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

Language | Haskell98 |

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

- class Eq a where
- type FilePath = String
- data Float :: *
- class Fractional a => Floating a where
- class Num a => Fractional a where
- (/) :: a -> a -> a
- recip :: a -> a
- fromRational :: Rational -> a

- class Functor f where
- fmap :: (a -> b) -> f a -> f b

- data IO a :: * -> *
- type IOError = IOException
- data Int :: *
- data Integer :: *
- class (Real a, Enum a) => Integral a where
- data Maybe a :: * -> *
- class Applicative m => Monad m where
- class Num a where
- class Eq a => Ord a where
- data Ordering :: *
- type Rational = Ratio Integer
- class Read a where
- type ReadS a = String -> [(a, String)]
- class (Num a, Ord a) => Real a where
- toRational :: a -> Rational

- class (RealFrac a, Floating a) => RealFloat a where
- floatRadix :: a -> Integer
- floatDigits :: a -> Int
- floatRange :: a -> (Int, Int)
- decodeFloat :: a -> (Integer, Int)
- encodeFloat :: Integer -> Int -> a
- exponent :: a -> Int
- significand :: a -> a
- scaleFloat :: Int -> a -> a
- isNaN :: a -> Bool
- isInfinite :: a -> Bool
- isDenormalized :: a -> Bool
- isNegativeZero :: a -> Bool
- isIEEE :: a -> Bool
- atan2 :: a -> a -> a

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

# Documentation

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

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

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

is the non-negative factor of both `gcd`

x y`x`

and `y`

of which
every common factor of `x`

and `y`

is also a factor; for example

, `gcd`

4 2 = 2

, `gcd`

(-4) 6 = 2

= `gcd`

0 4`4`

.

= `gcd`

0 0`0`

.
(That is, the common divisor that is "greatest" in the divisibility
preordering.)

Note: Since for signed fixed-width integer types,

,
the result may be negative if one of the arguments is `abs`

`minBound`

< 0

(and
necessarily is if the other is `minBound`

`0`

or

) for such types.`minBound`

($) :: (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

(.) :: (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.

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`

).

data Double :: *

Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.

data 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").

#### Examples

The type

is the type of values which can be either
a `Either`

`String`

`Int`

`String`

or an `Int`

. The `Left`

constructor can be used only on
`String`

s, and the `Right`

constructor can be used only on `Int`

s:

`>>>`

`let s = Left "foo" :: Either String Int`

`>>>`

Left "foo"`s`

`>>>`

`let n = Right 3 :: Either String Int`

`>>>`

Right 3`n`

`>>>`

s :: Either String Int`:type s`

`>>>`

n :: Either String Int`:type n`

The `fmap`

from our `Functor`

instance will ignore `Left`

values, but
will apply the supplied function to values contained in a `Right`

:

`>>>`

`let s = Left "foo" :: Either String Int`

`>>>`

`let n = Right 3 :: Either String Int`

`>>>`

Left "foo"`fmap (*2) s`

`>>>`

Right 6`fmap (*2) n`

The `Monad`

instance for `Either`

allows us to chain together multiple
actions which may fail, and fail overall if any of the individual
steps failed. First we'll write a function that can either parse an
`Int`

from a `Char`

, or fail.

`>>>`

`import Data.Char ( digitToInt, isDigit )`

`>>>`

let parseEither :: Char -> Either String Int parseEither c | isDigit c = Right (digitToInt c) | otherwise = Left "parse error"`:{`

`>>>`

`:}`

The following should work, since both `'1'`

and `'2'`

can be
parsed as `Int`

s.

`>>>`

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

`>>>`

`:}`

`>>>`

Right 3`parseMultiple`

But the following should fail overall, since the first operation where
we attempt to parse `'m'`

as an `Int`

will fail:

`>>>`

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

`>>>`

`:}`

`>>>`

Left "parse error"`parseMultiple`

Monad (Either e) | |

Functor (Either a) | |

Applicative (Either e) | |

Foldable (Either a) | |

Traversable (Either a) | |

Generic1 (Either a) | |

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

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

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

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

Generic (Either a b) | |

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

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

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

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]`

.

class Eq a where

The `Eq`

class defines equality (`==`

) and inequality (`/=`

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

,
and `Eq`

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

.

Eq Bool | |

Eq Char | |

Eq Double | |

Eq Float | |

Eq Int | |

Eq Integer | |

Eq Ordering | |

Eq Word | |

Eq () | |

Eq BigNat | |

Eq AsyncException | |

Eq ArrayException | |

Eq ExitCode | |

Eq IOErrorType | |

Eq MaskingState | |

Eq IOException | |

Eq Arity | |

Eq Fixity | |

Eq Associativity | |

Eq a => Eq [a] | |

Eq a => Eq (Ratio a) | |

Eq (U1 p) | |

Eq p => Eq (Par1 p) | |

Eq a => Eq (ZipList a) | |

Eq a => Eq (Maybe a) | |

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

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

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

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

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

Eq (Proxy k s) | |

Eq 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.

data Float :: *

Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.

class Fractional a => Floating a where

Trigonometric and hyperbolic functions and related functions.

class Num a => Fractional a where

Fractional numbers, supporting real division.

fromRational, (recip | (/))

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

fractional division

recip :: a -> a

reciprocal fraction

fromRational :: Rational -> a

Conversion from a `Rational`

(that is

).
A floating literal stands for an application of `Ratio`

`Integer`

`fromRational`

to a value of type `Rational`

, so such literals have type
`(`

.`Fractional`

a) => a

Integral a => Fractional (Ratio a) |

class Functor f where

The `Functor`

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

should satisfy the following laws:

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

The instances of `Functor`

for lists, `Maybe`

and `IO`

satisfy these laws.

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

Functor [] | |

Functor IO | |

Functor Id | |

Functor P | |

Functor ZipList | |

Functor ReadP | |

Functor Maybe | |

Functor ((->) r) | |

Functor (Either a) | |

Functor ((,) a) | |

Functor (StateL s) | |

Functor (StateR s) | |

Ix i => Functor (Array i) | |

Functor (Const m) | |

Monad m => Functor (WrappedMonad m) | |

Functor (Proxy *) | |

Arrow a => Functor (WrappedArrow a b) |

data IO a :: * -> *

A value of type

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

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 Int :: *

data Integer :: *

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

Integral numbers, supporting integer division.

quot :: a -> a -> a infixl 7

integer division truncated toward zero

rem :: a -> a -> a infixl 7

integer remainder, satisfying

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

div :: a -> a -> a infixl 7

integer division truncated toward negative infinity

mod :: a -> a -> a infixl 7

integer modulus, satisfying

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

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

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

conversion to `Integer`

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.

Monad Maybe | |

Functor Maybe | |

Applicative Maybe | |

Foldable Maybe | |

Traversable Maybe | |

Generic1 Maybe | |

Alternative Maybe | |

MonadPlus Maybe | |

Eq a => Eq (Maybe a) | |

Ord a => Ord (Maybe a) | |

Read a => Read (Maybe a) | |

Show a => Show (Maybe a) | |

Generic (Maybe a) | |

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

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 Applicative m => Monad m where

The `Monad`

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

expressions provide a convenient syntax for writing
monadic expressions.

Instances of `Monad`

should satisfy the following laws:

Furthermore, the `Monad`

and `Applicative`

operations should relate as follows:

The above laws imply:

and that `pure`

and (`<*>`

) satisfy the applicative functor laws.

The instances of `Monad`

for lists, `Maybe`

and `IO`

defined in the Prelude satisfy these laws.

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

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

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

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

return :: a -> m a

Inject a value into the monadic type.

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

expression.

class Num a where

Basic numeric class.

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

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

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

negate :: a -> a

Unary negation.

abs :: a -> a

Absolute value.

signum :: a -> a

Sign of a number.
The functions `abs`

and `signum`

should satisfy the law:

abs x * signum x == x

For real numbers, the `signum`

is either `-1`

(negative), `0`

(zero)
or `1`

(positive).

fromInteger :: Integer -> a

Conversion from an `Integer`

.
An integer literal represents the application of the function
`fromInteger`

to the appropriate value of type `Integer`

,
so such literals have type `(`

.`Num`

a) => a

The `Ord`

class is used for totally ordered datatypes.

Instances of `Ord`

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

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

instances. The `Ordering`

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

Minimal complete definition: either `compare`

or `<=`

.
Using `compare`

can be more efficient for complex types.

Ord Bool | |

Ord Char | |

Ord Double | |

Ord Float | |

Ord Int | |

Ord Integer | |

Ord Ordering | |

Ord Word | |

Ord () | |

Ord BigNat | |

Ord AsyncException | |

Ord ArrayException | |

Ord ExitCode | |

Ord Arity | |

Ord Fixity | |

Ord Associativity | |

Ord a => Ord [a] | |

Integral a => Ord (Ratio a) | |

Ord (U1 p) | |

Ord p => Ord (Par1 p) | |

Ord a => Ord (ZipList a) | |

Ord a => Ord (Maybe a) | |

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

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

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

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

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

Ord (Proxy k s) | |

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

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

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

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

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

Ord ((:~:) 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 :: *

class Read a where

Parsing of `String`

s, producing values.

Derived instances of `Read`

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

obey:

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

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

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

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

For example, given the declarations

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

the derived instance of `Read`

in Haskell 2010 is equivalent to

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

Note that right-associativity of `:^:`

is unused.

The derived instance in GHC is equivalent to

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

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

-> ReadS a |

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

Derived instances of `Read`

and `Show`

satisfy the following:

That is, `readsPrec`

parses the string produced by
`showsPrec`

, and delivers the value that
`showsPrec`

started with.

Read Bool | |

Read Char | |

Read Double | |

Read Float | |

Read Int | |

Read Integer | |

Read Ordering | |

Read Word | |

Read () | |

Read ExitCode | |

Read Arity | |

Read Fixity | |

Read Associativity | |

Read Lexeme | |

Read a => Read [a] | |

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

Read (U1 p) | |

Read p => Read (Par1 p) | |

Read a => Read (ZipList a) | |

Read a => Read (Maybe a) | |

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

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

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

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

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

Read (Proxy k s) | |

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

class (Num a, Ord a) => Real a where

toRational :: a -> Rational

the rational equivalent of its real argument with full precision

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

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

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

floatRadix :: a -> Integer

a constant function, returning the radix of the representation
(often `2`

)

floatDigits :: a -> Int

a constant function, returning the number of digits of
`floatRadix`

in the significand

floatRange :: a -> (Int, Int)

a constant function, returning the lowest and highest values the exponent may assume

decodeFloat :: a -> (Integer, Int)

The function `decodeFloat`

applied to a real floating-point
number returns the significand expressed as an `Integer`

and an
appropriately scaled exponent (an `Int`

). If

yields `decodeFloat`

x`(m,n)`

, then `x`

is equal in value to `m*b^^n`

, where `b`

is the floating-point radix, and furthermore, either `m`

and `n`

are both zero or else `b^(d-1) <= `

, where `abs`

m < b^d`d`

is
the value of

.
In particular, `floatDigits`

x

. If the type
contains a negative zero, also `decodeFloat`

0 = (0,0)

.
`decodeFloat`

(-0.0) = (0,0)*The result of* `decodeFloat`

x*is unspecified if either of*
`isNaN`

x*or* `isInfinite`

x*is* `True`

.

encodeFloat :: Integer -> Int -> a

`encodeFloat`

performs the inverse of `decodeFloat`

in the
sense that for finite `x`

with the exception of `-0.0`

,

.
`uncurry`

`encodeFloat`

(`decodeFloat`

x) = x

is one of the two closest representable
floating-point numbers to `encodeFloat`

m n`m*b^^n`

(or `±Infinity`

if overflow
occurs); usually the closer, but if `m`

contains too many bits,
the result may be rounded in the wrong direction.

`exponent`

corresponds to the second component of `decodeFloat`

.

and for finite nonzero `exponent`

0 = 0`x`

,

.
If `exponent`

x = snd (`decodeFloat`

x) + `floatDigits`

x`x`

is a finite floating-point number, it is equal in value to

, where `significand`

x * b ^^ `exponent`

x`b`

is the
floating-point radix.
The behaviour is unspecified on infinite or `NaN`

values.

significand :: a -> a

The first component of `decodeFloat`

, scaled to lie in the open
interval (`-1`

,`1`

), either `0.0`

or of absolute value `>= 1/b`

,
where `b`

is the floating-point radix.
The behaviour is unspecified on infinite or `NaN`

values.

scaleFloat :: Int -> a -> a

multiplies a floating-point number by an integer power of the radix

`True`

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

isInfinite :: a -> Bool

`True`

if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool

`True`

if the argument is too small to be represented in
normalized format

isNegativeZero :: a -> Bool

`True`

if the argument is an IEEE negative zero

`True`

if the argument is an IEEE floating point number

atan2 :: a -> a -> a

a version of arctangent taking two real floating-point arguments.
For real floating `x`

and `y`

,

computes the angle
(from the positive x-axis) of the vector from the origin to the
point `atan2`

y x`(x,y)`

.

returns a value in the range [`atan2`

y x`-pi`

,
`pi`

]. It follows the Common Lisp semantics for the origin when
signed zeroes are supported.

, with `atan2`

y 1`y`

in a type
that is `RealFloat`

, should return the same value as

.
A default definition of `atan`

y`atan2`

is provided, but implementors
can provide a more accurate implementation.

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

Extracting components of fractions.

properFraction :: Integral b => a -> (b, a)

The function `properFraction`

takes a real fractional number `x`

and returns a pair `(n,f)`

such that `x = n+f`

, and:

`n`

is an integral number with the same sign as`x`

; and`f`

is a fraction with the same type and sign as`x`

, and with absolute value less than`1`

.

The default definitions of the `ceiling`

, `floor`

, `truncate`

and `round`

functions are in terms of `properFraction`

.

truncate :: Integral b => a -> b

returns the integer nearest `truncate`

x`x`

between zero and `x`

returns the nearest integer to `round`

x`x`

;
the even integer if `x`

is equidistant between two integers

ceiling :: Integral b => a -> b

returns the least integer not less than `ceiling`

x`x`

returns the greatest integer not greater than `floor`

x`x`

class Show a where

Conversion of values to readable `String`

s.

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.

Show Bool | |

Show Char | |

Show Int | |

Show Integer | |

Show Ordering | |

Show Word | |

Show () | |

Show BlockedIndefinitelyOnMVar | |

Show BlockedIndefinitelyOnSTM | |

Show Deadlock | |

Show AllocationLimitExceeded | |

Show AssertionFailed | |

Show SomeAsyncException | |

Show AsyncException | |

Show ArrayException | |

Show ExitCode | |

Show IOErrorType | |

Show MaskingState | |

Show IOException | |

Show Arity | |

Show Fixity | |

Show Associativity | |

Show a => Show [a] | |

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

Show (U1 p) | |

Show p => Show (Par1 p) | |

Show a => Show (ZipList a) | |

Show a => Show (Maybe a) | |

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

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

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

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

Show a => Show (Const a b) | |

Show (Proxy k s) | |

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

raise a number to an integral power

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

The computation `appendFile`

`file str`

function appends the string `str`

,
to the file `file`

.

Note that `writeFile`

and `appendFile`

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

,
use the `show`

function to convert the value to a string first.

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

asTypeOf :: a -> a -> a

const :: a -> b -> a

Constant function.

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

Case analysis for the `Either`

type.
If the value is

, apply the first function to `Left`

a`a`

;
if it is

, apply the second function to `Right`

b`b`

.

#### Examples

We create two values of type

, one using the
`Either`

`String`

`Int`

`Left`

constructor and another using the `Right`

constructor. Then
we apply "either" the `length`

function (if we have a `String`

)
or the "times-two" function (if we have an `Int`

):

`>>>`

`let s = Left "foo" :: Either String Int`

`>>>`

`let n = Right 3 :: Either String Int`

`>>>`

3`either length (*2) s`

`>>>`

6`either length (*2) n`

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

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

f`f`

.

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

general coercion from integral types

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`

).

id :: a -> a

Identity function.

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

The `interact`

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

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

The `lex`

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

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

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

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

fails (i.e. returns `[]`

).

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

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

`lines`

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

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

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

.

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

The `maybe`

function takes a default value, a function, and a `Maybe`

value. If the `Maybe`

value is `Nothing`

, the function returns the
default value. Otherwise, it applies the function to the value inside
the `Just`

and returns the result.

#### Examples

Basic usage:

`>>>`

True`maybe False odd (Just 3)`

`>>>`

False`maybe False odd Nothing`

Read an integer from a string using `readMaybe`

. If we succeed,
return twice the integer; that is, apply `(*2)`

to it. If instead
we fail to parse an integer, return `0`

by default:

`>>>`

`import Text.Read ( readMaybe )`

`>>>`

10`maybe 0 (*2) (readMaybe "5")`

`>>>`

0`maybe 0 (*2) (readMaybe "")`

Apply `show`

to a `Maybe Int`

. If we have `Just n`

, we want to show
the underlying `Int`

`n`

. But if we have `Nothing`

, we return the
empty string instead of (for example) "Nothing":

`>>>`

"5"`maybe "" show (Just 5)`

`>>>`

""`maybe "" show Nothing`

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]])

product :: Foldable t => forall a. Num a => t a -> a

The `product`

function computes the product of the numbers of a
structure.

The `read`

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

readFile :: FilePath -> IO String

The `readFile`

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

.

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

general coercion to fractional types

seq :: a -> b -> b

The value of `seq a b`

is bottom if `a`

is bottom, and
otherwise equal to `b`

. `seq`

is usually introduced to
improve performance by avoiding unneeded laziness.

A note on evaluation order: the expression `seq a b`

does
*not* guarantee that `a`

will be evaluated before `b`

.
The only guarantee given by `seq`

is that the both `a`

and `b`

will be evaluated before `seq`

returns a value.
In particular, this means that `b`

may be evaluated before
`a`

. If you need to guarantee a specific order of evaluation,
you must use the function `pseq`

from the "parallel" package.

sequence :: Traversable t => forall m a. Monad m => t (m a) -> m (t a)

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

.

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

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

.

As of base 4.8.0.0, `sequence_`

is just `sequenceA_`

, specialized
to `Monad`

.

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.

sum :: Foldable t => forall a. Num a => t a -> a

The `sum`

function computes the sum of the numbers of a structure.

undefined :: a