Natural

Documentation

data Natural

Instances

Eq Natural

Defined in Natural

Methods

(==) :: Natural -> Natural -> Bool

(/=) :: Natural -> Natural -> Bool

Ord Natural

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

Defined in Natural

Methods

showsPrec :: Int -> Natural -> ShowS

show :: Natural -> String

showList :: [Natural] -> ShowS

Semigroup Natural

Defined in Natural

Methods

(<>) :: Natural -> Natural -> Natural

sconcat :: NonEmpty Natural -> Natural

stimes :: Integral b => b -> Natural -> Natural

Monoid Natural

Defined in Natural

Methods

mempty :: Natural

mappend :: Natural -> Natural -> Natural

mconcat :: [Natural] -> Natural

AsPositive Natural

Defined in Natural

Methods

_Positive :: Prism' Natural Positive

AsNatural Natural

Defined in Natural

Methods

_Natural :: Prism' Natural Natural

HasNatural Natural

Defined in Natural

Methods

natural :: Lens' Natural Natural

class HasNatural a where

Methods

natural :: Lens' a Natural

Instances

HasNatural MinNatural

Defined in Natural

Methods

natural :: Lens' MinNatural Natural

HasNatural MaxNatural

Defined in Natural

Methods

natural :: Lens' MaxNatural Natural

HasNatural ProductNatural

Defined in Natural

Methods

natural :: Lens' ProductNatural Natural

HasNatural Natural

Defined in Natural

Methods

natural :: Lens' Natural Natural

class AsNatural a where

Methods

_Natural :: Prism' a Natural

Instances

AsNatural Int

Defined in Natural

Methods

_Natural :: Prism' Int Natural

AsNatural Integer

Defined in Natural

Methods

_Natural :: Prism' Integer Natural

AsNatural Word

Defined in Natural

Methods

_Natural :: Prism' Word Natural

AsNatural MinNatural

Defined in Natural

Methods

_Natural :: Prism' MinNatural Natural

AsNatural MaxNatural

Defined in Natural

Methods

_Natural :: Prism' MaxNatural Natural

AsNatural ProductNatural

Defined in Natural

Methods

_Natural :: Prism' ProductNatural Natural

AsNatural Natural

Defined in Natural

Methods

_Natural :: Prism' Natural Natural

Integral a => AsNatural (Identity a)

Defined in Natural

Methods

_Natural :: Prism' (Identity a) Natural

Integral a => AsNatural (Const a b)

Defined in Natural

Methods

_Natural :: Prism' (Const a b) Natural

newtype ProductNatural

Constructors

ProductNatural Natural

Instances

Eq ProductNatural

Defined in Natural

Methods

(==) :: ProductNatural -> ProductNatural -> Bool

(/=) :: ProductNatural -> ProductNatural -> Bool

Ord ProductNatural

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

Defined in Natural

Methods

showsPrec :: Int -> ProductNatural -> ShowS

show :: ProductNatural -> String

showList :: [ProductNatural] -> ShowS

Semigroup ProductNatural

Defined in Natural

Methods

(<>) :: ProductNatural -> ProductNatural -> ProductNatural

sconcat :: NonEmpty ProductNatural -> ProductNatural

stimes :: Integral b => b -> ProductNatural -> ProductNatural

Monoid ProductNatural

Defined in Natural

Methods

mempty :: ProductNatural

mappend :: ProductNatural -> ProductNatural -> ProductNatural

mconcat :: [ProductNatural] -> ProductNatural

Wrapped ProductNatural

Defined in Natural

Associated Types

type Unwrapped ProductNatural

Methods

_Wrapped' :: Iso' ProductNatural (Unwrapped ProductNatural)

AsNatural ProductNatural

Defined in Natural

Methods

_Natural :: Prism' ProductNatural Natural

HasNatural ProductNatural

Defined in Natural

Methods

natural :: Lens' ProductNatural Natural

ProductNatural ~ a => Rewrapped ProductNatural a

Defined in Natural

type Unwrapped ProductNatural

Defined in Natural

type Unwrapped ProductNatural = Natural

newtype MaxNatural

Constructors

MaxNatural Natural

Instances

Eq MaxNatural

Defined in Natural

Methods

(==) :: MaxNatural -> MaxNatural -> Bool

(/=) :: MaxNatural -> MaxNatural -> Bool

Ord MaxNatural

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

Defined in Natural

Methods

showsPrec :: Int -> MaxNatural -> ShowS

show :: MaxNatural -> String

showList :: [MaxNatural] -> ShowS

Semigroup MaxNatural

Defined in Natural

Methods

(<>) :: MaxNatural -> MaxNatural -> MaxNatural

sconcat :: NonEmpty MaxNatural -> MaxNatural

stimes :: Integral b => b -> MaxNatural -> MaxNatural

Wrapped MaxNatural

Defined in Natural

Associated Types

type Unwrapped MaxNatural

Methods

_Wrapped' :: Iso' MaxNatural (Unwrapped MaxNatural)

AsNatural MaxNatural

Defined in Natural

Methods

_Natural :: Prism' MaxNatural Natural

HasNatural MaxNatural

Defined in Natural

Methods

natural :: Lens' MaxNatural Natural

MaxNatural ~ a => Rewrapped MaxNatural a

Defined in Natural

type Unwrapped MaxNatural

Defined in Natural

type Unwrapped MaxNatural = Natural

newtype MinNatural

Constructors

MinNatural Natural

Instances

Eq MinNatural

Defined in Natural

Methods

(==) :: MinNatural -> MinNatural -> Bool

(/=) :: MinNatural -> MinNatural -> Bool

Ord MinNatural

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

Defined in Natural

Methods

showsPrec :: Int -> MinNatural -> ShowS

show :: MinNatural -> String

showList :: [MinNatural] -> ShowS

Semigroup MinNatural

Defined in Natural

Methods

(<>) :: MinNatural -> MinNatural -> MinNatural

sconcat :: NonEmpty MinNatural -> MinNatural

stimes :: Integral b => b -> MinNatural -> MinNatural

Wrapped MinNatural

Defined in Natural

Associated Types

type Unwrapped MinNatural

Methods

_Wrapped' :: Iso' MinNatural (Unwrapped MinNatural)

AsNatural MinNatural

Defined in Natural

Methods

_Natural :: Prism' MinNatural Natural

HasNatural MinNatural

Defined in Natural

Methods

natural :: Lens' MinNatural Natural

MinNatural ~ a => Rewrapped MinNatural a

Defined in Natural

type Unwrapped MinNatural

Defined in Natural

type Unwrapped MinNatural = Natural

zero :: Prism' Natural ()

zero' :: Natural

successor :: Prism' Natural Natural

successor' :: Natural -> Natural

plus :: Natural -> Natural -> Natural

multiply :: Natural -> Natural -> Natural

square :: Natural -> Natural -> Natural

zeroOr :: AsNatural a => a -> Natural

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

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

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

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

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

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

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

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

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

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

minus :: Natural -> Natural -> Natural

list :: Iso' Natural [()]

data Positive

Instances

Eq Positive

Defined in Natural

Methods

(==) :: Positive -> Positive -> Bool

(/=) :: Positive -> Positive -> Bool

Ord Positive

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

Defined in Natural

Methods

showsPrec :: Int -> Positive -> ShowS

show :: Positive -> String

showList :: [Positive] -> ShowS

Semigroup Positive

Defined in Natural

Methods

(<>) :: Positive -> Positive -> Positive

sconcat :: NonEmpty Positive -> Positive

stimes :: Integral b => b -> Positive -> Positive

Monoid Positive

Defined in Natural

Methods

mempty :: Positive

mappend :: Positive -> Positive -> Positive

mconcat :: [Positive] -> Positive

AsPositive Positive

Defined in Natural

Methods

_Positive :: Prism' Positive Positive

HasPositive Positive

Defined in Natural

Methods

positive :: Lens' Positive Positive

class HasPositive a where

Methods

positive :: Lens' a Positive

Instances

HasPositive MinPositive

Defined in Natural

Methods

positive :: Lens' MinPositive Positive

HasPositive MaxPositive

Defined in Natural

Methods

positive :: Lens' MaxPositive Positive

HasPositive SumPositive

Defined in Natural

Methods

positive :: Lens' SumPositive Positive

HasPositive Positive

Defined in Natural

Methods

positive :: Lens' Positive Positive

class AsPositive a where

Methods

_Positive :: Prism' a Positive

Instances

AsPositive Int

Defined in Natural

Methods

_Positive :: Prism' Int Positive

AsPositive Integer

Defined in Natural

Methods

_Positive :: Prism' Integer Positive

AsPositive Word

Defined in Natural

Methods

_Positive :: Prism' Word Positive

AsPositive MinPositive

Defined in Natural

Methods

_Positive :: Prism' MinPositive Positive

AsPositive MaxPositive

Defined in Natural

Methods

_Positive :: Prism' MaxPositive Positive

AsPositive SumPositive

Defined in Natural

Methods

_Positive :: Prism' SumPositive Positive

AsPositive Positive

Defined in Natural

Methods

_Positive :: Prism' Positive Positive

AsPositive Natural

Defined in Natural

Methods

_Positive :: Prism' Natural Positive

Integral a => AsPositive (Identity a)

Defined in Natural

Methods

_Positive :: Prism' (Identity a) Positive

Integral a => AsPositive (Const a b)

Defined in Natural

Methods

_Positive :: Prism' (Const a b) Positive

newtype SumPositive

Constructors

SumPositive Positive

Instances

Eq SumPositive

Defined in Natural

Methods

(==) :: SumPositive -> SumPositive -> Bool

(/=) :: SumPositive -> SumPositive -> Bool

Ord SumPositive

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

Defined in Natural

Methods

showsPrec :: Int -> SumPositive -> ShowS

show :: SumPositive -> String

showList :: [SumPositive] -> ShowS

Semigroup SumPositive

Defined in Natural

Methods

(<>) :: SumPositive -> SumPositive -> SumPositive

sconcat :: NonEmpty SumPositive -> SumPositive

stimes :: Integral b => b -> SumPositive -> SumPositive

Wrapped SumPositive

Defined in Natural

Associated Types

type Unwrapped SumPositive

Methods

_Wrapped' :: Iso' SumPositive (Unwrapped SumPositive)

AsPositive SumPositive

Defined in Natural

Methods

_Positive :: Prism' SumPositive Positive

HasPositive SumPositive

Defined in Natural

Methods

positive :: Lens' SumPositive Positive

SumPositive ~ a => Rewrapped SumPositive a

Defined in Natural

type Unwrapped SumPositive

Defined in Natural

type Unwrapped SumPositive = Positive

newtype MaxPositive

Constructors

MaxPositive Positive

Instances

Eq MaxPositive

Defined in Natural

Methods

(==) :: MaxPositive -> MaxPositive -> Bool

(/=) :: MaxPositive -> MaxPositive -> Bool

Ord MaxPositive

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

Defined in Natural

Methods

showsPrec :: Int -> MaxPositive -> ShowS

show :: MaxPositive -> String

showList :: [MaxPositive] -> ShowS

Semigroup MaxPositive

Defined in Natural

Methods

(<>) :: MaxPositive -> MaxPositive -> MaxPositive

sconcat :: NonEmpty MaxPositive -> MaxPositive

stimes :: Integral b => b -> MaxPositive -> MaxPositive

Wrapped MaxPositive

Defined in Natural

Associated Types

type Unwrapped MaxPositive

Methods

_Wrapped' :: Iso' MaxPositive (Unwrapped MaxPositive)

AsPositive MaxPositive

Defined in Natural

Methods

_Positive :: Prism' MaxPositive Positive

HasPositive MaxPositive

Defined in Natural

Methods

positive :: Lens' MaxPositive Positive

MaxPositive ~ a => Rewrapped MaxPositive a

Defined in Natural

type Unwrapped MaxPositive

Defined in Natural

type Unwrapped MaxPositive = Positive

newtype MinPositive

Constructors

MinPositive Positive

Instances

Eq MinPositive

Defined in Natural

Methods

(==) :: MinPositive -> MinPositive -> Bool

(/=) :: MinPositive -> MinPositive -> Bool

Ord MinPositive

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

Defined in Natural

Methods

showsPrec :: Int -> MinPositive -> ShowS

show :: MinPositive -> String

showList :: [MinPositive] -> ShowS

Semigroup MinPositive

Defined in Natural

Methods

(<>) :: MinPositive -> MinPositive -> MinPositive

sconcat :: NonEmpty MinPositive -> MinPositive

stimes :: Integral b => b -> MinPositive -> MinPositive

Wrapped MinPositive

Defined in Natural

Associated Types

type Unwrapped MinPositive

Methods

_Wrapped' :: Iso' MinPositive (Unwrapped MinPositive)

AsPositive MinPositive

Defined in Natural

Methods

_Positive :: Prism' MinPositive Positive

HasPositive MinPositive

Defined in Natural

Methods

positive :: Lens' MinPositive Positive

MinPositive ~ a => Rewrapped MinPositive a

Defined in Natural

type Unwrapped MinPositive

Defined in Natural

type Unwrapped MinPositive = Positive

naturalPositive :: Iso' Natural (Maybe Positive)

one :: Prism' Positive ()

one' :: Positive

successor1 :: Prism' Positive Positive

successor1' :: Positive -> Positive

successorW :: Iso' Natural Positive

plus1 :: Positive -> Positive -> Positive

multiply1 :: Positive -> Positive -> Positive

square1 :: Positive -> Positive -> Positive

oneOr :: AsPositive a => a -> Positive

notZero :: Prism' Natural Positive

length1 :: Foldable1 f => f a -> Positive

replicate1 :: Positive -> a -> NonEmpty a

take1 :: Positive -> NonEmpty a -> NonEmpty a

drop1 :: Positive -> NonEmpty a -> [a]

splitAt1 :: Positive -> NonEmpty a -> (NonEmpty a, [a])

(!!!) :: NonEmpty a -> Positive -> Maybe a

findIndices1 :: (a -> Bool) -> NonEmpty a -> [Positive]

findIndex1 :: (a -> Bool) -> NonEmpty a -> Maybe Positive

elemIndices1 :: Eq a => a -> NonEmpty a -> [Positive]

elemIndex1 :: Eq a => a -> NonEmpty a -> Maybe Positive

minus1 :: Positive -> Positive -> Positive

list1 :: Iso' Positive (NonEmpty ())

plusone :: Natural -> Positive

minusone :: Positive -> Natural