Interval arithmetic in Python using Algebraic Data Types

More or less based on a Haskell package.

Contains an infix class released under PSF License.

Requires uxadt

sudo pip3 install uxadt

Supports arithmetic (add,sub,mul,div) and comparison.

Comparison using forall by default.

Use e.g., ltSome or leSome if x < y for some values of x and y

Equality is weird for intervals.

Addition:

>>> Interval(-1,3) + Interval(4,5)
Interval(3,8)
>>> Interval(1,3) + Empty()
Empty()
>>> Empty() + Interval(1,3)
Empty()

Multiplication:

>>> Interval(-1,3) * Interval(4,5)
Interval(-5,15)
>>> Interval(-3,3) * Interval(-5,2)
Interval(-15,15)
>>> Interval(1,3) * Empty()
Empty()
>>> Empty() * Interval(1,3)
Empty()

Unary minus operator

>>> -Interval(-1,3)
Interval(-3,1)
>>> -Empty()
Empty()

Binary minus operator

>>> Interval(3,6) - Interval(-4,2)
Interval(1,10)
>>> Empty() - Interval(1,2)
Empty()

Division

>>> Interval(1,3) / Interval(3,5)
Interval(0.2,1.0))
>>> Interval(1,3) / Interval(-1,1)
Interval(-inf,inf)
>>> Interval(1,3) / Interval(0,3)
Interval(0.3333333333333333, inf)

Inclusion

>>> 1 in Interval(0,2)
True
>>> -1 in Interval(0,2)
False
>>> 1 in Empty()
False