Question

Short and sharp:
Given two Boolean statements, what is the easiest way to calculate the equation of their intersection in a language like Lua?

(Red = Filter 1, Blue = Filter 2, Purple = Area of intersection)

Long and lamenting:

• Filter A: object.ID < 300

• Filter B: object.ID < 600

Filter A is a subset of Filter B, that is: Filter B will contain everything matched by Filter A, plus 0 or more objects.
On a Venn diagram, Filter A would be inside Filter B.

How can I calculate the equation of the area of intersection?

A more complicated example:

• Filter X: object.Col == 'GREEN' and (object.ID == 2 or object.ID == 64 or object.ID > 9001)
• Filter Y: (object.Col == 'RED' or object.Col == 'GREEN') and (object.ID == 3 or object.ID > 22)

Filter A intersects with Filter B.
On a Venn Diagram, they would overlap.
The equation for the overlapping area would be:
object.Col == 'GREEN' and (object.ID == 64 or object.ID > 9001)

How would this equation be calculated in a language such as Python or Haskell?

I wish to eventually make this in Lua, but if Python, Haskell or another language provided the functionality, I would be able to look at the source code and convert it over.

Here is how I am representing filters in Lua:

filter = DataFilter(
    {"and",
        {"or",
            {"==", "Col", "RED"},
            {"==", "Col", "GREEN"},
        },
        {"or",
            {"==", "ID", 3},
            {">" , "ID", 22},
        },
    }
)

Please point me in the right direction.

Answer 1

Wild guess: Bring the “Filters” into disjunctive normal form and reduce using appropriate methods (x == 8 contained in x > 5).