Plankton.Integral

Integral classes

Documentation

class Ring a => Integral a where

Integral laws

b == zero || b * (a `div` b) + (a `mod` b) == a

Minimal complete definition

divMod

Methods

div :: a -> a -> a infixl 7

mod :: a -> a -> a infixl 7

divMod :: a -> a -> (a, a)

Instances

Integral Int

Methods

div :: Int -> Int -> Int

mod :: Int -> Int -> Int

divMod :: Int -> Int -> (Int, Int)

Integral Integer

Methods

div :: Integer -> Integer -> Integer

mod :: Integer -> Integer -> Integer

divMod :: Integer -> Integer -> (Integer, Integer)

class ToInteger a where

toInteger is kept separate from Integral to help with compatability issues.

Minimal complete definition

toInteger

Methods

toInteger :: a -> Integer

Instances

ToInteger Int

Methods

toInteger :: Int -> Integer

ToInteger Integer

Methods

toInteger :: Integer -> Integer

class FromInteger a where

fromInteger is the most problematic of the Num class operators. Particularly heinous, it is assumed that any number type can be constructed from an Integer, so that the broad classes of objects that are composed of multiple elements is avoided in haskell.

Minimal complete definition

fromInteger

Methods

fromInteger :: Integer -> a

Instances

FromInteger Double

Methods

fromInteger :: Integer -> Double

FromInteger Float

Methods

fromInteger :: Integer -> Float

FromInteger Int

Methods

fromInteger :: Integer -> Int

FromInteger Integer

Methods

fromInteger :: Integer -> Integer

fromIntegral :: (ToInteger a, FromInteger b) => a -> b

coercion of Integrals

fromIntegral a == a