Copyright	Copyright (c) 2016 the Hakaru team
License	BSD3
Maintainer	wren@community.haskell.org
Stability	experimental
Portability	Haskell98 + CPP
Safe Haskell	Safe
Language	Haskell2010

Data.Number.Natural

Description

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

Synopsis

Documentation

data Natural Source #

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 Source #
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 Source #
Methods (==) :: Natural -> Natural -> Bool # (/=) :: Natural -> Natural -> Bool #
Integral Natural Source #
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 Source #
Methods (+) :: Natural -> Natural -> Natural # (-) :: Natural -> Natural -> Natural # (*) :: Natural -> Natural -> Natural # negate :: Natural -> Natural # abs :: Natural -> Natural # signum :: Natural -> Natural # fromInteger :: Integer -> Natural #
Ord Natural Source #
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 Source #
Methods readsPrec :: Int -> ReadS Natural # readList :: ReadS [Natural] # readPrec :: ReadPrec Natural # readListPrec :: ReadPrec [Natural] #
Real Natural Source #
Methods toRational :: Natural -> Rational #
Show Natural Source #
Methods showsPrec :: Int -> Natural -> ShowS # show :: Natural -> String # showList :: [Natural] -> ShowS #
Interp HNat Natural Source #
Methods reify :: ABT Hakaru Term abt => Head abt HNat -> Natural Source # reflect :: ABT Hakaru Term abt => Natural -> Head abt HNat Source #
Interp HProb NonNegativeRational Source #
Methods reify :: ABT Hakaru Term abt => Head abt HProb -> NonNegativeRational Source # reflect :: ABT Hakaru Term abt => NonNegativeRational -> Head abt HProb Source #

fromNatural :: Natural -> Integer Source #

Safely convert a natural number to an integer.

toNatural :: Integer -> Maybe Natural Source #

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

unsafeNatural :: Integer -> Natural Source #

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

newtype MaxNatural Source #

Constructors

MaxNatural
Fields unMaxNatural :: Natural

Instances

Monoid MaxNatural Source #
Methods mempty :: MaxNatural # mappend :: MaxNatural -> MaxNatural -> MaxNatural # mconcat :: [MaxNatural] -> MaxNatural #

type NonNegativeRational = Ratio Natural Source #

fromNonNegativeRational :: NonNegativeRational -> Rational Source #

Safely convert a non-negative rational to a rational.

toNonNegativeRational :: Rational -> Maybe NonNegativeRational Source #

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

unsafeNonNegativeRational :: Rational -> NonNegativeRational Source #

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