Prelude replacement, use the NoImplicitPrelude extension before importing this.
It deliberately omits all listhandling functions, import Data.List or use the generic versions.
 module Data.Bool
 bool :: a > a > Bool > a
 module Data.Maybe
 module Data.Either
 module Data.Eq
 module Data.Ord
 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]
 data Char
 type String = [Char]
 fst :: (a, b) > a
 snd :: (a, b) > b
 lines :: String > [String]
 words :: String > [String]
 unlines :: [String] > String
 unwords :: [String] > String
 class Show a where
 class Read a where
 read :: Read a => String > a
 data IO a
 putChar :: Char > IO ()
 putStr :: String > IO ()
 putStrLn :: String > IO ()
 print :: Show a => a > IO ()
 getChar :: IO Char
 getLine :: IO String
 readFile :: FilePath > IO String
 writeFile :: FilePath > String > IO ()
 appendFile :: FilePath > String > IO ()
 readIO :: Read a => String > IO a
 readLn :: Read a => IO a
 curry :: ((a, b) > c) > a > b > c
 uncurry :: (a > b > c) > (a, b) > c
 first :: Arrow a => forall b c d. a b c > a (b, d) (c, d)
 second :: Arrow a => forall b c d. a b c > a (d, b) (d, c)
 id :: a > a
 const :: a > b > a
 (.) :: (b > c) > (a > b) > a > c
 flip :: (a > b > c) > b > a > c
 ($) :: (t1 > t) > t1 > t
 until :: (a > Bool) > (a > a) > a > a
 data Int
 data Integer
 class Bounded a where
 class (Eq a, Show a) => Num a where
 class (Real a, Enum a) => Integral a where
 subtract :: Num a => a > a > a
 even :: Integral a => a > Bool
 odd :: Integral a => a > Bool
 (^) :: (Num a, Integral b) => a > b > a
 fromIntegral :: (Integral a, Num b) => a > b
 module Control.Applicative
 module Control.Monad
 module Data.Monoid
 (<>) :: Monoid a => a > a > a
 module Data.Foldable
 module Data.Traversable
 asTypeOf :: a > a > a
 error :: [Char] > a
 undefined :: a
 seq :: a > b > b
 ($!) :: (t1 > t) > t1 > t
Basic/legacy types
module Data.Bool
:: 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 lefttoright by fromEnum
from 0
through n1
.
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
andsucc
maxBound
should result in a runtime error.pred
minBound

fromEnum
andtoEnum
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
andenumFromThen
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 implementationdependent 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]
.
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 88591 (Latin1) 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
).
fst :: (a, b) > a
Extract the first component of a pair.
snd :: (a, b) > b
Extract the second component of a pair.
lines
breaks a string up into a list of strings at newline
characters. The resulting strings do not contain newlines.
words
breaks a string up into a list of words, which were delimited
by white space.
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 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 toplevel constructor in
x
is less thand
(associativity is ignored). Thus, ifd
is0
then the result is never surrounded in parentheses; ifd
is11
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 recordsyntax 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 rightassociativity of :^:
is ignored. For example,

produces the stringshow
(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 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 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 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 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 recordsyntax 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 rightassociativity 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 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.
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) 
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
is a computation which, when performed,
does some I/O before returning a value of type IO
aa
.
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 donotation
or the >>
and >>=
operations from the Monad
class.
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]])
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]])
Basic function composition
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
takes its (first) two arguments in the reverse order of flip
ff
.
Integer math
data Int
A fixedprecision integer type with at least the range [2^29 .. 2^291]
.
The exact range for a given implementation can be determined by using
Prelude.minBound
and Prelude.maxBound
from the Prelude.Bounded
class.
data Integer
Arbitraryprecision integers.
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 singleconstructor datatypes whose
constituent types are in Bounded
.
class (Eq a, Show a) => Num a where
Basic numeric class.
Minimal complete definition: all except negate
or ()
(+) :: 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
class (Real a, Enum a) => Integral a where
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)
divMod :: a > a > (a, a)
conversion to Integer
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
module Data.Foldable
module Data.Traversable
Misc.
asTypeOf :: a > a > a
undefined :: a
seq :: a > b > b
Evaluates its first argument to head normal form, and then returns its second argument as the result.