Safe Haskell	Safe
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 #

Instances

Enum Natural #
Instance details Defined in Data.Number.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 #
Instance details Defined in Data.Number.Natural Methods (==) :: Natural -> Natural -> Bool # (/=) :: Natural -> Natural -> Bool #
Integral Natural #
Instance details Defined in Data.Number.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 #
Instance details Defined in Data.Number.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 #
Instance details Defined in Data.Number.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 #
Real Natural #
Instance details Defined in Data.Number.Natural Methods toRational :: Natural -> Rational #
Show Natural #
Instance details Defined in Data.Number.Natural Methods showsPrec :: Int -> Natural -> ShowS # show :: Natural -> String # showList :: [Natural] -> ShowS #

infinity :: Natural #

The infinite natural number.