peano
Safe HaskellSafe-Inferred
LanguageHaskell2010

Data.Peano

Description

See Peano.

Synopsis

Documentation

data Peano Source #

The natural numbers in (lazy) unary notation.

Constructors

Zero 
Succ Peano 

Instances

Instances details
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 #

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

Enum Peano Source # 
Instance details

Defined in Data.Peano

Generic Peano Source # 
Instance details

Defined in Data.Peano

Associated Types

type Rep Peano 
Instance details

Defined in Data.Peano

type Rep Peano = D1 ('MetaData "Peano" "Data.Peano" "peano-0.1.1.0-inplace" 'False) (C1 ('MetaCons "Zero" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Succ" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Peano)))

Methods

from :: Peano -> Rep Peano x #

to :: Rep Peano x -> Peano #

Ix Peano Source # 
Instance details

Defined in Data.Peano

Num Peano Source # 
Instance details

Defined in Data.Peano

Read Peano Source # 
Instance details

Defined in Data.Peano

Integral Peano Source # 
Instance details

Defined in Data.Peano

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 #

type Rep Peano Source # 
Instance details

Defined in Data.Peano

type Rep Peano = D1 ('MetaData "Peano" "Data.Peano" "peano-0.1.1.0-inplace" 'False) (C1 ('MetaCons "Zero" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Succ" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Peano)))

infinity :: Peano Source #

The infinite number (ω).