Copyright	(c) Masahiro Sakai 2014
License	BSD-style
Maintainer	masahiro.sakai@gmail.com
Stability	provisional
Portability	non-portable (DeriveDataTypeable)
Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.ExtendedReal

Description

Extension of real numbers with positive/negative infinities (±∞). It is useful for describing various limiting behaviors in mathematics.

Remarks:

∞ - ∞ is left undefined as usual, but we define 0 × ∞ = 0 × -∞ = 0 by following the convention of probability or measure theory.

References:

Wikipedia contributors, "Extended real number line," Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Extended_real_number_line (accessed September 1, 2014).

Synopsis

data Extended r
- = NegInf
- | Finite !r
- | PosInf
inf :: Extended r
isFinite :: Extended r -> Bool
isInfinite :: Extended r -> Bool

Documentation

data Extended r Source #

Extended r is an extension of r with positive/negative infinity (±∞).

Constructors

NegInf	negative infinity (-∞)
Finite !r	finite value
PosInf	positive infinity (+∞)

Instances

Instances details

Functor Extended Source #
Instance details Defined in Data.ExtendedReal Methods fmap :: (a -> b) -> Extended a -> Extended b Source # (<$) :: a -> Extended b -> Extended a Source #
Bounded ( Extended r) Source #
Instance details Defined in Data.ExtendedReal Methods minBound :: Extended r Source # maxBound :: Extended r Source #
Eq r => Eq ( Extended r) Source #
Instance details Defined in Data.ExtendedReal Methods (==) :: Extended r -> Extended r -> Bool Source # (/=) :: Extended r -> Extended r -> Bool Source #
( Fractional r, Ord r) => Fractional ( Extended r) Source #	Note that `Extended r` is not a field, nor a ring.
Instance details Defined in Data.ExtendedReal Methods (/) :: Extended r -> Extended r -> Extended r Source # recip :: Extended r -> Extended r Source # fromRational :: Rational -> Extended r Source #
Data r => Data ( Extended r) Source #
Instance details Defined in Data.ExtendedReal Methods gfoldl :: ( forall d b. Data d => c (d -> b) -> d -> c b) -> ( forall g. g -> c g) -> Extended r -> c ( Extended r) Source # gunfold :: ( forall b r0. Data b => c (b -> r0) -> c r0) -> ( forall r1. r1 -> c r1) -> Constr -> c ( Extended r) Source # toConstr :: Extended r -> Constr Source # dataTypeOf :: Extended r -> DataType Source # dataCast1 :: Typeable t => ( forall d. Data d => c (t d)) -> Maybe (c ( Extended r)) Source # dataCast2 :: Typeable t => ( forall d e. ( Data d, Data e) => c (t d e)) -> Maybe (c ( Extended r)) Source # gmapT :: ( forall b. Data b => b -> b) -> Extended r -> Extended r Source # gmapQl :: (r0 -> r' -> r0) -> r0 -> ( forall d. Data d => d -> r') -> Extended r -> r0 Source # gmapQr :: forall r0 r'. (r' -> r0 -> r0) -> r0 -> ( forall d. Data d => d -> r') -> Extended r -> r0 Source # gmapQ :: ( forall d. Data d => d -> u) -> Extended r -> [u] Source # gmapQi :: Int -> ( forall d. Data d => d -> u) -> Extended r -> u Source # gmapM :: Monad m => ( forall d. Data d => d -> m d) -> Extended r -> m ( Extended r) Source # gmapMp :: MonadPlus m => ( forall d. Data d => d -> m d) -> Extended r -> m ( Extended r) Source # gmapMo :: MonadPlus m => ( forall d. Data d => d -> m d) -> Extended r -> m ( Extended r) Source #
( Num r, Ord r) => Num ( Extended r) Source #	Note that `Extended r` is not a field, nor a ring. `PosInf + NegInf` is left undefined as usual, but we define `0 * PosInf = 0 * NegInf = 0` by following the convention of probability or measure theory.
Instance details Defined in Data.ExtendedReal Methods (+) :: Extended r -> Extended r -> Extended r Source # (-) :: Extended r -> Extended r -> Extended r Source # (*) :: Extended r -> Extended r -> Extended r Source # negate :: Extended r -> Extended r Source # abs :: Extended r -> Extended r Source # signum :: Extended r -> Extended r Source # fromInteger :: Integer -> Extended r Source #
Ord r => Ord ( Extended r) Source #
Instance details Defined in Data.ExtendedReal Methods compare :: Extended r -> Extended r -> Ordering Source # (<) :: Extended r -> Extended r -> Bool Source # (<=) :: Extended r -> Extended r -> Bool Source # (>) :: Extended r -> Extended r -> Bool Source # (>=) :: Extended r -> Extended r -> Bool Source # max :: Extended r -> Extended r -> Extended r Source # min :: Extended r -> Extended r -> Extended r Source #
Read r => Read ( Extended r) Source #
Instance details Defined in Data.ExtendedReal Methods readsPrec :: Int -> ReadS ( Extended r) Source # readList :: ReadS [ Extended r] Source # readPrec :: ReadPrec ( Extended r) Source # readListPrec :: ReadPrec [ Extended r] Source #
Show r => Show ( Extended r) Source #
Instance details Defined in Data.ExtendedReal Methods showsPrec :: Int -> Extended r -> ShowS Source # show :: Extended r -> String Source # showList :: [ Extended r] -> ShowS Source #
NFData r => NFData ( Extended r) Source #
Instance details Defined in Data.ExtendedReal Methods rnf :: Extended r -> () Source #
Hashable r => Hashable ( Extended r) Source #
Instance details Defined in Data.ExtendedReal Methods hashWithSalt :: Int -> Extended r -> Int Source # hash :: Extended r -> Int Source #

inf :: Extended r Source #

Infinity (∞)

isFinite :: Extended r -> Bool Source #

isFinite x = not (isInfinite x) .

isInfinite :: Extended r -> Bool Source #

isInfinite x returns True iff x is PosInf or NegInf .