| Copyright | (c) The University of Glasgow 1994-2002 |
|---|---|
| License | see libraries/base/LICENSE |
| Maintainer | cvs-ghc@haskell.org |
| Stability | internal |
| Portability | non-portable (GHC Extensions) |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
GHC.Num
Synopsis
- class Num a where
- subtract :: Num a => a -> a -> a
- module GHC.Integer
- module GHC.Natural
Documentation
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 + xfromInteger0x + fromInteger 0=xnegategives the additive inversex + negate x=fromInteger 0- Associativity of
(*) (x * y) * z=x * (y * z)fromInteger1x * fromInteger 1=xandfromInteger 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.
Methods
Unary negation.
Absolute value.
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 # | Note that due to the presence of
Also note that due to the presence of -0,
Since: base-2.1 |
| Num Float # | Note that due to the presence of
Also note that due to the presence of -0,
Since: base-2.1 |
| Num Int # | Since: base-2.1 |
| Num Int8 # | Since: base-2.1 |
| Num Int16 # | Since: base-2.1 |
| Num Int32 # | Since: base-2.1 |
| Num Int64 # | Since: base-2.1 |
| Num Integer # | Since: base-2.1 |
| Num Natural # | Note that Since: base-4.8.0.0 |
| Num Word # | Since: base-2.1 |
| Num Word8 # | Since: base-2.1 |
| Num Word16 # | Since: base-2.1 |
| Num Word32 # | Since: base-2.1 |
| Num Word64 # | Since: base-2.1 |
| Num IntPtr # | |
| Num WordPtr # | |
| Num CUIntMax # | |
| Num CIntMax # | |
| Num CUIntPtr # | |
| Num CIntPtr # | |
| Num CSUSeconds # | |
Defined in Foreign.C.Types Methods (+) :: CSUSeconds -> CSUSeconds -> CSUSeconds # (-) :: CSUSeconds -> CSUSeconds -> CSUSeconds # (*) :: CSUSeconds -> CSUSeconds -> CSUSeconds # negate :: CSUSeconds -> CSUSeconds # abs :: CSUSeconds -> CSUSeconds # signum :: CSUSeconds -> CSUSeconds # fromInteger :: Integer -> CSUSeconds # | |
| Num CUSeconds # | |
Defined in Foreign.C.Types | |
| Num CTime # | |
| Num CClock # | |
| Num CSigAtomic # | |
Defined in Foreign.C.Types Methods (+) :: CSigAtomic -> CSigAtomic -> CSigAtomic # (-) :: CSigAtomic -> CSigAtomic -> CSigAtomic # (*) :: CSigAtomic -> CSigAtomic -> CSigAtomic # negate :: CSigAtomic -> CSigAtomic # abs :: CSigAtomic -> CSigAtomic # signum :: CSigAtomic -> CSigAtomic # fromInteger :: Integer -> CSigAtomic # | |
| Num CWchar # | |
| Num CSize # | |
| Num CPtrdiff # | |
| Num CDouble # | |
| Num CFloat # | |
| Num CBool # | |
| Num CULLong # | |
| Num CLLong # | |
| Num CULong # | |
| Num CLong # | |
| Num CUInt # | |
| Num CInt # | |
| Num CUShort # | |
| Num CShort # | |
| Num CUChar # | |
| Num CSChar # | |
| Num CChar # | |
| Num Fd # | |
| Num CKey # | |
| Num CId # | |
| Num CFsFilCnt # | |
Defined in System.Posix.Types | |
| Num CFsBlkCnt # | |
Defined in System.Posix.Types | |
| Num CClockId # | |
| Num CBlkCnt # | |
| Num CBlkSize # | |
| Num CRLim # | |
| Num CTcflag # | |
| Num CSpeed # | |
| Num CCc # | |
| Num CUid # | |
| Num CNlink # | |
| Num CGid # | |
| Num CSsize # | |
| Num CPid # | |
| Num COff # | |
| Num CMode # | |
| Num CIno # | |
| Num CDev # | |
| Integral a => Num (Ratio a) # | Since: base-2.0.1 |
| Num a => Num (Down a) # | Since: base-4.11.0.0 |
| Num a => Num (Product a) # | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
| Num a => Num (Sum a) # | Since: base-4.7.0.0 |
| Num a => Num (Identity a) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity | |
| Num a => Num (Max a) # | Since: base-4.9.0.0 |
| Num a => Num (Min a) # | Since: base-4.9.0.0 |
| HasResolution a => Num (Fixed a) # | Since: base-2.1 |
| RealFloat a => Num (Complex a) # | Since: base-2.1 |
| Num a => Num (Op a b) # | |
| Num (f a) => Num (Alt f a) # | Since: base-4.8.0.0 |
| (Applicative f, Num a) => Num (Ap f a) # | Since: base-4.12.0.0 |
| Num a => Num (Const a b) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
module GHC.Integer
module GHC.Natural