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

Data.Number.Nat

Description

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

Synopsis

data Nat
fromNat :: Nat -> Int
toNat :: Int -> Maybe Nat
unsafeNat :: Int -> Nat
newtype MaxNat = MaxNat {
- unMaxNat :: Nat
}

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

Instances details

Enum Nat Source #
Instance details Defined in Data.Number.Nat 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 #
Instance details Defined in Data.Number.Nat Methods (==) :: Nat -> Nat -> Bool # (/=) :: Nat -> Nat -> Bool #
Integral Nat Source #
Instance details Defined in Data.Number.Nat 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 #
Data Nat Source #
Instance details Defined in Data.Number.Nat Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Nat -> c Nat # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Nat # toConstr :: Nat -> Constr # dataTypeOf :: Nat -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Nat) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Nat) # gmapT :: (forall b. Data b => b -> b) -> Nat -> Nat # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Nat -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Nat -> r # gmapQ :: (forall d. Data d => d -> u) -> Nat -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Nat -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Nat -> m Nat # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Nat -> m Nat # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Nat -> m Nat #
Num Nat Source #
Instance details Defined in Data.Number.Nat 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 #
Instance details Defined in Data.Number.Nat 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 #
Instance details Defined in Data.Number.Nat Methods readsPrec :: Int -> ReadS Nat # readList :: ReadS [Nat] # readPrec :: ReadPrec Nat # readListPrec :: ReadPrec [Nat] #
Real Nat Source #
Instance details Defined in Data.Number.Nat Methods toRational :: Nat -> Rational #
Show Nat Source #
Instance details Defined in Data.Number.Nat 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

Instances details

Semigroup MaxNat Source #
Instance details Defined in Data.Number.Nat Methods (<>) :: MaxNat -> MaxNat -> MaxNat # sconcat :: NonEmpty MaxNat -> MaxNat # stimes :: Integral b => b -> MaxNat -> MaxNat #
Monoid MaxNat Source #
Instance details Defined in Data.Number.Nat Methods mempty :: MaxNat # mappend :: MaxNat -> MaxNat -> MaxNat # mconcat :: [MaxNat] -> MaxNat #