Safe Haskell	Safe
Language	Haskell2010

Natural

Documentation

data Natural Source #

Instances

Eq Natural Source #
Instance details Defined in Natural Methods (==) :: Natural -> Natural -> Bool # (/=) :: Natural -> Natural -> Bool #
Ord Natural Source #
Instance details Defined in Natural Methods compare :: Natural -> Natural -> Ordering # (<) :: Natural -> Natural -> Bool # (<=) :: Natural -> Natural -> Bool # (>) :: Natural -> Natural -> Bool # (>=) :: Natural -> Natural -> Bool # max :: Natural -> Natural -> Natural # min :: Natural -> Natural -> Natural #
Show Natural Source #
Instance details Defined in Natural Methods showsPrec :: Int -> Natural -> ShowS # show :: Natural -> String # showList :: [Natural] -> ShowS #
Semigroup Natural Source #
Instance details Defined in Natural Methods (<>) :: Natural -> Natural -> Natural # sconcat :: NonEmpty Natural -> Natural # stimes :: Integral b => b -> Natural -> Natural #
Monoid Natural Source #
Instance details Defined in Natural Methods mempty :: Natural # mappend :: Natural -> Natural -> Natural # mconcat :: [Natural] -> Natural #
AsPositive Natural Source #
Instance details Defined in Natural Methods _Positive :: Prism' Natural Positive Source #
AsNatural Natural Source #
Instance details Defined in Natural Methods _Natural :: Prism' Natural Natural Source #
HasNatural Natural Source #
Instance details Defined in Natural Methods natural :: Lens' Natural Natural Source #

class HasNatural a where Source #

Methods

natural :: Lens' a Natural Source #

Instances

HasNatural MinNatural Source #
Instance details Defined in Natural Methods natural :: Lens' MinNatural Natural Source #
HasNatural MaxNatural Source #
Instance details Defined in Natural Methods natural :: Lens' MaxNatural Natural Source #
HasNatural ProductNatural Source #
Instance details Defined in Natural Methods natural :: Lens' ProductNatural Natural Source #
HasNatural Natural Source #
Instance details Defined in Natural Methods natural :: Lens' Natural Natural Source #

class AsNatural a where Source #

Methods

_Natural :: Prism' a Natural Source #

Instances

AsNatural Int Source #
Instance details Defined in Natural Methods _Natural :: Prism' Int Natural Source #
AsNatural Integer Source #
Instance details Defined in Natural Methods _Natural :: Prism' Integer Natural Source #
AsNatural Word Source #
Instance details Defined in Natural Methods _Natural :: Prism' Word Natural Source #
AsNatural MinNatural Source #
Instance details Defined in Natural Methods _Natural :: Prism' MinNatural Natural Source #
AsNatural MaxNatural Source #
Instance details Defined in Natural Methods _Natural :: Prism' MaxNatural Natural Source #
AsNatural ProductNatural Source #
Instance details Defined in Natural Methods _Natural :: Prism' ProductNatural Natural Source #
AsNatural Natural Source #
Instance details Defined in Natural Methods _Natural :: Prism' Natural Natural Source #
Integral a => AsNatural (Identity a) Source #
Instance details Defined in Natural Methods _Natural :: Prism' (Identity a) Natural Source #
Integral a => AsNatural (Const a b) Source #
Instance details Defined in Natural Methods _Natural :: Prism' (Const a b) Natural Source #

newtype ProductNatural Source #

Constructors

ProductNatural Natural

Instances

Eq ProductNatural Source #
Instance details Defined in Natural Methods (==) :: ProductNatural -> ProductNatural -> Bool # (/=) :: ProductNatural -> ProductNatural -> Bool #
Ord ProductNatural Source #
Instance details Defined in Natural Methods compare :: ProductNatural -> ProductNatural -> Ordering # (<) :: ProductNatural -> ProductNatural -> Bool # (<=) :: ProductNatural -> ProductNatural -> Bool # (>) :: ProductNatural -> ProductNatural -> Bool # (>=) :: ProductNatural -> ProductNatural -> Bool # max :: ProductNatural -> ProductNatural -> ProductNatural # min :: ProductNatural -> ProductNatural -> ProductNatural #
Show ProductNatural Source #
Instance details Defined in Natural Methods showsPrec :: Int -> ProductNatural -> ShowS # show :: ProductNatural -> String # showList :: [ProductNatural] -> ShowS #
Semigroup ProductNatural Source #
Instance details Defined in Natural Methods (<>) :: ProductNatural -> ProductNatural -> ProductNatural # sconcat :: NonEmpty ProductNatural -> ProductNatural # stimes :: Integral b => b -> ProductNatural -> ProductNatural #
Monoid ProductNatural Source #
Instance details Defined in Natural Methods mempty :: ProductNatural # mappend :: ProductNatural -> ProductNatural -> ProductNatural # mconcat :: [ProductNatural] -> ProductNatural #
Wrapped ProductNatural Source #
Instance details Defined in Natural Associated Types type Unwrapped ProductNatural :: Type # Methods _Wrapped' :: Iso' ProductNatural (Unwrapped ProductNatural) #
AsNatural ProductNatural Source #
Instance details Defined in Natural Methods _Natural :: Prism' ProductNatural Natural Source #
HasNatural ProductNatural Source #
Instance details Defined in Natural Methods natural :: Lens' ProductNatural Natural Source #
ProductNatural ~ a => Rewrapped ProductNatural a Source #
Instance details Defined in Natural
type Unwrapped ProductNatural Source #
Instance details Defined in Natural type Unwrapped ProductNatural = Natural

newtype MaxNatural Source #

Constructors

MaxNatural Natural

Instances

Eq MaxNatural Source #
Instance details Defined in Natural Methods (==) :: MaxNatural -> MaxNatural -> Bool # (/=) :: MaxNatural -> MaxNatural -> Bool #
Ord MaxNatural Source #
Instance details Defined in Natural Methods compare :: MaxNatural -> MaxNatural -> Ordering # (<) :: MaxNatural -> MaxNatural -> Bool # (<=) :: MaxNatural -> MaxNatural -> Bool # (>) :: MaxNatural -> MaxNatural -> Bool # (>=) :: MaxNatural -> MaxNatural -> Bool # max :: MaxNatural -> MaxNatural -> MaxNatural # min :: MaxNatural -> MaxNatural -> MaxNatural #
Show MaxNatural Source #
Instance details Defined in Natural Methods showsPrec :: Int -> MaxNatural -> ShowS # show :: MaxNatural -> String # showList :: [MaxNatural] -> ShowS #
Semigroup MaxNatural Source #
Instance details Defined in Natural Methods (<>) :: MaxNatural -> MaxNatural -> MaxNatural # sconcat :: NonEmpty MaxNatural -> MaxNatural # stimes :: Integral b => b -> MaxNatural -> MaxNatural #
Wrapped MaxNatural Source #
Instance details Defined in Natural Associated Types type Unwrapped MaxNatural :: Type # Methods _Wrapped' :: Iso' MaxNatural (Unwrapped MaxNatural) #
AsNatural MaxNatural Source #
Instance details Defined in Natural Methods _Natural :: Prism' MaxNatural Natural Source #
HasNatural MaxNatural Source #
Instance details Defined in Natural Methods natural :: Lens' MaxNatural Natural Source #
MaxNatural ~ a => Rewrapped MaxNatural a Source #
Instance details Defined in Natural
type Unwrapped MaxNatural Source #
Instance details Defined in Natural type Unwrapped MaxNatural = Natural

newtype MinNatural Source #

Constructors

MinNatural Natural

Instances

Eq MinNatural Source #
Instance details Defined in Natural Methods (==) :: MinNatural -> MinNatural -> Bool # (/=) :: MinNatural -> MinNatural -> Bool #
Ord MinNatural Source #
Instance details Defined in Natural Methods compare :: MinNatural -> MinNatural -> Ordering # (<) :: MinNatural -> MinNatural -> Bool # (<=) :: MinNatural -> MinNatural -> Bool # (>) :: MinNatural -> MinNatural -> Bool # (>=) :: MinNatural -> MinNatural -> Bool # max :: MinNatural -> MinNatural -> MinNatural # min :: MinNatural -> MinNatural -> MinNatural #
Show MinNatural Source #
Instance details Defined in Natural Methods showsPrec :: Int -> MinNatural -> ShowS # show :: MinNatural -> String # showList :: [MinNatural] -> ShowS #
Semigroup MinNatural Source #
Instance details Defined in Natural Methods (<>) :: MinNatural -> MinNatural -> MinNatural # sconcat :: NonEmpty MinNatural -> MinNatural # stimes :: Integral b => b -> MinNatural -> MinNatural #
Wrapped MinNatural Source #
Instance details Defined in Natural Associated Types type Unwrapped MinNatural :: Type # Methods _Wrapped' :: Iso' MinNatural (Unwrapped MinNatural) #
AsNatural MinNatural Source #
Instance details Defined in Natural Methods _Natural :: Prism' MinNatural Natural Source #
HasNatural MinNatural Source #
Instance details Defined in Natural Methods natural :: Lens' MinNatural Natural Source #
MinNatural ~ a => Rewrapped MinNatural a Source #
Instance details Defined in Natural
type Unwrapped MinNatural Source #
Instance details Defined in Natural type Unwrapped MinNatural = Natural

zero :: Prism' Natural () Source #

zero' :: Natural Source #

successor :: Prism' Natural Natural Source #

successor' :: Natural -> Natural Source #

plus :: Natural -> Natural -> Natural Source #

multiply :: Natural -> Natural -> Natural Source #

square :: Natural -> Natural -> Natural Source #

zeroOr :: AsNatural a => a -> Natural Source #

length :: Foldable f => f a -> Natural Source #

replicate :: Natural -> a -> [a] Source #

take :: Natural -> [a] -> [a] Source #

drop :: Natural -> [a] -> [a] Source #

splitAt :: Natural -> [a] -> ([a], [a]) Source #

(!!) :: [a] -> Natural -> Maybe a Source #

findIndices :: (a -> Bool) -> [a] -> [Natural] Source #

findIndex :: (a -> Bool) -> [a] -> Maybe Natural Source #

elemIndices :: Eq a => a -> [a] -> [Natural] Source #

elemIndex :: Eq a => a -> [a] -> Maybe Natural Source #

minus :: Natural -> Natural -> Natural Source #

list :: Iso' Natural [()] Source #

data Positive Source #

Instances

Eq Positive Source #
Instance details Defined in Natural Methods (==) :: Positive -> Positive -> Bool # (/=) :: Positive -> Positive -> Bool #
Ord Positive Source #
Instance details Defined in Natural Methods compare :: Positive -> Positive -> Ordering # (<) :: Positive -> Positive -> Bool # (<=) :: Positive -> Positive -> Bool # (>) :: Positive -> Positive -> Bool # (>=) :: Positive -> Positive -> Bool # max :: Positive -> Positive -> Positive # min :: Positive -> Positive -> Positive #
Show Positive Source #
Instance details Defined in Natural Methods showsPrec :: Int -> Positive -> ShowS # show :: Positive -> String # showList :: [Positive] -> ShowS #
Semigroup Positive Source #
Instance details Defined in Natural Methods (<>) :: Positive -> Positive -> Positive # sconcat :: NonEmpty Positive -> Positive # stimes :: Integral b => b -> Positive -> Positive #
Monoid Positive Source #
Instance details Defined in Natural Methods mempty :: Positive # mappend :: Positive -> Positive -> Positive # mconcat :: [Positive] -> Positive #
AsPositive Positive Source #
Instance details Defined in Natural Methods _Positive :: Prism' Positive Positive Source #
HasPositive Positive Source #
Instance details Defined in Natural Methods positive :: Lens' Positive Positive Source #

class HasPositive a where Source #

Methods

positive :: Lens' a Positive Source #

Instances

HasPositive MinPositive Source #
Instance details Defined in Natural Methods positive :: Lens' MinPositive Positive Source #
HasPositive MaxPositive Source #
Instance details Defined in Natural Methods positive :: Lens' MaxPositive Positive Source #
HasPositive SumPositive Source #
Instance details Defined in Natural Methods positive :: Lens' SumPositive Positive Source #
HasPositive Positive Source #
Instance details Defined in Natural Methods positive :: Lens' Positive Positive Source #

class AsPositive a where Source #

Methods

_Positive :: Prism' a Positive Source #

Instances

AsPositive Int Source #
Instance details Defined in Natural Methods _Positive :: Prism' Int Positive Source #
AsPositive Integer Source #
Instance details Defined in Natural Methods _Positive :: Prism' Integer Positive Source #
AsPositive Word Source #
Instance details Defined in Natural Methods _Positive :: Prism' Word Positive Source #
AsPositive MinPositive Source #
Instance details Defined in Natural Methods _Positive :: Prism' MinPositive Positive Source #
AsPositive MaxPositive Source #
Instance details Defined in Natural Methods _Positive :: Prism' MaxPositive Positive Source #
AsPositive SumPositive Source #
Instance details Defined in Natural Methods _Positive :: Prism' SumPositive Positive Source #
AsPositive Positive Source #
Instance details Defined in Natural Methods _Positive :: Prism' Positive Positive Source #
AsPositive Natural Source #
Instance details Defined in Natural Methods _Positive :: Prism' Natural Positive Source #
Integral a => AsPositive (Identity a) Source #
Instance details Defined in Natural Methods _Positive :: Prism' (Identity a) Positive Source #
Integral a => AsPositive (Const a b) Source #
Instance details Defined in Natural Methods _Positive :: Prism' (Const a b) Positive Source #

newtype SumPositive Source #

Constructors

SumPositive Positive

Instances

Eq SumPositive Source #
Instance details Defined in Natural Methods (==) :: SumPositive -> SumPositive -> Bool # (/=) :: SumPositive -> SumPositive -> Bool #
Ord SumPositive Source #
Instance details Defined in Natural Methods compare :: SumPositive -> SumPositive -> Ordering # (<) :: SumPositive -> SumPositive -> Bool # (<=) :: SumPositive -> SumPositive -> Bool # (>) :: SumPositive -> SumPositive -> Bool # (>=) :: SumPositive -> SumPositive -> Bool # max :: SumPositive -> SumPositive -> SumPositive # min :: SumPositive -> SumPositive -> SumPositive #
Show SumPositive Source #
Instance details Defined in Natural Methods showsPrec :: Int -> SumPositive -> ShowS # show :: SumPositive -> String # showList :: [SumPositive] -> ShowS #
Semigroup SumPositive Source #
Instance details Defined in Natural Methods (<>) :: SumPositive -> SumPositive -> SumPositive # sconcat :: NonEmpty SumPositive -> SumPositive # stimes :: Integral b => b -> SumPositive -> SumPositive #
Wrapped SumPositive Source #
Instance details Defined in Natural Associated Types type Unwrapped SumPositive :: Type # Methods _Wrapped' :: Iso' SumPositive (Unwrapped SumPositive) #
AsPositive SumPositive Source #
Instance details Defined in Natural Methods _Positive :: Prism' SumPositive Positive Source #
HasPositive SumPositive Source #
Instance details Defined in Natural Methods positive :: Lens' SumPositive Positive Source #
SumPositive ~ a => Rewrapped SumPositive a Source #
Instance details Defined in Natural
type Unwrapped SumPositive Source #
Instance details Defined in Natural type Unwrapped SumPositive = Positive

newtype MaxPositive Source #

Constructors

MaxPositive Positive

Instances

Eq MaxPositive Source #
Instance details Defined in Natural Methods (==) :: MaxPositive -> MaxPositive -> Bool # (/=) :: MaxPositive -> MaxPositive -> Bool #
Ord MaxPositive Source #
Instance details Defined in Natural Methods compare :: MaxPositive -> MaxPositive -> Ordering # (<) :: MaxPositive -> MaxPositive -> Bool # (<=) :: MaxPositive -> MaxPositive -> Bool # (>) :: MaxPositive -> MaxPositive -> Bool # (>=) :: MaxPositive -> MaxPositive -> Bool # max :: MaxPositive -> MaxPositive -> MaxPositive # min :: MaxPositive -> MaxPositive -> MaxPositive #
Show MaxPositive Source #
Instance details Defined in Natural Methods showsPrec :: Int -> MaxPositive -> ShowS # show :: MaxPositive -> String # showList :: [MaxPositive] -> ShowS #
Semigroup MaxPositive Source #
Instance details Defined in Natural Methods (<>) :: MaxPositive -> MaxPositive -> MaxPositive # sconcat :: NonEmpty MaxPositive -> MaxPositive # stimes :: Integral b => b -> MaxPositive -> MaxPositive #
Wrapped MaxPositive Source #
Instance details Defined in Natural Associated Types type Unwrapped MaxPositive :: Type # Methods _Wrapped' :: Iso' MaxPositive (Unwrapped MaxPositive) #
AsPositive MaxPositive Source #
Instance details Defined in Natural Methods _Positive :: Prism' MaxPositive Positive Source #
HasPositive MaxPositive Source #
Instance details Defined in Natural Methods positive :: Lens' MaxPositive Positive Source #
MaxPositive ~ a => Rewrapped MaxPositive a Source #
Instance details Defined in Natural
type Unwrapped MaxPositive Source #
Instance details Defined in Natural type Unwrapped MaxPositive = Positive

newtype MinPositive Source #

Constructors

MinPositive Positive

Instances

Eq MinPositive Source #
Instance details Defined in Natural Methods (==) :: MinPositive -> MinPositive -> Bool # (/=) :: MinPositive -> MinPositive -> Bool #
Ord MinPositive Source #
Instance details Defined in Natural Methods compare :: MinPositive -> MinPositive -> Ordering # (<) :: MinPositive -> MinPositive -> Bool # (<=) :: MinPositive -> MinPositive -> Bool # (>) :: MinPositive -> MinPositive -> Bool # (>=) :: MinPositive -> MinPositive -> Bool # max :: MinPositive -> MinPositive -> MinPositive # min :: MinPositive -> MinPositive -> MinPositive #
Show MinPositive Source #
Instance details Defined in Natural Methods showsPrec :: Int -> MinPositive -> ShowS # show :: MinPositive -> String # showList :: [MinPositive] -> ShowS #
Semigroup MinPositive Source #
Instance details Defined in Natural Methods (<>) :: MinPositive -> MinPositive -> MinPositive # sconcat :: NonEmpty MinPositive -> MinPositive # stimes :: Integral b => b -> MinPositive -> MinPositive #
Wrapped MinPositive Source #
Instance details Defined in Natural Associated Types type Unwrapped MinPositive :: Type # Methods _Wrapped' :: Iso' MinPositive (Unwrapped MinPositive) #
AsPositive MinPositive Source #
Instance details Defined in Natural Methods _Positive :: Prism' MinPositive Positive Source #
HasPositive MinPositive Source #
Instance details Defined in Natural Methods positive :: Lens' MinPositive Positive Source #
MinPositive ~ a => Rewrapped MinPositive a Source #
Instance details Defined in Natural
type Unwrapped MinPositive Source #
Instance details Defined in Natural type Unwrapped MinPositive = Positive