Example of functional sets in Python

functional_sets_in_python.py

set_of_1 = lambda i: i == 1

set_of_1(1)

set_of_1(2)

empty = lambda i: False

empty(1)

union = lambda s1, s2: lambda i: s1(i) or s2(i)

intersect = lambda s1, s2: lambda i: s1(i) and s2(i)

set_of_5_3_2 = union(union(lambda x: x == 5, lambda x: x == 3), lambda x: x == 2)

set_of_5_3_2(5)

set_of_5_3_2(2)

set_of_5_3_2(1)

set_of_5_3_2_1 = union(set_of_1, set_of_5_3_2)

set_of_5_3_2_1(3)

set_of_5_3_2_1(1)

intersect(set_of_5_3_2, set_of_5_3_2_1)(1)

intersect(set_of_5_3_2, set_of_5_3_2_1)(5)

Python REPL output of the code above:

>>> 
>>> set_of_1 = lambda i: i == 1
>>> 
>>> set_of_1(1)
True
>>> 
>>> set_of_1(2)
False
>>> 
>>> empty = lambda i: False
>>> 
>>> empty(1)
False
>>> 
>>> union = lambda s1, s2: lambda i: s1(i) or s2(i)
>>> 
>>> intersect = lambda s1, s2: lambda i: s1(i) and s2(i)
>>> 
>>> set_of_5_3_2 = union(union(lambda x: x == 5, lambda x: x == 3), lambda x: x == 2)
>>> 
>>> set_of_5_3_2(5)
True
>>> 
>>> set_of_5_3_2(2)
True
>>> 
>>> set_of_5_3_2(1)
False
>>> 
>>> set_of_5_3_2_1 = union(set_of_1, set_of_5_3_2)
>>> 
>>> set_of_5_3_2_1(3)
True
>>> 
>>> set_of_5_3_2_1(1)
True
>>> 
>>> intersect(set_of_5_3_2, set_of_5_3_2_1)(1)
False
>>> 
>>> intersect(set_of_5_3_2, set_of_5_3_2_1)(5)
True
>>>