-----------------------------------

wtd

Fri Dec 10, 2021 7:31 pm


Algebra of conditionals

-----------------------------------

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.

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:

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:

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

Let's look at another example:

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".

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?

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.

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

Or just:

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