-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Integer, Natural, and Positive
--   
--   The base package contains two unbounded integral types: Integer (-∞,
--   ∞) and Natural (0, ∞). This package expands that integral repertoire
--   with the addition of Positive (1, ∞).
@package integer-types
@version 0.1.4.1

module Integer.BoundedBelow
class BoundedBelow a
minBound :: BoundedBelow a => a
instance Integer.BoundedBelow.BoundedBelow GHC.Num.Natural.Natural

module Integer.Sign
data Sign
MinusSign :: Sign
PlusSign :: Sign
negate :: Sign -> Sign
multiply :: Sign -> Sign -> Sign
instance GHC.Enum.Bounded Integer.Sign.Sign
instance GHC.Enum.Enum Integer.Sign.Sign
instance GHC.Show.Show Integer.Sign.Sign
instance GHC.Classes.Ord Integer.Sign.Sign
instance GHC.Classes.Eq Integer.Sign.Sign
instance Control.DeepSeq.NFData Integer.Sign.Sign
instance Data.Hashable.Class.Hashable Integer.Sign.Sign

module Integer.Signed
data Signed
Zero :: Signed
NonZero :: Sign -> Positive -> Signed
pattern Plus :: Positive -> Signed
pattern Minus :: Positive -> Signed

-- | A <a>Signed</a> that is either zero or negative; the <a>Natural</a>
--   gives the magnitude of the negative
pattern NotPlus :: Natural -> Signed

-- | A <a>Signed</a> that is either zero or positive
pattern NotMinus :: Natural -> Signed
toInteger :: Signed -> Integer
fromInteger :: Integer -> Signed
toNatural :: Signed -> Maybe Natural
fromNatural :: Natural -> Signed
toPositive :: Signed -> Maybe Positive
fromPositive :: Positive -> Signed
toInt :: Signed -> Maybe Int
fromInt :: Int -> Signed
toWord :: Signed -> Maybe Word
fromWord :: Word -> Signed
increase :: Natural -> Signed -> Signed
strictlyIncrease :: Positive -> Signed -> Signed
one :: Signed
addOne :: Signed -> Signed
subtractOne :: Signed -> Signed
instance GHC.Classes.Eq Integer.Signed.Signed
instance GHC.Classes.Ord Integer.Signed.Signed
instance Control.DeepSeq.NFData Integer.Signed.Signed
instance Data.Hashable.Class.Hashable Integer.Signed.Signed
instance GHC.Num.Num Integer.Signed.Signed
instance GHC.Enum.Enum Integer.Signed.Signed
instance GHC.Real.Real Integer.Signed.Signed
instance GHC.Real.Integral Integer.Signed.Signed
instance GHC.Show.Show Integer.Signed.Signed

module Integer.Positive
data Positive
toNatural :: Positive -> Natural
fromNatural :: Natural -> Maybe Positive
toInteger :: Positive -> Integer
fromInteger :: Integer -> Maybe Positive
toSigned :: Positive -> Signed
fromSigned :: Signed -> Maybe Positive
toInt :: Positive -> Maybe Int
fromInt :: Int -> Maybe Positive
toWord :: Positive -> Maybe Word
fromWord :: Word -> Maybe Positive
subtract :: Positive -> Positive -> Signed
increase :: Natural -> Positive -> Positive
one :: Positive
addOne :: Positive -> Positive
subtractOne :: Positive -> Natural
length :: NonEmpty a -> Positive

module Integer.Natural

-- | Natural number
--   
--   Invariant: numbers &lt;= 0xffffffffffffffff use the <a>NS</a>
--   constructor
data () => Natural
toPositive :: Natural -> Maybe Positive
fromPositive :: Positive -> Natural
toInteger :: Natural -> Integer
fromInteger :: Integer -> Maybe Natural
toSigned :: Natural -> Signed
fromSigned :: Signed -> Maybe Natural
toInt :: Natural -> Maybe Int
fromInt :: Int -> Maybe Natural
toWord :: Natural -> Maybe Word
fromWord :: Word -> Natural
subtract :: Natural -> Natural -> Signed
strictlyIncrease :: Positive -> Natural -> Natural
one :: Natural
addOne :: Natural -> Positive
subtractOne :: Natural -> Maybe Signed
length :: [a] -> Natural

module Integer.Integer

-- | Arbitrary precision integers. In contrast with fixed-size integral
--   types such as <a>Int</a>, the <a>Integer</a> 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 <a>Int</a>), <a>IS</a> constructor
--   is used. Otherwise <a>Integer</a> and <a>IN</a> constructors are used
--   to store a <a>BigNat</a> representing respectively the positive or the
--   negative value magnitude.
--   
--   Invariant: <a>Integer</a> and <a>IN</a> are used iff value doesn't fit
--   in <a>IS</a>
data () => Integer
toPositive :: Integer -> Maybe Positive
fromPositive :: Positive -> Integer
toNatural :: Integer -> Maybe Natural
fromNatural :: Natural -> Integer
toSigned :: Integer -> Signed
fromSigned :: Signed -> Integer
toInt :: Integer -> Maybe Int
fromInt :: Int -> Integer
toWord :: Integer -> Maybe Word
fromWord :: Word -> Integer
increase :: Natural -> Integer -> Integer
strictlyIncrease :: Positive -> Integer -> Integer

module Integer.Increase

-- | Class of numbers are closed under addition with <a>Natural</a>
class Increase a

-- | Addition
increase :: Increase a => Natural -> a -> a
instance Integer.Increase.Increase GHC.Num.Integer.Integer
instance Integer.Increase.Increase Integer.Signed.Signed
instance Integer.Increase.Increase GHC.Num.Natural.Natural
instance Integer.Increase.Increase Integer.Positive.Unsafe.Positive

module Integer.Finite
class ConvertWithFinite a
toWord :: ConvertWithFinite a => a -> Maybe Word
fromWord :: ConvertWithFinite a => Word -> Maybe a
toInt :: ConvertWithFinite a => a -> Maybe Int
fromInt :: ConvertWithFinite a => Int -> Maybe a
class (Bounded b, Integral b) => Finite b
toFinite :: (Finite b, ConvertWithFinite a) => a -> Maybe b
fromFinite :: (Finite b, ConvertWithFinite a) => b -> Maybe a
instance Integer.Finite.Finite GHC.Types.Int
instance Integer.Finite.Finite GHC.Types.Word
instance Integer.Finite.ConvertWithFinite GHC.Num.Natural.Natural
instance Integer.Finite.ConvertWithFinite Integer.Positive.Unsafe.Positive
instance Integer.Finite.ConvertWithFinite GHC.Num.Integer.Integer
instance Integer.Finite.ConvertWithFinite Integer.Signed.Signed

module Integer.Conversion
class IntegerNarrow a b
narrow :: IntegerNarrow a b => a -> Maybe b
class IntegerNarrow a b => IntegerConvert a b
convert :: IntegerConvert a b => a -> b
class (IntegerConvert a b, IntegerConvert b a) => IntegerEquiv a b

-- | Partial conversion between <a>Integral</a> types via <a>Integer</a>
--   
--   <pre>
--   yolo = <a>fromInteger</a> . <a>toInteger</a>
--   </pre>
yolo :: (Integral a, Num b) => a -> b
instance Integer.Conversion.IntegerEquiv GHC.Num.Integer.Integer GHC.Num.Integer.Integer
instance Integer.Conversion.IntegerEquiv GHC.Num.Natural.Natural GHC.Num.Natural.Natural
instance Integer.Conversion.IntegerEquiv Integer.Positive.Unsafe.Positive Integer.Positive.Unsafe.Positive
instance Integer.Conversion.IntegerEquiv Integer.Signed.Signed Integer.Signed.Signed
instance Integer.Conversion.IntegerEquiv GHC.Num.Integer.Integer Integer.Signed.Signed
instance Integer.Conversion.IntegerEquiv Integer.Signed.Signed GHC.Num.Integer.Integer
instance Integer.Conversion.IntegerConvert GHC.Num.Integer.Integer GHC.Num.Integer.Integer
instance Integer.Conversion.IntegerConvert GHC.Num.Natural.Natural GHC.Num.Natural.Natural
instance Integer.Conversion.IntegerConvert Integer.Positive.Unsafe.Positive Integer.Positive.Unsafe.Positive
instance Integer.Conversion.IntegerConvert Integer.Signed.Signed Integer.Signed.Signed
instance Integer.Conversion.IntegerConvert GHC.Num.Integer.Integer Integer.Signed.Signed
instance Integer.Conversion.IntegerNarrow GHC.Num.Integer.Integer Integer.Signed.Signed
instance Integer.Conversion.IntegerConvert Integer.Signed.Signed GHC.Num.Integer.Integer
instance Integer.Conversion.IntegerNarrow Integer.Signed.Signed GHC.Num.Integer.Integer
instance Integer.Conversion.IntegerNarrow GHC.Num.Natural.Natural GHC.Num.Integer.Integer
instance Integer.Conversion.IntegerConvert GHC.Num.Natural.Natural GHC.Num.Integer.Integer
instance Integer.Conversion.IntegerNarrow GHC.Num.Natural.Natural Integer.Signed.Signed
instance Integer.Conversion.IntegerConvert GHC.Num.Natural.Natural Integer.Signed.Signed
instance Integer.Conversion.IntegerNarrow Integer.Positive.Unsafe.Positive GHC.Num.Integer.Integer
instance Integer.Conversion.IntegerConvert Integer.Positive.Unsafe.Positive GHC.Num.Integer.Integer
instance Integer.Conversion.IntegerNarrow Integer.Positive.Unsafe.Positive GHC.Num.Natural.Natural
instance Integer.Conversion.IntegerConvert Integer.Positive.Unsafe.Positive GHC.Num.Natural.Natural
instance Integer.Conversion.IntegerNarrow Integer.Positive.Unsafe.Positive Integer.Signed.Signed
instance Integer.Conversion.IntegerConvert Integer.Positive.Unsafe.Positive Integer.Signed.Signed
instance Integer.Conversion.IntegerNarrow GHC.Num.Integer.Integer GHC.Num.Integer.Integer
instance Integer.Conversion.IntegerNarrow GHC.Num.Natural.Natural GHC.Num.Natural.Natural
instance Integer.Conversion.IntegerNarrow Integer.Positive.Unsafe.Positive Integer.Positive.Unsafe.Positive
instance Integer.Conversion.IntegerNarrow Integer.Signed.Signed Integer.Signed.Signed
instance Integer.Conversion.IntegerNarrow GHC.Num.Integer.Integer GHC.Num.Natural.Natural
instance Integer.Conversion.IntegerNarrow Integer.Signed.Signed GHC.Num.Natural.Natural
instance Integer.Conversion.IntegerNarrow GHC.Num.Integer.Integer Integer.Positive.Unsafe.Positive
instance Integer.Conversion.IntegerNarrow GHC.Num.Natural.Natural Integer.Positive.Unsafe.Positive
instance Integer.Conversion.IntegerNarrow Integer.Signed.Signed Integer.Positive.Unsafe.Positive

module Integer.AbsoluteDifference
class AbsoluteDifference a b
absoluteDifference :: AbsoluteDifference a b => a -> b -> Natural
instance Integer.AbsoluteDifference.AbsoluteDifference GHC.Num.Integer.Integer GHC.Num.Integer.Integer
instance Integer.AbsoluteDifference.AbsoluteDifference GHC.Num.Natural.Natural GHC.Num.Natural.Natural
instance Integer.AbsoluteDifference.AbsoluteDifference Integer.Positive.Unsafe.Positive Integer.Positive.Unsafe.Positive
instance Integer.AbsoluteDifference.AbsoluteDifference Integer.Signed.Signed Integer.Signed.Signed
instance Integer.AbsoluteDifference.AbsoluteDifference Integer.Positive.Unsafe.Positive GHC.Num.Natural.Natural
instance Integer.AbsoluteDifference.AbsoluteDifference GHC.Num.Natural.Natural Integer.Positive.Unsafe.Positive
instance Integer.AbsoluteDifference.AbsoluteDifference Integer.Signed.Signed GHC.Num.Natural.Natural
instance Integer.AbsoluteDifference.AbsoluteDifference GHC.Num.Natural.Natural Integer.Signed.Signed
instance Integer.AbsoluteDifference.AbsoluteDifference GHC.Num.Integer.Integer GHC.Num.Natural.Natural
instance Integer.AbsoluteDifference.AbsoluteDifference GHC.Num.Natural.Natural GHC.Num.Integer.Integer
instance Integer.AbsoluteDifference.AbsoluteDifference Integer.Signed.Signed Integer.Positive.Unsafe.Positive
instance Integer.AbsoluteDifference.AbsoluteDifference Integer.Positive.Unsafe.Positive Integer.Signed.Signed
instance Integer.AbsoluteDifference.AbsoluteDifference Integer.Signed.Signed GHC.Num.Integer.Integer
instance Integer.AbsoluteDifference.AbsoluteDifference GHC.Num.Integer.Integer Integer.Signed.Signed
instance Integer.AbsoluteDifference.AbsoluteDifference Integer.Positive.Unsafe.Positive GHC.Num.Integer.Integer
instance Integer.AbsoluteDifference.AbsoluteDifference GHC.Num.Integer.Integer Integer.Positive.Unsafe.Positive

module Integer.StrictlyIncrease

-- | Class of numbers that are closed under addition with <a>Positive</a>
class StrictlyIncrease a

-- | Addition
strictlyIncrease :: StrictlyIncrease a => Positive -> a -> a
instance Integer.StrictlyIncrease.StrictlyIncrease GHC.Num.Integer.Integer
instance Integer.StrictlyIncrease.StrictlyIncrease Integer.Signed.Signed
instance Integer.StrictlyIncrease.StrictlyIncrease GHC.Num.Natural.Natural
instance Integer.StrictlyIncrease.StrictlyIncrease Integer.Positive.Unsafe.Positive

module Integer.Subtraction

-- | Domain of a subtraction operation
class Subtraction a
subtractInteger :: Subtraction a => a -> a -> Integer
subtractSigned :: Subtraction a => a -> a -> Signed

-- | Codomain of a subtraction operation
class Subtraction' b
subtract :: (Subtraction' b, Subtraction a) => a -> a -> b
instance Integer.Subtraction.Subtraction' GHC.Num.Integer.Integer
instance Integer.Subtraction.Subtraction' Integer.Signed.Signed
instance Integer.Subtraction.Subtraction GHC.Num.Integer.Integer
instance Integer.Subtraction.Subtraction Integer.Signed.Signed
instance Integer.Subtraction.Subtraction GHC.Num.Natural.Natural
instance Integer.Subtraction.Subtraction Integer.Positive.Unsafe.Positive

module Integer

-- | Arbitrary precision integers. In contrast with fixed-size integral
--   types such as <a>Int</a>, the <a>Integer</a> 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 <a>Int</a>), <a>IS</a> constructor
--   is used. Otherwise <a>Integer</a> and <a>IN</a> constructors are used
--   to store a <a>BigNat</a> representing respectively the positive or the
--   negative value magnitude.
--   
--   Invariant: <a>Integer</a> and <a>IN</a> are used iff value doesn't fit
--   in <a>IS</a>
data () => Integer

-- | Natural number
--   
--   Invariant: numbers &lt;= 0xffffffffffffffff use the <a>NS</a>
--   constructor
data () => Natural
data Positive
data Signed
Zero :: Signed
NonZero :: Sign -> Positive -> Signed
pattern Minus :: Positive -> Signed
pattern Plus :: Positive -> Signed
data Sign
MinusSign :: Sign
PlusSign :: Sign

-- | Class of numbers are closed under addition with <a>Natural</a>
class Increase a

-- | Addition
increase :: Increase a => Natural -> a -> a

-- | Class of numbers that are closed under addition with <a>Positive</a>
class StrictlyIncrease a

-- | Addition
strictlyIncrease :: StrictlyIncrease a => Positive -> a -> a

-- | Domain of a subtraction operation
class Subtraction a
subtractInteger :: Subtraction a => a -> a -> Integer
subtractSigned :: Subtraction a => a -> a -> Signed

-- | Codomain of a subtraction operation
class Subtraction' b
subtract :: (Subtraction' b, Subtraction a) => a -> a -> b
class AbsoluteDifference a b
absoluteDifference :: AbsoluteDifference a b => a -> b -> Natural
class IntegerNarrow a b
narrow :: IntegerNarrow a b => a -> Maybe b
class IntegerNarrow a b => IntegerConvert a b
convert :: IntegerConvert a b => a -> b
class (IntegerConvert a b, IntegerConvert b a) => IntegerEquiv a b

-- | Partial conversion between <a>Integral</a> types via <a>Integer</a>
--   
--   <pre>
--   yolo = <a>fromInteger</a> . <a>toInteger</a>
--   </pre>
yolo :: (Integral a, Num b) => a -> b
class ConvertWithFinite a
toWord :: ConvertWithFinite a => a -> Maybe Word
fromWord :: ConvertWithFinite a => Word -> Maybe a
toInt :: ConvertWithFinite a => a -> Maybe Int
fromInt :: ConvertWithFinite a => Int -> Maybe a
class (Bounded b, Integral b) => Finite b
toFinite :: (Finite b, ConvertWithFinite a) => a -> Maybe b
fromFinite :: (Finite b, ConvertWithFinite a) => b -> Maybe a
class BoundedBelow a
minBound :: BoundedBelow a => a