Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Peano

Description

See Peano.

Synopsis

data Peano
- = Zero
- | Succ Peano
infinity :: Peano

Documentation

data Peano Source #

The natural numbers in (lazy) unary notation.

Constructors

Zero
Succ Peano

Instances

Instances details

Data Peano Source #
Instance details Defined in Data.Peano Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Peano -> c Peano gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Peano toConstr :: Peano -> Constr dataTypeOf :: Peano -> DataType dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Peano) dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Peano) gmapT :: (forall b. Data b => b -> b) -> Peano -> Peano gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Peano -> r gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Peano -> r gmapQ :: (forall d. Data d => d -> u) -> Peano -> [u] gmapQi :: Int -> (forall d. Data d => d -> u) -> Peano -> u gmapM :: Monad m => (forall d. Data d => d -> m d) -> Peano -> m Peano gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Peano -> m Peano gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Peano -> m Peano
Bounded Peano Source #
Instance details Defined in Data.Peano Methods minBound :: Peano maxBound :: Peano
Enum Peano Source #
Instance details Defined in Data.Peano Methods succ :: Peano -> Peano pred :: Peano -> Peano toEnum :: Int -> Peano fromEnum :: Peano -> Int enumFrom :: Peano -> [Peano] enumFromThen :: Peano -> Peano -> [Peano] enumFromTo :: Peano -> Peano -> [Peano] enumFromThenTo :: Peano -> Peano -> Peano -> [Peano]
Ix Peano Source #
Instance details Defined in Data.Peano Methods range :: (Peano, Peano) -> [Peano] index :: (Peano, Peano) -> Peano -> Int unsafeIndex :: (Peano, Peano) -> Peano -> Int inRange :: (Peano, Peano) -> Peano -> Bool rangeSize :: (Peano, Peano) -> Int unsafeRangeSize :: (Peano, Peano) -> Int
Num Peano Source #
Instance details Defined in Data.Peano Methods (+) :: Peano -> Peano -> Peano (-) :: Peano -> Peano -> Peano (*) :: Peano -> Peano -> Peano negate :: Peano -> Peano abs :: Peano -> Peano signum :: Peano -> Peano fromInteger :: Integer -> Peano
Read Peano Source #
Instance details Defined in Data.Peano Methods readsPrec :: Int -> ReadS Peano readList :: ReadS [Peano] readPrec :: ReadPrec Peano readListPrec :: ReadPrec [Peano]
Integral Peano Source #
Instance details Defined in Data.Peano Methods quot :: Peano -> Peano -> Peano rem :: Peano -> Peano -> Peano div :: Peano -> Peano -> Peano mod :: Peano -> Peano -> Peano quotRem :: Peano -> Peano -> (Peano, Peano) divMod :: Peano -> Peano -> (Peano, Peano) toInteger :: Peano -> Integer
Real Peano Source #
Instance details Defined in Data.Peano Methods toRational :: Peano -> Rational
Show Peano Source #
Instance details Defined in Data.Peano Methods showsPrec :: Int -> Peano -> ShowS show :: Peano -> String showList :: [Peano] -> ShowS
Eq Peano Source #
Instance details Defined in Data.Peano Methods (==) :: Peano -> Peano -> Bool (/=) :: Peano -> Peano -> Bool
Ord Peano Source #
Instance details Defined in Data.Peano Methods compare :: Peano -> Peano -> Ordering (<) :: Peano -> Peano -> Bool (<=) :: Peano -> Peano -> Bool (>) :: Peano -> Peano -> Bool (>=) :: Peano -> Peano -> Bool max :: Peano -> Peano -> Peano min :: Peano -> Peano -> Peano

infinity :: Peano Source #

The infinite number (ω).