GHC.Num
| 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 |
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 0is the additive identity-
x + fromInteger 0=x negategives the additive inverse-
x + negate x=fromInteger 0 - Associativity of
(*) -
(x * y) * z=x * (y * z) fromInteger 1is the multiplicative identity-
x * 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
(+) :: a -> a -> a infixl 6 Source
(-) :: a -> a -> a infixl 6 Source
(*) :: a -> a -> a infixl 7 Source
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 Source
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
subtract :: Num a => a -> a -> a Source
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.
module GHC.Integer
module GHC.Natural
© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.10.2/docs/html/libraries/base-4.14.1.0/GHC-Num.html
