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

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 #
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 #

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 #

Natural number

Invariant: numbers <= 0xffffffffffffffff use the NS constructor

Instances

Instances details

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 #
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] #
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 #
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 #
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] #
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 #
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 #
Eq Natural
Instance details Defined in GHC.Num.Natural Methods (==) :: Natural -> Natural -> Bool # (/=) :: Natural -> Natural -> Bool #
Ord Natural
Instance details Defined in GHC.Num.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 #
Lift Natural
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Quote m => Natural -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Natural -> Code m Natural #

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.

Integers are stored in a kind of sign-magnitude form, hence do not expect two's complement form when using bit operations.

If the value is small (fit into an Int), IS constructor is used. Otherwise IP and IN constructors are used to store a BigNat representing respectively the positive or the negative value magnitude.

Invariant: IP and IN are used iff value doesn't fit in IS

Instances

Instances details

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 #
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] #
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 #
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 #
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] #
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 #
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 #
Eq Integer
Instance details Defined in GHC.Num.Integer Methods (==) :: Integer -> Integer -> Bool # (/=) :: Integer -> Integer -> Bool #
Ord Integer
Instance details Defined in GHC.Num.Integer 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 #
Lift Integer
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Quote m => Integer -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Integer -> Code m Integer #

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