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.Nat

Description

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

Synopsis

Documentation

data Nat Source #

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

Instances

Enum Nat Source #
Methods succ :: Nat -> Nat # pred :: Nat -> Nat # toEnum :: Int -> Nat # fromEnum :: Nat -> Int # enumFrom :: Nat -> [Nat] # enumFromThen :: Nat -> Nat -> [Nat] # enumFromTo :: Nat -> Nat -> [Nat] # enumFromThenTo :: Nat -> Nat -> Nat -> [Nat] #
Eq Nat Source #
Methods (==) :: Nat -> Nat -> Bool # (/=) :: Nat -> Nat -> Bool #
Integral Nat Source #
Methods quot :: Nat -> Nat -> Nat # rem :: Nat -> Nat -> Nat # div :: Nat -> Nat -> Nat # mod :: Nat -> Nat -> Nat # quotRem :: Nat -> Nat -> (Nat, Nat) # divMod :: Nat -> Nat -> (Nat, Nat) # toInteger :: Nat -> Integer #
Num Nat Source #
Methods (+) :: Nat -> Nat -> Nat # (-) :: Nat -> Nat -> Nat # (*) :: Nat -> Nat -> Nat # negate :: Nat -> Nat # abs :: Nat -> Nat # signum :: Nat -> Nat # fromInteger :: Integer -> Nat #
Ord Nat Source #
Methods compare :: Nat -> Nat -> Ordering # (<) :: Nat -> Nat -> Bool # (<=) :: Nat -> Nat -> Bool # (>) :: Nat -> Nat -> Bool # (>=) :: Nat -> Nat -> Bool # max :: Nat -> Nat -> Nat # min :: Nat -> Nat -> Nat #
Read Nat Source #
Methods readsPrec :: Int -> ReadS Nat # readList :: ReadS [Nat] # readPrec :: ReadPrec Nat # readListPrec :: ReadPrec [Nat] #
Real Nat Source #
Methods toRational :: Nat -> Rational #
Show Nat Source #
Methods showsPrec :: Int -> Nat -> ShowS # show :: Nat -> String # showList :: [Nat] -> ShowS #

fromNat :: Nat -> Int Source #

Safely convert a natural number to an integer.

toNat :: Int -> Maybe Nat Source #

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

unsafeNat :: Int -> Nat Source #

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

newtype MaxNat Source #

Constructors

MaxNat
Fields unMaxNat :: Nat

Instances

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