Safe Haskell | Safe-Inferred |
---|---|
Language | Haskell2010 |
Prelude.Linear
Description
This module provides a replacement for Prelude
with
support for linear programming via linear versions of
standard data types, functions and type classes.
A simple example:
>>>
:set -XLinearTypes
>>>
:set -XNoImplicitPrelude
>>>
import Prelude.Linear
>>>
:{
boolToInt :: Bool %1-> Int boolToInt False = 0 boolToInt True = 1 :}
>>>
:{
makeInt :: Either Int Bool %1-> Int makeInt = either id boolToInt :}
This module is designed to be imported unqualifed.
Synopsis
- module Data.Bool.Linear
- data Char
- module Data.Maybe.Linear
- module Data.Either.Linear
- fst :: (a, b) -> a
- snd :: (a, b) -> b
- curry :: ((a, b) %1 -> c) %1 -> a %1 -> b %1 -> c
- uncurry :: (a %1 -> b %1 -> c) %1 -> (a, b) %1 -> c
- module Data.Ord.Linear
- 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 Bounded a where
- data Int
- data Integer
- data Float
- data Double
- type Rational = Ratio Integer
- data Word
- module Data.Num.Linear
- class (Num a, Ord a) => Real a where
- toRational :: a -> Rational
- class (Real a, Enum a) => Integral a where
- class Fractional a => Floating a where
- class Num a => Fractional a where
- (/) :: a -> a -> a
- recip :: a -> a
- fromRational :: Rational -> a
- class (Real a, Fractional a) => RealFrac a where
- 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
- subtract :: Num a => a -> a -> a
- even :: Integral a => a -> Bool
- odd :: Integral a => a -> Bool
- gcd :: Integral a => a -> a -> a
- lcm :: Integral a => a -> a -> a
- (^) :: (Num a, Integral b) => a -> b -> a
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- fromIntegral :: (Integral a, Num b) => a -> b
- realToFrac :: (Real a, Fractional b) => a -> b
- (<*) :: (Applicative f, Consumable b) => f a %1 -> f b %1 -> f a
- module Data.Monoid.Linear
- id :: a %1 -> a
- const :: a %1 -> b -> a
- (.) :: (b %1 -> c) %1 -> (a %1 -> b) %1 -> a %1 -> c
- flip :: (a %p -> b %q -> c) %r -> b %q -> a %p -> c
- ($) :: (a %1 -> b) %1 -> a %1 -> b
- (&) :: a %1 -> (a %1 -> b) %1 -> b
- until :: (a -> Bool) -> (a -> a) -> a -> a
- asTypeOf :: a %1 -> a -> a
- error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a
- errorWithoutStackTrace :: forall (r :: RuntimeRep) (a :: TYPE r). [Char] -> a
- undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a
- seq :: a -> b %1 -> b
- ($!) :: (a %1 -> b) %1 -> a %1 -> b
- module Data.List.Linear
- module Data.String
- type ShowS = String -> String
- class Show a where
- shows :: Show a => a -> ShowS
- showChar :: Char -> ShowS
- showString :: String -> ShowS
- showParen :: Bool -> ShowS -> ShowS
- type ReadS a = String -> [(a, String)]
- class Read a where
- reads :: Read a => ReadS a
- readParen :: Bool -> ReadS a -> ReadS a
- read :: Read a => String -> a
- lex :: ReadS String
- data IO a
- putChar :: Char -> IO ()
- putStr :: String -> IO ()
- putStrLn :: String -> IO ()
- print :: Show a => a -> IO ()
- getChar :: IO Char
- getLine :: IO String
- getContents :: IO String
- interact :: (String -> String) -> IO ()
- type FilePath = String
- readFile :: FilePath -> IO String
- writeFile :: FilePath -> String -> IO ()
- appendFile :: FilePath -> String -> IO ()
- readIO :: Read a => String -> IO a
- readLn :: Read a => IO a
- data Ur a where
- unur :: Ur a %1 -> a
- class Consumable a where
- consume :: a %1 -> ()
- class Consumable a => Dupable a where
- class Dupable a => Movable a where
- lseq :: Consumable a => a %1 -> b %1 -> b
- dup :: Dupable a => a %1 -> (a, a)
- dup3 :: Dupable a => a %1 -> (a, a, a)
- forget :: (a %1 -> b) %1 -> a -> b
Standard Types, Classes and Related Functions
Basic data types
module Data.Bool.Linear
The character type Char
is an enumeration whose values represent
Unicode (or equivalently ISO/IEC 10646) code points (i.e. 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
).
Instances
Bounded Char | Since: base-2.1 |
Enum Char | Since: base-2.1 |
Eq Char | |
Ord Char | |
Read Char | Since: base-2.1 |
Show Char | Since: base-2.1 |
Ix Char | Since: base-2.1 |
Storable Char | Since: base-2.1 |
Defined in Foreign.Storable | |
Hashable Char | |
Defined in Data.Hashable.Class | |
ErrorList Char | |
Defined in Control.Monad.Trans.Error | |
Consumable Char Source # | |
Defined in Data.Unrestricted.Internal.Instances | |
Dupable Char Source # | |
Movable Char Source # | |
Eq Char Source # | |
Ord Char Source # | |
Lift Char | |
Generic1 (URec Char :: k -> Type) | |
Foldable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UChar m -> m # foldMap :: Monoid m => (a -> m) -> UChar a -> m # foldMap' :: Monoid m => (a -> m) -> UChar a -> m # foldr :: (a -> b -> b) -> b -> UChar a -> b # foldr' :: (a -> b -> b) -> b -> UChar a -> b # foldl :: (b -> a -> b) -> b -> UChar a -> b # foldl' :: (b -> a -> b) -> b -> UChar a -> b # foldr1 :: (a -> a -> a) -> UChar a -> a # foldl1 :: (a -> a -> a) -> UChar a -> a # elem :: Eq a => a -> UChar a -> Bool # maximum :: Ord a => UChar a -> a # minimum :: Ord a => UChar a -> a # | |
Traversable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Char :: Type -> Type) | Since: base-4.9.0.0 |
Eq (URec Char p) | Since: base-4.9.0.0 |
Ord (URec Char p) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Show (URec Char p) | Since: base-4.9.0.0 |
Generic (URec Char p) | |
data URec Char (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 |
type Rep1 (URec Char :: k -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
type Rep (URec Char p) | Since: base-4.9.0.0 |
Defined in GHC.Generics |
module Data.Maybe.Linear
module Data.Either.Linear
Tuples
curry :: ((a, b) %1 -> c) %1 -> a %1 -> b %1 -> c Source #
Beware, curry
is not compatible with the standard one because it is
higher-order and we don't have multiplicity polymorphism yet.
uncurry :: (a %1 -> b %1 -> c) %1 -> (a, b) %1 -> c Source #
Beware, uncurry
is not compatible with the standard one because it is
higher-order and we don't have multiplicity polymorphism yet.
Basic type classes
module Data.Ord.Linear
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
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
Methods
the successor of a value. For numeric types, succ
adds 1.
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
.
Used in Haskell's translation of [n..]
with [n..] = enumFrom n
,
a possible implementation being enumFrom n = n : enumFrom (succ n)
.
For example:
enumFrom 4 :: [Integer] = [4,5,6,7,...]
enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]
enumFromThen :: a -> a -> [a] #
Used in Haskell's translation of [n,n'..]
with [n,n'..] = enumFromThen n n'
, a possible implementation being
enumFromThen n n' = n : n' : worker (f x) (f x n')
,
worker s v = v : worker s (s v)
, x = fromEnum n' - fromEnum n
and
f n y
| n > 0 = f (n - 1) (succ y)
| n < 0 = f (n + 1) (pred y)
| otherwise = y
For example:
enumFromThen 4 6 :: [Integer] = [4,6,8,10...]
enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]
enumFromTo :: a -> a -> [a] #
Used in Haskell's translation of [n..m]
with
[n..m] = enumFromTo n m
, a possible implementation being
enumFromTo n m
| n <= m = n : enumFromTo (succ n) m
| otherwise = []
.
For example:
enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
enumFromTo 42 1 :: [Integer] = []
enumFromThenTo :: a -> a -> a -> [a] #
Used in Haskell's translation of [n,n'..m]
with
[n,n'..m] = enumFromThenTo n n' m
, a possible implementation
being enumFromThenTo n n' m = worker (f x) (c x) n m
,
x = fromEnum n' - fromEnum n
, c x = bool (>=) ((x 0)
f n y
| n > 0 = f (n - 1) (succ y)
| n < 0 = f (n + 1) (pred y)
| otherwise = y
and
worker s c v m
| c v m = v : worker s c (s v) m
| otherwise = []
For example:
enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]
enumFromThenTo 6 8 2 :: [Int] = []
Instances
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
.
Instances
Bounded Bool | Since: base-2.1 |
Bounded Char | Since: base-2.1 |
Bounded Int | Since: base-2.1 |
Bounded Ordering | Since: base-2.1 |
Bounded Word | Since: base-2.1 |
Bounded Word8 | Since: base-2.1 |
Bounded Word16 | Since: base-2.1 |
Bounded Word32 | Since: base-2.1 |
Bounded Word64 | Since: base-2.1 |
Bounded VecCount | Since: base-4.10.0.0 |
Bounded VecElem | Since: base-4.10.0.0 |
Bounded () | Since: base-2.1 |
Bounded Any | Since: base-2.1 |
Bounded All | Since: base-2.1 |
Bounded SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Bounded SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Bounded DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Bounded Associativity | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Bounded WordPtr | |
Bounded IntPtr | |
Bounded GeneralCategory | Since: base-2.1 |
Defined in GHC.Unicode | |
Bounded Extension | |
Bounded m => Bounded (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
Bounded a => Bounded (Min a) | Since: base-4.9.0.0 |
Bounded a => Bounded (Max a) | Since: base-4.9.0.0 |
Bounded a => Bounded (Last a) | Since: base-4.9.0.0 |
Bounded a => Bounded (First a) | Since: base-4.9.0.0 |
Bounded a => Bounded (Identity a) | Since: base-4.9.0.0 |
Bounded a => Bounded (Sum a) | Since: base-2.1 |
Bounded a => Bounded (Product a) | Since: base-2.1 |
Bounded a => Bounded (Dual a) | Since: base-2.1 |
Bounded a => Bounded (Down a) | Swaps Since: base-4.14.0.0 |
(Bounded a, Bounded b) => Bounded (a, b) | Since: base-2.1 |
Bounded (Proxy t) | Since: base-4.7.0.0 |
(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) | Since: base-2.1 |
Bounded a => Bounded (Const a b) | Since: base-4.9.0.0 |
a ~ b => Bounded (a :~: b) | Since: base-4.7.0.0 |
(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) | Since: base-2.1 |
a ~~ b => Bounded (a :~~: b) | Since: base-4.10.0.0 |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) | Since: base-2.1 |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) | Since: base-2.1 |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) | Since: base-2.1 |
(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) | Since: base-2.1 |
(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) | Since: base-2.1 |
(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) | Since: base-2.1 |
(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) | Since: base-2.1 |
(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) | Since: base-2.1 |
(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) | Since: base-2.1 |
(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) | Since: base-2.1 |
(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) | Since: base-2.1 |
Numbers
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
minBound
and maxBound
from the Bounded
class.
Instances
Bounded Int | Since: base-2.1 |
Enum Int | Since: base-2.1 |
Eq Int | |
Integral Int | Since: base-2.0.1 |
Num Int | Since: base-2.1 |
Ord Int | |
Read Int | Since: base-2.1 |
Real Int | Since: base-2.0.1 |
Defined in GHC.Real Methods toRational :: Int -> Rational # | |
Show Int | Since: base-2.1 |
Ix Int | Since: base-2.1 |
Storable Int | Since: base-2.1 |
Defined in Foreign.Storable | |
Hashable Int | |
Defined in Data.Hashable.Class | |
Consumable Int Source # | |
Defined in Data.Unrestricted.Internal.Instances | |
Dupable Int Source # | |
Movable Int Source # | |
Eq Int Source # | |
Ord Int Source # | |
Num Int Source # | |
FromInteger Int Source # | |
Defined in Data.Num.Linear Methods fromInteger :: Integer %1 -> Int Source # | |
Ring Int Source # | |
Defined in Data.Num.Linear | |
Semiring Int Source # | |
Defined in Data.Num.Linear | |
MultIdentity Int Source # | |
Defined in Data.Num.Linear | |
Multiplicative Int Source # | |
AdditiveGroup Int Source # | |
AddIdentity Int Source # | |
Defined in Data.Num.Linear | |
Additive Int Source # | |
Representable Int Source # | |
KnownRepresentable Int Source # | |
Defined in Foreign.Marshal.Pure | |
Lift Int | |
Generic1 (URec Int :: k -> Type) | |
Foldable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UInt m -> m # foldMap :: Monoid m => (a -> m) -> UInt a -> m # foldMap' :: Monoid m => (a -> m) -> UInt a -> m # foldr :: (a -> b -> b) -> b -> UInt a -> b # foldr' :: (a -> b -> b) -> b -> UInt a -> b # foldl :: (b -> a -> b) -> b -> UInt a -> b # foldl' :: (b -> a -> b) -> b -> UInt a -> b # foldr1 :: (a -> a -> a) -> UInt a -> a # foldl1 :: (a -> a -> a) -> UInt a -> a # elem :: Eq a => a -> UInt a -> Bool # maximum :: Ord a => UInt a -> a # | |
Traversable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Int :: Type -> Type) | Since: base-4.9.0.0 |
Eq (URec Int p) | Since: base-4.9.0.0 |
Ord (URec Int p) | Since: base-4.9.0.0 |
Show (URec Int p) | Since: base-4.9.0.0 |
Generic (URec Int p) | |
type AsKnown Int Source # | |
Defined in Foreign.Marshal.Pure | |
data URec Int (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 |
type Rep1 (URec Int :: k -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
type Rep (URec Int p) | Since: base-4.9.0.0 |
Defined in GHC.Generics |
Arbitrary precision integers. In contrast with fixed-size integral types
such as Int
, the Integer
type represents the entire infinite range of
integers.
Integers are stored in a kind of sign-magnitude form, hence do not expect two's complement form when using bit operations.
If the value is small (fit into an Int
), IS
constructor is used.
Otherwise Integer
and IN
constructors are used to store a BigNat
representing respectively the positive or the negative value magnitude.
Invariant: Integer
and IN
are used iff value doesn't fit in IS
Instances
Enum Integer | Since: base-2.1 |
Eq Integer | |
Integral Integer | Since: base-2.0.1 |
Defined in GHC.Real | |
Num Integer | Since: base-2.1 |
Ord Integer | |
Read Integer | Since: base-2.1 |
Real Integer | Since: base-2.0.1 |
Defined in GHC.Real Methods toRational :: Integer -> Rational # | |
Show Integer | Since: base-2.1 |
Ix Integer | Since: base-2.1 |
Defined in GHC.Ix | |
Hashable Integer | |
Defined in Data.Hashable.Class | |
Lift Integer | |
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.
Instances
Eq Float | Note that due to the presence of
Also note that
|
Floating Float | Since: base-2.1 |
Ord Float | Note that due to the presence of
Also note that, due to the same,
|
Read Float | Since: base-2.1 |
RealFloat Float | Since: base-2.1 |
Defined in GHC.Float Methods floatRadix :: Float -> Integer # floatDigits :: Float -> Int # floatRange :: Float -> (Int, Int) # decodeFloat :: Float -> (Integer, Int) # encodeFloat :: Integer -> Int -> Float # significand :: Float -> Float # scaleFloat :: Int -> Float -> Float # isInfinite :: Float -> Bool # isDenormalized :: Float -> Bool # isNegativeZero :: Float -> Bool # | |
Storable Float | Since: base-2.1 |
Hashable Float | Note: prior to The Since: hashable-1.3.0.0 |
Defined in Data.Hashable.Class | |
Lift Float | |
Generic1 (URec Float :: k -> Type) | |
Foldable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UFloat m -> m # foldMap :: Monoid m => (a -> m) -> UFloat a -> m # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m # foldr :: (a -> b -> b) -> b -> UFloat a -> b # foldr' :: (a -> b -> b) -> b -> UFloat a -> b # foldl :: (b -> a -> b) -> b -> UFloat a -> b # foldl' :: (b -> a -> b) -> b -> UFloat a -> b # foldr1 :: (a -> a -> a) -> UFloat a -> a # foldl1 :: (a -> a -> a) -> UFloat a -> a # elem :: Eq a => a -> UFloat a -> Bool # maximum :: Ord a => UFloat a -> a # minimum :: Ord a => UFloat a -> a # | |
Traversable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Float :: Type -> Type) | Since: base-4.9.0.0 |
Eq (URec Float p) | |
Ord (URec Float p) | |
Defined in GHC.Generics | |
Show (URec Float p) | |
Generic (URec Float p) | |
data URec Float (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 |
type Rep1 (URec Float :: k -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
type Rep (URec Float p) | |
Defined in GHC.Generics |
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.
Instances
Eq Double | Note that due to the presence of
Also note that
|
Floating Double | Since: base-2.1 |
Ord Double | Note that due to the presence of
Also note that, due to the same,
|
Read Double | Since: base-2.1 |
RealFloat Double | Since: base-2.1 |
Defined in GHC.Float Methods floatRadix :: Double -> Integer # floatDigits :: Double -> Int # floatRange :: Double -> (Int, Int) # decodeFloat :: Double -> (Integer, Int) # encodeFloat :: Integer -> Int -> Double # significand :: Double -> Double # scaleFloat :: Int -> Double -> Double # isInfinite :: Double -> Bool # isDenormalized :: Double -> Bool # isNegativeZero :: Double -> Bool # | |
Storable Double | Since: base-2.1 |
Hashable Double | Note: prior to The Since: hashable-1.3.0.0 |
Defined in Data.Hashable.Class | |
Consumable Double Source # | |
Defined in Data.Unrestricted.Internal.Instances | |
Dupable Double Source # | |
Movable Double Source # | |
Eq Double Source # | |
Ord Double Source # | |
Num Double Source # | |
FromInteger Double Source # | |
Defined in Data.Num.Linear Methods fromInteger :: Integer %1 -> Double Source # | |
Ring Double Source # | |
Defined in Data.Num.Linear | |
Semiring Double Source # | |
Defined in Data.Num.Linear | |
MultIdentity Double Source # | |
Defined in Data.Num.Linear | |
Multiplicative Double Source # | |
AdditiveGroup Double Source # | |
AddIdentity Double Source # | |
Defined in Data.Num.Linear | |
Additive Double Source # | |
Lift Double | |
Generic1 (URec Double :: k -> Type) | |
Foldable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UDouble m -> m # foldMap :: Monoid m => (a -> m) -> UDouble a -> m # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m # foldr :: (a -> b -> b) -> b -> UDouble a -> b # foldr' :: (a -> b -> b) -> b -> UDouble a -> b # foldl :: (b -> a -> b) -> b -> UDouble a -> b # foldl' :: (b -> a -> b) -> b -> UDouble a -> b # foldr1 :: (a -> a -> a) -> UDouble a -> a # foldl1 :: (a -> a -> a) -> UDouble a -> a # elem :: Eq a => a -> UDouble a -> Bool # maximum :: Ord a => UDouble a -> a # minimum :: Ord a => UDouble a -> a # | |
Traversable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Double :: Type -> Type) | Since: base-4.9.0.0 |
Eq (URec Double p) | Since: base-4.9.0.0 |
Ord (URec Double p) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods compare :: URec Double p -> URec Double p -> Ordering # (<) :: URec Double p -> URec Double p -> Bool # (<=) :: URec Double p -> URec Double p -> Bool # (>) :: URec Double p -> URec Double p -> Bool # (>=) :: URec Double p -> URec Double p -> Bool # | |
Show (URec Double p) | Since: base-4.9.0.0 |
Generic (URec Double p) | |
data URec Double (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 |
type Rep1 (URec Double :: k -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
type Rep (URec Double p) | Since: base-4.9.0.0 |
Defined in GHC.Generics |
Instances
Bounded Word | Since: base-2.1 |
Enum Word | Since: base-2.1 |
Eq Word | |
Integral Word | Since: base-2.1 |
Num Word | Since: base-2.1 |
Ord Word | |
Read Word | Since: base-4.5.0.0 |
Real Word | Since: base-2.1 |
Defined in GHC.Real Methods toRational :: Word -> Rational # | |
Show Word | Since: base-2.1 |
Ix Word | Since: base-4.6.0.0 |
Storable Word | Since: base-2.1 |
Defined in Foreign.Storable | |
Hashable Word | |
Defined in Data.Hashable.Class | |
Representable Word Source # | |
KnownRepresentable Word Source # | |
Defined in Foreign.Marshal.Pure | |
Lift Word | |
Generic1 (URec Word :: k -> Type) | |
Foldable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UWord m -> m # foldMap :: Monoid m => (a -> m) -> UWord a -> m # foldMap' :: Monoid m => (a -> m) -> UWord a -> m # foldr :: (a -> b -> b) -> b -> UWord a -> b # foldr' :: (a -> b -> b) -> b -> UWord a -> b # foldl :: (b -> a -> b) -> b -> UWord a -> b # foldl' :: (b -> a -> b) -> b -> UWord a -> b # foldr1 :: (a -> a -> a) -> UWord a -> a # foldl1 :: (a -> a -> a) -> UWord a -> a # elem :: Eq a => a -> UWord a -> Bool # maximum :: Ord a => UWord a -> a # minimum :: Ord a => UWord a -> a # | |
Traversable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Word :: Type -> Type) | Since: base-4.9.0.0 |
Eq (URec Word p) | Since: base-4.9.0.0 |
Ord (URec Word p) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
Show (URec Word p) | Since: base-4.9.0.0 |
Generic (URec Word p) | |
type AsKnown Word Source # | |
Defined in Foreign.Marshal.Pure | |
data URec Word (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 |
type Rep1 (URec Word :: k -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
type Rep (URec Word p) | Since: base-4.9.0.0 |
Defined in GHC.Generics |
module Data.Num.Linear
class (Num a, Ord a) => Real a where #
Methods
toRational :: a -> Rational #
the rational equivalent of its real argument with full precision
Instances
Real Int | Since: base-2.0.1 |
Defined in GHC.Real Methods toRational :: Int -> Rational # | |
Real Integer | Since: base-2.0.1 |
Defined in GHC.Real Methods toRational :: Integer -> Rational # | |
Real Natural | Since: base-4.8.0.0 |
Defined in GHC.Real Methods toRational :: Natural -> Rational # | |
Real Word | Since: base-2.1 |
Defined in GHC.Real Methods toRational :: Word -> Rational # | |
Real Word8 | Since: base-2.1 |
Defined in GHC.Word Methods toRational :: Word8 -> Rational # | |
Real Word16 | Since: base-2.1 |
Defined in GHC.Word Methods toRational :: Word16 -> Rational # | |
Real Word32 | Since: base-2.1 |
Defined in GHC.Word Methods toRational :: Word32 -> Rational # | |
Real Word64 | Since: base-2.1 |
Defined in GHC.Word Methods toRational :: Word64 -> Rational # | |
Real WordPtr | |
Defined in Foreign.Ptr Methods toRational :: WordPtr -> Rational # | |
Real IntPtr | |
Defined in Foreign.Ptr Methods toRational :: IntPtr -> Rational # | |
Integral a => Real (Ratio a) | Since: base-2.0.1 |
Defined in GHC.Real Methods toRational :: Ratio a -> Rational # | |
Real a => Real (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity Methods toRational :: Identity a -> Rational # | |
Real a => Real (Down a) | Since: base-4.14.0.0 |
Defined in Data.Ord Methods toRational :: Down a -> Rational # | |
Real a => Real (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods toRational :: Const a b -> Rational # |
class (Real a, Enum a) => Integral a where #
Integral numbers, supporting integer division.
The Haskell Report defines no laws for Integral
. However, Integral
instances are customarily expected to define a Euclidean domain and have the
following properties for the div
/mod
and quot
/rem
pairs, given
suitable Euclidean functions f
and g
:
x
=y * quot x y + rem x y
withrem x y
=fromInteger 0
org (rem x y)
<g y
x
=y * div x y + mod x y
withmod x y
=fromInteger 0
orf (mod x y)
<f y
An example of a suitable Euclidean function, for Integer
's instance, is
abs
.
Methods
quot :: a -> a -> a infixl 7 #
integer division truncated toward zero
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
integer division truncated toward negative infinity
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
conversion to Integer
Instances
Integral Int | Since: base-2.0.1 |
Integral Integer | Since: base-2.0.1 |
Defined in GHC.Real | |
Integral Natural | Since: base-4.8.0.0 |
Defined in GHC.Real | |
Integral Word | Since: base-2.1 |
Integral Word8 | Since: base-2.1 |
Integral Word16 | Since: base-2.1 |
Integral Word32 | Since: base-2.1 |
Integral Word64 | Since: base-2.1 |
Integral WordPtr | |
Defined in Foreign.Ptr | |
Integral IntPtr | |
Defined in Foreign.Ptr | |
Integral a => Integral (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity Methods quot :: Identity a -> Identity a -> Identity a # rem :: Identity a -> Identity a -> Identity a # div :: Identity a -> Identity a -> Identity a # mod :: Identity a -> Identity a -> Identity a # quotRem :: Identity a -> Identity a -> (Identity a, Identity a) # divMod :: Identity a -> Identity a -> (Identity a, Identity a) # | |
Integral a => Integral (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods quot :: Const a b -> Const a b -> Const a b # rem :: Const a b -> Const a b -> Const a b # div :: Const a b -> Const a b -> Const a b # mod :: Const a b -> Const a b -> Const a b # quotRem :: Const a b -> Const a b -> (Const a b, Const a b) # divMod :: Const a b -> Const a b -> (Const a b, Const a b) # |
class Fractional a => Floating a where #
Trigonometric and hyperbolic functions and related functions.
The Haskell Report defines no laws for Floating
. However, (
, +
)(
and *
)exp
are customarily expected to define an exponential field and have
the following properties:
exp (a + b)
=exp a * exp b
exp (fromInteger 0)
=fromInteger 1
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
Instances
class Num a => Fractional a where #
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.
Minimal complete definition
fromRational, (recip | (/))
Methods
Fractional division.
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
Instances
Integral a => Fractional (Ratio a) | Since: base-2.0.1 |
RealFloat a => Fractional (Complex a) | Since: base-2.1 |
Fractional a => Fractional (Identity a) | Since: base-4.9.0.0 |
Fractional a => Fractional (Down a) | Since: base-4.14.0.0 |
Fractional a => Fractional (Const a b) | Since: base-4.9.0.0 |
class (Real a, Fractional a) => RealFrac a where #
Extracting components of fractions.
Minimal complete definition
Methods
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 asx
; andf
is a fraction with the same type and sign asx
, and with absolute value less than1
.
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
xx
between zero and x
round :: Integral b => a -> b #
returns the nearest integer to round
xx
;
the even integer if x
is equidistant between two integers
ceiling :: Integral b => a -> b #
returns the least integer not less than ceiling
xx
floor :: Integral b => a -> b #
returns the greatest integer not greater than floor
xx
class (RealFrac a, Floating a) => RealFloat a where #
Efficient, machine-independent access to the components of a floating-point number.
Minimal complete definition
floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE
Methods
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^dd
is
the value of
.
In particular, floatDigits
x
. If the type
contains a negative zero, also decodeFloat
0 = (0,0)
.
The result of decodeFloat
(-0.0) = (0,0)
is unspecified if either of
decodeFloat
x
or isNaN
x
is isInfinite
xTrue
.
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 nm*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 = 0x
,
.
If exponent
x = snd (decodeFloat
x) + floatDigits
xx
is a finite floating-point number, it is equal in value to
, where significand
x * b ^^ exponent
xb
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
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 1y
in a type
that is RealFloat
, should return the same value as
.
A default definition of atan
yatan2
is provided, but implementors
can provide a more accurate implementation.
Instances
Numeric functions
gcd :: Integral a => a -> a -> a #
is the non-negative factor of both gcd
x yx
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 44
.
= gcd
0 00
.
(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
lcm :: Integral a => a -> a -> a #
is the smallest positive integer that both lcm
x yx
and y
divide.
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 #
raise a number to an integral power
fromIntegral :: (Integral a, Num b) => a -> b #
general coercion from integral types
realToFrac :: (Real a, Fractional b) => a -> b #
general coercion to fractional types
Monads and functors
(<*) :: (Applicative f, Consumable b) => f a %1 -> f b %1 -> f a Source #
Linearly typed replacement for the standard (<*)
function.
Semigroups and monoids
module Data.Monoid.Linear
Miscellaneous functions
(.) :: (b %1 -> c) %1 -> (a %1 -> b) %1 -> a %1 -> c Source #
Beware: (.)
is not compatible with the standard one because it is
higher-order and we don't have multiplicity polymorphism yet.
flip :: (a %p -> b %q -> c) %r -> b %q -> a %p -> c Source #
Replacement for the flip function with generalized multiplicities.
($) :: (a %1 -> b) %1 -> a %1 -> b infixr 0 Source #
Beware: ($)
is not compatible with the standard one because it is
higher-order and we don't have multiplicity polymorphism yet.
until :: (a -> Bool) -> (a -> a) -> a -> a #
yields the result of applying until
p ff
until p
holds.
error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a #
error
stops execution and displays an error message.
errorWithoutStackTrace :: forall (r :: RuntimeRep) (a :: TYPE r). [Char] -> a #
A variant of error
that does not produce a stack trace.
Since: base-4.9.0.0
undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a #
seq :: a -> b %1 -> b Source #
seq x y
only forces x
to head normal form, therefore is not guaranteed
to consume x
when the resulting computation is consumed. Therefore, seq
cannot be linear in it's first argument.
List operations
module Data.List.Linear
Functions on strings
module Data.String
Converting to and from String
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)"
.
Methods
Arguments
:: 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.