Safe Haskell | Safe-Inferred |
---|---|

Language | Haskell98 |

The only point of this module is to reexport items that we want from the standard Prelude.

- (!!) :: [a] -> Int -> a
- ($) :: (a -> b) -> a -> b
- ($!) :: (a -> b) -> a -> b
- (&&) :: Bool -> Bool -> Bool
- (++) :: [a] -> [a] -> [a]
- (.) :: (b -> c) -> (a -> b) -> a -> c
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- data Bool :: *
- class Bounded a where
- data Char :: *
- data Either a b :: * -> * -> *
- class Enum a where
- succ :: a -> a
- pred :: a -> a
- toEnum :: Int -> a
- fromEnum :: a -> Int
- enumFrom :: a -> [a]
- enumFromThen :: a -> a -> [a]
- enumFromTo :: a -> a -> [a]
- enumFromThenTo :: a -> a -> a -> [a]

- class Eq a where
- type FilePath = String
- class Functor f where
- fmap :: (a -> b) -> f a -> f b

- data IO a :: * -> *
- type IOError = IOException
- data Maybe a :: * -> *
- class Monad m where
- class Eq a => Ord a where
- data Ordering :: *
- class Read a where
- type ReadS a = String -> [(a, String)]
- class Show a where
- type ShowS = String -> String
- type String = [Char]
- all :: (a -> Bool) -> [a] -> Bool
- and :: [Bool] -> Bool
- any :: (a -> Bool) -> [a] -> Bool
- appendFile :: FilePath -> String -> IO ()
- asTypeOf :: a -> a -> a
- break :: (a -> Bool) -> [a] -> ([a], [a])
- concat :: [[a]] -> [a]
- concatMap :: (a -> [b]) -> [a] -> [b]
- const :: a -> b -> a
- curry :: ((a, b) -> c) -> a -> b -> c
- cycle :: [a] -> [a]
- drop :: Int -> [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- elem :: Eq a => a -> [a] -> Bool
- error :: [Char] -> a
- filter :: (a -> Bool) -> [a] -> [a]
- flip :: (a -> b -> c) -> b -> a -> c
- foldl :: (b -> a -> b) -> b -> [a] -> b
- foldl1 :: (a -> a -> a) -> [a] -> a
- foldr :: (a -> b -> b) -> b -> [a] -> b
- foldr1 :: (a -> a -> a) -> [a] -> a
- fst :: (a, b) -> a
- getChar :: IO Char
- getContents :: IO String
- getLine :: IO String
- head :: [a] -> a
- id :: a -> a
- init :: [a] -> [a]
- interact :: (String -> String) -> IO ()
- ioError :: IOError -> IO a
- iterate :: (a -> a) -> a -> [a]
- last :: [a] -> a
- length :: [a] -> Int
- lex :: ReadS String
- lines :: String -> [String]
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- map :: (a -> b) -> [a] -> [b]
- mapM :: Monad m => (a -> m b) -> [a] -> m [b]
- mapM_ :: Monad m => (a -> m b) -> [a] -> m ()
- maximum :: Ord a => [a] -> a
- maybe :: b -> (a -> b) -> Maybe a -> b
- minimum :: Ord a => [a] -> a
- not :: Bool -> Bool
- notElem :: Eq a => a -> [a] -> Bool
- null :: [a] -> Bool
- or :: [Bool] -> Bool
- otherwise :: Bool
- print :: Show a => a -> IO ()
- putChar :: Char -> IO ()
- putStr :: String -> IO ()
- putStrLn :: String -> IO ()
- read :: Read a => String -> a
- readFile :: FilePath -> IO String
- readIO :: Read a => String -> IO a
- readLn :: Read a => IO a
- readParen :: Bool -> ReadS a -> ReadS a
- reads :: Read a => ReadS a
- realToFrac :: (Real a, Fractional b) => a -> b
- repeat :: a -> [a]
- replicate :: Int -> a -> [a]
- reverse :: [a] -> [a]
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- seq :: a -> b -> b
- sequence :: Monad m => [m a] -> m [a]
- sequence_ :: Monad m => [m a] -> m ()
- showChar :: Char -> ShowS
- showParen :: Bool -> ShowS -> ShowS
- showString :: String -> ShowS
- shows :: Show a => a -> ShowS
- snd :: (a, b) -> b
- span :: (a -> Bool) -> [a] -> ([a], [a])
- splitAt :: Int -> [a] -> ([a], [a])
- tail :: [a] -> [a]
- take :: Int -> [a] -> [a]
- takeWhile :: (a -> Bool) -> [a] -> [a]
- uncurry :: (a -> b -> c) -> (a, b) -> c
- undefined :: a
- unlines :: [String] -> String
- until :: (a -> Bool) -> (a -> a) -> a -> a
- unwords :: [String] -> String
- unzip :: [(a, b)] -> ([a], [b])
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- userError :: String -> IOError
- words :: String -> [String]
- writeFile :: FilePath -> String -> IO ()
- zip :: [a] -> [b] -> [(a, b)]
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- (||) :: Bool -> Bool -> Bool
- catch :: IO a -> (IOError -> IO a) -> IO a
- ifThenElse :: Bool -> a -> a -> a

# Documentation

(!!) :: [a] -> Int -> a infixl 9

List index (subscript) operator, starting from 0.
It is an instance of the more general `genericIndex`

,
which takes an index of any integral type.

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

Application operator. This operator is redundant, since ordinary
application `(f x)`

means the same as `(f `

. However, `$`

x)`$`

has
low, right-associative binding precedence, so it sometimes allows
parentheses to be omitted; for example:

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

It is also useful in higher-order situations, such as

,
or `map`

(`$`

0) xs

.`zipWith`

(`$`

) fs xs

(++) :: [a] -> [a] -> [a] infixr 5

Append two lists, i.e.,

[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn] [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]

If the first list is not finite, the result is the first list.

(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9

Function composition.

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1

Same as `>>=`

, but with the arguments interchanged.

data Bool :: *

class Bounded a where

The `Bounded`

class is used to name the upper and lower limits of a
type. `Ord`

is not a superclass of `Bounded`

since types that are not
totally ordered may also have upper and lower bounds.

The `Bounded`

class may be derived for any enumeration type;
`minBound`

is the first constructor listed in the `data`

declaration
and `maxBound`

is the last.
`Bounded`

may also be derived for single-constructor datatypes whose
constituent types are in `Bounded`

.

data Char :: *

The character type `Char`

is an enumeration whose values represent
Unicode (or equivalently ISO/IEC 10646) characters (see
http://www.unicode.org/ for details). This set extends the ISO 8859-1
(Latin-1) character set (the first 256 characters), which is itself an extension
of the ASCII character set (the first 128 characters). A character literal in
Haskell has type `Char`

.

To convert a `Char`

to or from the corresponding `Int`

value defined
by Unicode, use `toEnum`

and `fromEnum`

from the
`Enum`

class respectively (or equivalently `ord`

and `chr`

).

Bounded Char | |

Enum Char | |

Eq Char | |

Ord Char | |

Read Char | |

Show Char | |

Ix Char | |

Generic Char | |

Arbitrary Char | |

CoArbitrary Char | |

Storable Char | |

NFData Char | |

Random Char | |

ErrorList Char | |

Monad m => Stream ByteString m Char | |

Monad m => Stream ByteString m Char | |

Monad m => Stream Text m Char | |

Monad m => Stream Text m Char | |

type Rep Char = D1 D_Char (C1 C_Char (S1 NoSelector (Rec0 Char))) |

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

The `Either`

type represents values with two possibilities: a value of
type

is either `Either`

a b

or `Left`

a

.`Right`

b

The `Either`

type is sometimes used to represent a value which is
either correct or an error; by convention, the `Left`

constructor is
used to hold an error value and the `Right`

constructor is used to
hold a correct value (mnemonic: "right" also means "correct").

Error e => Alternative (Either e) | |

Monad (Either e) | |

Functor (Either a) | |

Error e => MonadPlus (Either e) | |

Applicative (Either e) | |

Foldable (Either a) | |

Generic1 (Either a) | |

(Eq a, Eq b) => Eq (Either a b) | |

(Ord a, Ord b) => Ord (Either a b) | |

(Read a, Read b) => Read (Either a b) | |

(Show a, Show b) => Show (Either a b) | |

Generic (Either a b) | |

(Arbitrary a, Arbitrary b) => Arbitrary (Either a b) | |

(CoArbitrary a, CoArbitrary b) => CoArbitrary (Either a b) | |

(NFData a, NFData b) => NFData (Either a b) | |

Typeable (* -> * -> *) Either | |

type Rep1 (Either a) = D1 D1Either ((:+:) (C1 C1_0Either (S1 NoSelector (Rec0 a))) (C1 C1_1Either (S1 NoSelector Par1))) | |

type Rep (Either a b) = D1 D1Either ((:+:) (C1 C1_0Either (S1 NoSelector (Rec0 a))) (C1 C1_1Either (S1 NoSelector (Rec0 b)))) | |

type (==) (Either k k1) a b = EqEither k k1 a b |

class Enum a where

Class `Enum`

defines operations on sequentially ordered types.

The `enumFrom`

... methods are used in Haskell's translation of
arithmetic sequences.

Instances of `Enum`

may be derived for any enumeration type (types
whose constructors have no fields). The nullary constructors are
assumed to be numbered left-to-right by `fromEnum`

from `0`

through `n-1`

.
See Chapter 10 of the *Haskell Report* for more details.

For any type that is an instance of class `Bounded`

as well as `Enum`

,
the following should hold:

- The calls

and`succ`

`maxBound`

should result in a runtime error.`pred`

`minBound`

`fromEnum`

and`toEnum`

should give a runtime error if the result value is not representable in the result type. For example,

is an error.`toEnum`

7 ::`Bool`

`enumFrom`

and`enumFromThen`

should be defined with an implicit bound, thus:

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

succ :: a -> a

the successor of a value. For numeric types, `succ`

adds 1.

pred :: a -> a

the predecessor of a value. For numeric types, `pred`

subtracts 1.

Convert from an `Int`

.

Convert to an `Int`

.
It is implementation-dependent what `fromEnum`

returns when
applied to a value that is too large to fit in an `Int`

.

enumFrom :: a -> [a]

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

.

enumFromThen :: a -> a -> [a]

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

.

enumFromTo :: a -> a -> [a]

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

.

enumFromThenTo :: a -> a -> a -> [a]

Used in Haskell's translation of `[n,n'..m]`

.

Enum Bool | |

Enum Char | |

Enum Double | |

Enum Float | |

Enum Int | |

Enum Int8 | |

Enum Int16 | |

Enum Int32 | |

Enum Int64 | |

Enum Integer | |

Enum Ordering | |

Enum Word | |

Enum Word8 | |

Enum Word16 | |

Enum Word32 | |

Enum Word64 | |

Enum () | |

Enum GeneralCategory | |

Enum CChar | |

Enum CSChar | |

Enum CUChar | |

Enum CShort | |

Enum CUShort | |

Enum CInt | |

Enum CUInt | |

Enum CLong | |

Enum CULong | |

Enum CLLong | |

Enum CULLong | |

Enum CFloat | |

Enum CDouble | |

Enum CPtrdiff | |

Enum CSize | |

Enum CWchar | |

Enum CSigAtomic | |

Enum CClock | |

Enum CTime | |

Enum CUSeconds | |

Enum CSUSeconds | |

Enum CIntPtr | |

Enum CUIntPtr | |

Enum CIntMax | |

Enum CUIntMax | |

Enum Message | |

Enum NominalDiffTime | |

Enum Day | |

Enum Dimension | |

Enum T | |

Integral a => Enum (Ratio a) | |

(Enum a, C a) => Enum (T a) | |

(Ord a, Num a, Enum a) => Enum (T a) | |

Enum a => Enum (T a) | |

Enum a => Enum (T a) | |

(~) k a b => Enum ((:~:) k a b) |

class Eq a where

The `Eq`

class defines equality (`==`

) and inequality (`/=`

).
All the basic datatypes exported by the Prelude are instances of `Eq`

,
and `Eq`

may be derived for any datatype whose constituents are also
instances of `Eq`

.

Eq Bool | |

Eq Char | |

Eq Double | |

Eq Float | |

Eq Int | |

Eq Int8 | |

Eq Int16 | |

Eq Int32 | |

Eq Int64 | |

Eq Integer | |

Eq Ordering | |

Eq Word | |

Eq Word8 | |

Eq Word16 | |

Eq Word32 | |

Eq Word64 | |

Eq () | |

Eq SpecConstrAnnotation | |

Eq AsyncException | |

Eq ArrayException | |

Eq ExitCode | |

Eq IOErrorType | |

Eq GeneralCategory | |

Eq CChar | |

Eq CSChar | |

Eq CUChar | |

Eq CShort | |

Eq CUShort | |

Eq CInt | |

Eq CUInt | |

Eq CLong | |

Eq CULong | |

Eq CLLong | |

Eq CULLong | |

Eq CFloat | |

Eq CDouble | |

Eq CPtrdiff | |

Eq CSize | |

Eq CWchar | |

Eq CSigAtomic | |

Eq CClock | |

Eq CTime | |

Eq CUSeconds | |

Eq CSUSeconds | |

Eq CIntPtr | |

Eq CUIntPtr | |

Eq CIntMax | |

Eq CUIntMax | |

Eq MaskingState | |

Eq IOException | |

Eq All | |

Eq Any | |

Eq Arity | |

Eq Fixity | |

Eq Associativity | |

Eq Lexeme | |

Eq Number | |

Eq Message | |

Eq ParseError | |

Eq SourcePos | |

Eq Text | |

Eq Text | |

Eq LocalTime | |

Eq TimeOfDay | |

Eq TimeZone | |

Eq UTCTime | |

Eq NominalDiffTime | |

Eq Day | |

Eq T | |

Eq Dimension | |

Eq T | |

Eq T | |

Eq T | |

Eq a => Eq [a] | |

Eq a => Eq (Ratio a) | |

Eq (Ptr a) | |

Eq (FunPtr a) | |

Eq (U1 p) | |

Eq p => Eq (Par1 p) | |

Eq a => Eq (Complex a) | |

Eq a => Eq (ZipList a) | |

Eq a => Eq (Dual a) | |

Eq a => Eq (Sum a) | |

Eq a => Eq (Product a) | |

Eq a => Eq (First a) | |

Eq a => Eq (Last a) | |

Eq a => Eq (Maybe a) | |

Eq a => Eq (Set a) | |

C a => Eq (T a) | |

Eq a => Eq (T a) | |

Eq a => Eq (ToOrd a) | |

Eq a => Eq (Max a) | |

Eq a => Eq (Min a) | |

Eq a => Eq (LCM a) | |

Eq a => Eq (GCD a) | |

Eq a => Eq (T a) | |

Eq a => Eq (T a) | |

Eq a => Eq (T a) | |

Ix i => Eq (T i) | These instances may need more work They involve converting a permutation to a table. |

Eq i => Eq (Cycle i) | |

(Eq a, C a) => Eq (T a) | |

(Eq a, C a) => Eq (T a) | |

Eq a => Eq (T a) | |

Eq a => Eq (T a) | |

(Eq a, C a, C a) => Eq (T a) | |

Eq a => Eq (T a) | |

(Eq a, C a) => Eq (T a) | |

(Eq a, C a) => Eq (T a) | |

Eq a => Eq (T a) | |

(Eq a, C a) => Eq (T a) | |

Eq a => Eq (T a) | |

Eq (T a) | |

Eq a => Eq (T a) | |

C a => Eq (T a) | |

Eq a => Eq (Valuable a) | |

(Eq a, Eq b) => Eq (Either a b) | |

Eq (f p) => Eq (Rec1 f p) | |

(Eq a, Eq b) => Eq (a, b) | |

(Ix i, Eq e) => Eq (Array i e) | |

(Eq k, Eq a) => Eq (Map k a) | |

(Eq a, Eq b) => Eq (T a b) | |

Eq a => Eq (T u a) | |

Eq v => Eq (T a v) | |

(Eq i, Eq a) => Eq (T i a) | |

Eq v => Eq (T a v) | |

Eq c => Eq (K1 i c p) | |

(Eq (f p), Eq (g p)) => Eq ((:+:) f g p) | |

(Eq (f p), Eq (g p)) => Eq ((:*:) f g p) | |

Eq (f (g p)) => Eq ((:.:) f g p) | |

(Eq a, Eq b, Eq c) => Eq (a, b, c) | |

Eq (STArray s i e) | |

Eq ((:~:) k a b) | |

Eq (f p) => Eq (M1 i c f p) | |

(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) | |

(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) | |

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) | |

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) | |

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) | |

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) | |

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) | |

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) | |

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) | |

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) | |

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |

File and directory names are values of type `String`

, whose precise
meaning is operating system dependent. Files can be opened, yielding a
handle which can then be used to operate on the contents of that file.

class Functor f where

The `Functor`

class is used for types that can be mapped over.
Instances of `Functor`

should satisfy the following laws:

fmap id == id fmap (f . g) == fmap f . fmap g

The instances of `Functor`

for lists, `Maybe`

and `IO`

satisfy these laws.

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

Functor [] | |

Functor IO | |

Functor Rose | |

Functor Gen | |

Functor ZipList | |

Functor Handler | |

Functor ReadPrec | |

Functor ReadP | |

Functor Maybe | |

Functor Identity | |

Functor Consumed | |

Functor PprM | |

Functor T | |

Functor T | |

Functor T | |

Functor T | |

Functor T | |

Functor T | |

Functor T | When you use |

Functor T | |

Functor T | |

Functor T | |

Functor ((->) r) | |

Functor (Either a) | |

Functor ((,) a) | |

Ix i => Functor (Array i) | |

Functor (Const m) | |

Monad m => Functor (WrappedMonad m) | |

Functor (Map k) | |

Functor (Box r) | |

Functor (Access r) | |

Functor (T v) | |

Functor (T a) | |

Functor (T a) | |

Functor (T i) | |

Functor (T a) | |

Arrow a => Functor (WrappedArrow a b) | |

Functor m => Functor (ErrorT e m) | |

Functor (Reply s u) | |

Functor (ParsecT s u m) |

data IO a :: * -> *

A value of type

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

a`a`

.

There is really only one way to "perform" an I/O action: bind it to
`Main.main`

in your program. When your program is run, the I/O will
be performed. It isn't possible to perform I/O from an arbitrary
function, unless that function is itself in the `IO`

monad and called
at some point, directly or indirectly, from `Main.main`

.

`IO`

is a monad, so `IO`

actions can be combined using either the do-notation
or the `>>`

and `>>=`

operations from the `Monad`

class.

type IOError = IOException

The Haskell 2010 type for exceptions in the `IO`

monad.
Any I/O operation may raise an `IOError`

instead of returning a result.
For a more general type of exception, including also those that arise
in pure code, see Control.Exception.Exception.

In Haskell 2010, this is an opaque type.

data Maybe a :: * -> *

The `Maybe`

type encapsulates an optional value. A value of type

either contains a value of type `Maybe`

a`a`

(represented as

),
or it is empty (represented as `Just`

a`Nothing`

). Using `Maybe`

is a good way to
deal with errors or exceptional cases without resorting to drastic
measures such as `error`

.

The `Maybe`

type is also a monad. It is a simple kind of error
monad, where all errors are represented by `Nothing`

. A richer
error monad can be built using the `Either`

type.

Alternative Maybe | |

Monad Maybe | |

Functor Maybe | |

MonadPlus Maybe | |

Applicative Maybe | |

Foldable Maybe | |

Generic1 Maybe | |

Eq a => Eq (Maybe a) | |

Ord a => Ord (Maybe a) | |

Read a => Read (Maybe a) | |

Show a => Show (Maybe a) | |

Generic (Maybe a) | |

Arbitrary a => Arbitrary (Maybe a) | |

CoArbitrary a => CoArbitrary (Maybe a) | |

Monoid a => Monoid (Maybe a) | Lift a semigroup into |

NFData a => NFData (Maybe a) | |

type Rep1 Maybe = D1 D1Maybe ((:+:) (C1 C1_0Maybe U1) (C1 C1_1Maybe (S1 NoSelector Par1))) | |

type Rep (Maybe a) = D1 D1Maybe ((:+:) (C1 C1_0Maybe U1) (C1 C1_1Maybe (S1 NoSelector (Rec0 a)))) | |

type (==) (Maybe k) a b = EqMaybe k a b |

class Monad m where

The `Monad`

class defines the basic operations over a *monad*,
a concept from a branch of mathematics known as *category theory*.
From the perspective of a Haskell programmer, however, it is best to
think of a monad as an *abstract datatype* of actions.
Haskell's `do`

expressions provide a convenient syntax for writing
monadic expressions.

Minimal complete definition: `>>=`

and `return`

.

Instances of `Monad`

should satisfy the following laws:

return a >>= k == k a m >>= return == m m >>= (\x -> k x >>= h) == (m >>= k) >>= h

Instances of both `Monad`

and `Functor`

should additionally satisfy the law:

fmap f xs == xs >>= return . f

The instances of `Monad`

for lists, `Maybe`

and `IO`

defined in the Prelude satisfy these laws.

(>>=) :: m a -> (a -> m b) -> m b infixl 1

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

(>>) :: m a -> m b -> m b infixl 1

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

return :: a -> m a

Inject a value into the monadic type.

Fail with a message. This operation is not part of the
mathematical definition of a monad, but is invoked on pattern-match
failure in a `do`

expression.

The `Ord`

class is used for totally ordered datatypes.

Instances of `Ord`

can be derived for any user-defined
datatype whose constituent types are in `Ord`

. The declared order
of the constructors in the data declaration determines the ordering
in derived `Ord`

instances. The `Ordering`

datatype allows a single
comparison to determine the precise ordering of two objects.

Minimal complete definition: either `compare`

or `<=`

.
Using `compare`

can be more efficient for complex types.

Ord Bool | |

Ord Char | |

Ord Double | |

Ord Float | |

Ord Int | |

Ord Int8 | |

Ord Int16 | |

Ord Int32 | |

Ord Int64 | |

Ord Integer | |

Ord Ordering | |

Ord Word | |

Ord Word8 | |

Ord Word16 | |

Ord Word32 | |

Ord Word64 | |

Ord () | |

Ord AsyncException | |

Ord ArrayException | |

Ord ExitCode | |

Ord GeneralCategory | |

Ord CChar | |

Ord CSChar | |

Ord CUChar | |

Ord CShort | |

Ord CUShort | |

Ord CInt | |

Ord CUInt | |

Ord CLong | |

Ord CULong | |

Ord CLLong | |

Ord CULLong | |

Ord CFloat | |

Ord CDouble | |

Ord CPtrdiff | |

Ord CSize | |

Ord CWchar | |

Ord CSigAtomic | |

Ord CClock | |

Ord CTime | |

Ord CUSeconds | |

Ord CSUSeconds | |

Ord CIntPtr | |

Ord CUIntPtr | |

Ord CIntMax | |

Ord CUIntMax | |

Ord All | |

Ord Any | |

Ord Arity | |

Ord Fixity | |

Ord Associativity | |

Ord Message | |

Ord SourcePos | |

Ord Text | |

Ord Text | |

Ord LocalTime | |

Ord TimeOfDay | |

Ord TimeZone | |

Ord UTCTime | |

Ord NominalDiffTime | |

Ord Day | |

Ord Dimension | |

Ord T | |

Ord T | |

Ord T | |

Ord a => Ord [a] | |

Integral a => Ord (Ratio a) | |

Ord (Ptr a) | |

Ord (FunPtr a) | |

Ord (U1 p) | |

Ord p => Ord (Par1 p) | |

Ord a => Ord (ZipList a) | |

Ord a => Ord (Dual a) | |

Ord a => Ord (Sum a) | |

Ord a => Ord (Product a) | |

Ord a => Ord (First a) | |

Ord a => Ord (Last a) | |

Ord a => Ord (Maybe a) | |

Ord a => Ord (Set a) | |

C a => Ord (T a) | |

Ord a => Ord (T a) | |

C a => Ord (ToOrd a) | |

(Ord a, C a) => Ord (T a) | |

Ord a => Ord (T a) | |

Ix i => Ord (T i) | |

(Ord a, C a) => Ord (T a) | |

(Ord a, C a) => Ord (T a) | |

Ord a => Ord (T a) | |

Ord a => Ord (T a) | |

(Ord a, C a) => Ord (T a) | |

Ord a => Ord (T a) | |

C a => Ord (T a) | |

Ord a => Ord (Valuable a) | |

(Ord a, Ord b) => Ord (Either a b) | |

Ord (f p) => Ord (Rec1 f p) | |

(Ord a, Ord b) => Ord (a, b) | |

(Ix i, Ord e) => Ord (Array i e) | |

(Ord k, Ord v) => Ord (Map k v) | |

Ord a => Ord (T u a) | |

Ord v => Ord (T a v) | |

(Ord i, Ord a) => Ord (T i a) | |

Ord v => Ord (T a v) | |

Ord c => Ord (K1 i c p) | |

(Ord (f p), Ord (g p)) => Ord ((:+:) f g p) | |

(Ord (f p), Ord (g p)) => Ord ((:*:) f g p) | |

Ord (f (g p)) => Ord ((:.:) f g p) | |

(Ord a, Ord b, Ord c) => Ord (a, b, c) | |

Ord ((:~:) k a b) | |

Ord (f p) => Ord (M1 i c f p) | |

(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) | |

(Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) | |

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) | |

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) | |

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) | |

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) | |

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) | |

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) | |

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) | |

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) | |

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |

data Ordering :: *

Bounded Ordering | |

Enum Ordering | |

Eq Ordering | |

Ord Ordering | |

Read Ordering | |

Show Ordering | |

Ix Ordering | |

Generic Ordering | |

Arbitrary Ordering | |

CoArbitrary Ordering | |

Monoid Ordering | |

type Rep Ordering = D1 D1Ordering ((:+:) (C1 C1_0Ordering U1) ((:+:) (C1 C1_1Ordering U1) (C1 C1_2Ordering U1))) | |

type (==) Ordering a b = EqOrdering a b |

class Read a where

Parsing of `String`

s, producing values.

Minimal complete definition: `readsPrec`

(or, for GHC only, `readPrec`

)

Derived instances of `Read`

make the following assumptions, which
derived instances of `Show`

obey:

- If the constructor is defined to be an infix operator, then the
derived
`Read`

instance will parse only infix applications of the constructor (not the prefix form). - Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
- If the constructor is defined using record syntax, the derived
`Read`

will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration. - The derived
`Read`

instance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.

For example, given the declarations

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

the derived instance of `Read`

in Haskell 2010 is equivalent to

instance (Read a) => Read (Tree a) where readsPrec d r = readParen (d > app_prec) (\r -> [(Leaf m,t) | ("Leaf",s) <- lex r, (m,t) <- readsPrec (app_prec+1) s]) r ++ readParen (d > up_prec) (\r -> [(u:^:v,w) | (u,s) <- readsPrec (up_prec+1) r, (":^:",t) <- lex s, (v,w) <- readsPrec (up_prec+1) t]) r where app_prec = 10 up_prec = 5

Note that right-associativity of `:^:`

is unused.

The derived instance in GHC is equivalent to

instance (Read a) => Read (Tree a) where readPrec = parens $ (prec app_prec $ do Ident "Leaf" <- lexP m <- step readPrec return (Leaf m)) +++ (prec up_prec $ do u <- step readPrec Symbol ":^:" <- lexP v <- step readPrec return (u :^: v)) where app_prec = 10 up_prec = 5 readListPrec = readListPrecDefault

:: Int | the operator precedence of the enclosing
context (a number from |

-> ReadS a |

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

Derived instances of `Read`

and `Show`

satisfy the following:

That is, `readsPrec`

parses the string produced by
`showsPrec`

, and delivers the value that
`showsPrec`

started with.

Read Bool | |

Read Char | |

Read Double | |

Read Float | |

Read Int | |

Read Int8 | |

Read Int16 | |

Read Int32 | |

Read Int64 | |

Read Integer | |

Read Ordering | |

Read Word | |

Read Word8 | |

Read Word16 | |

Read Word32 | |

Read Word64 | |

Read () | |

Read StdGen | |

Read ExitCode | |

Read GeneralCategory | |

Read CChar | |

Read CSChar | |

Read CUChar | |

Read CShort | |

Read CUShort | |

Read CInt | |

Read CUInt | |

Read CLong | |

Read CULong | |

Read CLLong | |

Read CULLong | |

Read CFloat | |

Read CDouble | |

Read CPtrdiff | |

Read CSize | |

Read CWchar | |

Read CSigAtomic | |

Read CClock | |

Read CTime | |

Read CUSeconds | |

Read CSUSeconds | |

Read CIntPtr | |

Read CUIntPtr | |

Read CIntMax | |

Read CUIntMax | |

Read All | |

Read Any | |

Read Arity | |

Read Fixity | |

Read Associativity | |

Read Lexeme | |

Read Text | |

Read Text | |

Read LocalTime | |

Read ZonedTime | |

Read TimeOfDay | |

Read TimeZone | |

Read UTCTime | |

Read Day | |

Read T | |

Read a => Read [a] | |

(Integral a, Read a) => Read (Ratio a) | |

Read (U1 p) | |

Read p => Read (Par1 p) | |

Read a => Read (Complex a) | |

Read a => Read (ZipList a) | |

Read a => Read (Dual a) | |

Read a => Read (Sum a) | |

Read a => Read (Product a) | |

Read a => Read (First a) | |

Read a => Read (Last a) | |

Read a => Read (Maybe a) | |

(Read a, Ord a) => Read (Set a) | |

(Read a, C a) => Read (T a) | |

Read a => Read (T a) | |

Read i => Read (Cycle i) | |

(Read a, C a) => Read (T a) | |

Read a => Read (T a) | |

Read a => Read (T a) | |

Read a => Read (T a) | |

(Read a, Read b) => Read (Either a b) | |

Read (f p) => Read (Rec1 f p) | |

(Read a, Read b) => Read (a, b) | |

(Ix a, Read a, Read b) => Read (Array a b) | |

(Ord k, Read k, Read e) => Read (Map k e) | |

(Read v, Ord a, C a, C a v) => Read (T a v) | |

Read c => Read (K1 i c p) | |

(Read (f p), Read (g p)) => Read ((:+:) f g p) | |

(Read (f p), Read (g p)) => Read ((:*:) f g p) | |

Read (f (g p)) => Read ((:.:) f g p) | |

(Read a, Read b, Read c) => Read (a, b, c) | |

(~) k a b => Read ((:~:) k a b) | |

Read (f p) => Read (M1 i c f p) | |

(Read a, Read b, Read c, Read d) => Read (a, b, c, d) | |

(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) | |

(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |

(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |

class Show a where

Conversion of values to readable `String`

s.

Minimal complete definition: `showsPrec`

or `show`

.

Derived instances of `Show`

have the following properties, which
are compatible with derived instances of `Read`

:

- The result of
`show`

is a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used. - If the constructor is defined to be an infix operator, then
`showsPrec`

will produce infix applications of the constructor. - the representation will be enclosed in parentheses if the
precedence of the top-level constructor in
`x`

is less than`d`

(associativity is ignored). Thus, if`d`

is`0`

then the result is never surrounded in parentheses; if`d`

is`11`

it is always surrounded in parentheses, unless it is an atomic expression. - If the constructor is defined using record syntax, then
`show`

will produce the record-syntax form, with the fields given in the same order as the original declaration.

For example, given the declarations

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

the derived instance of `Show`

is equivalent to

instance (Show a) => Show (Tree a) where showsPrec d (Leaf m) = showParen (d > app_prec) $ showString "Leaf " . showsPrec (app_prec+1) m where app_prec = 10 showsPrec d (u :^: v) = showParen (d > up_prec) $ showsPrec (up_prec+1) u . showString " :^: " . showsPrec (up_prec+1) v where up_prec = 5

Note that right-associativity of `:^:`

is ignored. For example,

produces the string`show`

(Leaf 1 :^: Leaf 2 :^: Leaf 3)`"Leaf 1 :^: (Leaf 2 :^: Leaf 3)"`

.

:: Int | the operator precedence of the enclosing
context (a number from |

-> a | the value to be converted to a |

-> ShowS |

Convert a value to a readable `String`

.

`showsPrec`

should satisfy the law

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

Derived instances of `Read`

and `Show`

satisfy the following:

That is, `readsPrec`

parses the string produced by
`showsPrec`

, and delivers the value that `showsPrec`

started with.

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

The computation `appendFile`

`file str`

function appends the string `str`

,
to the file `file`

.

Note that `writeFile`

and `appendFile`

write a literal string
to a file. To write a value of any printable type, as with `print`

,
use the `show`

function to convert the value to a string first.

main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])

asTypeOf :: a -> a -> a

break :: (a -> Bool) -> [a] -> ([a], [a])

`break`

, applied to a predicate `p`

and a list `xs`

, returns a tuple where
first element is longest prefix (possibly empty) of `xs`

of elements that
*do not satisfy* `p`

and second element is the remainder of the list:

break (> 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4]) break (< 9) [1,2,3] == ([],[1,2,3]) break (> 9) [1,2,3] == ([1,2,3],[])

concat :: [[a]] -> [a]

Concatenate a list of lists.

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

Map a function over a list and concatenate the results.

const :: a -> b -> a

Constant function.

cycle :: [a] -> [a]

`cycle`

ties a finite list into a circular one, or equivalently,
the infinite repetition of the original list. It is the identity
on infinite lists.

`drop`

`n xs`

returns the suffix of `xs`

after the first `n`

elements, or `[]`

if `n > `

:`length`

xs

drop 6 "Hello World!" == "World!" drop 3 [1,2,3,4,5] == [4,5] drop 3 [1,2] == [] drop 3 [] == [] drop (-1) [1,2] == [1,2] drop 0 [1,2] == [1,2]

It is an instance of the more general `genericDrop`

,
in which `n`

may be of any integral type.

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

`filter`

, applied to a predicate and a list, returns the list of
those elements that satisfy the predicate; i.e.,

filter p xs = [ x | x <- xs, p x]

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

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

f`f`

.

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

`foldl`

, 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:

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

The list must be finite.

foldl1 :: (a -> a -> a) -> [a] -> a

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

`foldr`

, 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:

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

foldr1 :: (a -> a -> a) -> [a] -> a

fst :: (a, b) -> a

Extract the first component of a pair.

getContents :: IO String

The `getContents`

operation returns all user input as a single string,
which is read lazily as it is needed
(same as `hGetContents`

`stdin`

).

head :: [a] -> a

Extract the first element of a list, which must be non-empty.

id :: a -> a

Identity function.

init :: [a] -> [a]

Return all the elements of a list except the last one. The list must be non-empty.

interact :: (String -> String) -> IO ()

The `interact`

function takes a function of type `String->String`

as its argument. The entire input from the standard input device is
passed to this function as its argument, and the resulting string is
output on the standard output device.

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

`iterate`

`f x`

returns an infinite list of repeated applications
of `f`

to `x`

:

iterate f x == [x, f x, f (f x), ...]

last :: [a] -> a

Extract the last element of a list, which must be finite and non-empty.

*O(n)*. `length`

returns the length of a finite list as an `Int`

.
It is an instance of the more general `genericLength`

,
the result type of which may be any kind of number.

The `lex`

function reads a single lexeme from the input, discarding
initial white space, and returning the characters that constitute the
lexeme. If the input string contains only white space, `lex`

returns a
single successful `lexeme' consisting of the empty string. (Thus

.) If there is no legal lexeme at the
beginning of the input string, `lex`

"" = [("","")]`lex`

fails (i.e. returns `[]`

).

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

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

`lines`

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

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

`map`

`f xs`

is the list obtained by applying `f`

to each element
of `xs`

, i.e.,

map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] map f [x1, x2, ...] == [f x1, f x2, ...]

The `print`

function outputs a value of any printable type to the
standard output device.
Printable types are those that are instances of class `Show`

; `print`

converts values to strings for output using the `show`

operation and
adds a newline.

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

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

The `read`

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

readFile :: FilePath -> IO String

The `readFile`

function reads a file and
returns the contents of the file as a string.
The file is read lazily, on demand, as with `getContents`

.

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

general coercion to fractional types

`replicate`

`n x`

is a list of length `n`

with `x`

the value of
every element.
It is an instance of the more general `genericReplicate`

,
in which `n`

may be of any integral type.

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

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

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

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

seq :: a -> b -> b

Evaluates its first argument to head normal form, and then returns its second argument as the result.

sequence :: Monad m => [m a] -> m [a]

Evaluate each action in the sequence from left to right, and collect the results.

sequence_ :: Monad m => [m a] -> m ()

Evaluate each action in the sequence from left to right, and ignore the results.

utility function converting a `Char`

to a show function that
simply prepends the character unchanged.

showString :: String -> ShowS

utility function converting a `String`

to a show function that
simply prepends the string unchanged.

snd :: (a, b) -> b

Extract the second component of a pair.

span :: (a -> Bool) -> [a] -> ([a], [a])

`span`

, applied to a predicate `p`

and a list `xs`

, returns a tuple where
first element is longest prefix (possibly empty) of `xs`

of elements that
satisfy `p`

and second element is the remainder of the list:

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

splitAt :: Int -> [a] -> ([a], [a])

`splitAt`

`n xs`

returns a tuple where first element is `xs`

prefix of
length `n`

and second element is the remainder of the list:

splitAt 6 "Hello World!" == ("Hello ","World!") splitAt 3 [1,2,3,4,5] == ([1,2,3],[4,5]) splitAt 1 [1,2,3] == ([1],[2,3]) splitAt 3 [1,2,3] == ([1,2,3],[]) splitAt 4 [1,2,3] == ([1,2,3],[]) splitAt 0 [1,2,3] == ([],[1,2,3]) splitAt (-1) [1,2,3] == ([],[1,2,3])

It is equivalent to `(`

when `take`

n xs, `drop`

n xs)`n`

is not `_|_`

(`splitAt _|_ xs = _|_`

).
`splitAt`

is an instance of the more general `genericSplitAt`

,
in which `n`

may be of any integral type.

tail :: [a] -> [a]

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

`take`

`n`

, applied to a list `xs`

, returns the prefix of `xs`

of length `n`

, or `xs`

itself if `n > `

:`length`

xs

take 5 "Hello World!" == "Hello" take 3 [1,2,3,4,5] == [1,2,3] take 3 [1,2] == [1,2] take 3 [] == [] take (-1) [1,2] == [] take 0 [1,2] == []

It is an instance of the more general `genericTake`

,
in which `n`

may be of any integral type.

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

`takeWhile`

, applied to a predicate `p`

and a list `xs`

, returns the
longest prefix (possibly empty) of `xs`

of elements that satisfy `p`

:

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

undefined :: a

unzip :: [(a, b)] -> ([a], [b])

`unzip`

transforms a list of pairs into a list of first components
and a list of second components.

unzip3 :: [(a, b, c)] -> ([a], [b], [c])

`words`

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

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

The computation `writeFile`

`file str`

function writes the string `str`

,
to the file `file`

.

zip :: [a] -> [b] -> [(a, b)]

`zip`

takes two lists and returns a list of corresponding pairs.
If one input list is short, excess elements of the longer list are
discarded.

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

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

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

ifThenElse :: Bool -> a -> a -> a

The same as `if'`

, but the name is chosen
such that it can be used for GHC-7.0's rebindable if-then-else syntax.