Safe Haskell	Safe-Inferred
Language	Haskell98

Data.Number.Natural

Description

Lazy natural numbers. Addition and multiplication recurses over the first argument, i.e., 1 + n is the way to write the constant time successor function.

Note that (+) and (*) are not commutative for lazy natural numbers when considering bottom.

Synopsis

data Natural
infinity :: Natural

Documentation

data Natural Source #

Instances

Instances details

Enum Natural Source #
Instance details Defined in Data.Number.Natural Methods succ :: Natural -> Natural Source # pred :: Natural -> Natural Source # toEnum :: Int -> Natural Source # fromEnum :: Natural -> Int Source # enumFrom :: Natural -> [Natural] Source # enumFromThen :: Natural -> Natural -> [Natural] Source # enumFromTo :: Natural -> Natural -> [Natural] Source # enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] Source #
Num Natural Source #
Instance details Defined in Data.Number.Natural Methods (+) :: Natural -> Natural -> Natural Source # (-) :: Natural -> Natural -> Natural Source # (*) :: Natural -> Natural -> Natural Source # negate :: Natural -> Natural Source # abs :: Natural -> Natural Source # signum :: Natural -> Natural Source # fromInteger :: Integer -> Natural Source #
Integral Natural Source #
Instance details Defined in Data.Number.Natural Methods quot :: Natural -> Natural -> Natural Source # rem :: Natural -> Natural -> Natural Source # div :: Natural -> Natural -> Natural Source # mod :: Natural -> Natural -> Natural Source # quotRem :: Natural -> Natural -> (Natural, Natural) Source # divMod :: Natural -> Natural -> (Natural, Natural) Source # toInteger :: Natural -> Integer Source #
Real Natural Source #
Instance details Defined in Data.Number.Natural Methods toRational :: Natural -> Rational Source #
Show Natural Source #
Instance details Defined in Data.Number.Natural Methods showsPrec :: Int -> Natural -> ShowS Source # show :: Natural -> String Source # showList :: [Natural] -> ShowS Source #
Eq Natural Source #
Instance details Defined in Data.Number.Natural Methods (==) :: Natural -> Natural -> Bool Source # (/=) :: Natural -> Natural -> Bool Source #
Ord Natural Source #
Instance details Defined in Data.Number.Natural Methods compare :: Natural -> Natural -> Ordering Source # (<) :: Natural -> Natural -> Bool Source # (<=) :: Natural -> Natural -> Bool Source # (>) :: Natural -> Natural -> Bool Source # (>=) :: Natural -> Natural -> Bool Source # max :: Natural -> Natural -> Natural Source # min :: Natural -> Natural -> Natural Source #

infinity :: Natural Source #

The infinite natural number.