Safe Haskell	None
Language	Haskell98

Algebra.ToInteger

Contents

Orphan instances

Synopsis

class (C a, C a) => C a where
- toInteger :: a -> Integer
fromIntegral :: (C a, C b) => a -> b
ringPower :: (C a, C b) => b -> a -> a
fieldPower :: (C a, C b) => b -> a -> a

Documentation

class (C a, C a) => C a where #

The two classes C and C exist to allow convenient conversions, primarily between the built-in types. They should satisfy

  fromInteger .  toInteger === id
   toRational .  toInteger === toRational

Conversions must be lossless, that is, they do not round in any way. For rounding see Algebra.RealRing.

I think that the RealIntegral superclass is too restrictive. Non-negative numbers are not a ring, but can be easily converted to Integers.

Methods

toInteger :: a -> Integer #

Instances

C Int #
Instance details Defined in Algebra.ToInteger Methods toInteger :: Int -> Integer #
C Int8 #
Instance details Defined in Algebra.ToInteger Methods toInteger :: Int8 -> Integer #
C Int16 #
Instance details Defined in Algebra.ToInteger Methods toInteger :: Int16 -> Integer #
C Int32 #
Instance details Defined in Algebra.ToInteger Methods toInteger :: Int32 -> Integer #
C Int64 #
Instance details Defined in Algebra.ToInteger Methods toInteger :: Int64 -> Integer #
C Integer #
Instance details Defined in Algebra.ToInteger Methods toInteger :: Integer -> Integer #
C Word #
Instance details Defined in Algebra.ToInteger Methods toInteger :: Word -> Integer #
C Word8 #
Instance details Defined in Algebra.ToInteger Methods toInteger :: Word8 -> Integer #
C Word16 #
Instance details Defined in Algebra.ToInteger Methods toInteger :: Word16 -> Integer #
C Word32 #
Instance details Defined in Algebra.ToInteger Methods toInteger :: Word32 -> Integer #
C Word64 #
Instance details Defined in Algebra.ToInteger Methods toInteger :: Word64 -> Integer #
C T #
Instance details Defined in Number.Peano Methods toInteger :: T -> Integer #
C a => C (T a) #
Instance details Defined in Number.NonNegative Methods toInteger :: T a -> Integer #
Integral a => C (T a) #
Instance details Defined in MathObj.Wrapper.Haskell98 Methods toInteger :: T a -> Integer #
(C a, C a) => C (T a) #
Instance details Defined in Number.NonNegativeChunky Methods toInteger :: T a -> Integer #
C a => C (T a) #
Instance details Defined in MathObj.Wrapper.NumericPrelude Methods toInteger :: T a -> Integer #

fromIntegral :: (C a, C b) => a -> b #

ringPower :: (C a, C b) => b -> a -> a #

A prefix function of '(Algebra.Ring.^)' with a parameter order that fits the needs of partial application and function composition. It has generalised exponent.

See: Argument order of expNat on http://www.haskell.org/pipermail/haskell-cafe/2006-September/018022.html

fieldPower :: (C a, C b) => b -> a -> a #

A prefix function of '(Algebra.Field.^-)'. It has a generalised exponent.

Orphan instances

(C a, C a) => C (T a) #
Instance details Methods toRational :: T a -> Rational #