Data.ExtendedReal

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.orgwiki/Extended_real_number_line (accessed September 1, 2014).

Documentation

data Extended r

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

Constructors

NegInf

negative infinity (-∞)

Finite !r

finite value

PosInf

positive infinity (+∞)

Instances

Functor Extended

Bounded (Extended r)

Eq r => Eq (Extended r)

(Fractional r, Ord r) => Fractional (Extended r)

Note that Extended r is not a field, nor a ring.

Data r => Data (Extended r)

(Num r, Ord r) => Num (Extended r)

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.

Ord r => Ord (Extended r)

Read r => Read (Extended r)

Show r => Show (Extended r)

NFData r => NFData (Extended r)

Hashable r => Hashable (Extended r)

Typeable (* -> *) Extended

inf :: Extended r

Infinity (∞)

isFinite :: Extended r -> Bool

isFinite x = not (isInfinite x).

isInfinite :: Extended r -> Bool

isInfinite x returns True iff x is PosInf or NegInf.