Safe Haskell	Trustworthy
Language	Haskell2010

NatOptics.Positive

Contents

Type constructor
Optics
Re-exports

Synopsis

data Positive number
refine :: (Num n, Ord n) => Prism' n (Positive n)
natPrism :: (Integral n, Bits n) => Prism' Natural (Positive n)
intPrism :: (Integral n, Bits n) => Prism' Integer (Positive n)
textPrism :: (Integral n, Bits n) => Prism' Text (Positive n)
stringPrism :: (Integral n, Bits n) => Prism' String (Positive n)
data Natural
data Integer
type Prism' s a = Optic' A_Prism NoIx s a
view :: forall k (is :: IxList) s a. Is k A_Getter => Optic' k is s a -> s -> a
review :: forall k (is :: IxList) t b. Is k A_Review => Optic' k is t b -> b -> t
preview :: forall k (is :: IxList) s a. Is k An_AffineFold => Optic' k is s a -> s -> Maybe a

Type constructor

data Positive number Source #

Instances

Instances details

Eq number => Eq (Positive number) Source #
Instance details Defined in NatOptics.Positive.Unsafe Methods (==) :: Positive number -> Positive number -> Bool # (/=) :: Positive number -> Positive number -> Bool #
Ord number => Ord (Positive number) Source #
Instance details Defined in NatOptics.Positive.Unsafe Methods compare :: Positive number -> Positive number -> Ordering # (<) :: Positive number -> Positive number -> Bool # (<=) :: Positive number -> Positive number -> Bool # (>) :: Positive number -> Positive number -> Bool # (>=) :: Positive number -> Positive number -> Bool # max :: Positive number -> Positive number -> Positive number # min :: Positive number -> Positive number -> Positive number #
Show number => Show (Positive number) Source #
Instance details Defined in NatOptics.Positive.Unsafe Methods showsPrec :: Int -> Positive number -> ShowS # show :: Positive number -> String # showList :: [Positive number] -> ShowS #

Optics

refine :: (Num n, Ord n) => Prism' n (Positive n) Source #

For any numeric type n, Positive n is a subset of n.

Examples:

preview refine (-1 :: Integer) = Nothing
preview refine (0 :: Integer) = Nothing
preview refine (1 :: Integer) = Just (Positive 1)
preview refine (2 :: Integer) = Just (Positive 2)

natPrism :: (Integral n, Bits n) => Prism' Natural (Positive n) Source #

For any integral type n, Positive n is a subset of Natural.

intPrism :: (Integral n, Bits n) => Prism' Integer (Positive n) Source #

For any integral type n, Positive n is a subset of Integer.

textPrism :: (Integral n, Bits n) => Prism' Text (Positive n) Source #

stringPrism :: (Integral n, Bits n) => Prism' String (Positive n) Source #

Re-exports

data Natural #

Type representing arbitrary-precision non-negative integers.

>>> 2^100 :: Natural
1267650600228229401496703205376

Operations whose result would be negative throw (Underflow :: ArithException),

>>> -1 :: Natural
*** Exception: arithmetic underflow

Since: base-4.8.0.0

Instances

Instances details

Enum Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Enum Methods succ :: Natural -> Natural # pred :: Natural -> Natural # toEnum :: Int -> Natural # fromEnum :: Natural -> Int # enumFrom :: Natural -> [Natural] # enumFromThen :: Natural -> Natural -> [Natural] # enumFromTo :: Natural -> Natural -> [Natural] # enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] #
Eq Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural Methods (==) :: Natural -> Natural -> Bool # (/=) :: Natural -> Natural -> Bool #
Integral Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods quot :: Natural -> Natural -> Natural # rem :: Natural -> Natural -> Natural # div :: Natural -> Natural -> Natural # mod :: Natural -> Natural -> Natural # quotRem :: Natural -> Natural -> (Natural, Natural) # divMod :: Natural -> Natural -> (Natural, Natural) # toInteger :: Natural -> Integer #
Num Natural	Note that `Natural`'s `Num` instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though. Since: base-4.8.0.0
Instance details Defined in GHC.Num Methods (+) :: Natural -> Natural -> Natural # (-) :: Natural -> Natural -> Natural # (*) :: Natural -> Natural -> Natural # negate :: Natural -> Natural # abs :: Natural -> Natural # signum :: Natural -> Natural # fromInteger :: Integer -> Natural #
Ord Natural	Since: base-4.8.0.0
Instance details Defined in GHC.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 #
Read Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Natural # readList :: ReadS [Natural] # readPrec :: ReadPrec Natural # readListPrec :: ReadPrec [Natural] #
Real Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods toRational :: Natural -> Rational #
Show Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Natural -> ShowS # show :: Natural -> String # showList :: [Natural] -> ShowS #
Ix Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Ix Methods range :: (Natural, Natural) -> [Natural] # index :: (Natural, Natural) -> Natural -> Int # unsafeIndex :: (Natural, Natural) -> Natural -> Int # inRange :: (Natural, Natural) -> Natural -> Bool # rangeSize :: (Natural, Natural) -> Int # unsafeRangeSize :: (Natural, Natural) -> Int #
Bits Natural	Since: base-4.8.0
Instance details Defined in Data.Bits Methods (.&.) :: Natural -> Natural -> Natural # (.\|.) :: Natural -> Natural -> Natural # xor :: Natural -> Natural -> Natural # complement :: Natural -> Natural # shift :: Natural -> Int -> Natural # rotate :: Natural -> Int -> Natural # zeroBits :: Natural # bit :: Int -> Natural # setBit :: Natural -> Int -> Natural # clearBit :: Natural -> Int -> Natural # complementBit :: Natural -> Int -> Natural # testBit :: Natural -> Int -> Bool # bitSizeMaybe :: Natural -> Maybe Int # bitSize :: Natural -> Int # isSigned :: Natural -> Bool # shiftL :: Natural -> Int -> Natural # unsafeShiftL :: Natural -> Int -> Natural # shiftR :: Natural -> Int -> Natural # unsafeShiftR :: Natural -> Int -> Natural # rotateL :: Natural -> Int -> Natural # rotateR :: Natural -> Int -> Natural # popCount :: Natural -> Int #

data Integer #

Arbitrary precision integers. In contrast with fixed-size integral types such as Int, the Integer type represents the entire infinite range of integers.

For more information about this type's representation, see the comments in its implementation.

Instances

Instances details

Enum Integer	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Integer -> Integer # pred :: Integer -> Integer # toEnum :: Int -> Integer # fromEnum :: Integer -> Int # enumFrom :: Integer -> [Integer] # enumFromThen :: Integer -> Integer -> [Integer] # enumFromTo :: Integer -> Integer -> [Integer] # enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] #
Eq Integer
Instance details Defined in GHC.Integer.Type Methods (==) :: Integer -> Integer -> Bool # (/=) :: Integer -> Integer -> Bool #
Integral Integer	Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Integer -> Integer -> Integer # rem :: Integer -> Integer -> Integer # div :: Integer -> Integer -> Integer # mod :: Integer -> Integer -> Integer # quotRem :: Integer -> Integer -> (Integer, Integer) # divMod :: Integer -> Integer -> (Integer, Integer) # toInteger :: Integer -> Integer #
Num Integer	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Integer -> Integer -> Integer # (-) :: Integer -> Integer -> Integer # (*) :: Integer -> Integer -> Integer # negate :: Integer -> Integer # abs :: Integer -> Integer # signum :: Integer -> Integer # fromInteger :: Integer -> Integer #
Ord Integer
Instance details Defined in GHC.Integer.Type Methods compare :: Integer -> Integer -> Ordering # (<) :: Integer -> Integer -> Bool # (<=) :: Integer -> Integer -> Bool # (>) :: Integer -> Integer -> Bool # (>=) :: Integer -> Integer -> Bool # max :: Integer -> Integer -> Integer # min :: Integer -> Integer -> Integer #
Read Integer	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Integer # readList :: ReadS [Integer] # readPrec :: ReadPrec Integer # readListPrec :: ReadPrec [Integer] #
Real Integer	Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Integer -> Rational #
Show Integer	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Integer -> ShowS # show :: Integer -> String # showList :: [Integer] -> ShowS #
Ix Integer	Since: base-2.1
Instance details Defined in GHC.Ix Methods range :: (Integer, Integer) -> [Integer] # index :: (Integer, Integer) -> Integer -> Int # unsafeIndex :: (Integer, Integer) -> Integer -> Int # inRange :: (Integer, Integer) -> Integer -> Bool # rangeSize :: (Integer, Integer) -> Int # unsafeRangeSize :: (Integer, Integer) -> Int #
Bits Integer	Since: base-2.1
Instance details Defined in Data.Bits Methods (.&.) :: Integer -> Integer -> Integer # (.\|.) :: Integer -> Integer -> Integer # xor :: Integer -> Integer -> Integer # complement :: Integer -> Integer # shift :: Integer -> Int -> Integer # rotate :: Integer -> Int -> Integer # zeroBits :: Integer # bit :: Int -> Integer # setBit :: Integer -> Int -> Integer # clearBit :: Integer -> Int -> Integer # complementBit :: Integer -> Int -> Integer # testBit :: Integer -> Int -> Bool # bitSizeMaybe :: Integer -> Maybe Int # bitSize :: Integer -> Int # isSigned :: Integer -> Bool # shiftL :: Integer -> Int -> Integer # unsafeShiftL :: Integer -> Int -> Integer # shiftR :: Integer -> Int -> Integer # unsafeShiftR :: Integer -> Int -> Integer # rotateL :: Integer -> Int -> Integer # rotateR :: Integer -> Int -> Integer # popCount :: Integer -> Int #

type Prism' s a = Optic' A_Prism NoIx s a #

Type synonym for a type-preserving prism.

view :: forall k (is :: IxList) s a. Is k A_Getter => Optic' k is s a -> s -> a #

View the value pointed to by a getter.

If you want to view a type-modifying optic that is insufficiently polymorphic to be type-preserving, use getting.

review :: forall k (is :: IxList) t b. Is k A_Review => Optic' k is t b -> b -> t #

Retrieve the value targeted by a Review.

>>> review _Left "hi"
Left "hi"

preview :: forall k (is :: IxList) s a. Is k An_AffineFold => Optic' k is s a -> s -> Maybe a #

Retrieve the value targeted by an AffineFold.

>>> let _Right = prism Right $ either (Left . Left) Right

>>> preview _Right (Right 'x')
Just 'x'

>>> preview _Right (Left 'y')
Nothing