled.
--   
--   Non-I/O exceptions are not caught by this variant; to catch all
--   exceptions, use <a>try</a> from <a>Control.Exception</a>.
try :: IO a -> IO (Either IOError a)

-- | The <a>bracket</a> function captures a common allocate, compute,
--   deallocate idiom in which the deallocation step must occur even in the
--   case of an error during computation. This is similar to
--   try-catch-finally in Java.
--   
--   This version handles only IO errors, as defined by Haskell 98. The
--   version of <tt>bracket</tt> in <a>Control.Exception</a> handles all
--   exceptions, and should be used instead.
bracket :: IO a -> (a -> IO b) -> (a -> IO c) -> IO c

-- | A variant of <a>bracket</a> where the middle computation doesn't want
--   <tt>x</tt>.
--   
--   This version handles only IO errors, as defined by Haskell 98. The
--   version of <tt>bracket_</tt> in <a>Control.Exception</a> handles all
--   exceptions, and should be used instead.
bracket_ :: IO a -> (a -> IO b) -> IO c -> IO c
data IO a :: * -> *

-- | File and directory names are values of type <a>String</a>, 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 FilePath = String

-- | The Haskell 98 type for exceptions in the <a>IO</a> monad. Any I/O
--   operation may raise an <a>IOError</a> instead of returning a result.
--   For a more general type of exception, including also those that arise
--   in pure code, see <a>Control.Exception.Exception</a>.
--   
--   In Haskell 98, this is an opaque type.
type IOError = IOException

-- | Raise an <a>IOError</a> in the <a>IO</a> monad.
ioError :: IOError -> IO a

-- | Construct an <a>IOError</a> value with a string describing the error.
--   The <a>fail</a> method of the <a>IO</a> instance of the <a>Monad</a>
--   class raises a <a>userError</a>, thus:
--   
--   <pre>
--   instance Monad IO where 
--     ...
--     fail s = ioError (userError s)
--   </pre>
userError :: String -> IOError

-- | The <a>catch</a> function establishes a handler that receives any
--   <a>IOError</a> raised in the action protected by <a>catch</a>. An
--   <a>IOError</a> is caught by the most recent handler established by one
--   of the exception handling functions. These handlers are not selective:
--   all <a>IOError</a>s are caught. Exception propagation must be
--   explicitly provided in a handler by re-raising any unwanted
--   exceptions. For example, in
--   
--   <pre>
--   f = catch g (\e -&gt; if IO.isEOFError e then return [] else ioError e)
--   </pre>
--   
--   the function <tt>f</tt> returns <tt>[]</tt> when an end-of-file
--   exception (cf. <a>isEOFError</a>) occurs in <tt>g</tt>; otherwise, the
--   exception is propagated to the next outer handler.
--   
--   When an exception propagates outside the main program, the Haskell
--   system prints the associated <a>IOError</a> value and exits the
--   program.
--   
--   Non-I/O exceptions are not caught by this variant; to catch all
--   exceptions, use <a>catch</a> from <a>Control.Exception</a>.
catch :: IO a -> (IOError -> IO a) -> IO a

-- | The <a>interact</a> function takes a function of type
--   <tt>String-&gt;String</tt> 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.
interact :: (String -> String) -> IO ()

-- | Write a character to the standard output device (same as
--   <a>hPutChar</a> <a>stdout</a>).
putChar :: Char -> IO ()

-- | Write a string to the standard output device (same as <a>hPutStr</a>
--   <a>stdout</a>).
putStr :: String -> IO ()

-- | The same as <a>putStr</a>, but adds a newline character.
putStrLn :: String -> IO ()

-- | The <a>print</a> function outputs a value of any printable type to the
--   standard output device. Printable types are those that are instances
--   of class <a>Show</a>; <a>print</a> converts values to strings for
--   output using the <a>show</a> operation and adds a newline.
--   
--   For example, a program to print the first 20 integers and their powers
--   of 2 could be written as:
--   
--   <pre>
--   main = print ([(n, 2^n) | n &lt;- [0..19]])
--   </pre>
print :: Show a => a -> IO ()

-- | Read a character from the standard input device (same as
--   <a>hGetChar</a> <a>stdin</a>).
getChar :: IO Char

-- | Read a line from the standard input device (same as <a>hGetLine</a>
--   <a>stdin</a>).
getLine :: IO String

-- | The <a>getContents</a> operation returns all user input as a single
--   string, which is read lazily as it is needed (same as
--   <a>hGetContents</a> <a>stdin</a>).
getContents :: IO String

-- | The <a>readFile</a> function reads a file and returns the contents of
--   the file as a string. The file is read lazily, on demand, as with
--   <a>getContents</a>.
readFile :: FilePath -> IO String

-- | The computation <a>writeFile</a> <tt>file str</tt> function writes the
--   string <tt>str</tt>, to the file <tt>file</tt>.
writeFile :: FilePath -> String -> IO ()

-- | The computation <a>appendFile</a> <tt>file str</tt> function appends
--   the string <tt>str</tt>, to the file <tt>file</tt>.
--   
--   Note that <a>writeFile</a> and <a>appendFile</a> write a literal
--   string to a file. To write a value of any printable type, as with
--   <a>print</a>, use the <a>show</a> function to convert the value to a
--   string first.
--   
--   <pre>
--   main = appendFile "squares" (show [(x,x*x) | x &lt;- [0,0.1..2]])
--   </pre>
appendFile :: FilePath -> String -> IO ()

-- | The <a>readIO</a> function is similar to <a>read</a> except that it
--   signals parse failure to the <a>IO</a> monad instead of terminating
--   the program.
readIO :: Read a => String -> IO a

-- | The <a>readLn</a> function combines <a>getLine</a> and <a>readIO</a>.
readLn :: Read a => IO a

module Char

-- | Selects the first 128 characters of the Unicode character set,
--   corresponding to the ASCII character set.
isAscii :: Char -> Bool

-- | Selects the first 256 characters of the Unicode character set,
--   corresponding to the ISO 8859-1 (Latin-1) character set.
isLatin1 :: Char -> Bool

-- | Selects control characters, which are the non-printing characters of
--   the Latin-1 subset of Unicode.
isControl :: Char -> Bool

-- | Selects printable Unicode characters (letters, numbers, marks,
--   punctuation, symbols and spaces).
isPrint :: Char -> Bool

-- | Returns <a>True</a> for any Unicode space character, and the control
--   characters <tt>\t</tt>, <tt>\n</tt>, <tt>\r</tt>, <tt>\f</tt>,
--   <tt>\v</tt>.
isSpace :: Char -> Bool

-- | Selects upper-case or title-case alphabetic Unicode characters
--   (letters). Title case is used by a small number of letter ligatures
--   like the single-character form of <i>Lj</i>.
isUpper :: Char -> Bool

-- | Selects lower-case alphabetic Unicode characters (letters).
isLower :: Char -> Bool

-- | Selects alphabetic Unicode characters (lower-case, upper-case and
--   title-case letters, plus letters of caseless scripts and modifiers
--   letters). This function is equivalent to <a>isLetter</a>.
isAlpha :: Char -> Bool

-- | Selects ASCII digits, i.e. <tt>'0'</tt>..<tt>'9'</tt>.
isDigit :: Char -> Bool

-- | Selects ASCII octal digits, i.e. <tt>'0'</tt>..<tt>'7'</tt>.
isOctDigit :: Char -> Bool

-- | Selects ASCII hexadecimal digits, i.e. <tt>'0'</tt>..<tt>'9'</tt>,
--   <tt>'a'</tt>..<tt>'f'</tt>, <tt>'A'</tt>..<tt>'F'</tt>.
isHexDigit :: Char -> Bool

-- | Selects alphabetic or numeric digit Unicode characters.
--   
--   Note that numeric digits outside the ASCII range are selected by this
--   function but not by <a>isDigit</a>. Such digits may be part of
--   identifiers but are not used by the printer and reader to represent
--   numbers.
isAlphaNum :: Char -> Bool

-- | Convert a single digit <a>Char</a> to the corresponding <a>Int</a>.
--   This function fails unless its argument satisfies <a>isHexDigit</a>,
--   but recognises both upper and lower-case hexadecimal digits (i.e.
--   <tt>'0'</tt>..<tt>'9'</tt>, <tt>'a'</tt>..<tt>'f'</tt>,
--   <tt>'A'</tt>..<tt>'F'</tt>).
digitToInt :: Char -> Int

-- | Convert an <a>Int</a> in the range <tt>0</tt>..<tt>15</tt> to the
--   corresponding single digit <a>Char</a>. This function fails on other
--   inputs, and generates lower-case hexadecimal digits.
intToDigit :: Int -> Char

-- | Convert a letter to the corresponding upper-case letter, if any. Any
--   other character is returned unchanged.
toUpper :: Char -> Char

-- | Convert a letter to the corresponding lower-case letter, if any. Any
--   other character is returned unchanged.
toLower :: Char -> Char

-- | The <a>fromEnum</a> method restricted to the type <a>Char</a>.
ord :: Char -> Int

-- | The <a>toEnum</a> method restricted to the type <a>Char</a>.
chr :: Int -> Char

-- | Read a string representation of a character, using Haskell
--   source-language escape conventions, and convert it to the character
--   that it encodes. For example:
--   
--   <pre>
--   readLitChar "\\nHello"  =  [('\n', "Hello")]
--   </pre>
readLitChar :: ReadS Char

-- | Convert a character to a string using only printable characters, using
--   Haskell source-language escape conventions. For example:
--   
--   <pre>
--   showLitChar '\n' s  =  "\\n" ++ s
--   </pre>
showLitChar :: Char -> ShowS

-- | Read a string representation of a character, using Haskell
--   source-language escape conventions. For example:
--   
--   <pre>
--   lexLitChar  "\\nHello"  =  [("\\n", "Hello")]
--   </pre>
lexLitChar :: ReadS String
data Char :: *

-- | A <a>String</a> is a list of characters. String constants in Haskell
--   are values of type <a>String</a>.
type String = [Char]

module Int

module Ix

-- | The <a>Ix</a> class is used to map a contiguous subrange of values in
--   a type onto integers. It is used primarily for array indexing (see the
--   array package).
--   
--   The first argument <tt>(l,u)</tt> of each of these operations is a
--   pair specifying the lower and upper bounds of a contiguous subrange of
--   values.
--   
--   An implementation is entitled to assume the following laws about these
--   operations:
--   
--   <ul>
--   <li><tt><a>inRange</a> (l,u) i == <a>elem</a> i (<a>range</a>
--   (l,u))</tt> <tt> </tt></li>
--   <li><tt><a>range</a> (l,u) <a>!!</a> <a>index</a> (l,u) i == i</tt>,
--   when <tt><a>inRange</a> (l,u) i</tt></li>
--   <li><tt><a>map</a> (<a>index</a> (l,u)) (<a>range</a> (l,u))) ==
--   [0..<a>rangeSize</a> (l,u)-1]</tt> <tt> </tt></li>
--   <li><tt><a>rangeSize</a> (l,u) == <a>length</a> (<a>range</a>
--   (l,u))</tt> <tt> </tt></li>
--   </ul>
--   
--   Minimal complete instance: <a>range</a>, <a>index</a> and
--   <a>inRange</a>.
class Ord a => Ix a
range :: Ix a => (a, a) -> [a]
index :: Ix a => (a, a) -> a -> Int
inRange :: Ix a => (a, a) -> a -> Bool
rangeSize :: Ix a => (a, a) -> Int

-- | The size of the subrange defined by a bounding pair.
rangeSize :: Ix a => (a, a) -> Int

module Array

-- | The type of immutable non-strict (boxed) arrays with indices in
--   <tt>i</tt> and elements in <tt>e</tt>.
data Array i e :: * -> * -> *

-- | Construct an array with the specified bounds and containing values for
--   given indices within these bounds.
--   
--   The array is undefined (i.e. bottom) if any index in the list is out
--   of bounds. The Haskell 98 Report further specifies that if any two
--   associations in the list have the same index, the value at that index
--   is undefined (i.e. bottom). However in GHC's implementation, the value
--   at such an index is the value part of the last association with that
--   index in the list.
--   
--   Because the indices must be checked for these errors, <a>array</a> is
--   strict in the bounds argument and in the indices of the association
--   list, but non-strict in the values. Thus, recurrences such as the
--   following are possible:
--   
--   <pre>
--   a = array (1,100) ((1,1) : [(i, i * a!(i-1)) | i &lt;- [2..100]])
--   </pre>
--   
--   Not every index within the bounds of the array need appear in the
--   association list, but the values associated with indices that do not
--   appear will be undefined (i.e. bottom).
--   
--   If, in any dimension, the lower bound is greater than the upper bound,
--   then the array is legal, but empty. Indexing an empty array always
--   gives an array-bounds error, but <a>bounds</a> still yields the bounds
--   with which the array was constructed.
array :: Ix i => (i, i) -> [(i, e)] -> Array i e

-- | Construct an array from a pair of bounds and a list of values in index
--   order.
listArray :: Ix i => (i, i) -> [e] -> Array i e

-- | The value at the given index in an array.
(!) :: Ix i => Array i e -> i -> e

-- | The bounds with which an array was constructed.
bounds :: Ix i => Array i e -> (i, i)

-- | The list of indices of an array in ascending order.
indices :: Ix i => Array i e -> [i]

-- | The list of elements of an array in index order.
elems :: Ix i => Array i e -> [e]

-- | The list of associations of an array in index order.
assocs :: Ix i => Array i e -> [(i, e)]

-- | The <a>accumArray</a> function deals with repeated indices in the
--   association list using an <i>accumulating function</i> which combines
--   the values of associations with the same index. For example, given a
--   list of values of some index type, <tt>hist</tt> produces a histogram
--   of the number of occurrences of each index within a specified range:
--   
--   <pre>
--   hist :: (Ix a, Num b) =&gt; (a,a) -&gt; [a] -&gt; Array a b
--   hist bnds is = accumArray (+) 0 bnds [(i, 1) | i&lt;-is, inRange bnds i]
--   </pre>
--   
--   If the accumulating function is strict, then <a>accumArray</a> is
--   strict in the values, as well as the indices, in the association list.
--   Thus, unlike ordinary arrays built with <a>array</a>, accumulated
--   arrays should not in general be recursive.
accumArray :: Ix i => (e -> a -> e) -> e -> (i, i) -> [(i, a)] -> Array i e

-- | Constructs an array identical to the first argument except that it has
--   been updated by the associations in the right argument. For example,
--   if <tt>m</tt> is a 1-origin, <tt>n</tt> by <tt>n</tt> matrix, then
--   
--   <pre>
--   m//[((i,i), 0) | i &lt;- [1..n]]
--   </pre>
--   
--   is the same matrix, except with the diagonal zeroed.
--   
--   Repeated indices in the association list are handled as for
--   <a>array</a>: Haskell 98 specifies that the resulting array is
--   undefined (i.e. bottom), but GHC's implementation uses the last
--   association for each index.
(//) :: Ix i => Array i e -> [(i, e)] -> Array i e

-- | <tt><a>accum</a> f</tt> takes an array and an association list and
--   accumulates pairs from the list into the array with the accumulating
--   function <tt>f</tt>. Thus <a>accumArray</a> can be defined using
--   <a>accum</a>:
--   
--   <pre>
--   accumArray f z b = accum f (array b [(i, z) | i &lt;- range b])
--   </pre>
accum :: Ix i => (e -> a -> e) -> Array i e -> [(i, a)] -> Array i e

-- | <a>ixmap</a> allows for transformations on array indices. It may be
--   thought of as providing function composition on the right with the
--   mapping that the original array embodies.
--   
--   A similar transformation of array values may be achieved using
--   <a>fmap</a> from the <a>Array</a> instance of the <a>Functor</a>
--   class.
ixmap :: (Ix i, Ix j) => (i, i) -> (i -> j) -> Array j e -> Array i e
