I already thought about this some time ago, but for some reason (that I don't remember ATM), it wasn't that easy to implement in this context. So I decided against it. When I find the time, I might take a look at it again...

Thinking about it, I remember my actual problem with it. This logic applies to AND and OR when they are boolean operators. But in BASIC V2, what they actually are, are bitwise AND and OR operators. That means, that

if x=5 and y=12 then...

can easily be optimized to

if x=5 then if y=12 then...

(which is the same as you've suggested, but in BASIC source code)

but something like

if a and 8 then...

can't. Or more complex:

if (b>2)*-8 and 2*b then ...

can't either. Right now, I'm lacking a clever idea how to separate these cases correctly without going overboard with it...hmm...

thinking about it... when evaluating the AST, your expression nodes might also include a isBoolean property that bubbles up to the root, e.g.

b<2 => return { ..., isBoolean: true }
b * 4  => return { ..., isBoolean: false }
expr1 AND expr2 => return { ..., isBoolean: expr1.isBoolean AND expr2.isBoolean }
expr1 OR expr2 => return { ..., isBoolean: expr1.isBoolean AND expr2.isBoolean }

then you can check the root node of your IF expression and if it's isBoolean you can apply short circuit optimization. Something like this.