Algebra of conditionals

[wtd]

Let's examine the algebra of conditionals. We'll use Python syntax with symbols because it's pretty. We'll also assume for now that we don't have any statements outside nested conditionals.

A sample nested conditional.

Python:

if A:     if B:         if C:             X     elif D:         Y     else:         Z else:     W

How can we flatten this?

We know we have to "and" the previous level with any nested conditions.

So, as a first step:

Python:

if A:     if B and C:         X     elif D:         Y     else:         Z else:     W

But we can go right down to a single level with ease:

Python:

if A and B and C:     X elif A and D:     Y elif A:     Z else:     W

Let's look at another example:

Python:

if A:     X elif B:     Y elif C:     Y elif D:     Z else:     Z

When two consecutive branches of a conditional yield the same result, we can "or" them together. If one of the consecutive conditions that leads to the same result is "else", we can just use "else".

Python:

if A:     X elif B or C:     Y else:     Z

But what happens if they're not consecutive. What if other branches lie in between?

Python:

if A:     X elif not B:     Y elif C:     X else:     Z

We can still "or" those together, but we have to "and" the negation of each intermediate condition.

Python:

if A or C and not (not B):     X elif not B:     Y else:     Z

Or just:

Python:

if A or C and B:     X elif not B:     Y else:     Z