Safe Haskell	Safe
Language	Haskell2010

Data.Nat

Contents

Natural, Nat numbers
Showing
Aliases

Description

Nat numbers.

This module is designed to be imported qualified.

Synopsis

data Nat
- = Z
- | S Nat
toNatural :: Nat -> Natural
fromNatural :: Natural -> Nat
cata :: a -> (a -> a) -> Nat -> a
explicitShow :: Nat -> String
explicitShowsPrec :: Int -> Nat -> ShowS
nat0 :: Nat
nat1 :: Nat
nat2 :: Nat
nat3 :: Nat
nat4 :: Nat
nat5 :: Nat
nat6 :: Nat
nat7 :: Nat
nat8 :: Nat
nat9 :: Nat

Natural, Nat numbers

data Nat Source #

Nat natural numbers.

Better than GHC's built-in Nat for some use cases.

Constructors

Z
S Nat

Instances

Enum Nat Source #
Instance details Defined in Data.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.Nat Methods (==) :: Nat -> Nat -> Bool # (/=) :: Nat -> Nat -> Bool #
Integral Nat Source #
Instance details Defined in Data.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.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 Source #
Instance details Defined in Data.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.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 #
Real Nat Source #
Instance details Defined in Data.Nat Methods toRational :: Nat -> Rational #
Show Nat Source #	`Nat` is printed as `Natural`. To see explicit structure, use `explicitShow` or `explicitShowsPrec`
Instance details Defined in Data.Nat Methods showsPrec :: Int -> Nat -> ShowS # show :: Nat -> String # showList :: [Nat] -> ShowS #
NFData Nat Source #
Instance details Defined in Data.Nat Methods rnf :: Nat -> () #
Hashable Nat Source #
Instance details Defined in Data.Nat Methods hashWithSalt :: Int -> Nat -> Int # hash :: Nat -> Int #
TestEquality SNat Source #
Instance details Defined in Data.Type.Nat Methods testEquality :: SNat a -> SNat b -> Maybe (a :~: b) #

toNatural :: Nat -> Natural Source #

Convert Nat to Natural

>>> toNatural 0
0

>>> toNatural 2
2

>>> toNatural $ S $ S $ Z
2

fromNatural :: Natural -> Nat Source #

Convert Natural to Nat

>>> fromNatural 4
4

>>> explicitShow (fromNatural 4)
"S (S (S (S Z)))"

cata :: a -> (a -> a) -> Nat -> a Source #

Fold Nat.

>>> cata [] ('x' :) 2
"xx"

Showing

explicitShow :: Nat -> String Source #

show displaying a structure of Nat.

>>> explicitShow 0
"Z"

>>> explicitShow 2
"S (S Z)"

explicitShowsPrec :: Int -> Nat -> ShowS Source #

showsPrec displaying a structure of Nat.

Aliases

nat0 :: Nat Source #

nat1 :: Nat Source #

nat2 :: Nat Source #

nat3 :: Nat Source #

nat4 :: Nat Source #

nat5 :: Nat Source #

nat6 :: Nat Source #

nat7 :: Nat Source #

nat8 :: Nat Source #

nat9 :: Nat Source #