connections-0.1.0: Orders, Galois connections, and lattices.

Safe HaskellSafe
LanguageHaskell2010

Data.Connection.Ratio

Contents

Synopsis

Documentation

data Ratio a #

Rational numbers, with numerator and denominator of some Integral type.

Note that Ratio's instances inherit the deficiencies from the type parameter's. For example, Ratio Natural's Num instance has similar problems to Natural's.

Constructors

!a :% !a 
Instances
Preorder Rational Source # 
Instance details

Defined in Data.Order

Preorder Positive Source # 
Instance details

Defined in Data.Order

Connection k () Rational Source # 
Instance details

Defined in Data.Connection.Class

Methods

conn :: Conn k () Rational Source #

Connection k () Positive Source # 
Instance details

Defined in Data.Connection.Class

Methods

conn :: Conn k () Positive Source #

Connection k Rational Double Source # 
Instance details

Defined in Data.Connection.Class

Connection k Rational Float Source # 
Instance details

Defined in Data.Connection.Class

Connection k Rational (Extended Integer) Source # 
Instance details

Defined in Data.Connection.Class

Connection k Rational (Extended Int) Source # 
Instance details

Defined in Data.Connection.Class

Connection k Rational (Extended Int64) Source # 
Instance details

Defined in Data.Connection.Class

Connection k Rational (Extended Int32) Source # 
Instance details

Defined in Data.Connection.Class

Connection k Rational (Extended Int16) Source # 
Instance details

Defined in Data.Connection.Class

Connection k Rational (Extended Int8) Source # 
Instance details

Defined in Data.Connection.Class

Connection k (Rational, Rational) Rational Source # 
Instance details

Defined in Data.Connection.Class

Connection k (Positive, Positive) Positive Source # 
Instance details

Defined in Data.Connection.Class

Integral a => Enum (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

succ :: Ratio a -> Ratio a #

pred :: Ratio a -> Ratio a #

toEnum :: Int -> Ratio a #

fromEnum :: Ratio a -> Int #

enumFrom :: Ratio a -> [Ratio a] #

enumFromThen :: Ratio a -> Ratio a -> [Ratio a] #

enumFromTo :: Ratio a -> Ratio a -> [Ratio a] #

enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a] #

Eq a => Eq (Ratio a)

Since: base-2.1

Instance details

Defined in GHC.Real

Methods

(==) :: Ratio a -> Ratio a -> Bool #

(/=) :: Ratio a -> Ratio a -> Bool #

Integral a => Fractional (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

(/) :: Ratio a -> Ratio a -> Ratio a #

recip :: Ratio a -> Ratio a #

fromRational :: Rational -> Ratio a #

Integral a => Num (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

(+) :: Ratio a -> Ratio a -> Ratio a #

(-) :: Ratio a -> Ratio a -> Ratio a #

(*) :: Ratio a -> Ratio a -> Ratio a #

negate :: Ratio a -> Ratio a #

abs :: Ratio a -> Ratio a #

signum :: Ratio a -> Ratio a #

fromInteger :: Integer -> Ratio a #

Integral a => Ord (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

compare :: Ratio a -> Ratio a -> Ordering #

(<) :: Ratio a -> Ratio a -> Bool #

(<=) :: Ratio a -> Ratio a -> Bool #

(>) :: Ratio a -> Ratio a -> Bool #

(>=) :: Ratio a -> Ratio a -> Bool #

max :: Ratio a -> Ratio a -> Ratio a #

min :: Ratio a -> Ratio a -> Ratio a #

(Integral a, Read a) => Read (Ratio a)

Since: base-2.1

Instance details

Defined in GHC.Read

Integral a => Real (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

toRational :: Ratio a -> Rational #

Integral a => RealFrac (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

properFraction :: Integral b => Ratio a -> (b, Ratio a) #

truncate :: Integral b => Ratio a -> b #

round :: Integral b => Ratio a -> b #

ceiling :: Integral b => Ratio a -> b #

floor :: Integral b => Ratio a -> b #

Show a => Show (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

showsPrec :: Int -> Ratio a -> ShowS #

show :: Ratio a -> String #

showList :: [Ratio a] -> ShowS #

RationalUniverse a => Universe (Ratio a) 
Instance details

Defined in Data.Universe.Class

Methods

universe :: [Ratio a] #

reduce :: Integral a => Ratio a -> Ratio a Source #

A total version of reduce.

shiftd :: Num a => a -> Ratio a -> Ratio a Source #

Shift by n 'units of least precision' where the ULP is determined by the denominator

This is an analog of shift for rationals.

Rational

Positive