Safe Haskell	Safe-Inferred
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

Instances details

Enum Nat Source #
Instance details Defined in Data.Nat Methods succ :: Nat -> Nat Source # pred :: Nat -> Nat Source # toEnum :: Int -> Nat Source # fromEnum :: Nat -> Int Source # enumFrom :: Nat -> [ Nat ] Source # enumFromThen :: Nat -> Nat -> [ Nat ] Source # enumFromTo :: Nat -> Nat -> [ Nat ] Source # enumFromThenTo :: Nat -> Nat -> Nat -> [ Nat ] Source #
Eq Nat Source #
Instance details Defined in Data.Nat Methods (==) :: Nat -> Nat -> Bool Source # (/=) :: Nat -> Nat -> Bool Source #
Integral Nat Source #
Instance details Defined in Data.Nat Methods quot :: Nat -> Nat -> Nat Source # rem :: Nat -> Nat -> Nat Source # div :: Nat -> Nat -> Nat Source # mod :: Nat -> Nat -> Nat Source # quotRem :: Nat -> Nat -> ( Nat , Nat ) Source # divMod :: Nat -> Nat -> ( Nat , Nat ) Source # toInteger :: Nat -> Integer Source #
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 Source # gunfold :: ( forall b r. Data b => c (b -> r) -> c r) -> ( forall r. r -> c r) -> Constr -> c Nat Source # toConstr :: Nat -> Constr Source # dataTypeOf :: Nat -> DataType Source # dataCast1 :: Typeable t => ( forall d. Data d => c (t d)) -> Maybe (c Nat ) Source # dataCast2 :: Typeable t => ( forall d e. ( Data d, Data e) => c (t d e)) -> Maybe (c Nat ) Source # gmapT :: ( forall b. Data b => b -> b) -> Nat -> Nat Source # gmapQl :: (r -> r' -> r) -> r -> ( forall d. Data d => d -> r') -> Nat -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> ( forall d. Data d => d -> r') -> Nat -> r Source # gmapQ :: ( forall d. Data d => d -> u) -> Nat -> [u] Source # gmapQi :: Int -> ( forall d. Data d => d -> u) -> Nat -> u Source # gmapM :: Monad m => ( forall d. Data d => d -> m d) -> Nat -> m Nat Source # gmapMp :: MonadPlus m => ( forall d. Data d => d -> m d) -> Nat -> m Nat Source # gmapMo :: MonadPlus m => ( forall d. Data d => d -> m d) -> Nat -> m Nat Source #
Num Nat Source #
Instance details Defined in Data.Nat Methods (+) :: Nat -> Nat -> Nat Source # (-) :: Nat -> Nat -> Nat Source # (*) :: Nat -> Nat -> Nat Source # negate :: Nat -> Nat Source # abs :: Nat -> Nat Source # signum :: Nat -> Nat Source # fromInteger :: Integer -> Nat Source #
Ord Nat Source #
Instance details Defined in Data.Nat Methods compare :: Nat -> Nat -> Ordering Source # (<) :: Nat -> Nat -> Bool Source # (<=) :: Nat -> Nat -> Bool Source # (>) :: Nat -> Nat -> Bool Source # (>=) :: Nat -> Nat -> Bool Source # max :: Nat -> Nat -> Nat Source # min :: Nat -> Nat -> Nat Source #
Real Nat Source #
Instance details Defined in Data.Nat Methods toRational :: Nat -> Rational Source #
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 Source # show :: Nat -> String Source # showList :: [ Nat ] -> ShowS Source #
Function Nat Source #
Instance details Defined in Data.Nat Methods function :: ( Nat -> b) -> Nat :-> b Source #
Arbitrary Nat Source #
Instance details Defined in Data.Nat Methods arbitrary :: Gen Nat Source # shrink :: Nat -> [ Nat ] Source #
CoArbitrary Nat Source #
Instance details Defined in Data.Nat Methods coarbitrary :: Nat -> Gen b -> Gen b Source #
NFData Nat Source #
Instance details Defined in Data.Nat Methods rnf :: Nat -> () Source #
Hashable Nat Source #
Instance details Defined in Data.Nat Methods hashWithSalt :: Int -> Nat -> Int Source # hash :: Nat -> Int Source #
TestEquality SNat Source #
Instance details Defined in Data.Type.Nat Methods testEquality :: forall (a :: k) (b :: k). SNat a -> SNat b -> Maybe (a :~: b) Source #

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 #