Data.Number.Nat

The implementations of all functions except for rem, quot, div, mod are supposed to be as non-strict as possible.

Datatype

data Nat

Natural numbers and zero

Constructors

Zero

Constructor representing zero

Pos Nat1

A natural number

Instances

Enum Nat

Eq Nat

Integral Nat

Num Nat

Ord Nat

Read Nat

Real Nat

Show Nat

Helper Functions

cmpNatLT :: Nat -> Nat -> Ordering

This function is used to implement lazy instances of compare and (<), (<=), (>), (>=). It is used to transfer information to more significant bits. Instead of yielding EQ it yields LT if the numbers are equal.

fromNat :: Num n => Nat -> n

This is used for the implementation of toInteger and fromEnum.

toNat :: (Integral n, Num n) => n -> Nat

This is used for the implementation of fromInteger and toEnum.

Example Implementations using Nat

length :: [a] -> Nat

take :: Nat -> [a] -> [a]

drop :: Nat -> [a] -> [a]

replicate :: Nat -> a -> [a]

Example Implementations using Num

lengthNum :: (Enum n, Num n) => [a] -> n

takeNum :: (Enum n, Num n) => n -> [a] -> [a]

dropNum :: (Enum n, Num n) => n -> [a] -> [a]

replicateNum :: (Enum n, Num n) => n -> a -> [a]

divmodNat1 :: Nat1 -> Nat1 -> (Nat, Nat)