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GHC 9.10.3 · lts/ghc-9.10.x · 248f8f0 · 2026-10-05

Moduleintervals-0.9.2Haskell2010

Numeric.Interval

Interval arithmetic

  • 1 type
  • 49 values
  • Packageintervals-0.9.2
  • Exports50
  • LanguageHaskell2010
  • LicenceBSD-3-Clause
  • SourceInterval.hs
datadata Interval a
#
Instances16Generic1, Eq, Floating, Fractional, Data, Num, …
valuewhole :: Fractional a => Interval a
#

The whole real number line

Example1 expression
whole-Infinity ... Infinity
valueempty :: Interval a
#

An empty interval

Example1 expression
emptyEmpty
valuenull :: Interval a -> Bool
#

Check if an interval is empty

Example1 expression
null (1 ... 5)False
Example1 expression
null (1 ... 1)False
Example1 expression
null emptyTrue
valuesingleton :: a -> Interval a
#

A singleton point

Example1 expression
singleton 11 ... 1
valuemember :: Ord a => a -> Interval a -> Bool
#

Determine if a point is in the interval.

Example1 expression
member 3.2 (1.0 ... 5.0)True
Example1 expression
member 5 (1.0 ... 5.0)True
Example1 expression
member 1 (1.0 ... 5.0)True
Example1 expression
member 8 (1.0 ... 5.0)False
Example1 expression
member 5 emptyFalse
valuenotMember :: Ord a => a -> Interval a -> Bool
#

Determine if a point is not included in the interval

Example1 expression
notMember 8 (1.0 ... 5.0)True
Example1 expression
notMember 1.4 (1.0 ... 5.0)False

And of course, nothing is a member of the empty interval.

Example1 expression
notMember 5 emptyTrue
valueelem :: Ord a => a -> Interval a -> Bool
#

Deprecated. Use member instead.

Determine if a point is in the interval.

Example1 expression
elem 3.2 (1.0 ... 5.0)True
Example1 expression
elem 5 (1.0 ... 5.0)True
Example1 expression
elem 1 (1.0 ... 5.0)True
Example1 expression
elem 8 (1.0 ... 5.0)False
Example1 expression
elem 5 emptyFalse
valuenotElem :: Ord a => a -> Interval a -> Bool
#

Deprecated. Use notMember instead.

Determine if a point is not included in the interval

Example1 expression
notElem 8 (1.0 ... 5.0)True
Example1 expression
notElem 1.4 (1.0 ... 5.0)False

And of course, nothing is a member of the empty interval.

Example1 expression
notElem 5 emptyTrue
valueinf :: Interval a -> a
#

The infimum (lower bound) of an interval

Example1 expression
inf (1.0 ... 20.0)1.0
Example1 expression
inf empty*** Exception: empty interval
valuesup :: Interval a -> a
#

The supremum (upper bound) of an interval

Example1 expression
sup (1.0 ... 20.0)20.0
Example1 expression
sup empty*** Exception: empty interval
valuesingular :: Ord a => Interval a -> Bool
#

Is the interval a singleton point? N.B. This is fairly fragile and likely will not hold after even a few operations that only involve singletons

Example1 expression
singular (singleton 1)True
Example1 expression
singular (1.0 ... 20.0)False
valuewidth :: Num a => Interval a -> a
#

Calculate the width of an interval.

Example1 expression
width (1 ... 20)19
Example1 expression
width (singleton 1)0
Example1 expression
width empty0
valuemidpoint :: Fractional a => Interval a -> a
#

Nearest point to the midpoint of the interval.

Example1 expression
midpoint (10.0 ... 20.0)15.0
Example1 expression
midpoint (singleton 5.0)5.0
Example1 expression
midpoint empty*** Exception: empty interval
valueintersection :: Ord a => Interval a -> Interval a -> Interval a
#

Calculate the intersection of two intervals.

Example1 expression
intersection (1 ... 10 :: Interval Double) (5 ... 15 :: Interval Double)5.0 ... 10.0
valuehull :: Ord a => Interval a -> Interval a -> Interval a
#

Calculate the convex hull of two intervals

Example1 expression
hull (0 ... 10 :: Interval Double) (5 ... 15 :: Interval Double)0.0 ... 15.0
Example1 expression
hull (15 ... 85 :: Interval Double) (0 ... 10 :: Interval Double)0.0 ... 85.0
valuebisect :: Fractional a => Interval a -> (Interval a, Interval a)
#

Bisect an interval at its midpoint.

Example1 expression
bisect (10.0 ... 20.0)(10.0 ... 15.0,15.0 ... 20.0)
Example1 expression
bisect (singleton 5.0)(5.0 ... 5.0,5.0 ... 5.0)
Example1 expression
bisect Empty(Empty,Empty)
valuemagnitude :: (Num a, Ord a) => Interval a -> a
#

Magnitude

Example1 expression
magnitude (1 ... 20)20
Example1 expression
magnitude (-20 ... 10)20
Example1 expression
magnitude (singleton 5)5

throws EmptyInterval if the interval is empty.

Example1 expression
magnitude empty*** Exception: empty interval
valuemignitude :: (Num a, Ord a) => Interval a -> a
#

"mignitude"

Example1 expression
mignitude (1 ... 20)1
Example1 expression
mignitude (-20 ... 10)0
Example1 expression
mignitude (singleton 5)5

throws EmptyInterval if the interval is empty.

Example1 expression
mignitude empty*** Exception: empty interval
valuedistance :: (Num a, Ord a) => Interval a -> Interval a -> a
#

Hausdorff distance between intervals.

Example1 expression
distance (1 ... 7) (6 ... 10)0
Example1 expression
distance (1 ... 7) (15 ... 24)8
Example1 expression
distance (1 ... 7) (-10 ... -2)3
Example1 expression
distance Empty (1 ... 1)*** Exception: empty interval
valueinflate :: (Num a, Ord a) => a -> Interval a -> Interval a
#

Inflate an interval by enlarging it at both ends.

Example1 expression
inflate 3 (-1 ... 7)-4 ... 10
Example1 expression
inflate (-2) (0 ... 4)-2 ... 6
Example1 expression
inflate 1 emptyEmpty
valuedeflate :: (Num a, Ord a) => a -> Interval a -> Interval a
#

Deflate an interval by shrinking it from both ends.

Example1 expression
deflate 3.0 (-4.0 ... 10.0)-1.0 ... 7.0
Example1 expression
deflate 2.0 (-1.0 ... 1.0)Empty
Example1 expression
deflate 1.0 emptyEmpty
valuescale :: (Fractional a, Ord a) => a -> Interval a -> Interval a
#

Scale an interval about its midpoint.

Example1 expression
scale 1.1 (-6.0 ... 4.0)-6.5 ... 4.5
Example1 expression
scale (-2.0) (-1.0 ... 1.0)Empty
Example1 expression
scale 3.0 emptyEmpty
valuesymmetric :: (Num a, Ord a) => a -> Interval a
#

Construct a symmetric interval.

Example1 expression
symmetric 3-3 ... 3
Example1 expression
symmetric (-2)-2 ... 2
valuecontains :: Ord a => Interval a -> Interval a -> Bool
#

Check if interval X totally contains interval Y

Example1 expression
(20 ... 40 :: Interval Double) `contains` (25 ... 35 :: Interval Double)True
Example1 expression
(20 ... 40 :: Interval Double) `contains` (15 ... 35 :: Interval Double)False
valueisSubsetOf :: Ord a => Interval a -> Interval a -> Bool
#

Flipped version of contains. Check if interval X a subset of interval Y

Example1 expression
(25 ... 35 :: Interval Double) `isSubsetOf` (20 ... 40 :: Interval Double)True
Example1 expression
(20 ... 40 :: Interval Double) `isSubsetOf` (15 ... 35 :: Interval Double)False
value(<!) :: Ord a => Interval a -> Interval a -> Bool
#

For all x in X, y in Y. x < y

Example1 expression
(5 ... 10 :: Interval Double) <! (20 ... 30 :: Interval Double)True
Example1 expression
(5 ... 10 :: Interval Double) <! (10 ... 30 :: Interval Double)False
Example1 expression
(20 ... 30 :: Interval Double) <! (5 ... 10 :: Interval Double)False
value(<=!) :: Ord a => Interval a -> Interval a -> Bool
#

For all x in X, y in Y. x <= y

Example1 expression
(5 ... 10 :: Interval Double) <=! (20 ... 30 :: Interval Double)True
Example1 expression
(5 ... 10 :: Interval Double) <=! (10 ... 30 :: Interval Double)True
Example1 expression
(20 ... 30 :: Interval Double) <=! (5 ... 10 :: Interval Double)False
value(==!) :: Eq a => Interval a -> Interval a -> Bool
#

For all x in X, y in Y. x == y

Only singleton intervals or empty intervals can return true

Example1 expression
(singleton 5 :: Interval Double) ==! (singleton 5 :: Interval Double)True
Example1 expression
(5 ... 10 :: Interval Double) ==! (5 ... 10 :: Interval Double)False
value(/=!) :: Ord a => Interval a -> Interval a -> Bool
#

For all x in X, y in Y. x /= y

Example1 expression
(5 ... 15 :: Interval Double) /=! (20 ... 40 :: Interval Double)True
Example1 expression
(5 ... 15 :: Interval Double) /=! (15 ... 40 :: Interval Double)False
value(>=!) :: Ord a => Interval a -> Interval a -> Bool
#

For all x in X, y in Y. x >= y

Example1 expression
(20 ... 40 :: Interval Double) >=! (10 ... 20 :: Interval Double)True
Example1 expression
(5 ... 20 :: Interval Double) >=! (15 ... 40 :: Interval Double)False
value(>!) :: Ord a => Interval a -> Interval a -> Bool
#

For all x in X, y in Y. x > y

Example1 expression
(20 ... 40 :: Interval Double) >! (10 ... 19 :: Interval Double)True
Example1 expression
(5 ... 20 :: Interval Double) >! (15 ... 40 :: Interval Double)False
valueifloat :: Interval Float -> Interval Float
#

id function. Useful for type specification

Example1 expression
:t ifloat (1 ... 3)ifloat (1 ... 3) :: Interval Float