Prelude.Classy

Prelude replacement, use the NoImplicitPrelude extension before importing this.

It deliberately omits all list-handling functions, import Data.List or use the generic versions.

Basic/legacy types

module Data.Bool

bool

Arguments

:: a

Returned if the bool is True

-> a

Returned if the bool is False

-> Bool

-> a

An either/maybe equivalent for Bool, often known as if'

module Data.Maybe

module Data.Either

module Data.Eq

module Data.Ord

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 succ maxBound and pred minBound should result in a runtime error.
• fromEnum and toEnum should give a runtime error if the result value is not representable in the result type. For example, toEnum 7 :: Bool is an error.
• 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

Methods

succ :: a -> a

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

pred :: a -> a

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

toEnum :: Int -> a

Convert from an Int.

fromEnum :: a -> Int

Convert to an Int. It is implementation-dependent what fromEnum returns when applied to a value that is too large to fit in an Int.

enumFrom :: a -> [a]

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

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

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

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

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

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

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

Instances

Enum Bool

Enum Char

Enum Double

Enum Float

Enum Int

Enum Integer

Enum Ordering

Enum ()

Integral a => Enum (Ratio a)

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 charachers), 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 Prelude.toEnum and Prelude.fromEnum from the Prelude.Enum class respectively (or equivalently ord and chr).

Instances

Bounded Char

Enum Char

Read Char

Show Char

type String = [Char]

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

fst :: (a, b) -> a

Extract the first component of a pair.

snd :: (a, b) -> b

Extract the second component of a pair.

lines :: String -> [String]

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

words :: String -> [String]

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

unlines :: [String] -> String

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

unwords :: [String] -> String

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

class Show a where

Conversion of values to readable Strings.

Minimal complete definition: showsPrec or show.

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

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

For example, given the declarations

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

the derived instance of Show is equivalent to

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

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

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

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

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

Methods

showsPrec

Arguments

:: Int

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

-> a

the value to be converted to a String

-> ShowS

Convert a value to a readable String.

showsPrec should satisfy the law

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

Derived instances of Text.Read.Read and Show satisfy the following:

• (x,"") is an element of (Text.Read.readsPrec d (showsPrec d x "")).

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

show :: a -> String

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

showList :: [a] -> ShowS

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

Instances

Show Bool

Show Char

Show Double

Show Float

Show Int

Show Integer

Show Ordering

Show ()

Show All

Show Any

Show a => Show [a]

Integral a => Show (Ratio a)

Show a => Show (Dual a)

Show a => Show (Sum a)

Show a => Show (Product a)

Show a => Show (First a)

Show a => Show (Last a)

Show a => Show (Maybe a)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

class Read a where

Parsing of Strings, producing values.

Minimal complete definition: readsPrec (or, for GHC only, readPrec)

Derived instances of Read make the following assumptions, which derived instances of Text.Show.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 98 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

Methods

readsPrec

Arguments

:: Int

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

-> ReadS a

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

Derived instances of Read and Text.Show.Show satisfy the following:

• (x,"") is an element of (readsPrec d (Text.Show.showsPrec d x "")).

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

readList :: ReadS [a]

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

Instances

Read Bool

Read Char

Read Double

Read Float

Read Int

Read Integer

Read Ordering

Read ()

Read All

Read Any

Read Lexeme

Read a => Read [a]

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

Read a => Read (Dual a)

Read a => Read (Sum a)

Read a => Read (Product a)

Read a => Read (First a)

Read a => Read (Last a)

Read a => Read (Maybe a)

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

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

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

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

(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)

read :: Read a => String -> a

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

Basic I/O

data IO a

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

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

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

Instances

Monad IO

Functor IO

Applicative IO

putChar :: Char -> IO ()

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

putStr :: String -> IO ()

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

putStrLn :: String -> IO ()

The same as putStr, but adds a newline character.

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

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

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

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

getChar :: IO Char

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

getLine :: IO String

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

readFile :: FilePath -> IO String

The readFile function reads a file and returns the contents of the file as a string. The file is read strictly, as with getContents.

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

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

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]])

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

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

readLn :: Read a => IO a

The readLn function combines getLine and readIO.

Basic function composition

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

curry converts an uncurried function to a curried function.

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

uncurry converts a curried function to a function on pairs.

first :: Arrow a => forall b c d. a b c -> a (b, d) (c, d)

Send the first component of the input through the argument arrow, and copy the rest unchanged to the output.

second :: Arrow a => forall b c d. a b c -> a (d, b) (d, c)

A mirror image of first.

The default definition may be overridden with a more efficient version if desired.

id :: a -> a

Identity function.

const :: a -> b -> a

Constant function.

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

Function composition.

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

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

($) :: (t1 -> t) -> t1 -> t

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

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

Integer math

data Int

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

Instances

Bounded Int

Enum Int

Eq Int

Integral Int

Num Int

Ord Int

Read Int

Real Int

Show Int

data Integer

Arbitrary-precision integers.

Instances

Enum Integer

Integral Integer

Num Integer

Read Integer

Real Integer

Show Integer

class Bounded a where

The Bounded class is used to name the upper and lower limits of a type. Ord is not a superclass of Bounded since types that are not totally ordered may also have upper and lower bounds.

The Bounded class may be derived for any enumeration type; minBound is the first constructor listed in the data declaration and maxBound is the last. Bounded may also be derived for single-constructor datatypes whose constituent types are in Bounded.

Methods

minBound :: a

maxBound :: a

Instances

Bounded Bool

Bounded Char

Bounded Int

Bounded Ordering

Bounded ()

Bounded All

Bounded Any

Bounded a => Bounded (Dual a)

Bounded a => Bounded (Sum a)

Bounded a => Bounded (Product a)

(Bounded a, Bounded b) => Bounded (a, b)

(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c)

(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d)

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e)

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f)

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

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

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

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

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

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

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

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

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

class (Eq a, Show a) => Num a where

Basic numeric class.

Minimal complete definition: all except negate or (-)

Methods

(+) :: a -> a -> a

(*) :: a -> a -> a

(-) :: a -> a -> a

negate :: a -> a

Unary negation.

abs :: a -> a

Absolute value.

signum :: a -> a

Sign of a number. The functions abs and signum should satisfy the law:

 abs x * signum x == x

For real numbers, the signum is either -1 (negative), 0 (zero) or 1 (positive).

fromInteger :: Integer -> a

Conversion from an Integer. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer, so such literals have type (Num a) => a.

Instances

Num Double

Num Float

Num Int

Num Integer

Integral a => Num (Ratio a)

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

Integral numbers, supporting integer division.

Minimal complete definition: quotRem and toInteger

Methods

quot :: a -> a -> a

integer division truncated toward zero

rem :: a -> a -> a

integer remainder, satisfying

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

div :: a -> a -> a

integer division truncated toward negative infinity

mod :: a -> a -> a

integer modulus, satisfying

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

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

simultaneous quot and rem

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

simultaneous div and mod

toInteger :: a -> Integer

conversion to Integer

Instances

Integral Int

Integral Integer

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

the same as flip (-).

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

even :: Integral a => a -> Bool

odd :: Integral a => a -> Bool

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

raise a number to a non-negative integral power

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

general coercion from integral types

Monad hierarchy

module Control.Applicative

module Control.Monad

Monoids, Foldables and other goodies

module Data.Monoid

(<>) :: Monoid a => a -> a -> a

module Data.Foldable

module Data.Traversable

Misc.

asTypeOf :: a -> a -> a

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

error :: [Char] -> a

error stops execution and displays an error message.

undefined :: a

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

seq :: a -> b -> b

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

($!) :: (t1 -> t) -> t1 -> t