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).