Data.Number.Natural

A data type for natural numbers (aka non-negative integers).

Documentation

data Natural

Natural numbers, with unbounded-width à la Integer. N.B., the Num instance will throw errors on subtraction, negation, and fromInteger when the result is not a natural number.

Instances

Enum Natural

Methods

succ :: Natural -> Natural

pred :: Natural -> Natural

toEnum :: Int -> Natural

fromEnum :: Natural -> Int

enumFrom :: Natural -> [Natural]

enumFromThen :: Natural -> Natural -> [Natural]

enumFromTo :: Natural -> Natural -> [Natural]

enumFromThenTo :: Natural -> Natural -> Natural -> [Natural]

Eq Natural

Methods

(==) :: Natural -> Natural -> Bool

(/=) :: Natural -> Natural -> Bool

Integral Natural

Methods

quot :: Natural -> Natural -> Natural

rem :: Natural -> Natural -> Natural

div :: Natural -> Natural -> Natural

mod :: Natural -> Natural -> Natural

quotRem :: Natural -> Natural -> (Natural, Natural)

divMod :: Natural -> Natural -> (Natural, Natural)

toInteger :: Natural -> Integer

Num Natural

Methods

(+) :: Natural -> Natural -> Natural

(-) :: Natural -> Natural -> Natural

(*) :: Natural -> Natural -> Natural

negate :: Natural -> Natural

abs :: Natural -> Natural

signum :: Natural -> Natural

fromInteger :: Integer -> Natural

Ord Natural

Methods

compare :: Natural -> Natural -> Ordering

(<) :: Natural -> Natural -> Bool

(<=) :: Natural -> Natural -> Bool

(>) :: Natural -> Natural -> Bool

(>=) :: Natural -> Natural -> Bool

max :: Natural -> Natural -> Natural

min :: Natural -> Natural -> Natural

Read Natural

Methods

readsPrec :: Int -> ReadS Natural

readList :: ReadS [Natural]

readPrec :: ReadPrec Natural

readListPrec :: ReadPrec [Natural]

Real Natural

Methods

toRational :: Natural -> Rational

Show Natural

Methods

showsPrec :: Int -> Natural -> ShowS

show :: Natural -> String

showList :: [Natural] -> ShowS

Interp HNat Natural

Methods

reify :: ABT Term abt => Head abt HNat -> Natural

reflect :: ABT Term abt => Natural -> Head abt HNat

Interp HProb NonNegativeRational

Methods

reify :: ABT Term abt => Head abt HProb -> NonNegativeRational

reflect :: ABT Term abt => NonNegativeRational -> Head abt HProb

fromNatural :: Natural -> Integer

Safely convert a natural number to an integer.

toNatural :: Integer -> Maybe Natural

Safely convert an integer to a natural number. Returns Nothing if the integer is negative.

unsafeNatural :: Integer -> Natural

Unsafely convert an integer to a natural number. Throws an error if the integer is negative.

newtype MaxNatural

Constructors

MaxNatural

Fields

• unMaxNatural :: Natural

Instances

Semigroup MaxNatural

Methods

(<>) :: MaxNatural -> MaxNatural -> MaxNatural

sconcat :: NonEmpty MaxNatural -> MaxNatural

stimes :: Integral b => b -> MaxNatural -> MaxNatural

Monoid MaxNatural

Methods

mempty :: MaxNatural

mappend :: MaxNatural -> MaxNatural -> MaxNatural

mconcat :: [MaxNatural] -> MaxNatural

type NonNegativeRational = Ratio Natural

fromNonNegativeRational :: NonNegativeRational -> Rational

Safely convert a non-negative rational to a rational.

toNonNegativeRational :: Rational -> Maybe NonNegativeRational

Safely convert a rational to a non-negative rational. Returns Nothing if the argument is negative.

unsafeNonNegativeRational :: Rational -> NonNegativeRational

Unsafely convert a rational to a non-negative rational. Throws an error if the argument is negative.