Haskell has several number types including Int, Integer, Float, Double, Ratio, and Complex. Int and Integer are integral types with Int having a fixed precision and Integer having arbitrary precision. Float and Double are floating point types with single and double precision respectively. Ratio represents rational numbers using the Ratio type. Complex represents complex numbers using the Complex type. The various number types instantiate typeclasses like Num, Fractional, Floating, Real, and RealFrac that define common numeric operations.

1. Haskell
Number System
Jaiyalas

2. Basic Number
Type Precision Instance Data Structure
Single- Integral,
Int minBound ... -1 | 0 | 1 ... maxBound
Precision Bounded
Arbitrary-
Integer Integral ... -1 | 0 | 1 ...
Precision
Single-
Float RealFloat -
Precision
Double-
Double RealFloat -
Precision

3. More Number
Type Precision Instance Data Structure
Ratio (Integral a) => Ratio a = !a :% !a
- RealFrac
(Rational) Rational = Ratio Integer
Complex - Floating (RealFloat a) => Complex a = !a :+ !a

4. Type : Integer
Show
Num Fractional Floating
Eq RealFloat
Real RealFrac
Ord
Integral
Enum

5. Type : Int
Show
Num Fractional Floating
Eq RealFloat
Real RealFrac
Ord
Integral Bounded
Enum

6. Type : Rational
Show
Num Fractional Floating
Eq RealFloat
Real RealFrac
Ord
Integral
Enum

7. Type : Complex
Show
Num Fractional Floating
Eq RealFloat
Real RealFrac
Ord
Integral
Enum

8. Type : Float & Double
Show
Num Fractional Floating
Eq RealFloat
Real RealFrac
Ord
Integral
Enum

9. Casting Functions
fromInteger (Num a) => Integer -> a
toInteger (Integral a) => a -> Integer
fromRational (Fractional a) => Rational -> a
toRational (RealFrac a) => a -> Rational
(Integral a, Num b) => a -> b
fromIntegral
fromInteger . toInteger
fromRealFrac (RealFrac a, Fractional b) => a -> b
(realToFrac) fromRational . toRational

10. Using Number
Focus on properties Class provided
Focus on a particular type

11. Using Number
Focus on properties Class provided
func :: (Fractional α) => α -> α
Focus on a particular type
func :: Double -> Double

12. Using Number
Focus on properties Class provided
func :: (Fractional α) => α -> α
- α can be Float, Double,
Rational or Complex
Focus on a particular type
func :: Double -> Double
- Can be Double only

13. Using Number
Focus on what Fractional can do
func :: (Fractional α) => α -> α
- α can be Float, Double,
Rational or Complex
Focus on what Double can do
func :: Double -> Double
- Can be Double only

14. Using Number
Focus on what Fractional can do
func :: (Fractional α) => α -> α
- α can be Float, Double,
Rational or Complex
Focus on what Double can do
func :: Double -> Double
- Can be Double only

15. Using Number
Focus on what Fractional can do
func :: (Fractional α) => α -> α
- α can be Float, Double,
Rational or Complex
Focus on what Double can do
func :: Double -> Double
- Can be Double only

16. THX.