Data.Number.Nat

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

Documentation

data Nat

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

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

Methods

(==) :: Nat -> Nat -> Bool

(/=) :: Nat -> Nat -> Bool

Integral 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

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 :: (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

Methods

(+) :: Nat -> Nat -> Nat

(-) :: Nat -> Nat -> Nat

(*) :: Nat -> Nat -> Nat

negate :: Nat -> Nat

abs :: Nat -> Nat

signum :: Nat -> Nat

fromInteger :: Integer -> Nat

Ord 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

Methods

readsPrec :: Int -> ReadS Nat

readList :: ReadS [Nat]

readPrec :: ReadPrec Nat

readListPrec :: ReadPrec [Nat]

Real Nat

Methods

toRational :: Nat -> Rational

Show Nat

Methods

showsPrec :: Int -> Nat -> ShowS

show :: Nat -> String

showList :: [Nat] -> ShowS

fromNat :: Nat -> Int

Safely convert a natural number to an integer.

toNat :: Int -> Maybe Nat

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

unsafeNat :: Int -> Nat

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

newtype MaxNat

Constructors

MaxNat

Fields

• unMaxNat :: Nat

Instances

Semigroup MaxNat

Methods

(<>) :: MaxNat -> MaxNat -> MaxNat

sconcat :: NonEmpty MaxNat -> MaxNat

stimes :: Integral b => b -> MaxNat -> MaxNat

Monoid MaxNat

Methods

mempty :: MaxNat

mappend :: MaxNat -> MaxNat -> MaxNat

mconcat :: [MaxNat] -> MaxNat