Safe Haskell | None |
---|---|
Language | Haskell2010 |
Synopsis
- (.) :: (b -> c) -> (a -> b) -> a -> c
- const :: a -> b -> a
- id :: a -> a
- outl :: (a, b) -> a
- outr :: (a, b) -> b
- swap :: (a, b) -> (b, a)
- assocl :: (a, (b, c)) -> ((a, b), c)
- assocr :: ((a, b), c) -> (a, (b, c))
- dupl :: (a, (b, c)) -> ((a, b), (a, c))
- dupr :: ((a, b), c) -> ((a, c), (b, c))
- pair :: (a -> b, a -> c) -> a -> (b, c)
- cross :: (a -> c, b -> d) -> (a, b) -> (c, d)
- cond :: (a -> Bool) -> (a -> b, a -> b) -> a -> b
- curry :: ((a, b) -> c) -> a -> b -> c
- uncurry :: (a -> b -> c) -> (a, b) -> c
- false :: a -> Bool
- true :: a -> Bool
- (&&) :: Bool -> Bool -> Bool
- (||) :: Bool -> Bool -> Bool
- not :: Bool -> Bool
- otherwise :: Bool
- leq :: Ord a => (a, a) -> Bool
- less :: Ord a => (a, a) -> Bool
- eql :: Ord a => (a, a) -> Bool
- neq :: Ord a => (a, a) -> Bool
- gtr :: Ord a => (a, a) -> Bool
- geq :: Ord a => (a, a) -> Bool
- meet :: (a -> Bool, a -> Bool) -> a -> Bool
- join :: (a -> Bool, a -> Bool) -> a -> Bool
- wok :: ((b, a) -> c) -> (a, b) -> c
- zero :: a -> Natural
- succ :: Natural -> Natural
- pred :: Natural -> Natural
- plus :: Num a => (a, a) -> a
- minus :: Num a => (a, a) -> a
- times :: Num a => (a, a) -> a
- divide :: Fractional a => (a, a) -> a
- negative :: (Ord a, Num a) => a -> Bool
- positive :: (Ord a, Num a) => a -> Bool
- (++) :: [a] -> [a] -> [a]
- null :: [a] -> Bool
- nil :: t -> [a]
- wrap :: a -> [a]
- cons :: (a, [a]) -> [a]
- cat :: ([a], [a]) -> [a]
- concat :: [[a]] -> [a]
- snoc :: ([a], a) -> [a]
- head :: [a] -> a
- tail :: [a] -> [a]
- split :: [a] -> (a, [a])
- last :: [a] -> a
- init :: [a] -> [a]
- inits :: [a] -> [[a]]
- tails :: [a] -> [[a]]
- splits :: [a] -> [([a], [a])]
- cpp :: ([a], [b]) -> [(a, b)]
- cpl :: ([a], b) -> [(a, b)]
- cpr :: (a, [b]) -> [(a, b)]
- cplist :: [[a]] -> [[a]]
- minlist :: ((a, a) -> Bool) -> [a] -> a
- bmin :: ((a, a) -> Bool) -> (a, a) -> a
- maxlist :: ((a, a) -> Bool) -> [a] -> a
- bmax :: ((a, a) -> Bool) -> (a, a) -> a
- thinlist :: ((a, a) -> Bool) -> [a] -> [a]
- length :: [a] -> Natural
- sum :: Num a => [a] -> a
- trans :: [[a]] -> [[a]]
- list :: (a -> b) -> [a] -> [b]
- filter :: (a -> Bool) -> [a] -> [a]
- catalist :: (b, (a, b) -> b) -> [a] -> b
- cata1list :: (a -> b, (a, b) -> b) -> [a] -> b
- cata2list :: ((a, a) -> b, (a, b) -> b) -> [a] -> b
- loop :: ((a, b) -> a) -> (a, [b]) -> a
- merge :: ((a, a) -> Bool) -> ([a], [a]) -> [a]
- zip :: ([a], [b]) -> [(a, b)]
- unzip :: [(a, b)] -> ([a], [b])
- words :: String -> [String]
- lines :: String -> [String]
- unwords :: [String] -> String
- unlines :: [String] -> String
- ord :: Char -> Int
- chr :: Int -> Char
- (==) :: Eq a => a -> a -> Bool
- (/=) :: Eq a => a -> a -> Bool
- (<=) :: Ord a => a -> a -> Bool
- (<) :: Ord a => a -> a -> Bool
- (>=) :: Ord a => a -> a -> Bool
- (>) :: Ord a => a -> a -> Bool
- (+) :: Num a => a -> a -> a
- (-) :: Num a => a -> a -> a
- (/) :: Fractional a => a -> a -> a
- div :: Integral a => a -> a -> a
- mod :: Integral a => a -> a -> a
- (*) :: Num a => a -> a -> a
- negate :: Num a => a -> a
- primPrint :: Show a => a -> IO ()
- strict :: (a -> b) -> a -> b
- error :: HasCallStack => [Char] -> a
- show :: Show a => a -> String
- flip :: (a -> b -> c) -> b -> a -> c
- type String = [Char]
- class Num a
- class Num a => Fractional a
- class Show a
- data Natural
- module GHC.Types
Documentation
divide :: Fractional a => (a, a) -> a Source #
(/) :: Fractional a => a -> a -> a infixl 7 #
fractional division
mod :: Integral a => a -> a -> a infixl 7 #
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
error :: HasCallStack => [Char] -> a #
error
stops execution and displays an error message.
Basic numeric class.
The Haskell Report defines no laws for Num
. However, '(+)' and '(*)' are
customarily expected to define a ring and have the following properties:
- Associativity of (+)
(x + y) + z
=x + (y + z)
- Commutativity of (+)
x + y
=y + x
fromInteger 0
is the additive identityx + fromInteger 0
=x
negate
gives the additive inversex + negate x
=fromInteger 0
- Associativity of (*)
(x * y) * z
=x * (y * z)
fromInteger 1
is the multiplicative identityx * fromInteger 1
=x
andfromInteger 1 * x
=x
- Distributivity of (*) with respect to (+)
a * (b + c)
=(a * b) + (a * c)
and(b + c) * a
=(b * a) + (c * a)
Note that it isn't customarily expected that a type instance of both Num
and Ord
implement an ordered ring. Indeed, in base
only Integer
and
Rational
do.
class Num a => Fractional a #
Fractional numbers, supporting real division.
The Haskell Report defines no laws for Fractional
. However, '(+)' and
'(*)' are customarily expected to define a division ring and have the
following properties:
recip
gives the multiplicative inversex * recip x
=recip x * x
=fromInteger 1
Note that it isn't customarily expected that a type instance of
Fractional
implement a field. However, all instances in base
do.
fromRational, (recip | (/))
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 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 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 stringshow
(Leaf 1 :^: Leaf 2 :^: Leaf 3)"Leaf 1 :^: (Leaf 2 :^: Leaf 3)"
.
Instances
Show Bool | Since: base-2.1 |
Show Char | Since: base-2.1 |
Show Int | Since: base-2.1 |
Show Integer | Since: base-2.1 |
Show Natural | Since: base-4.8.0.0 |
Show Ordering | Since: base-2.1 |
Show Word | Since: base-2.1 |
Show RuntimeRep | Since: base-4.11.0.0 |
Defined in GHC.Show showsPrec :: Int -> RuntimeRep -> ShowS # show :: RuntimeRep -> String # showList :: [RuntimeRep] -> ShowS # | |
Show VecCount | Since: base-4.11.0.0 |
Show VecElem | Since: base-4.11.0.0 |
Show CallStack | Since: base-4.9.0.0 |
Show () | Since: base-2.1 |
Show TyCon | Since: base-2.1 |
Show Module | Since: base-4.9.0.0 |
Show TrName | Since: base-4.9.0.0 |
Show KindRep | |
Show TypeLitSort | Since: base-4.11.0.0 |
Defined in GHC.Show showsPrec :: Int -> TypeLitSort -> ShowS # show :: TypeLitSort -> String # showList :: [TypeLitSort] -> ShowS # | |
Show SrcLoc | Since: base-4.9.0.0 |
Show a => Show [a] | Since: base-2.1 |
Show a => Show (Maybe a) | Since: base-2.1 |
Show a => Show (Ratio a) | Since: base-2.0.1 |
Show a => Show (NonEmpty a) | Since: base-4.11.0.0 |
(Show a, Show b) => Show (a, b) | Since: base-2.1 |
(Show a, Show b, Show c) => Show (a, b, c) | Since: base-2.1 |
(Show a, Show b, Show c, Show d) => Show (a, b, c, d) | Since: base-2.1 |
(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e) | Since: base-2.1 |
(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f) | Since: base-2.1 |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g) | Since: base-2.1 |
(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) | Since: base-2.1 |
(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) | Since: base-2.1 |
(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) | Since: base-2.1 |
(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) | Since: base-2.1 |
(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) | Since: base-2.1 |
(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) | Since: base-2.1 |
(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) | Since: base-2.1 |
(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) | Since: base-2.1 |
Type representing arbitrary-precision non-negative integers.
>>>
2^100 :: Natural
1267650600228229401496703205376
Operations whose result would be negative
,throw
(Underflow
:: ArithException
)
>>>
-1 :: Natural
*** Exception: arithmetic underflow
Since: base-4.8.0.0
Instances
Eq Natural | Since: base-4.8.0.0 |
Integral Natural | Since: base-4.8.0.0 |
Defined in GHC.Real | |
Num Natural | Note that Since: base-4.8.0.0 |
Ord Natural | Since: base-4.8.0.0 |
Real Natural | Since: base-4.8.0.0 |
Defined in GHC.Real toRational :: Natural -> Rational # | |
Show Natural | Since: base-4.8.0.0 |
module GHC.Types